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What is Logical Thinking? A Beginner's Guide 

What is Logical Thinking? A Beginner's Guide: Discover the essence of Logical Thinking in this detailed guide. Unveil its importance in problem-solving, decision-making, and analytical reasoning. Learn techniques to develop this crucial skill, understand common logical fallacies, and explore how Logical Thinking can be applied effectively in various aspects of life and work.

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Whether you're solving a complex problem, engaging in critical discussions, or just navigating your daily routines, Logical Thinking plays a pivotal role in ensuring that your thoughts and actions are rational and coherent. In this blog, we will discuss What is Logical Thinking in detail, its importance, and its components. You'll also learn about the various ways that make up Logical Thinking and how to develop this essential skill.    

Table of contents  

1)  Understanding Logical Thinking 

2)  Components of Logical Thinking 

3)  Why is Logical Thinking important? 

4)  What are Logical Thinking skills?   

5)  Developing Logical Thinking skills 

6)  Exercises to improve Logical Thinking 

7)  Conclusion 

Understanding Logical Thinking  

Logical Thinking is the capacity to employ reason and systematic processes to analyse information, establish connections, and reach well-founded conclusions. It entails a structured and rational approach to problem-solving and decision-making. 

For example, consider a scenario where you're presented with a puzzle. To logically think through it, you would assess the provided clues, break down the problem into smaller elements, and systematically find potential solutions. You'd avoid hasty or emotion-driven judgments and rely on evidence and sound reasoning to arrive at the correct answer, showcasing the essence of Logical Thinking in problem-solving.

C omponents of Logical Thinking  

After knowing What is Logic al Thinking, let’s move on to the key components of Logical Thinking. Logical Thinking comprises several key components that work together to facilitate reasoned analysis and problem-solving. Here are the following key components of Logical Thinking.  

1)  Deductive reasoning : Deductive reasoning involves drawing specific conclusions from general premises or facts. It's like moving from a broad idea to a more specific conclusion. For example, if all humans are mortal, and Socrates is a human, then you can logically conclude that Socrates is mortal. 

2)   I nductive reasoning : Inductive reasoning is the procedure of forming general conclusions based on specific observations or evidence. It's the opposite of deductive reasoning. For instance, if you observe that the sun has risen every day, you might inductively reason that the sun will rise again tomorrow.  

3)  Causal inference : Causal inference is the ability to identify cause-and-effect relationships between events, actions, or variables. It involves understanding that one event or action can lead to another event as a consequence . In essence, it's the recognition that a specific cause produces a particular effect.  

4)  Analogy : Analogical reasoning or analogy involves drawing similarities and making comparisons between two or more situations, objects, or concepts. It's a way of applying knowledge or understanding from one context to another by recognising shared features or characteristics. Analogical reasoning is powerful because it allows you to transfer what you know in one domain to another, making it easier to comprehend and solve new problems. 

Why is Logical Thinking Important?  

1)  Effective problem-solving : Logical Thinking equips individuals with the ability to dissect complex problems, identify patterns, and devise systematic solutions. Whether it's troubleshooting a technical issue or resolving personal dilemmas, Logical Thinking ensures that problems are approached with a structured and efficient methodology. 

2)  Enhanced decision-making : Making sound decisions is a cornerstone of success in both personal and professional life. Logical Thinking allows individuals to evaluate options, consider consequences, and choose the most rational course of action. This is particularly critical in high-stakes situations. 

3)   Critical thinking : Logical Thinking is at the core of critical thinking. It encourages individuals to question assumptions, seek evidence, and challenge existing beliefs. This capacity for critical analysis fosters a deeper understanding of complex issues and prevents the acceptance of unfounded or biased information. 

4)  Effective communication : In discussions and debates, Logical Thinking helps individuals express their ideas and viewpoints clearly and persuasively. It enables individuals to construct well-structured arguments, provide evidence, and counter opposing views, fostering productive and respectful communication. 

5)  Academic and professional success : Logical Thinking is highly valued in educational settings and the workplace. It allows students to excel academically by tackling challenging coursework and assignments. In the professional world, it's a key attribute for problem-solving, innovation, and career advancement. 

6)  Avoiding Logical fallacies : Logical Thinking equips individuals with the ability to recognise and avoid common logical fallacies such as circular reasoning, straw man arguments, and ad hominem attacks. This safeguards them from being deceived or manipulated by flawed or deceptive arguments. 

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What are Logical Thinking skills ?  

Logical Thinking skills are cognitive abilities that allow individuals to process information, analyse it systematically, and draw reasonable conclusions. These skills enable people to approach problems, decisions, and challenges with a structured and rational mindset .  

Developing Logical Thinking skills  

Developing strong Logical Thinking skills is essential for improved problem-solving, decision-making, and critical analysis. Here are some key strategies to help you enhance your Logical Thinking abilities.   

1)  Practice critical thinking : Engage in activities that require critical thinking, such as analysing articles, solving puzzles, or evaluating arguments. Regular practice sharpens your analytical skills.  

2)  L earn formal logic : Study the principles of formal logic, which provide a structured approach to reasoning. This can include topics like syllogisms, propositional logic, and predicate logic. 

3)  I dentify assumptions : When faced with a problem or argument, be aware of underlying assumptions. Question these assumptions and consider how they impact the overall reasoning. 

4)  B reak down problems : When tackling complex problems, break them down into smaller, more manageable components. Analyse each component individually before looking at the problem as a whole . 

5)   Seek diverse perspectives : Engage in discussions and debates with people who hold different viewpoints. This helps you consider a range of perspectives and strengthens your ability to construct and counter -arguments. 

6)  Read widely : Reading a variety of materials, from academic articles to literature, exposes you to different modes of reasoning and argumentation. This broadens your thinking and enhances your ability to connect ideas.  

7)  Solve puzzles and brain teasers : Engaging in puzzles, riddles, and brain teasers challenges your mind and encourages creative problem-solving. It's an enjoyable way to exercise your Logical Thinking. 

8)  Develop mathematical skills : Mathematics is a discipline that heavily relies on Logical Thinking. Learning and practising mathematical concepts and problem-solving techniques can significantly boost your logical reasoning skills. 

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Exercises to improve Logical Thinking  

Enhancing your Logical Thinking skills is achievable through various exercises and activities. Here are some practical exercises to help you strengthen your Logical Thinking abilities:  

1)   Sudoku puzzles : Solve Sudoku puzzles, as they require logical deduction to fill in the missing numbers.  

2)   Crossword puzzles : Crosswords challenge your vocabulary and logical word placement.  

3)  Brain teasers : Engage in brain teasers and riddles that encourage creative problem-solving.  

4)  Chess and board games : Play strategic board games like chess, checkers, or strategic video games that require forward thinking and planning.  

5)  Logical argumentation : Engage in debates or discussions where you must construct reasoned arguments and counter opposing viewpoints.  

6)  Coding and programming : Learn coding and programming languages which promote structured and Logical Thinking in problem-solving. 

7)  Mathematical challenges : Solve mathematical problems and equations, as mathematics is inherently logical.  

8)   Mensa puzzles : Work on Mensa puzzles, which are designed to test and strengthen Logical Thinking skills. 

9)  Logic games : Play logic-based games like Minesweeper or Mastermind.  

10)   Logical analogy exercises : Practice solving analogy exercises, which test your ability to find relationships between words or concepts.  

11)  Visual logic puzzles : Tackle visual logic puzzles like nonograms or logic grid puzzles. 

12)  Critical reading : Read books, articles, or academic papers and critically analyse the arguments and evidence presented. 

13)  Coding challenges : Participate in online coding challenges and competitions that require logical problem-solving in coding. 

14)  Scientific method : Conduct simple science experiments or projects, applying the scientific method to develop hypotheses and draw logical conclusions.  

15)   Poker or card games : Play card games like poker, where you must strategi se and make logical decisions based on probabilities and information. 

16)  Analyse real-world situations : Analyse real-world situations or news stories, evaluating the information, causes, and potential consequences. 

These exercises will help you practice and enhance your Logical Thinking skills in a fun and engaging way, making them an integral part of your problem-solving and decision-making toolkit. 

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Concluson  

In this blog, we have discussed What is Logical Thinking, its importance, its components and ways to improve this skill. When you learn how to think logically, you start gathering each and every information as much as possible, analyse the facts, and methodically choose the best way to go forward with your decision. Logical Thinking is considered the most important tool in brainstorming ideas, assessing issues and finding solutions. 

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How to Think Logically (And Permanently Solve Serious Problems)

Anthony Metivier | March 5, 2024 | Podcast , Thinking

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Yes, but not so fast.

You want to make sure you’re using the right kinds of logic for the problems at hand.

For example, you might need a non-classical logic instead of classical logic to approach a particular problem.

You see, logical thinkers do what I’m doing now:

They put the brakes on when they encounter problems and start to spin those problems around.

Why? Because logic itself often involves digging deeper and analyzing different perspectives.

For example, one of the forms of logical thinking you’re about to discover would have you instantly ask… 

Is there more than one kind of logic for solving life’s problems quickly? Or can I explore alternatives outside of logic? 

A logical thinker might do the same thing to the very idea of a “problem” itself.

This is done by “mentally rotating” the topic at hand and seeing how it might in fact not be a problem at all.

It might be a path to a solution. 

How to Think Logically: 9 Ways to Improve Your Logical Thinking Skills

At the end of the day, using the right form of logic is more about the best possible solution than the problem, but we do need to make sure we understand the problem first.

If you’ve listened to Elon Musk talk about first principles thinking, that’s a form of logic he’s using to help humans thrive on distant planets after earth dies. And communicate better here on our precious planet while we still can.

Those are real problems, and the right forms of logic are needed.

The best part?

There are a whole lot more ways to think logically to solve global and personal problems alike, so let’s get started 

One: Take A Deep Dive Into Logical Thinking

Improving logical reasoning begins by knowing the types of logic at your disposal.

Exploring the history of logic is well worth your time because it will help you see how humans discovered these principles and refined them over time through practice . 

As you’ll soon discover, many cultures have identified and used logical forms such as:

• Philosophical logic
• Informal logic
• Formal logic
• Modal logic
• Mathematical logic
• Paraconsistent logic
• Semantic logic
• Inferential logic
• Systematic logic

Related to this, you have the difference between what philosopher Elijah Millgram calls theoretical reasoning vs. practical reasoning. The first involves figuring out the facts, the second is the process of determining what courses of action to take based on what is ideally a set of accurate facts.

Now, usually what people who want to think more logically are actually after is the first category, or philosophical logic . This is also called “reasoning” and includes the skills of:

• Causal inference

Deductive reasoning is what we think of when we think of Sherlock Holmes , who builds his cases by arguing from general principles. He uses these to describe a specific series of events and solve various mysteries. 

Inductive reasoning is essentially the reverse of this process. Instead of using general principles to arrive at specifics, you use specific details to generalize. For example, you might notice that I post on this blog almost every week, and use inductive reasoning to logically determine that I am a consistent blogger. 

Causal inference helps you understand the scientific reason why and how things change. For example, why are you reading this article? I can logically infer that it is because you want to experience change and become a better thinker.

(Or maybe you want to experience more, such as all of these 11 benefits of critical thinking .)

Analogy or analogical reasoning involves making comparisons based on established examples or models. 

For example, we know that nearly every memory champion openly admits that they have normal memory that doesn’t work especially well without using mnemonic devices . By analogy, we can infer that any person with average memory abilities can become a memory champion. 

How long should you study logic? I’d suggest at least 90 days so you can get the bird’s eye overview and enough of the granular details.

Logical thinkers always make sure they have a bird’s eye view and the granular details at the same time.

Plus, as you’ll soon discover on this page, there are other fields you can read from to improve your logical thinking.

Two: Understand the Problems You’re Trying to Solve Deeply

Ever taken a quiz and realized you answered before thinking about the question? You could have gotten it correctly, but your impulses took over and you lost precious points. 

It’s not that you were being illogical. You just didn’t take the time to fully understand the question, and the reason why you failed to do so might have been logical. For example, from one perspective, in some contexts it might be perfectly logical to rush through an exam if you’re running out of time. 

But generally, we want to be sure that we deeply understand the problems we face. That is why Abraham Lincoln famously said:

“Give me six hours to chop down a tree and I will spend the first four sharpening the axe.” 

Lincoln is using an analogy here, one in which the “axe” stands in as an analogy. It speaks to spending the time needed to make sure you’re using the right tools for the job. Moreover, you make sure they are in top shape before you use them.

All the more reason to learn more about the different forms of logic. It will put more tools in your tool box and enable you to keep them sharp.

Here are 9 more critical thinking strategies to help you keep your axe sharp.

Three: Learn More About Language

A lot of people struggle to think logically because they don’t understand enough about what words mean.

Logical thinking involves nuance, so the more you know about words and their meanings, the greater mental precision in decision-making you’ll enjoy. 

To improve, here’s how to memorize vocabulary . It will help you add more meanings to words and add more definitions to those you already know. Learning word origins and how prefixes and suffixes work will help you too.

On top of learning more about words and their meanings, learning about language and logic will help, such as studying syllogisms and logical fallacies .

Go deep and learn as much as you can about fallacies so you really know your stuff. It’s easy to fall into thinking traps if you don’t.

For example, some people like to accuse others of slippery slope fallacy, without realizing that there are actually six kinds of this fallacy. 

If you want to think logically, it pays to be thorough. That’s why we’ll focus on thoroughness next.

Four: Read Quickly Without Sacrificing Thoroughness

Improving vocabulary is huge for improving logical thinking, and it will help you read faster .

But to improve your logical skills over time, you need to read thoroughly. 

I suggest you read bigger books and more of them, starting with the key textbooks in your field of interest. 

By going for the biggest and most authoritative books, you’ll be reading more logically .

Establishing foundations in your mind by reading authoritative textbooks will help you develop pattern recognition. This skill leads to faster use of the logical forms of inference we discussed in the first part of this article.

Five: Listen To Long Form Content

Short form content is causing people to make snap judgments and interrupt people before they’ve heard the full story. Logical thinkers protect themselves by practicing listening for long periods of time.

Not only is it helpful to read longer books, but you’ll learn to think much more logically when you listen to logical people think out loud.

Debates are a great way to do this and the Internet makes it possible to find many of them. 

It’s important to pay attention to both sides of the argument, however.

As you listen, practice thinking yourself by mentally rehearsing the evidence you would provide in support of your views. Also think about how you would respond.

Another tip:

Notice the holes in the arguments proposed by the debaters and list out the ways you would fill in the gaps. 

And if you want to remember more of what goes on during debates, Memory Palace Mastery is here to help.

Six: Expand Your Competence Using Multiple Media

I’ve just suggested that you experience “thinking out loud” and model it yourself.

But you’ll want to go beyond completing logical exercises in your mind. You should also:

To practice speaking logically, engage in as many discussions as you can about real problems. Sure, there’s a place for talking about movies and sports. But if you want to know how to think more logically, you’ve got to practice it yourself in real time.

Writing is always key for developing logical thinking, so I suggest you keep a journal. This simple practice will help you see your own thinking process and improve it over time. 

Combined, you will have many opportunities for self-analysis. If you can record your conversations and look at transcripts of them, all the better. 

Seven: Ask Better Questions

A lot of us ask the typical W5 questions and let it rest at that:

But to practice thinking logically, you want to go beyond these questions. Ask in addition to these questions: 

• According to whom?
• According to what precedent?
• Where isn’t this true?
• When hasn’t this been the case?

There are many variations on these questions you can ask, and I cover more along these lines in our community’s post on how to think faster .

Eight: Learn Game Theory

One of the lesser known ways to learn logical thinking is to study games and metagames. 

In brief, game theory studies areas of competition where people regularly make decisions. These decisions are influenced by other people in the area and in turn influence others. 

By modeling the ways people interact in competitive contexts, you can learn to think more logically and avoid cognitive biases that harm your performance in life. 

You’ll enjoy avoiding many problems because game theory helps train your mind to anticipate the possible outcomes of various decisions. By thinking through consequences in advance, you save yourself a lot of trouble.

Note: You can perform game theory on the past as well by thinking through what would have happened had people acted differently. This philosophical approach is called working through the counterfactuals of a historical situation and can be used on your personal life and large groups.

Some people think that game theory has limited value for everyday life, but I don’t think they’re being… logical about that. We all find ourselves in situations where we are influenced to act in certain ways and understanding these pressures will help you respond in much better ways. 

A key example is by using the Monty Hall Problem or Three Door Problem to make decisions . 

Logical exercises like The Monty Hall Problem help you think through what to do when you face choices in life.

Some people squabble over whether it is in fact logical to use this problem in life, but I can attest to its value.

For example, when I see an opportunity to do something different and feel like I want to default to my previous choices, I bring this game theoretical example to mind and remind myself to travel the “path less travelled.” 

Is the math on my side?

I think so, because I’ve gone on many adventures that logic dictates could not have happened had I chosen to stick with the same thing.

To learn more about these situations, check out the stories I share in The Victorious Mind: How to Master Memory, Meditation and Mental Well-Being .

Nine: Use Rules And Embrace Limitations

 I didn’t use to like rules. In some ways I still don’t.

But one day I was enjoying dinner with Tony Buzan, memory expert, mind map innovator and co-founder of the World Memory Championships. 

I told him about how I sometimes would switch memory systems while under time trials for numbers and playing cards. 

He said, “The rules will set you free.” 

Tony Buzan with Anthony Metivier and Phil Chambers

This is important because life, as in memory training, often gives us the opportunity to use multiple techniques.

For example, when remembering numbers, we could choose the Dominic System or the Major System , though as I discovered, it doesn’t pay off to switch from one to the other during a time trial.

But by willing to limit ourselves and stick to the “rules” of just one system, we can improve our performance.

This is true in life too, where you can learn certain rules of thumb and stick to them.

To take another example, learning the logic of Chip and Dan Heath’s W.R.A.P. technique and practicing it over time has been a tremendously helpful problem solving model for me. In fact, it’s probably the approach that has improved my critical thinking the fastest .

In fact, it’s so helpful, it is “illogical” to forget not to use it when making decisions. That’s why I memorized it using a special memory technique called ars combinatoria , something that was very important in the history of how logical thinking developed.

What rules of thumb that help you “limit” yourself to a productive form of thinking and decision making can you adopt? 

Thinking Logically Is A Rewarding Process To Enjoy For Life

Have you enjoyed learning these nine ways to improve your logical thinking? 

I hope so and hope you will make practicing some of these approaches a personal hobby.

You can easily practice logical thinking while meditating or working with an alternative to logic like Zen.

As a final tip, it would only be logical for me to recommend the opposite of logic. 

You see, there are practices like Zen which evolved to help us see and experience the limits of logic. Zen turns language against itself to help us experience mental relief from the problems we think so hard about. 

One of the best critical thinking books that situates the topic in the larger realm of computational thinking for both humans and machines is Gödel Escher Bach . For a collection of koans to explore, The Gateless Gate by Mumon is an interesting source.

I mention the opposite of logic not only because it is logical to do so. To fully experience the rewards of logical thinking, you need to be able to step outside of thinking altogether. 

Questioning deeply is not enough. We need to question the process of questioning itself as a lifelong learning habit.

So on that note, let the questioning begin. Let me know which of these ways to improve your thinking you’re going to try out and what questions about logic do you still have?

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7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

• Concepts and inferences (7.1)
• Procedural knowledge (7.1)
• Metacognition (7.1)
• Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
• Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
• Fixation:  functional fixedness, mental set  (7.3)
• Algorithms, heuristics, and the role of confirmation bias (7.3)
• Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

• Identify which type of knowledge a piece of information is (7.1)
• Recognize examples of deductive and inductive reasoning (7.2)
• Recognize judgments that have probably been influenced by the availability heuristic (7.2)
• Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

• Use the principles of critical thinking to evaluate information (7.1)
• Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
• Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

• Take a few minutes to write down everything that you know about dogs.
• Do you believe that:
• Psychic ability exists?
• Hypnosis is an altered state of consciousness?
• Magnet therapy is effective for relieving pain?
• Aerobic exercise is an effective treatment for depression?
• UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

• Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
• Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
• Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

• Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

• What percentage of kidnappings are committed by strangers?
• Which area of the house is riskiest: kitchen, bathroom, or stairs?
• What is the most common cancer in the US?
• What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

• Statement #1: The forecaster on Channel 2 said it is going to rain today.
• Statement #2: The forecaster on Channel 5 said it is going to rain today.
• Statement #3: It is very cloudy and humid.
• Statement #4: You just heard thunder.
• Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

• A particular class will be interesting/useful/difficult
• You will be able to finish writing a paper by next week if you go out tonight
• Your laptop’s battery will last through the next trip to the library
• You will not miss anything important if you skip class tomorrow
• Your instructor will not notice if you skip class tomorrow
• You will be able to find a book that you will need for a paper
• There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

• What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

• Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

• Please take a few minutes to list a number of problems that you are facing right now.
• Now write about a problem that you recently solved.
• What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

• Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
• Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
• Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
• Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
• Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
• Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

Introduction to Psychology Copyright © 2020 by Ken Gray; Elizabeth Arnott-Hill; and Or'Shaundra Benson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Logical Thinking

What is logical thinking.

Logical thinking is a fundamental cognitive ability that allows individuals to analyze, reason, and make sound decisions based on objective facts and evidence. It entails the ability to think critically, systematically, and coherentlWithin the context of problem-solving and decision-making, logical thinking enables individuals to identify patterns, recognize relationships, and draw logical conclusions.

Key Features of Logical Thinking

1. Deductive Reasoning: Logical thinking involves deducing specific conclusions from general principles or premises. It follows a top-down approach, using logic and established rules to reach valid conclusions.

2. Inductive Reasoning: This component of logical thinking involves inferring general principles or conclusions from specific observations or instances. Inductive reasoning utilizes patterns, data, and examples to arrive at probable conclusions.

3. Analytical Skills: Logical thinking requires strong analytical skills to break down complex problems or situations into smaller, more manageable components. By breaking down the elements and identifying the relationships between them, individuals can better understand the larger picture and draw logical conclusions.

4. Critical Thinking: Logical thinking relies heavily on critical thinking to evaluate arguments, ideas, and evidence objectively. It involves questioning assumptions, identifying biases, and applying logical principles to assess the validity of statements and arguments.

5. Problem-solving: Individuals with strong logical thinking skills excel in problem-solving. They can approach problems analytically, logically, and systematically, breaking them down into smaller parts, assessing possible solutions, and choosing the most effective course of action.

6. Decision-making: Logical thinking is closely linked to effective decision-making. By evaluating all available information, assessing potential outcomes, and considering the logical consequences of each option, individuals can make informed decisions that are rational and objective.

Why is Logical Thinking Important?

Logical thinking is a crucial skillset in various aspects of life and work. Whether in academic pursuits, professional endeavors, or everyday situations, honing logical thinking abilities can lead to better problem-solving, more effective decision-making, and improved overall cognitive functioning.

In academic settings, logical thinking enables students to excel in subjects such as mathematics, science, and philosophy, where reasoning and analytical skills are paramount. In the workplace, logical thinking is highly valued across disciplines, including business, engineering, law, and technology, as it allows employees to solve complex problems and make sound decisions based on objective analysis.

Furthermore, logical thinking fosters a more rational and critical approach to information, discouraging the acceptance of fallacious arguments or misinformation. It promotes a deeper understanding of complex issues and encourages individuals to challenge assumptions, leading to a more well-informed and intellectually engaged society.

Why Assess a Candidate's Logical Thinking Skill Level?

Assessing a candidate's logical thinking skill level is essential for organizations seeking to hire individuals who can approach complex problems with precision and make informed decisions based on objective analysis. Evaluating logical thinking abilities during the hiring process can provide numerous benefits, including:

Better Problem-Solving: Logical thinking is directly linked to effective problem-solving. By assessing a candidate's logical thinking skills, organizations can identify individuals who possess the ability to analyze and break down complex problems into manageable components, leading to more efficient and innovative solutions.

Enhanced Decision-Making: Logical thinking enables individuals to weigh evidence, consider multiple perspectives, and draw logical conclusions. By assessing a candidate's logical thinking abilities, organizations can identify individuals who can make well-informed and rational decisions based on objective analysis, minimizing the risks associated with subjective or biased decision-making.

Improved Critical Thinking: Critical thinking is closely intertwined with logical thinking. By evaluating a candidate's logical thinking abilities, organizations can gauge their capacity to evaluate arguments, identify logical fallacies, and assess the validity of information. This ensures that organizations hire individuals who can think critically and approach information with a logical and analytical mindset.

Efficient Resource Allocation: Assessing a candidate's logical thinking skill level helps organizations allocate resources more effectively. Individuals with strong logical thinking abilities can analyze situations, identify potential challenges or risks, and develop well-structured action plans. This allows organizations to optimize their resources and mitigate potential setbacks or roadblocks.

Promotion of Innovation: Logical thinking is crucial for fostering innovation and creativity within organizations. Candidates with strong logical thinking skills are more likely to think outside the box, consider alternative solutions, and explore new possibilities. Assessing logical thinking abilities can help organizations identify individuals who can bring fresh perspectives and contribute to innovative problem-solving.

Reduced Errors and Mistakes: Effective logical thinking minimizes errors and mistakes in decision-making and problem-solving processes. By assessing a candidate's logical thinking skills, organizations can ensure that they hire individuals who can critically evaluate information, identify inconsistencies, and avoid errors that may have significant consequences in critical or sensitive situations.

By assessing a candidate's logical thinking skill level, organizations can ensure that they hire individuals who possess the cognitive abilities necessary for success in problem-solving, decision-making, and critical analysis. Alooba's comprehensive assessment platform can help organizations evaluate logical thinking skills effectively and identify top-quality candidates to drive their success.

Assessing a Candidate's Logical Thinking Skill Level with Alooba

Alooba's advanced assessment platform offers a seamless solution for evaluating a candidate's logical thinking skill level. With our comprehensive range of assessment tools and features, organizations can confidently and efficiently assess candidates' logical thinking abilities. Here's how Alooba can help:

Customizable Tests : Alooba allows organizations to create customized logical thinking tests tailored to their specific needs. Whether it's deductive reasoning, inductive reasoning, analytical skills, or critical thinking, organizations can design tests that accurately measure a candidate's logical thinking abilities.

Versatile Test Formats : Alooba offers various test formats designed to assess logical thinking skills effectively. From multiple-choice tests that evaluate a candidate's conceptual understanding to practical assessments where candidates analyze data or write SQL statements, Alooba covers a wide range of logical thinking scenarios.

Objective Evaluation : Alooba's assessment platform utilizes an autograding system for objective evaluation of logical thinking tests. This ensures consistent and fair assessment results, enabling organizations to compare and rank candidates based on their logical thinking abilities accurately.

In-depth Assessments : For a more comprehensive evaluation of logical thinking skills, Alooba provides in-depth assessments. These assessments allow candidates to demonstrate their logical thinking abilities through tasks such as diagramming, coding, or written responses. Expert evaluators manually assess these tasks, providing valuable insights into a candidate's capabilities.

Alooba Interview Product : Alooba's structured interviews with predefined topics and questions offer an additional avenue to assess a candidate's logical thinking skills. Interviewers can use a marking guide for objective evaluation, ensuring consistency in the assessment process.

Alooba's Vision : Alooba's vision is to create a world where everyone can get the job they deserve. By assessing candidates' logical thinking skill level, organizations can make fair and informed hiring decisions, matching top-quality candidates with the opportunities they deserve.

With Alooba's comprehensive assessment platform, organizations can confidently evaluate and measure a candidate's logical thinking skill level. Save time, streamline your hiring process, and discover the candidates with the logical thinking abilities your organization needs to excel. Unleash the power of logical thinking assessments with Alooba.

Components of Logical Thinking

Logical thinking encompasses various subtopics, each contributing to an individual's overall proficiency in this valuable cognitive skill. Understanding the components of logical thinking provides a comprehensive view of the abilities necessary for effective problem-solving and decision-making. Here are some key components to consider:

Deductive Reasoning : Deductive reasoning involves drawing specific conclusions from general principles or premises. It requires individuals to apply logical rules and principles to reach valid and sound conclusions based on the given information.

Inductive Reasoning : Inductive reasoning involves making general conclusions based on specific observations or instances. Individuals utilize patterns, data, and examples to infer broader principles, allowing them to form probable conclusions.

Analytical Skills : Analytical skills are crucial for logical thinking, enabling individuals to break down complex problems or situations into smaller, more manageable components. This component focuses on identifying relationships, patterns, and underlying structures to gain a deeper understanding of the overall problem.

Critical Thinking : Critical thinking is closely associated with logical thinking, requiring individuals to assess, analyze, and evaluate arguments and evidence objectively. It involves questioning assumptions, identifying biases, and employing logical principles to determine the validity and soundness of statements and arguments.

Problem-Solving Strategies : Logical thinking plays a significant role in effective problem-solving strategies. It involves the systematic and coherent approach of breaking down problems, identifying the core issues, exploring possible solutions, and selecting the most appropriate course of action.

Decision-Making Processes : Logical thinking provides the foundation for robust decision-making processes. It allows individuals to evaluate all available information objectively, consider potential outcomes, and analyze the logical consequences of each decision. Logical thinking ensures rational and informed decision-making.

Pattern Recognition : Pattern recognition is vital in logical thinking, as it involves the ability to identify regularities, repetitions, and systematic relationships within data or information. Individuals proficient in pattern recognition can detect underlying structures and use them to draw logical insights.

Logical Communication : Logical thinking also extends to effective communication. It includes the ability to present ideas, arguments, and solutions in a logical and coherent manner, allowing others to understand and follow the train of thought.

By understanding and developing these key components, individuals can enhance their logical thinking skills, enabling them to approach problems and decision-making with precision and clarity. With Alooba's assessment platform, you can measure and evaluate these components to identify candidates who possess strong logical thinking abilities, ensuring you make informed hiring decisions.

Practical Applications of Logical Thinking

Logical thinking is a versatile cognitive skill that finds application in various aspects of life, work, and decision-making processes. By utilizing logical thinking, individuals can approach challenges, solve problems, and navigate complex situations with clarity and sound judgment. Here are some practical applications where logical thinking is commonly employed:

Problem-Solving: Logical thinking is essential for effective problem-solving. Whether it's troubleshooting technical issues, resolving conflicts, or finding innovative solutions, logical thinking enables individuals to break down problems, analyze the components, and apply logical reasoning to identify the most suitable course of action.

Critical Analysis: Logical thinking plays a significant role in critical analysis. It helps individuals evaluate information, arguments, and evidence objectively, enabling them to identify flaws, inconsistencies, or biases. By employing logical thinking, individuals can make informed judgments and arrive at well-supported conclusions.

Decision-Making: Logical thinking provides a foundation for rational decision-making. It allows individuals to consider all available information, assess potential outcomes, and analyze the logical implications of each decision. Logical thinking helps individuals make sound decisions based on objective analysis, minimizing the influence of emotions or biases.

Scientific and Mathematical Reasoning: Logical thinking is fundamental in scientific and mathematical reasoning processes. It involves following logical steps, applying rules and principles, and drawing logical conclusions. In fields such as physics, computer science, and mathematics, logical thinking ensures rigorous and accurate problem-solving.

Data Analysis: Logical thinking is crucial in data analysis. It enables individuals to identify patterns, make connections between variables, and draw logical insights from large datasets. By applying logical thinking, individuals can derive meaningful information from data, leading to informed decisions and insights.

Strategic Planning: Logical thinking is invaluable in strategic planning processes. It assists individuals in assessing the current situation, identifying goals, analyzing potential options, and formulating logical strategies. Logical thinking ensures that plans are coherent, feasible, and aligned with the organization's objectives.

Communication: Logical thinking enhances effective communication. It enables individuals to organize their thoughts in a logical and coherent manner, ensuring clear and concise communication of ideas, arguments, and instructions. Logical thinking helps individuals convey their message effectively and facilitate understanding.

By recognizing the practical applications of logical thinking, individuals and organizations can harness this cognitive skill to their advantage. Alooba's assessment platform allows you to evaluate and identify candidates with strong logical thinking skills, ensuring you have the right talent to tackle complex challenges and make informed decisions.

Roles that Require Strong Logical Thinking Skills

Logical thinking is a valuable skillset that plays a crucial role in numerous job functions. Certain roles particularly benefit from individuals who possess strong logical thinking skills. Here are some of the key roles where logical thinking abilities are highly relevant:

Data Analyst : Data analysts rely on logical thinking to interpret and analyze complex data sets. They apply logical reasoning to identify patterns, draw meaningful insights, and make data-driven recommendations.

Data Scientist : Data scientists leverage logical thinking to apply statistical models, algorithms, and machine learning techniques. They use logical reasoning to process data, test hypotheses, and develop predictive models.

Data Engineer : Data engineers employ logical thinking to design, construct, and maintain data systems. They utilize logical reasoning to develop efficient database architectures and ensure data integrity.

Insights Analyst : Insights analysts rely on logical thinking to interpret market trends, consumer behavior, and business performance. They use logical reasoning to draw meaningful conclusions from data and provide valuable insights.

Marketing Analyst : Marketing analysts utilize logical thinking to evaluate marketing strategies, measure campaign effectiveness, and analyze customer data. They apply logical reasoning to optimize marketing initiatives and drive business growth.

Product Analyst : Product analysts use logical thinking to assess market trends, user feedback, and product performance. They apply logical reasoning to identify opportunities for improvement and make data-informed decisions for product development.

Analytics Engineer : Analytics engineers employ logical thinking to design and develop systems for data analysis. They apply logical reasoning to implement data pipelines, automate data processes, and ensure accurate data reporting.

Artificial Intelligence Engineer : Artificial intelligence engineers rely on logical thinking to develop intelligent systems and algorithms. They apply logical reasoning to design and optimize algorithms for machine learning and decision-making.

Back-End Engineer : Back-end engineers use logical thinking to develop and maintain server-side applications. They apply logical reasoning to ensure seamless data flow, optimize system performance, and resolve technical issues.

Data Architect : Data architects employ logical thinking to design and structure data systems. They use logical reasoning to create data models, define data governance policies, and ensure data accuracy and integrity.

Data Governance Analyst : Data governance analysts rely on logical thinking to establish and enforce data management policies. They apply logical reasoning to ensure compliance, data quality, and secure data access.

Deep Learning Engineer : Deep learning engineers utilize logical thinking to design and implement deep learning models. They use logical reasoning to optimize neural networks, analyze model performance, and improve complex algorithms.

These roles showcase the significance of logical thinking in various job functions. By evaluating candidates' logical thinking skills using Alooba's assessment platform, organizations can identify top talent for these roles and ensure that their teams possess the necessary cognitive abilities to excel in these positions.

Associated Roles

Analytics engineer.

Analytics Engineers are responsible for preparing data for analytical or operational uses. These professionals bridge the gap between data engineering and data analysis, ensuring data is not only available but also accessible, reliable, and well-organized. They typically work with data warehousing tools, ETL (Extract, Transform, Load) processes, and data modeling, often using SQL, Python, and various data visualization tools. Their role is crucial in enabling data-driven decision making across all functions of an organization.

Artificial Intelligence Engineer

Artificial Intelligence Engineers are responsible for designing, developing, and deploying intelligent systems and solutions that leverage AI and machine learning technologies. They work across various domains such as healthcare, finance, and technology, employing algorithms, data modeling, and software engineering skills. Their role involves not only technical prowess but also collaboration with cross-functional teams to align AI solutions with business objectives. Familiarity with programming languages like Python, frameworks like TensorFlow or PyTorch, and cloud platforms is essential.

Back-End Engineer

Back-End Engineers focus on server-side web application logic and integration. They write clean, scalable, and testable code to connect the web application with the underlying services and databases. These professionals work in a variety of environments, including cloud platforms like AWS and Azure, and are proficient in programming languages such as Java, C#, and NodeJS. Their expertise extends to database management, API development, and implementing security and data protection solutions. Collaboration with front-end developers and other team members is key to creating cohesive and efficient applications.

Data Analyst

Data Analysts draw meaningful insights from complex datasets with the goal of making better decisions. Data Analysts work wherever an organization has data - these days that could be in any function, such as product, sales, marketing, HR, operations, and more.

Data Architect

Data Architects are responsible for designing, creating, deploying, and managing an organization's data architecture. They define how data is stored, consumed, integrated, and managed by different data entities and IT systems, as well as any applications using or processing that data. Data Architects ensure data solutions are built for performance and design analytics applications for various platforms. Their role is pivotal in aligning data management and digital transformation initiatives with business objectives.

Data Engineer

Data Engineers are responsible for moving data from A to B, ensuring data is always quickly accessible, correct and in the hands of those who need it. Data Engineers are the data pipeline builders and maintainers.

Data Governance Analyst

Data Governance Analysts play a crucial role in managing and protecting an organization's data assets. They establish and enforce policies and standards that govern data usage, quality, and security. These analysts collaborate with various departments to ensure data compliance and integrity, and they work with data management tools to maintain the organization's data framework. Their goal is to optimize data practices for accuracy, security, and efficiency.

Data Scientist

Data Scientists are experts in statistical analysis and use their skills to interpret and extract meaning from data. They operate across various domains, including finance, healthcare, and technology, developing models to predict future trends, identify patterns, and provide actionable insights. Data Scientists typically have proficiency in programming languages like Python or R and are skilled in using machine learning techniques, statistical modeling, and data visualization tools such as Tableau or PowerBI.

Deep Learning Engineer

Deep Learning Engineers’ role centers on the development and optimization of AI models, leveraging deep learning techniques. They are involved in designing and implementing algorithms, deploying models on various platforms, and contributing to cutting-edge research. This role requires a blend of technical expertise in Python, PyTorch or TensorFlow, and a deep understanding of neural network architectures.

Insights Analyst

Insights Analysts play a pivotal role in transforming complex data sets into actionable insights, driving business growth and efficiency. They specialize in analyzing customer behavior, market trends, and operational data, utilizing advanced tools such as SQL, Python, and BI platforms like Tableau and Power BI. Their expertise aids in decision-making across multiple channels, ensuring data-driven strategies align with business objectives.

Marketing Analyst

Marketing Analysts specialize in interpreting data to enhance marketing efforts. They analyze market trends, consumer behavior, and campaign performance to inform marketing strategies. Proficient in data analysis tools and techniques, they bridge the gap between data and marketing decision-making. Their role is crucial in tailoring marketing efforts to target audiences effectively and efficiently.

Product Analyst

Product Analysts utilize data to optimize product strategies and enhance user experiences. They work closely with product teams, leveraging skills in SQL, data visualization (e.g., Tableau), and data analysis to drive product development. Their role includes translating business requirements into technical specifications, conducting A/B testing, and presenting data-driven insights to inform product decisions. Product Analysts are key in understanding customer needs and driving product innovation.

Other names for Logical Thinking include Problem Solving , and Critical Thinking .

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For data engineering & analytics these take-home assignments we were doing ourselves are a bit time consuming so we wanted to automate that and also reduce the time candidates were spending on the assessment.

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Fluency, Reasoning and Problem Solving: What This Looks Like In Every Math Lesson

Neil Almond

Fluency, reasoning and problem solving are central strands of mathematical competency, as recognized by the National Council of Teachers of Mathematics (NCTM) and the National Research Council’s report ‘Adding It Up’.

They are key components to the Standards of Mathematical Practice, standards that are interwoven into every mathematics lesson. Here we look at how these three approaches or elements of math can be interwoven in a child’s math education through elementary and middle school.

We look at what fluency, reasoning and problem solving are, how to teach them, and how to know how a child is progressing in each – as well as what to do when they’re not, and what to avoid.

The hope is that this blog will help elementary and middle school teachers think carefully about their practice and the pedagogical choices they make around the teaching of what the common core refers to as ‘mathematical practices’, and reasoning and problem solving in particular.

Before we can think about what this would look like in Common Core math examples and other state-specific math frameworks, we need to understand the background to these terms.

What is fluency in math?

What is reasoning in math, what is problem solving in math, mathematical problem solving is a learned skill, performance vs learning: what to avoid when teaching fluency, reasoning, and problem solving.

• What IS ‘performance vs learning’?
• Teaching to “cover the curriculum” hinders development of strong problem solving skills.
• Fluency and reasoning – Best practice in a lesson, a unit, and a semester

Best practice for problem solving in a lesson, a unit, and a semester 

Fluency, reasoning and problem solving should not be taught by rote .

The Ultimate Guide to Problem Solving Techniques

Develop problem solving skills in the classroom with this free, downloadable worksheet

Fluency in math is a fairly broad concept. The basics of mathematical fluency – as defined by the Common Core State Standards for math – involve knowing key mathematical skills and being able to carry them out flexibly, accurately and efficiently.

But true fluency in math (at least up to middle school) means being able to apply the same skill to multiple contexts, and being able to choose the most appropriate method for a particular task.

Fluency in math lessons means we teach the content using a range of representations, to ensure that all students understand and have sufficient time to practice what is taught.

Read more: How the best schools develop math fluency

Reasoning in math is the process of applying logical thinking to a situation to derive the correct problem solving strategy for a given question, and using this method to develop and describe a solution.

Put more simply, mathematical reasoning is the bridge between fluency and problem solving. It allows students to use the former to accurately carry out the latter.

Read more: Developing math reasoning: the mathematical skills required and how to teach them .

It’s sometimes easier to start off with what problem solving is not. Problem solving is not necessarily just about answering word problems in math. If a child already has a readily available method to solve this sort of problem, problem solving has not occurred. Problem solving in math is finding a way to apply knowledge and skills you have to answer unfamiliar types of problems.

Read more: Math problem solving: strategies and resources for primary school teachers .

We are all problem solvers

First off, problem solving should not be seen as something that some students can do and some cannot. Every single person is born with an innate level of problem-solving ability.

Early on as a species on this planet, we solved problems like recognizing faces we know, protecting ourselves against other species, and as babies the problem of getting food (by crying relentlessly until we were fed).

All these scenarios are a form of what the evolutionary psychologist David Geary (1995) calls biologically primary knowledge. We have been solving these problems for millennia and they are so ingrained in our DNA that we learn them without any specific instruction.

Why then, if we have this innate ability, does actually teaching problem solving seem so hard?

As you might have guessed, the domain of mathematics is far from innate. Math doesn’t just happen to us; we need to learn it. It needs to be passed down from experts that have the knowledge to novices who do not.

This is what Geary calls biologically secondary knowledge. Solving problems (within the domain of math) is a mixture of both primary and secondary knowledge.

The issue is that problem solving in domains that are classified as biologically secondary knowledge (like math) can only be improved by practicing elements of that domain.

So there is no generic problem-solving skill that can be taught in isolation and transferred to other areas.

This will have important ramifications for pedagogical choices, which I will go into more detail about later on in this blog.

The educationalist Dylan Wiliam had this to say on the matter: ‘for…problem solving, the idea that students can learn these skills in one context and apply them in another is essentially wrong.’ (Wiliam, 2018) So what is the best method of teaching problem solving to elementary and middle school math students?

The answer is that we teach them plenty of domain specific biological secondary knowledge – in this case, math. Our ability to successfully problem solve requires us to have a deep understanding of content and fluency of facts and mathematical procedures.

Here is what cognitive psychologist Daniel Willingham (2010) has to say:

‘Data from the last thirty years leads to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.

The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).’

Colin Foster (2019), a reader in Mathematics Education in the Mathematics Education Center at Loughborough University, UK, says, ‘I think of fluency and mathematical reasoning, not as ends in themselves, but as means to support students in the most important goal of all: solving problems.’

In that paper he produces this pyramid:

This is important for two reasons:

1)    It splits up reasoning skills and problem solving into two different entities

2)    It demonstrates that fluency is not something to be rushed through to get to the ‘problem solving’ stage but is rather the foundation of problem solving.

In my own work I adapt this model and turn it into a cone shape, as education seems to have a problem with pyramids and gross misinterpretation of them (think Bloom’s taxonomy).

Notice how we need plenty of fluency of facts, concepts, procedures and mathematical language.

Having this fluency will help with improving logical reasoning skills, which will then lend themselves to solving mathematical problems – but only if it is truly learnt and there is systematic retrieval of this information carefully planned across the curriculum.

I mean to make no sweeping generalization here; this was my experience both at university when training and from working in schools.

At some point, schools become obsessed with the ridiculous notion of moving students through content at an accelerated rate. I have heard it used in all manner of educational contexts while training and being a teacher. ‘You will need to show ‘accelerated progress in math’ in this lesson,’ ‘School officials will be looking for ‘accelerated progress’ etc.

I have no doubt that all of this came from a good place and from those wanting the best possible outcomes – but it is misguided.

I remember being told that we needed to get students onto the problem solving questions as soon as possible to demonstrate this mystical ‘accelerated progress’.

This makes sense; you have a group of students and you have taken them from not knowing something to working out pretty sophisticated 2-step or multi-step word problems within an hour. How is that not ‘accelerated progress?’

This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the students to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; give the students some reasoning and word problem questions and that was it.

I wondered if I was the only one who had been taught this while at university so I did a quick poll on Twitter and found that was not the case.

I know these numbers won’t be big enough for a representative sample but it still shows that others are familiar with this approach.

The issue with the lesson framework I mentioned above is that it does not take into account ‘performance vs learning.’

What IS ‘performance vs learning’?

The premise is that performance in a lesson is not a good proxy for learning.

Yes, those students were performing well after I had modeled a mathematical procedure for them, and managed to get questions correct.

But if problem solving depends on a deep knowledge of mathematics, this approach to lesson structure is going to be very ineffective.

As mentioned earlier, the reasoning and problem solving questions were based on the same math content as the fluency exercises, making it more likely that students would solve problems correctly whether they fully understood them or not.

Chances are that all they’d need to do is find the numbers in the questions and use the same method they used in the fluency section to get their answers (a process referred to as “number plucking”) – not exactly high level problem solving skills.

Teaching to “cover the curriculum” hinders development of strong problem solving skills.

This is one of my worries with ‘math mastery schemes’ that block content so that, in some circumstances, it is not looked at again until the following year (and with new objectives).

The pressure for teachers to ‘get through the curriculum’ results in many opportunities to revisit content being missed in the classroom.

Students are unintentionally forced to skip ahead in the fluency, reasoning, problem solving chain without proper consolidation of the earlier processes.

As David Didau (2019) puts it, ‘When novices face a problem for which they do not have a conveniently stored solution, they have to rely on the costlier means-end analysis.

This is likely to lead to cognitive overload because it involves trying to work through and hold in mind multiple possible solutions.

It’s a bit like trying to juggle five objects at once without previous practice. Solving problems is an inefficient way to get better at problem solving.’

Fluency and reasoning – Best practice in a lesson, a unit, and a semester

By now I hope you have realized that when it comes to problem solving, fluency is king. As such we should look to mastery math based teaching to ensure that the fluency that students need is there.

The answer to what fluency looks like will obviously depend on many factors, including the content being taught and the grade you find yourself teaching.

But we should not consider rushing them on to problem solving or logical reasoning in the early stages of this new content as it has not been learnt, only performed.

I would say that in the early stages of learning, content that requires the end goal of being fluent should take up the majority of lesson time – approximately 60%. The rest of the time should be spent rehearsing and retrieving other knowledge that is at risk of being forgotten about.

This blog on mental math strategies students should learn at each grade level is a good place to start when thinking about the core aspects of fluency that students should achieve.

Little and often is a good mantra when we think about fluency, particularly when revisiting the key mathematical skills of number bond fluency or multiplication fluency. So when it comes to what fluency could look like throughout the day, consider all the opportunities to get students practicing.

They could chant multiplication facts when transitioning. If a lesson in another subject has finished earlier than expected, use that time to quiz students on number bonds. Have fluency exercises as part of the morning work.

Read more: How to teach multiplication for instant recall

What about best practice over a longer period?

Thinking about what fluency could look like across a unit of work would again depend on the unit itself.

Look at this unit below from a popular scheme of work.

They recommend 20 days to cover 9 objectives. One of these specifically mentions problem solving so I will forget about that one at the moment – so that gives 8 objectives.

I would recommend that the fluency of this unit look something like this:

This type of structure is heavily borrowed from Mark McCourt’s phased learning idea from his book ‘Teaching for Mastery.’

This should not be seen as something set in stone; it would greatly depend on the needs of the class in front of you. But it gives an idea of what fluency could look like across a unit of lessons – though not necessarily all math lessons.

When we think about a semester, we can draw on similar ideas to the one above except that your lessons could also pull on content from previous units from that semester.

So lesson one may focus 60% on the new unit and 40% on what was learnt in the previous unit.

The structure could then follow a similar pattern to the one above.

When an adult first learns something new, we cannot solve a problem with it straight away. We need to become familiar with the idea and practice before we can make connections, reason and problem solve with it.

The same is true for students. Indeed, it could take up to two years ‘between the mathematics a student can use in imitative exercises and that they have sufficiently absorbed and connected to use autonomously in non-routine problem solving.’ (Burkhardt, 2017).

Practice with facts that are secure

So when we plan for reasoning and problem solving, we need to be looking at content from 2 years ago to base these questions on.

You could get students in 3rd grade to solve complicated place value problems with the numbers they should know from 1st or 2nd grade. This would lessen the cognitive load , freeing up valuable working memory so they can actually focus on solving the problems using content they are familiar with.

Increase complexity gradually

Once they practice solving these types of problems, they can draw on this knowledge later when solving problems with more difficult numbers.

This is what Mark McCourt calls the ‘Behave’ phase. In his book he writes:

‘Many teachers find it an uncomfortable – perhaps even illogical – process to plan the ‘Behave’ phase as one that relates to much earlier learning rather than the new idea, but it is crucial to do so if we want to bring about optimal gains in learning, understanding and long term recall.’  (Mark McCourt, 2019)

This just shows the fallacy of ‘accelerated progress’; in the space of 20 minutes some teachers are taught to move students from fluency through to non-routine problem solving, or we are somehow not catering to the needs of the child.

When considering what problem solving lessons could look like, here’s an example structure based on the objectives above.

It is important to reiterate that this is not something that should be set in stone. Key to getting the most out of this teaching for mastery approach is ensuring your students (across abilities) are interested and engaged in their work.

Depending on the previous attainment and abilities of the children in your class, you may find that a few have come across some of the mathematical ideas you have been teaching, and so they are able to problem solve effectively with these ideas.

Equally likely is encountering students on the opposite side of the spectrum, who may not have fully grasped the concept of place value and will need to go further back than 2 years and solve even simpler problems.

In order to have the greatest impact on class performance, you will have to account for these varying experiences in your lessons.

Read more: 

• Math Mastery Toolkit : A Practical Guide To Mastery Teaching And Learning
• Problem Solving and Reasoning Questions and Answers
• Get to Grips with Math Problem Solving For Elementary Students
• Mixed Ability Teaching for Mastery: Classroom How To
• 21 Math Challenges To Really Stretch Your More Able Students
• Why You Should Be Incorporating Stem Sentences Into Your Elementary Math Teaching

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by primary school lead teacher Neil Almond and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.

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Ultimate guide to metacognition [free].

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The development of the reasoning brain and how to foster logical reasoning skills

Early childhood development / Effective lifelong learning / Learning mathematics

Executive summary

Learning to reason logically is necessary for the growth of critical and scientific thinking in children. Yet, both psychological and neural evidence indicates that logical reasoning is hard even for educated adults. Here, we examine the factors that scaffold the emergence of logical reasoning in children. Evidence suggests that the development of reasoning with concrete information can be accounted for by the development of both world knowledge and self-regulation. The transition from concrete to abstract reasoning, however, is a challenge for children. Children’s development of reasoning may be supported by encouraging both divergent thinking and reasoning at levels of abstraction that are just above reasoners’ current levels, alongside activities in which children reason with others.

Introduction

It is often argued that one of the most fundamental goals of education is to nurture critical thinking, that is, to teach children to employ good reasoning skills when developing their beliefs. Therefore, fostering logical reasoning should be an important goal for education: Children should learn to provide logical reasons for their opinions and should be able to distinguish between good and bad arguments. This is likely to be important for their effective exercise of citizenship as adults. For example, logical reasoning could tell you that it is unwarranted to conclude “All Muslims are terrorists” from the assertions “All the 9/11 perpetrators are Muslims” and “All the 9/11 perpetrators are terrorists.” Yet, many educated adults still draw such a conclusion, most likely because fear and bias can overcome rational thinking. This suggests that logical reasoning is hard even for educated adults, a conclusion that is supported by a wealth of psychological studies. Perhaps the most striking demonstration of the difficulty of logical reasoning was discovered by the psychologist Peter Wason in 1966 1 . Wason designed a task in which he presented participants with four playing cards, each with a letter on one side and a number on the other side. For example, the cards could be as follow:

A         B         2          3

Participants were then shown the conditional rule “If a card has the letter A on one side, then it has the number 2 on the other side.” The task consisted of selecting those cards that had to be turned over to discover whether the rule was true or false. Since Wason’s study, that task has been performed many times, and the results are always the same. Most people select either the A card alone or sometimes both the cards A and 2. However, very few adults, even highly educated, typically choose the 3 card. This is despite the fact that discovering what is on the other side of the 3 card is necessary to evaluate whether the rule is true or false (i.e., if there is an A on the other side of the 3, the rule is false). This reasoning failure has puzzled psychologists for decades because it questions the long-standing assumption that human beings are inherently rational. Why is it so hard for participants to select the 3 card? Neuroscience research suggests that it is because it is much more difficult for the brain to focus on the elements that are absent from the rule (e.g., 3) than on the elements that are present (e.g., A) 2 . Thus, selecting the 3 card requires much more extensive brain activation in several brain regions (primarily involved in attention and concentration) to overcome that tendency (see Figure 1). So, how can we get people to activate more of their reasoning brain and act more rationally on this task? One of the first ideas that comes to mind would be to teach them logic. Cheng and colleagues 3 have tested this. The researchers presented the Wason selection task to college students before and after they took a whole-semester introductory class in logic (about 40 hours of lectures). Surprisingly, they found no difference in the students’ poor performance between the beginning and the end of the semester. In other words, a whole semester of learning about logic did not help students make any less error on the task! What, then, can train the reasoning brain? To answer that question, it is interesting to turn to what we know about the development of logical reasoning in children.

Figure 1. The reasoning brain. Location of the brain regions (in red, blue, and white) that are activated when participants reason with elements that are not present in the rule in the Wason card task. Activations are displayed on pictures of the brain taken using a magnetic resonance imaging scanner. (Reproduced from Ref. 2 )

The development of concrete logical reasoning in children

It is clear that even young children can use some logical reasoning when concrete information is involved. For instance, most 6-year-olds can draw the conclusion “The person is hurt” from the statements “If the person breaks his arm, the person will be hurt” and “The person breaks his arm.” However, the reasoning abilities of young children are limited. For example, many 6-year-olds would also draw the conclusion “The person broke his arm” from the statements “If the person breaks his arm, the person will be hurt” and “The person is hurt.” This, however, is an invalid conclusion because there may be many other reasons why a person could be hurt. Children will progressively understand this and will make this type of reasoning error less and less as they get older. By the time they reach the end of elementary school, most children are able to refrain from concluding “The person broke his arm” from the statements “If the person breaks his arm, the person will be hurt” and “The person is hurt” 4 . Critically, this increased reasoning ability is mirrored by an increase in the ability to think about alternate causes for a given consequence. For example, older children are much more able than younger children to think about the many other reasons why someone would be hurt, like getting sick, breaking a leg, cutting a finger, etc. In other words, better reasoning ability with age is associated with a better ability to consider alternatives from stored knowledge. Clearly, however, children differ in terms of what they know about the world. This predicts that those who have better world knowledge and can think about more alternatives should be better reasoners than the others. And this is exactly what has been shown in several studies 4 .

Interestingly, the importance of world knowledge for reasoning has a paradoxical effect: It can make children poorer reasoners on some occasions. For example, children who can think about a lot of alternatives would be less inclined to draw the logically valid conclusion “The person will be tired” from the statements “If a person goes to sleep late, then he will be tired” and “The person goes to sleep late.” This is because a child with significant world knowledge can think of several circumstances that would make the conclusion unwarranted, such as waking up later the next day. Thus, more world knowledge needs to be associated with more ability to suppress the alternatives that might come to mind if the task requires it. This self-regulation ability relies on a part of the brain that also massively develops during childhood, i.e., the prefrontal cortex (see Figure 2). Overall, then, the development of concrete logical reasoning in children can be largely accounted for by the development of both world knowledge and self-regulation skills that are associated with the frontal cortex.

Figure 2. The prefrontal cortex. Location of the prefrontal cortex on a 3D rendering of the human brain. Polygon data were generated by Database Center for Life Science(DBCLS),  distributed under a CC-BY-SA-2.1-jp license.

From concrete to abstract reasoning

There is, however, an important difference between the reasoning skills described above and the task developed by Peter Wason about the four cards. What we just described relates to reasoning with very concrete information, whereas the card task involves reasoning with purely abstract information. Abstract reasoning is difficult because it requires one to manipulate information without any referent in the real world. Knowledge is of no help. In fact, neuroscience research indicates that abstract and concrete reasoning rely on two different parts of the brain 5 (see Figure 3). The ability to reason logically with an abstract premise is generally only found during late adolescence 4 . Transitioning from concrete to abstract reasoning may require extensive practice with concrete reasoning. With mastery, children may extract from the reasoning process abstract strategies that could be applied to abstract information. A recent study, however, suggests a trick to help facilitate this transition in children 6 . The researchers discovered that abstract reasoning in 12- to 15-year-olds is much improved when these adolescents are previously engaged in a task in which they have to reason with information that is concrete but empirically false, such as “If a shirt is rubbed with mud, then the shirt will be clean.” No such effect was observed when adolescents are asked to reason with concrete information that is empirically true, such as “If a shirt is washed with detergent, then the shirt will be clean.” Therefore, reasoning with information that contradicts what we know about the world might constitute an intermediary step in transitioning from concrete to abstract reasoning.

Figure 3. Brain regions activated when reasoning with concrete (left) and abstract (right) information. Activations are displayed on pictures of the brain taken using a magnetic resonance imaging scanner. (Reproduced from Ref. 5 )

What can we do to foster logical reasoning skills?

What, then, can we do to help foster the development of logical reasoning skills in children? The research described above suggests several potentially fruitful ways. First, it is clear that the development of concrete reasoning—the very first type of reasoning children can engage in—relies on an increased ability to think about counter-examples for a given statement. This implies that knowledge about the world is critical to the emergence of logical reasoning in children, at least when concrete information is involved. Therefore, all activities that would expand such world knowledge (e.g., reading informational books, learning new vocabulary, exploring new environments and places) are likely to be beneficial to the development of children’s reasoning skills. Second, it is important to consider that the more world knowledge a child possesses, the more he/she will need to juggle with this knowledge. For example, generating counter-examples when solving a reasoning problem will require maintaining pieces of information in memory for a short period of time, a type of memory called working memory . World knowledge can also sometimes be detrimental to reasoning and needs to be inhibited , such as when recognizing that the conclusion “The person will be tired” logically follows from the statements “If a person goes to sleep late, then he will be tired” and “The person goes to sleep late” (even if one might think of several conditions that would make the conclusion untrue based on what we know about the world). Fostering these types of self-regulation skills (working memory and inhibition) should thus be beneficial to the development of logical reasoning. Several studies suggest that these functions could be promoted by targeting children’s emotional and social development, such as in curricula involving social pretend play (requiring children to act out of character and adjusting to improvisation of others), self-discipline, orderliness, and meditation exercises 7 . Studies also indicate positive effects of various physical activities emphasizing self-control and mindfulness, such as yoga or traditional martial arts 7 . Third, studies indicate that the transition from concrete to abstract reasoning occurring around adolescence is challenging. Although more research is needed in this domain, one promising way to help this transition is by encouraging children’s thinking about alternatives with content that contradicts what they know about the world (e.g., “If a shirt is rubbed with mud, then the shirt will be clean”). In sum, as stated by Henry Markovits, “the best way to encourage the development of more abstract ways of logical reasoning is to gradually encourage both divergent thinking and reasoning at levels of abstraction that are just above reasoners’ current levels” 4 .

Fostering the development of logical reasoning should be an important goal of education. Yet, studies indicate that logical reasoning is hard even for educated adults and relies on the activation of an extensive network of brain regions. Neuroscience studies also demonstrate that reasoning with concrete information involves brain regions that qualitatively differ from those involved in reasoning with more abstract information, explaining why transitioning from concrete to abstract reasoning is challenging for children. We nonetheless reviewed here the more recent research on the development of reasoning skills and suggest several important factors that scaffold children’s reasoning abilities, such as world knowledge and self-regulation functions. On a final note, it is important to consider that logical reasoning is not something that we always do on our own, isolated from our peers. In fact, some have argued that the very function of reasoning is to argue with our peers (i.e., to find the best arguments to convince others and to evaluate arguments made by others) 8 . This idea is interesting from an educational point of view because it suggests that reasoning with others might be easier than reasoning in isolation—a hypothesis validated by several studies. For example, performance on the card task developed by Peter Wason is much higher when participants solve it as a group rather than alone 8 . Therefore, encouraging activities in which children reason with others might also be a fruitful avenue for stimulating the reasoning brain.

• Wason, P. C. Reasoning. In New Horizons in Psychology (ed. Foss, B. M.). (Penguin: Harmondsworth, 1966).
• Prado, J., & Noveck, I. A. Overcoming perceptual features in logical reasoning: A parametric functional magnetic resonance imaging study. J Cogn Neurosci . 19(4): 642-57 (2007).
• Cheng, P. W. et al. Pragmatic versus syntactic approaches to training deductive reasoning. Cogn Psychol . 18(3): 293-328 (1986).
• Markovits, H. How to develop a logical reasoner. In The Developmental Psychology of Reasoning and Decision-Making (ed. Markovits, H.) 148-164. (Psychology Press: Hove, UK, 2014).
• Goel, V. Anatomy of deductive reasoning. Trends Cogn. Sci. (Reg. Ed.) 11(10): 435-41 (2007).
• Markovits, H., & Lortie-Forgues, H. Conditional reasoning with false premises facilitates the transition between familiar and abstract reasoning. Child Development 82(2): 646-660 (2011).
• Diamond, A., & Lee, K. Interventions shown to aid executive function development in children 4 to 12 years old. Science 333(6045): 959-964 (2011).
• Mercier, H., & Sperber, D. Why do humans reason? Arguments for an argumentative theory. Behav Brain Sci . 34(2): 57-74; discussion 74-111 (2011).

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Struggling to overcome challenges in your life? We all face problems, big and small, on a regular basis.

So how do you tackle them effectively? What are some key problem-solving strategies and skills that can guide you?

Effective problem-solving requires breaking issues down logically, generating solutions creatively, weighing choices critically, and adapting plans flexibly based on outcomes. Useful strategies range from leveraging past solutions that have worked to visualizing problems through diagrams. Core skills include analytical abilities, innovative thinking, and collaboration.

Want to improve your problem-solving skills? Keep reading to find out 17 effective problem-solving strategies, key skills, common obstacles to watch for, and tips on improving your overall problem-solving skills.

Key Takeaways:

• Effective problem-solving requires breaking down issues logically, generating multiple solutions creatively, weighing choices critically, and adapting plans based on outcomes.
• Useful problem-solving strategies range from leveraging past solutions to brainstorming with groups to visualizing problems through diagrams and models.
• Core skills include analytical abilities, innovative thinking, decision-making, and team collaboration to solve problems.
• Common obstacles include fear of failure, information gaps, fixed mindsets, confirmation bias, and groupthink.
• Boosting problem-solving skills involves learning from experts, actively practicing, soliciting feedback, and analyzing others’ success.
• Onethread’s project management capabilities align with effective problem-solving tenets – facilitating structured solutions, tracking progress, and capturing lessons learned.

What Is Problem-Solving?

Problem-solving is the process of understanding an issue, situation, or challenge that needs to be addressed and then systematically working through possible solutions to arrive at the best outcome.

It involves critical thinking, analysis, logic, creativity, research, planning, reflection, and patience in order to overcome obstacles and find effective answers to complex questions or problems.

The ultimate goal is to implement the chosen solution successfully.

What Are Problem-Solving Strategies?

Problem-solving strategies are like frameworks or methodologies that help us solve tricky puzzles or problems we face in the workplace, at home, or with friends.

Imagine you have a big jigsaw puzzle. One strategy might be to start with the corner pieces. Another could be looking for pieces with the same colors. 

Just like in puzzles, in real life, we use different plans or steps to find solutions to problems. These strategies help us think clearly, make good choices, and find the best answers without getting too stressed or giving up.

Why Is It Important To Know Different Problem-Solving Strategies?

Knowing different problem-solving strategies is important because different types of problems often require different approaches to solve them effectively. Having a variety of strategies to choose from allows you to select the best method for the specific problem you are trying to solve.

This improves your ability to analyze issues thoroughly, develop solutions creatively, and tackle problems from multiple angles. Knowing multiple strategies also aids in overcoming roadblocks if your initial approach is not working.

Here are some reasons why you need to know different problem-solving strategies:

• Different Problems Require Different Tools: Just like you can’t use a hammer to fix everything, some problems need specific strategies to solve them.
• Improves Creativity: Knowing various strategies helps you think outside the box and come up with creative solutions.
• Saves Time: With the right strategy, you can solve problems faster instead of trying things that don’t work.
• Reduces Stress: When you know how to tackle a problem, it feels less scary and you feel more confident.
• Better Outcomes: Using the right strategy can lead to better solutions, making things work out better in the end.
• Learning and Growth: Each time you solve a problem, you learn something new, which makes you smarter and better at solving future problems.

Knowing different ways to solve problems helps you tackle anything that comes your way, making life a bit easier and more fun!

17 Effective Problem-Solving Strategies

Effective problem-solving strategies include breaking the problem into smaller parts, brainstorming multiple solutions, evaluating the pros and cons of each, and choosing the most viable option. 

Critical thinking and creativity are essential in developing innovative solutions. Collaboration with others can also provide diverse perspectives and ideas. 

By applying these strategies, you can tackle complex issues more effectively.

Now, consider a challenge you’re dealing with. Which strategy could help you find a solution? Here we will discuss key problem strategies in detail.

1. Use a Past Solution That Worked

This strategy involves looking back at previous similar problems you have faced and the solutions that were effective in solving them.

It is useful when you are facing a problem that is very similar to something you have already solved. The main benefit is that you don’t have to come up with a brand new solution – you already know the method that worked before will likely work again.

However, the limitation is that the current problem may have some unique aspects or differences that mean your old solution is not fully applicable.

The ideal process is to thoroughly analyze the new challenge, identify the key similarities and differences versus the past case, adapt the old solution as needed to align with the current context, and then pilot it carefully before full implementation.

An example is using the same negotiation tactics from purchasing your previous home when putting in an offer on a new house. Key terms would be adjusted but overall it can save significant time versus developing a brand new strategy.

2. Brainstorm Solutions

This involves gathering a group of people together to generate as many potential solutions to a problem as possible.

It is effective when you need creative ideas to solve a complex or challenging issue. By getting input from multiple people with diverse perspectives, you increase the likelihood of finding an innovative solution.

The main limitation is that brainstorming sessions can sometimes turn into unproductive gripe sessions or discussions rather than focusing on productive ideation —so they need to be properly facilitated.

The key to an effective brainstorming session is setting some basic ground rules upfront and having an experienced facilitator guide the discussion. Rules often include encouraging wild ideas, avoiding criticism of ideas during the ideation phase, and building on others’ ideas.

For instance, a struggling startup might hold a session where ideas for turnaround plans are generated and then formalized with financials and metrics.

3. Work Backward from the Solution

This technique involves envisioning that the problem has already been solved and then working step-by-step backward toward the current state.

This strategy is particularly helpful for long-term, multi-step problems. By starting from the imagined solution and identifying all the steps required to reach it, you can systematically determine the actions needed. It lets you tackle a big hairy problem through smaller, reversible steps.

A limitation is that this approach may not be possible if you cannot accurately envision the solution state to start with.

The approach helps drive logical systematic thinking for complex problem-solving, but should still be combined with creative brainstorming of alternative scenarios and solutions.

An example is planning for an event – you would imagine the successful event occurring, then determine the tasks needed the week before, two weeks before, etc. all the way back to the present.

4. Use the Kipling Method

This method, named after author Rudyard Kipling, provides a framework for thoroughly analyzing a problem before jumping into solutions.

It consists of answering six fundamental questions: What, Where, When, How, Who, and Why about the challenge. Clearly defining these core elements of the problem sets the stage for generating targeted solutions.

The Kipling method enables a deep understanding of problem parameters and root causes before solution identification. By jumping to brainstorm solutions too early, critical information can be missed or the problem is loosely defined, reducing solution quality.

Answering the six fundamental questions illuminates all angles of the issue. This takes time but pays dividends in generating optimal solutions later tuned precisely to the true underlying problem.

The limitation is that meticulously working through numerous questions before addressing solutions can slow progress.

The best approach blends structured problem decomposition techniques like the Kipling method with spurring innovative solution ideation from a diverse team. 

An example is using this technique after a technical process failure – the team would systematically detail What failed, Where/When did it fail, How it failed (sequence of events), Who was involved, and Why it likely failed before exploring preventative solutions.

5. Try Different Solutions Until One Works (Trial and Error)

This technique involves attempting various potential solutions sequentially until finding one that successfully solves the problem.

Trial and error works best when facing a concrete, bounded challenge with clear solution criteria and a small number of discrete options to try. By methodically testing solutions, you can determine the faulty component.

A limitation is that it can be time-intensive if the working solution set is large.

The key is limiting the variable set first. For technical problems, this boundary is inherent and each element can be iteratively tested. But for business issues, artificial constraints may be required – setting decision rules upfront to reduce options before testing.

Furthermore, hypothesis-driven experimentation is far superior to blind trial and error – have logic for why Option A may outperform Option B.

Examples include fixing printer jams by testing different paper tray and cable configurations or resolving website errors by tweaking CSS/HTML line-by-line until the code functions properly.

6. Use Proven Formulas or Frameworks (Heuristics)

Heuristics refers to applying existing problem-solving formulas or frameworks rather than addressing issues completely from scratch.

This allows leveraging established best practices rather than reinventing the wheel each time.

It is effective when facing recurrent, common challenges where proven structured approaches exist.

However, heuristics may force-fit solutions to non-standard problems.

For example, a cost-benefit analysis can be used instead of custom weighting schemes to analyze potential process improvements.

Onethread allows teams to define, save, and replicate configurable project templates so proven workflows can be reliably applied across problems with some consistency rather than fully custom one-off approaches each time.

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7. Trust Your Instincts (Insight Problem-Solving)

Insight is a problem-solving technique that involves waiting patiently for an unexpected “aha moment” when the solution pops into your mind.

It works well for personal challenges that require intuitive realizations over calculated logic. The unconscious mind makes connections leading to flashes of insight when relaxing or doing mundane tasks unrelated to the actual problem.

Benefits include out-of-the-box creative solutions. However, the limitations are that insights can’t be forced and may never come at all if too complex. Critical analysis is still required after initial insights.

A real-life example would be a writer struggling with how to end a novel. Despite extensive brainstorming, they feel stuck. Eventually while gardening one day, a perfect unexpected plot twist sparks an ideal conclusion. However, once written they still carefully review if the ending flows logically from the rest of the story.

8. Reverse Engineer the Problem

This approach involves deconstructing a problem in reverse sequential order from the current undesirable outcome back to the initial root causes.

By mapping the chain of events backward, you can identify the origin of where things went wrong and establish the critical junctures for solving it moving ahead. Reverse engineering provides diagnostic clarity on multi-step problems.

However, the limitation is that it focuses heavily on autopsying the past versus innovating improved future solutions.

An example is tracing back from a server outage, through the cascade of infrastructure failures that led to it finally terminating at the initial script error that triggered the crisis. This root cause would then inform the preventative measure.

9. Break Down Obstacles Between Current and Goal State (Means-End Analysis)

This technique defines the current problem state and the desired end goal state, then systematically identifies obstacles in the way of getting from one to the other.

By mapping the barriers or gaps, you can then develop solutions to address each one. This methodically connects the problem to solutions.

A limitation is that some obstacles may be unknown upfront and only emerge later.

For example, you can list down all the steps required for a new product launch – current state through production, marketing, sales, distribution, etc. to full launch (goal state) – to highlight where resource constraints or other blocks exist so they can be addressed.

Onethread allows dividing big-picture projects into discrete, manageable phases, milestones, and tasks to simplify execution just as problems can be decomposed into more achievable components. Features like dependency mapping further reinforce interconnections.

Using Onethread’s issues and subtasks feature, messy problems can be decomposed into manageable chunks.

10. Ask “Why” Five Times to Identify the Root Cause (The 5 Whys)

This technique involves asking “Why did this problem occur?” and then responding with an answer that is again met with asking “Why?” This process repeats five times until the root cause is revealed.

Continually asking why digs deeper from surface symptoms to underlying systemic issues.

It is effective for getting to the source of problems originating from human error or process breakdowns.

However, some complex issues may have multiple tangled root causes not solvable through this approach alone.

An example is a retail store experiencing a sudden decline in customers. Successively asking why five times may trace an initial drop to parking challenges, stemming from a city construction project – the true starting point to address.

11. Evaluate Strengths, Weaknesses, Opportunities, and Threats (SWOT Analysis)

This involves analyzing a problem or proposed solution by categorizing internal and external factors into a 2×2 matrix: Strengths, Weaknesses as the internal rows; Opportunities and Threats as the external columns.

Systematically identifying these elements provides balanced insight to evaluate options and risks. It is impactful when evaluating alternative solutions or developing strategy amid complexity or uncertainty.

The key benefit of SWOT analysis is enabling multi-dimensional thinking when rationally evaluating options. Rather than getting anchored on just the upsides or the existing way of operating, it urges a systematic assessment through four different lenses:

• Internal Strengths: Our core competencies/advantages able to deliver success
• Internal Weaknesses: Gaps/vulnerabilities we need to manage
• External Opportunities: Ways we can differentiate/drive additional value
• External Threats: Risks we must navigate or mitigate

Multiperspective analysis provides the needed holistic view of the balanced risk vs. reward equation for strategic decision making amid uncertainty.

However, SWOT can feel restrictive if not tailored and evolved for different issue types.

Teams should view SWOT analysis as a starting point, augmenting it further for distinct scenarios.

An example is performing a SWOT analysis on whether a small business should expand into a new market – evaluating internal capabilities to execute vs. risks in the external competitive and demand environment to inform the growth decision with eyes wide open.

12. Compare Current vs Expected Performance (Gap Analysis)

This technique involves comparing the current state of performance, output, or results to the desired or expected levels to highlight shortfalls.

By quantifying the gaps, you can identify problem areas and prioritize address solutions.

Gap analysis is based on the simple principle – “you can’t improve what you don’t measure.” It enables facts-driven problem diagnosis by highlighting delta to goals, not just vague dissatisfaction that something seems wrong. And measurement immediately suggests improvement opportunities – address the biggest gaps first.

This data orientation also supports ROI analysis on fixing issues – the return from closing larger gaps outweighs narrowly targeting smaller performance deficiencies.

However, the approach is only effective if robust standards and metrics exist as the benchmark to evaluate against. Organizations should invest upfront in establishing performance frameworks.

Furthermore, while numbers are invaluable, the human context behind problems should not be ignored – quantitative versus qualitative gap assessment is optimally blended.

For example, if usage declines are noted during software gap analysis, this could be used as a signal to improve user experience through design.

13. Observe Processes from the Frontline (Gemba Walk)

A Gemba walk involves going to the actual place where work is done, directly observing the process, engaging with employees, and finding areas for improvement.

By experiencing firsthand rather than solely reviewing abstract reports, practical problems and ideas emerge.

The limitation is Gemba walks provide anecdotes not statistically significant data. It complements but does not replace comprehensive performance measurement.

An example is a factory manager inspecting the production line to spot jam areas based on direct reality rather than relying on throughput dashboards alone back in her office. Frontline insights prove invaluable.

14. Analyze Competitive Forces (Porter’s Five Forces)

This involves assessing the marketplace around a problem or business situation via five key factors: competitors, new entrants, substitute offerings, suppliers, and customer power.

Evaluating these forces illuminates risks and opportunities for strategy development and issue resolution. It is effective for understanding dynamic external threats and opportunities when operating in a contested space.

However, over-indexing on only external factors can overlook the internal capabilities needed to execute solutions.

A startup CEO, for example, may analyze market entry barriers, whitespace opportunities, and disruption risks across these five forces to shape new product rollout strategies and marketing approaches.

15. Think from Different Perspectives (Six Thinking Hats)

The Six Thinking Hats is a technique developed by Edward de Bono that encourages people to think about a problem from six different perspectives, each represented by a colored “thinking hat.”

The key benefit of this strategy is that it pushes team members to move outside their usual thinking style and consider new angles. This brings more diverse ideas and solutions to the table.

It works best for complex problems that require innovative solutions and when a team is stuck in an unproductive debate. The structured framework keeps the conversation flowing in a positive direction.

Limitations are that it requires training on the method itself and may feel unnatural at first. Team dynamics can also influence success – some members may dominate certain “hats” while others remain quiet.

A real-life example is a software company debating whether to build a new feature. The white hat focuses on facts, red on gut feelings, black on potential risks, yellow on benefits, green on new ideas, and blue on process. This exposes more balanced perspectives before deciding.

Onethread centralizes diverse stakeholder communication onto one platform, ensuring all voices are incorporated when evaluating project tradeoffs, just as problem-solving should consider multifaceted solutions.

16. Visualize the Problem (Draw it Out)

Drawing out a problem involves creating visual representations like diagrams, flowcharts, and maps to work through challenging issues.

This strategy is helpful when dealing with complex situations with lots of interconnected components. The visuals simplify the complexity so you can thoroughly understand the problem and all its nuances.

Key benefits are that it allows more stakeholders to get on the same page regarding root causes and it sparks new creative solutions as connections are made visually.

However, simple problems with few variables don’t require extensive diagrams. Additionally, some challenges are so multidimensional that fully capturing every aspect is difficult.

A real-life example would be mapping out all the possible causes leading to decreased client satisfaction at a law firm. An intricate fishbone diagram with branches for issues like service delivery, technology, facilities, culture, and vendor partnerships allows the team to trace problems back to their origins and brainstorm targeted fixes.

17. Follow a Step-by-Step Procedure (Algorithms)

An algorithm is a predefined step-by-step process that is guaranteed to produce the correct solution if implemented properly.

Using algorithms is effective when facing problems that have clear, binary right and wrong answers. Algorithms work for mathematical calculations, computer code, manufacturing assembly lines, and scientific experiments.

Key benefits are consistency, accuracy, and efficiency. However, they require extensive upfront development and only apply to scenarios with strict parameters. Additionally, human error can lead to mistakes.

For example, crew members of fast food chains like McDonald’s follow specific algorithms for food prep – from grill times to ingredient amounts in sandwiches, to order fulfillment procedures. This ensures uniform quality and service across all locations. However, if a step is missed, errors occur.

The Problem-Solving Process

The problem-solving process typically includes defining the issue, analyzing details, creating solutions, weighing choices, acting, and reviewing results.

In the above, we have discussed several problem-solving strategies. For every problem-solving strategy, you have to follow these processes. Here’s a detailed step-by-step process of effective problem-solving:

Step 1: Identify the Problem

The problem-solving process starts with identifying the problem. This step involves understanding the issue’s nature, its scope, and its impact. Once the problem is clearly defined, it sets the foundation for finding effective solutions.

Identifying the problem is crucial. It means figuring out exactly what needs fixing. This involves looking at the situation closely, understanding what’s wrong, and knowing how it affects things. It’s about asking the right questions to get a clear picture of the issue. 

This step is important because it guides the rest of the problem-solving process. Without a clear understanding of the problem, finding a solution is much harder. It’s like diagnosing an illness before treating it. Once the problem is identified accurately, you can move on to exploring possible solutions and deciding on the best course of action.

Step 2: Break Down the Problem

Breaking down the problem is a key step in the problem-solving process. It involves dividing the main issue into smaller, more manageable parts. This makes it easier to understand and tackle each component one by one.

After identifying the problem, the next step is to break it down. This means splitting the big issue into smaller pieces. It’s like solving a puzzle by handling one piece at a time. 

By doing this, you can focus on each part without feeling overwhelmed. It also helps in identifying the root causes of the problem. Breaking down the problem allows for a clearer analysis and makes finding solutions more straightforward. 

Each smaller problem can be addressed individually, leading to an effective resolution of the overall issue. This approach not only simplifies complex problems but also aids in developing a systematic plan to solve them.

Step 3: Come up with potential solutions

Coming up with potential solutions is the third step in the problem-solving process. It involves brainstorming various options to address the problem, considering creativity and feasibility to find the best approach.

After breaking down the problem, it’s time to think of ways to solve it. This stage is about brainstorming different solutions. You look at the smaller issues you’ve identified and start thinking of ways to fix them. This is where creativity comes in. 

You want to come up with as many ideas as possible, no matter how out-of-the-box they seem. It’s important to consider all options and evaluate their pros and cons. This process allows you to gather a range of possible solutions. 

Later, you can narrow these down to the most practical and effective ones. This step is crucial because it sets the stage for deciding on the best solution to implement. It’s about being open-minded and innovative to tackle the problem effectively.

Step 4: Analyze the possible solutions

Analyzing the possible solutions is the fourth step in the problem-solving process. It involves evaluating each proposed solution’s advantages and disadvantages to determine the most effective and feasible option.

After coming up with potential solutions, the next step is to analyze them. This means looking closely at each idea to see how well it solves the problem. You weigh the pros and cons of every solution.

Consider factors like cost, time, resources, and potential outcomes. This analysis helps in understanding the implications of each option. It’s about being critical and objective, ensuring that the chosen solution is not only effective but also practical.

This step is vital because it guides you towards making an informed decision. It involves comparing the solutions against each other and selecting the one that best addresses the problem.

By thoroughly analyzing the options, you can move forward with confidence, knowing you’ve chosen the best path to solve the issue.

Step 5: Implement and Monitor the Solutions

Implementing and monitoring the solutions is the final step in the problem-solving process. It involves putting the chosen solution into action and observing its effectiveness, making adjustments as necessary.

Once you’ve selected the best solution, it’s time to put it into practice. This step is about action. You implement the chosen solution and then keep an eye on how it works. Monitoring is crucial because it tells you if the solution is solving the problem as expected. 

If things don’t go as planned, you may need to make some changes. This could mean tweaking the current solution or trying a different one. The goal is to ensure the problem is fully resolved. 

This step is critical because it involves real-world application. It’s not just about planning; it’s about doing and adjusting based on results. By effectively implementing and monitoring the solutions, you can achieve the desired outcome and solve the problem successfully.

Why This Process is Important

Following a defined process to solve problems is important because it provides a systematic, structured approach instead of a haphazard one. Having clear steps guides logical thinking, analysis, and decision-making to increase effectiveness. Key reasons it helps are:

• Clear Direction: This process gives you a clear path to follow, which can make solving problems less overwhelming.
• Better Solutions: Thoughtful analysis of root causes, iterative testing of solutions, and learning orientation lead to addressing the heart of issues rather than just symptoms.
• Saves Time and Energy: Instead of guessing or trying random things, this process helps you find a solution more efficiently.
• Improves Skills: The more you use this process, the better you get at solving problems. It’s like practicing a sport. The more you practice, the better you play.
• Maximizes collaboration: Involving various stakeholders in the process enables broader inputs. Their communication and coordination are streamlined through organized brainstorming and evaluation.
• Provides consistency: Standard methodology across problems enables building institutional problem-solving capabilities over time. Patterns emerge on effective techniques to apply to different situations.

The problem-solving process is a powerful tool that can help us tackle any challenge we face. By following these steps, we can find solutions that work and learn important skills along the way.

Key Skills for Efficient Problem Solving

Efficient problem-solving requires breaking down issues logically, evaluating options, and implementing practical solutions.

Key skills include critical thinking to understand root causes, creativity to brainstorm innovative ideas, communication abilities to collaborate with others, and decision-making to select the best way forward. Staying adaptable, reflecting on outcomes, and applying lessons learned are also essential.

With practice, these capacities will lead to increased personal and team effectiveness in systematically addressing any problem.

 Let’s explore the powers you need to become a problem-solving hero!

Critical Thinking and Analytical Skills

Critical thinking and analytical skills are vital for efficient problem-solving as they enable individuals to objectively evaluate information, identify key issues, and generate effective solutions. 

These skills facilitate a deeper understanding of problems, leading to logical, well-reasoned decisions. By systematically breaking down complex issues and considering various perspectives, individuals can develop more innovative and practical solutions, enhancing their problem-solving effectiveness.

Communication Skills

Effective communication skills are essential for efficient problem-solving as they facilitate clear sharing of information, ensuring all team members understand the problem and proposed solutions. 

These skills enable individuals to articulate issues, listen actively, and collaborate effectively, fostering a productive environment where diverse ideas can be exchanged and refined. By enhancing mutual understanding, communication skills contribute significantly to identifying and implementing the most viable solutions.

Decision-Making

Strong decision-making skills are crucial for efficient problem-solving, as they enable individuals to choose the best course of action from multiple alternatives. 

These skills involve evaluating the potential outcomes of different solutions, considering the risks and benefits, and making informed choices. Effective decision-making leads to the implementation of solutions that are likely to resolve problems effectively, ensuring resources are used efficiently and goals are achieved.

Planning and Prioritization

Planning and prioritization are key for efficient problem-solving, ensuring resources are allocated effectively to address the most critical issues first. This approach helps in organizing tasks according to their urgency and impact, streamlining efforts towards achieving the desired outcome efficiently.

Emotional Intelligence

Emotional intelligence enhances problem-solving by allowing individuals to manage emotions, understand others, and navigate social complexities. It fosters a positive, collaborative environment, essential for generating creative solutions and making informed, empathetic decisions.

Leadership skills drive efficient problem-solving by inspiring and guiding teams toward common goals. Effective leaders motivate their teams, foster innovation, and navigate challenges, ensuring collective efforts are focused and productive in addressing problems.

Time Management

Time management is crucial in problem-solving, enabling individuals to allocate appropriate time to each task. By efficiently managing time, one can ensure that critical problems are addressed promptly without neglecting other responsibilities.

Data Analysis

Data analysis skills are essential for problem-solving, as they enable individuals to sift through data, identify trends, and extract actionable insights. This analytical approach supports evidence-based decision-making, leading to more accurate and effective solutions.

Research Skills

Research skills are vital for efficient problem-solving, allowing individuals to gather relevant information, explore various solutions, and understand the problem’s context. This thorough exploration aids in developing well-informed, innovative solutions.

Becoming a great problem solver takes practice, but with these skills, you’re on your way to becoming a problem-solving hero. 

How to Improve Your Problem-Solving Skills?

Improving your problem-solving skills can make you a master at overcoming challenges. Learn from experts, practice regularly, welcome feedback, try new methods, experiment, and study others’ success to become better.

Learning from Experts

Improving problem-solving skills by learning from experts involves seeking mentorship, attending workshops, and studying case studies. Experts provide insights and techniques that refine your approach, enhancing your ability to tackle complex problems effectively.

To enhance your problem-solving skills, learning from experts can be incredibly beneficial. Engaging with mentors, participating in specialized workshops, and analyzing case studies from seasoned professionals can offer valuable perspectives and strategies. 

Experts share their experiences, mistakes, and successes, providing practical knowledge that can be applied to your own problem-solving process. This exposure not only broadens your understanding but also introduces you to diverse methods and approaches, enabling you to tackle challenges more efficiently and creatively.

Improving problem-solving skills through practice involves tackling a variety of challenges regularly. This hands-on approach helps in refining techniques and strategies, making you more adept at identifying and solving problems efficiently.

One of the most effective ways to enhance your problem-solving skills is through consistent practice. By engaging with different types of problems on a regular basis, you develop a deeper understanding of various strategies and how they can be applied. 

This hands-on experience allows you to experiment with different approaches, learn from mistakes, and build confidence in your ability to tackle challenges.

Regular practice not only sharpens your analytical and critical thinking skills but also encourages adaptability and innovation, key components of effective problem-solving.

Openness to Feedback

Being open to feedback is like unlocking a secret level in a game. It helps you boost your problem-solving skills. Improving problem-solving skills through openness to feedback involves actively seeking and constructively responding to critiques. 

This receptivity enables you to refine your strategies and approaches based on insights from others, leading to more effective solutions. 

Learning New Approaches and Methodologies

Learning new approaches and methodologies is like adding new tools to your toolbox. It makes you a smarter problem-solver. Enhancing problem-solving skills by learning new approaches and methodologies involves staying updated with the latest trends and techniques in your field. 

This continuous learning expands your toolkit, enabling innovative solutions and a fresh perspective on challenges.

Experimentation

Experimentation is like being a scientist of your own problems. It’s a powerful way to improve your problem-solving skills. Boosting problem-solving skills through experimentation means trying out different solutions to see what works best. This trial-and-error approach fosters creativity and can lead to unique solutions that wouldn’t have been considered otherwise.

Analyzing Competitors’ Success

Analyzing competitors’ success is like being a detective. It’s a smart way to boost your problem-solving skills. Improving problem-solving skills by analyzing competitors’ success involves studying their strategies and outcomes. Understanding what worked for them can provide valuable insights and inspire effective solutions for your own challenges. 

Challenges in Problem-Solving

Facing obstacles when solving problems is common. Recognizing these barriers, like fear of failure or lack of information, helps us find ways around them for better solutions.

Fear of Failure

Fear of failure is like a big, scary monster that stops us from solving problems. It’s a challenge many face. Because being afraid of making mistakes can make us too scared to try new solutions. 

How can we overcome this? First, understand that it’s okay to fail. Failure is not the opposite of success; it’s part of learning. Every time we fail, we discover one more way not to solve a problem, getting us closer to the right solution. Treat each attempt like an experiment. It’s not about failing; it’s about testing and learning.

Lack of Information

Lack of information is like trying to solve a puzzle with missing pieces. It’s a big challenge in problem-solving. Because without all the necessary details, finding a solution is much harder. 

How can we fix this? Start by gathering as much information as you can. Ask questions, do research, or talk to experts. Think of yourself as a detective looking for clues. The more information you collect, the clearer the picture becomes. Then, use what you’ve learned to think of solutions. 

Fixed Mindset

A fixed mindset is like being stuck in quicksand; it makes solving problems harder. It means thinking you can’t improve or learn new ways to solve issues. 

How can we change this? First, believe that you can grow and learn from challenges. Think of your brain as a muscle that gets stronger every time you use it. When you face a problem, instead of saying “I can’t do this,” try thinking, “I can’t do this yet.” Look for lessons in every challenge and celebrate small wins. 

Everyone starts somewhere, and mistakes are just steps on the path to getting better. By shifting to a growth mindset, you’ll see problems as opportunities to grow. Keep trying, keep learning, and your problem-solving skills will soar!

Jumping to Conclusions

Jumping to conclusions is like trying to finish a race before it starts. It’s a challenge in problem-solving. That means making a decision too quickly without looking at all the facts. 

How can we avoid this? First, take a deep breath and slow down. Think about the problem like a puzzle. You need to see all the pieces before you know where they go. Ask questions, gather information, and consider different possibilities. Don’t choose the first solution that comes to mind. Instead, compare a few options. 

Feeling Overwhelmed

Feeling overwhelmed is like being buried under a mountain of puzzles. It’s a big challenge in problem-solving. When we’re overwhelmed, everything seems too hard to handle. 

How can we deal with this? Start by taking a step back. Breathe deeply and focus on one thing at a time. Break the big problem into smaller pieces, like sorting puzzle pieces by color. Tackle each small piece one by one. It’s also okay to ask for help. Sometimes, talking to someone else can give you a new perspective. 

Confirmation Bias

Confirmation bias is like wearing glasses that only let you see what you want to see. It’s a challenge in problem-solving. Because it makes us focus only on information that agrees with what we already believe, ignoring anything that doesn’t. 

How can we overcome this? First, be aware that you might be doing it. It’s like checking if your glasses are on right. Then, purposely look for information that challenges your views. It’s like trying on a different pair of glasses to see a new perspective. Ask questions and listen to answers, even if they don’t fit what you thought before.

Groupthink is like everyone in a group deciding to wear the same outfit without asking why. It’s a challenge in problem-solving. It means making decisions just because everyone else agrees, without really thinking it through. 

How can we avoid this? First, encourage everyone in the group to share their ideas, even if they’re different. It’s like inviting everyone to show their unique style of clothes. 

Listen to all opinions and discuss them. It’s okay to disagree; it helps us think of better solutions. Also, sometimes, ask someone outside the group for their thoughts. They might see something everyone in the group missed.

Overcoming obstacles in problem-solving requires patience, openness, and a willingness to learn from mistakes. By recognizing these barriers, we can develop strategies to navigate around them, leading to more effective and creative solutions.

What are the most common problem-solving techniques?

The most common techniques include brainstorming, the 5 Whys, mind mapping, SWOT analysis, and using algorithms or heuristics. Each approach has its strengths, suitable for different types of problems.

What’s the best problem-solving strategy for every situation?

There’s no one-size-fits-all strategy. The best approach depends on the problem’s complexity, available resources, and time constraints. Combining multiple techniques often yields the best results.

How can I improve my problem-solving skills?

Improve your problem-solving skills by practicing regularly, learning from experts, staying open to feedback, and continuously updating your knowledge on new approaches and methodologies.

Are there any tools or resources to help with problem-solving?

Yes, tools like mind mapping software, online courses on critical thinking, and books on problem-solving techniques can be very helpful. Joining forums or groups focused on problem-solving can also provide support and insights.

What are some common mistakes people make when solving problems?

Common mistakes include jumping to conclusions without fully understanding the problem, ignoring valuable feedback, sticking to familiar solutions without considering alternatives, and not breaking down complex problems into manageable parts.

Final Words

Mastering problem-solving strategies equips us with the tools to tackle challenges across all areas of life. By understanding and applying these techniques, embracing a growth mindset, and learning from both successes and obstacles, we can transform problems into opportunities for growth. Continuously improving these skills ensures we’re prepared to face and solve future challenges more effectively.

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The Most Important Logical Thinking Skills (With Examples)

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Find a Job You Really Want In

Logical thinking skills like critical-thinking, research, and creative thinking are valuable assets in the workplace. These skills are sought after by many employers, who want employees that take into account facts and data before deciding on an important course of action. This is because such solutions will ensure the organization’s processes can continue to operate efficiently.

So, if you’re a job seeker or employee looking to explore and brush up on your logical thinking skills, you’re in luck. This article will cover examples of logical thinking skills in the workplace, as well as what you can do to showcase those skills on your resume and in interviews.

Key Takeaways:

Logical thinking is problem solving based on reasoning that follows a strictly structured progression of analysis.

Critical thinking, research, creativity, mathematics, reading, active listening, and organization are all important logical thinking skills in the workplace.

Logical thinking provides objectivity for decision making that multiple people can accept.

Deduction follows valid premises to reach a logical conclusion.

It can be very helpful to demonstrate logical thinking skills at a job interview.

What is logical thinking?

10 examples of logical thinking skills, examples of logical thinking in the workplace, what is deductive reasoning, logical thinking in a job interview, logical thinking skills faq, final thoughts.

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Logical thinking is the ability to reason out an issue after observing and analyzing it from all angles . You can then form a conclusion that makes the most sense. It also includes the ability to take note of reactions and feedback to aid in the formation of the conclusion.

Logical thinking skills enable you to present your justification for the actions you take, the strategies you use, and the decisions you make. You can easily stand in front of your clients, peers, and supervisors and defend your product, service, and course of action if the necessity arises.

Logical thinking is an excellent way of solving complex problems. You can break the problem into smaller parts; solve them individually in a sequence, then present the complete solution. However, it is not infallible.

So, when a problem in the workplace feels overwhelming, you may want to think about it logically first.

Logical thinking skills are a skill set that enables you to reason logically when solving problems. They enable you to provide well-reasoned answers to any issues that arise. They also empower you to make decisions that most people will consider rational.

Critical-thinking skills. If you are a critical thinker, then you can analyze and evaluate a problem before making judgments. You need to improve your critical thinking process to become a logical thinker.

Your critical thinking skills will improve your ability to solve problems. You will be the go-to employee concerning crises. People can rely on you to be reasonable whenever an issue arises instead of letting biases rule you.

Research skills. If you are a good researcher , then you can search and locate data that can be useful when presenting information on your preferred subject.

The more relevant information you have about a particular subject, the more accurate your conclusions are likely to be. The sources you use must be reputable and relevant.

For this reason, your ability to ferret out information will affect how well you can reason logically.

Creative thinking skills. If you are a creative thinker , then you can find innovative solutions to problems.

You are the kind of person that can think outside the box when brainstorming ideas and potential solutions. Your thinking is not rigid. Instead, you tend to look at issues in ways other people have not thought of before.

While logical thinking is based on data and facts, that doesn’t mean it is rigid. You can creatively find ways of sourcing that data or experimenting so that you can form logical conclusions. Your strategic thinking skills will also help enable you to analyze reactions or collect feedback .

Mathematical skills. If you are skilled in mathematics , then you can work well with numbers and represent mathematical ideas using visual symbols. Your brain must be able to compute information.

Business is a numbers game. That means you must have some knowledge of mathematics. You must be able to perform basic mathematical tasks involving addition, subtractions, divisions, multiplications, etc.

So, to become a logical thinker, you must be comfortable working with numbers. You will encounter them in many business-related complex problems. And your ability to understand them will determine whether you can reach an accurate logical conclusion that helps your organization.

Reading skills. If you are a good reader , then you can make sense of the letters and symbols that you see. Your ability to read will determine your competency concerning your logical thinking and reasoning skills.

And that skill set will come in handy when you are presented with different sets of work-related statements from which you are meant to conclude. Such statements may be part of your company policy, technical manual, etc.

Active listening skills. Active listening is an important communication skill to have. If you are an active listener, then you can hear, understand what is being said, remember it, and respond to it if necessary.

Not all instructions are written. You may need to listen to someone to get the information you need to solve problems before you write it down. In that case, your active listening skills will determine how well you can remember the information so that you can use it to reason things out logically.

Information ordering skills. If you have information ordering skills, then you can arrange things based on a specified order following the set rules or conditions. These things may include mathematical operations, words, pictures, etc.

Different organizations have different business processes. The workflow in one organization will be not similar to that of another organization even if both belong to the same industry.

Your ability to order information will depend on an organization’s culture . And it will have a major impact on how you can think and reason concerning solutions to your company problems.

If you follow the wrong order, then no matter how good your problem-solving techniques are your conclusions may be wrong for your organization.

Persuasion skills. Logical thinking can be useful when persuading others, especially in the workplace.

For example, lets say one of your co-workers wants to take a project in an impulsive direction, which will increase the budget. However, after you do your research, you realize a budget increase would be impossible.

You can then use your logical thinking skills to explain the situation to your co-worker , including details facts and numbers, which will help dissuade them from making an uninformed decision.

Decision making skills. Decision making skills go hand and hand with logical thinking, as being able to think logically about solutions and research topics will make it far easier to make informed decisions.

After all, no one likes making a decision that feels like a shot in the dark, so knowing crucial information about the options aviable to you, and thinking about them logically, can improve your confidence around decision making.

Confidence skills. Confidence that stems from an emotional and irrational place will always be fragile, but when you have more knowledge available to you through logical thinking, you can be more confident in your confidence skills.

For instance, if an employee asked you to answer an important question, you will have a lot more confidence in your answer if you can think logically about it, as opposed to having an air of uncertainty.

To improve your logic skills, it would be wise to practice how to solve problems based on facts and data. Below are examples of logical thinking in the workplace that will help you understand this kind of reasoning so that you can improve your thinking:

The human resource department in your organization has determined that leadership skills are important for anyone looking to go into a senior management position. So, it decides that it needs proof of leadership before hiring anyone internally. To find the right person for the senior management position , every candidate must undertake a project that involves a team of five. Whoever leads the winning team will get the senior managerial position.

This example shows a logical conclusion that is reached by your organization’s human resource department. In this case, your HR department has utilized logical thinking to determine the best internal candidate for the senior manager position.

It could be summarized as follows:

Statement 1: People with excellent leadership skills that produce winning teams make great senior managers. Statement 2: Candidate A is an excellent leader that has produced a winning team. Conclusion: Candidate A will make an excellent senior manager .

A marketing company researches working women on behalf of one of their clients – a robotics company. They find out that these women feel overwhelmed with responsibilities at home and in the workplace. As a result, they do not have enough time to clean, take care of their children, and stay productive in the workplace. A robotics company uses this research to create a robot cleaner that can be operated remotely . Then they advertise this cleaner specifically to working women with the tag line, “Working women can do it all with a little bit of help.” As a result of this marketing campaign, their revenues double within a year.

This example shows a logical conclusion reached by a robotics company after receiving the results of marketing research on working women. In this case, logical thinking has enabled the company to come up with a new marketing strategy for their cleaning product.

Statement 1: Working women struggle to keep their homes clean. Statement 2: Robot cleaners can take over cleaning duties for women who struggle to keep their homes clean. Conclusion: Robot cleaner can help working women keep their homes clean.

CalcX. Inc. has created a customer survey concerning its new finance software. The goal of the survey is to determine what customers like best about the software. After reading through over 100 customer reviews and ratings, it emerges that 60% of customers love the new user interface because it’s easy to navigate. CalcX. Inc. then decides to improve its marketing strategy. It decides to train every salesperson to talk about the easy navigation feature and how superior it is to the competition. So, every time a client objects to the price, the sales rep could admit that it is expensive, but the excellent user interface makes up for the price. At the end of the year, it emerges that this strategy has improved sales revenues by 10%.

The above example shows how logical thinking has helped CalcX. Sell more software and improve its bottom line.

Statement 1: If the majority of customers like a particular software feature, then sales reps should use it to overcome objections and increase revenues. Statement 2: 60% of the surveyed customers like the user interface of the new software, and; they think it makes navigation easier. Conclusion: The sales reps should market the new software’s user interface and the fact that it is easy to navigate to improve the company’s bottom line.

A political candidate hires a focus group to discuss hot-button issues they feel strongly about. It emerges that the group is torn on sexual reproductive health issues, but most support the issue of internal security . However, nearly everyone is opposed to the lower wages being paid due to the current economic crisis. Based on the results of this research, the candidate decides to focus on improving the economy and security mechanisms in the country. He also decides to let go of the sexual productive health issues because it would potentially cause him to lose some support.

In this case, the political candidate has made logical conclusions on what topics he should use to campaign for his seat with minimal controversies so that he doesn’t lose many votes.

This situation could be summarized as follows:

Statement 1: Most people find sexual reproductive health issues controversial and cannot agree. Statement 2: Most people feel that the internal security of the country is in jeopardy and something should be done about it. Statement 3: Most people want higher wages and an improved economy. Statement 4: Political candidates who want to win must avoid controversy and speak up on things that matter to people. Conclusion: To win, political candidates must focus on higher wages, an improved economy, and the internal security of the country while avoiding sexual reproductive health matters.

Deductive reasoning is an aspect of logical reasoning. It is a top-down reasoning approach that enables you to form a specific logical conclusion based on generalities. Therefore, you can use one or more statements, usually referred to as premises, to conclude something.

For example:

Statement 1: All mothers are women Statement 2: Daisy is a mother. Conclusion: Daisy is a woman.

Based on the above examples, all mothers are classified as women, and since Daisy is a mother, then it’s logical to deduce that she is a woman too.

It’s worth noting though, that deductive reasoning does not always produce an accurate conclusion based on reality.

Statement 1: All caregivers in this room are nurses. Statement 2: This dog, Tom, is a caregiver . Conclusion: This dog, Tom, is a nurse .

From the above example, we have deduced that Tom, the dog, is a nurse simply because the first statement stated that all caregivers are nurses. And yet, in reality, we know that dogs cannot be nurses. They do not have the mental capacity to become engaged in the profession.

For this reason, you must bear in mind that an argument can be validly based on the conditions but it can also be unsound if some statements are based on a fallacy.

Since logical thinking is so important in the workplace, most job interviewers will want to see you demonstrate this skill at the job interview. It is very important to keep in mind your logical thinking skills when you talk about yourself at the interview.

There are many ways in which an interviewer may ask you to demonstrate your logical thinking skills. For example:

You may have to solve an example problem. If the interviewer provides you a problem similar to one you might find at your job, make sure to critically analyze the problem to deduce a solution.

You may be asked about a previous problem or conflict you had to solve. This classic question provides you the opportunity to show your skills in action, so make sure to highlight the objectivity and logic of your problem solving.

Show your logic when talking about yourself. When given the opportunity to talk about yourself, highlight how logic comes into play in your decision making. This could be in how you picked the job position, why you choose your career or education, or what it is about yourself that makes you a great candidate.

Why is it important to think logically?

It’s important to think logically because it allows you to analyze a situation and come up with a logical solution. It allows for you to reason through the important decisions and solve problems with a better understanding of what needs to be done. This is necessary for developing a strong career.

Why is logic important?

Logic is important because it helps develop critical thinking skills. Critical thinking skills are important because they help you analyze and evaluate a problem before you make a decision. It also helps you improve your problem-solving skills to allow you to make better decisions.

How do you improve your logical thinking skills?

When improving your logical thinking skills make sure you spend time on a creative hobby and practice questioning. Creative hobbies can help reduce stress levels, and lower stress leads to having an easier time focusing on tasks and making logical thinking. Creative hobbies can include things like drawing, painting, and writing.

Another way to improve your logical thinking is to start asking questions about things. Asking questions allows for you to discover new things and learn about new topics you may not have thought about before.

What are logical thinking skills you need to succeed at work?

There are many logical thinking skills you need to succeed in the workplace. Our top four picks include:

Observation

Active Listening

Problem-solving

Logical thinking skills are valuable skills to have. You need to develop them so that you can become an asset to any organization that hires you. Be sure to include them in your resume and cover letter .

And if you make it to the interview, also ensure that you highlight these skills. You can do all this by highlighting the career accomplishments that required you to use logical thinking in the workplace.

It’s Your Yale – Consider Critical Thinking Skills to Articulate Your Work Quality

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Roger Raber has been a content writer at Zippia for over a year and has authored several hundred articles. Having retired after 28 years of teaching writing and research at both the high school and college levels, Roger enjoys providing career details that help inform people who are curious about a new job or career. Roger holds a BA in English from Cleveland State University and a MA from Marygrove college.

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Problem solving is clearly a key feature of human intelligence. Human intelligence does not, in the main, rely on behaviour patterns fixed by evolution and nor does it depend on habit learning. To understand human intelligence, we need to study how humans can solve both ill-defined and well-defined problems. ‘Problem solving’ considers both types of problems and the different approaches used to solve them: the computational approach, insight, and expertise. It also looks at dual-process theory and explains that fast, intuitive processes can be both a source of error and also a cause of success, depending on the context and the prior knowledge of the problem solver.

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How logical reasoning works

What is logical reasoning?

Logical reasoning is the process of using rational and systematic series of steps to come to a conclusion for a given statement. The situations that ask for logical reasoning require structure, a relationship between given facts and chains of reasoning that are sensible. Because you have to study a problem objectively with logical reasoning, analysing is an important factor within the process. Logical reasoning starts with a proposition or statement. This statement can be both true or false.  

Why is logical reasoning important?

Logical reasoning, in combination with other cognitive skills, is an important skill you use during all kinds of daily situations. It helps you make important decisions, discern the truth, solve problems, come up with new ideas and set achievable goals. Logical reasoning is also an important aspect of measuring intelligence during an IQ-test.  

The three types of logical reasoning

Logical reasoning can be divided into deductive-, inductive- and abductive reasoning. While inductive reasoning starts with a specific instance and moves into a generalized conclusion, deductive reasoning goes from a generalized principle that is known to be true to a specific conclusion that is true. And abductive reasoning is making a probable conclusion from what you know.  

We’ll explain each type of logical reasoning further:

Inductive reasoning

With inductive reasoning, a number of specific observations lead to a general rule. With this method, the premises are viewed as supplying some evidence for the truth of a conclusion. With inductive reasoning, there is an element of probability. In other words, forming a generalization based on what is known or observed.   While this sounds like the theory you will use during a debate or discussion, this is something you do every day in much simpler situations as well. We’ll explain this type of logical reasoning with an example: There are 28 balls within a basket, which are either red or white. To estimate the amount of red and white balls, you take a sample of four balls. The sample you took, exists out of three red and one white ball. Using good inductive generalization would be that there are 21 red and 7 white balls in the basket. As already explained, the conclusion drawn from his type of reasoning isn’t certain but is probable based on the evidence given (the sample of balls you took). Questions which require to perform inductive reasoning are a part of IQ-tests. An example of a little more complex question like just explained with the balls is the one of the image below. To come to a conclusion to solve this problem, both inductive reasoning and pattern recognition skills are required. Looking at the sequence of tiles with different patterns of dots, which tile should be on the place of the question mark? A, B, C, D, E or F?  

Deductive reasoning

With deductive reasoning, factual statements are used to come to a logical conclusion. If all the premises (factual statements) are true, the terms are clear and all the rules of deductive logic are followed to come to a conclusion, then the conclusion will also be true. In this case, the conclusion isn’t probable, but certain. Deductive reasoning is also known as “top-down” logic, because it (in most cases) starts with a general statement and will end with a specific conclusion.

We’ll explain deductive reasoning with an example, with 2 given premises:

It’s dangerous to drive while it’s freezing (premise 1)

It is currently freezing outside (premise 2)

So, we now know that it is dangerous to drive when it is freezing, and it is currently freezing outside. Using deductive reasoning, these two premises can help us form necessarily true conclusion, which is:

It is currently dangerous to drive outside (conclusion)

Situations in which you use deductive reasoning can come in many forms, such as mathematics. Whether you are designing your own garden or managing your time, you use deductive reasoning while doing math daily. An example is solving the following math problem:

All corners of a rectangle are always 180° (premise 1)

The following rectangle has one right angle, which is always 90° (premise 2)

The second angle is 60° (premise 3)  

How much degrees is the third angle (X)? To answer this question, you can use the three premises to come to the conclusion how much degrees the third hook is. The conclusion should be 180° (premise 1) -90° (premise 2) - 60° (premise 3) = 30° (conclusion)

Abductive reasoning

With abductive reasoning, the major premise is evident but the minor premise(s) is probable. Therefore, defining a conclusion would also make this conclusion probable. You start with an observation, followed by finding the most likely explanation for the observations. In other words, it is a type of logical reasoning you use when you form a conclusion with the (little) information that is known. An example of using abductive reasoning to come to a conclusion is a decision made by a jury. In this case, a group of people have to come to a solution based on the available evidence and witness testimonies. Based on this possibly incomplete information, they form a conclusion. A more common example is when you wake up in the morning, and you head downstairs. In the kitchen, you find a plate on the table, a half-eaten sandwich and half a glass of milk. From the premises that are available, you will come up with the most likely explanation for this. Which could be that your partner woke up before you and left in a hurry, without finishing his or her breakfast.  

How does logical thinking relate to problem-solving?

As previously mentioned, the different types of logical reasoning (inductive, deductive and abductive) help you to form conclusions based on the current situation and known facts. This very closely correlates to problem-solving, as finding the most probable solution to resolve a problem is a similar conclusion. Logical thinking, and thereby problem solving, goes through the following five steps to draw a conclusion and/or find a solution:

Collecting information about the current situation. Determining what the current problem is, and what premises apply. Let’s say you want to go out for a drive, but it’s freezing outside.

Analyzing this information. What information is relevant to the situation, and what isn’t. In this case, the fact that it’s freezing is relevant for your safety on the road. The fact that you might get cold isn’t, as you’d be in your car.

Forming a conclusion. What can you conclude from this information? The roads might be more dangerous because it’s freezing.

Support your conclusion. You might look at traffic information to see that there have been more accidents today, in which case, that supports the conclusion that driving is more dangerous today.

• Defend your conclusion. Is this conclusion correct for your case? If you don’t have winter tires it would be more accurate than when you do.  

How to improve logical thinking and problem-solving skills?

Because there are so many different situations in which you use logical thinking and problem-solving, this isn’t a cognitive skill you can train specifically. Luckily, there are many methods that might help you to improve your logical thinking skills. These include methods to keep your general cognitive abilities healthy as well as methods to train your logical thinking skills. These are:

Learning something new

Social interaction

Healthy nutrition

Ensure enough sleep

Avoid stress

Preferably no alcohol

Spend time on creative hobbies

Practice questioning

Try to anticipate the outcome of your decisions

Brain training to challenge your logical reasoning skills

Experimental Psychology, Cognition, and Human Aging pp 596–659 Cite as

Thinking: Problem Solving and Reasoning

• Donald H. Kausler 2  

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1 Citations

Bourne et al. (1979) reminded us that real-life problems come in all shapes and sizes. Earlier we observed that these real-life problems are faced by adults of all ages. Our concern is with what happens to problem-solving proficiency over the course of the adult segment of the life span and with what accounts for age changes in proficiency. To study problem-solving behavior in the laboratory, psychologists have introduced a number of specific problem situations that are intended to simulate a myriad of problem situations encountered in the real world. Several of these problems are given in Table 11.1. Our initial step will be to examine the processes that have been postulated by both associationists and cognitive psychologists to enter into the solving of these kinds of problems (see Bourne, Dominowski, Loftus, & Healy, 1986; Bourne et al., 1979; Glass, Holyoak, & Santa, 1979; and Newell & Simon, 1972; for more detailed reviews). Along the way, we will indicate likely candidates for age sensitivity.

ArticleNote Problems come in all shapes and sizes but generally share the characteristic that the individual must discover what to do in order to achieve a goal. Whether looking for the screwdriver that isn’t where it’s supposed to be, searching for a friend’s house in an unfamiliar neighborhood, trying to figure out why the car won’t start, or working on a mathematics exam in school, a person faces a situation in which the correct response is somewhat uncertain. (Bourne, Dominowski, & Loftus, 1979, p. 232)

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Kausler, D.H. (1991). Thinking: Problem Solving and Reasoning. In: Experimental Psychology, Cognition, and Human Aging. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9695-6_11

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Cognition and Instruction/Problem Solving, Critical Thinking and Argumentation

We are constantly surrounded by ambiguities, falsehoods, challenges or situations in our daily lives that require our Critical Thinking , Problem Solving Skills , and Argumentation skills . While these three terms are often used interchangeably, they are notably different. Critical thinking enables us to actively engage with information that we are presented with through all of our senses, and to think deeply about such information. This empowers us to analyse, critique, and apply knowledge, as well as create new ideas. Critical thinking can be considered the overarching cognitive skill of problem solving and argumentation. With critical thinking, although there are logical conclusions we can arrive at, there is not necessarily a 'right' idea. What may seem 'right' is often very subjective. Problem solving is a form of critical thinking that confronts learners with decisions to be made about best possible solutions, with no specific right answer for well-defined and ill-defined problems. One method of engaging with Problem Solving is with tutor systems such as Cognitive Tutor which can modify problems for individual students as well as track their progress in learning. Particular to Problem Solving is Project Based Learning which focuses the learner on solving a driving question, placing the student in the centre of learning experience by conducting an extensive investigation. Problem Based Learning focuses on real-life problems that motivate the student with experiential learning. Further, Design Thinking uses a specific scaffold system to encourage learners to develop a prototype to solve a real-world problem through a series of steps. Empathy, practical design principles, and refinement of prototyping demonstrate critical thought throughout this process. Likewise, argumentation is a critical thinking process that does not necessarily involve singular answers, hence the requirement for negotiation in argumentative thought. More specifically, argumentation involves using reasoning to support or refute a claim or idea. In comparison problem solving may lead to one solution that could be considered to be empirical.

This chapter provides a theoretical overview of these three key topics: the qualities of each, their relationship to each other, as well as practical classroom applications.

Learning Outcomes:

• Defining Critical Thought and its interaction with knowledge
• Defining Problem Solving and how it uses Critical Thought to develop solutions to problems
• Introduce a Cognitive Tutor as a cognitive learning tool that employs problem solving to enhance learning
• Explore Project Based Learning as a specific method of Problem Solving
• Examine Design Thinking as a sub-set of Project Based Learning and its scaffold process for learning
• Define Argumentation and how it employs a Critical Though process
• Examine specific methodologies and instruments of application for argumentation
• 1.1 Defining critical thinking
• 1.2 Critical thinking as a western construct
• 1.3 Critical thinking in other parts of the world
• 1.4 Disposition and critical thinking
• 1.5 Self-regulation and critical thinking
• 1.6.1 Venn Diagrams
• 1.6.2.1 The classroom environment
• 1.6.3.1 Socratic Method
• 1.6.3.2 Bloom’s Taxonomy
• 1.6.3.3 Norman Webb’s Depth of Knowledge
• 1.6.3.4 Williams Model
• 1.6.3.5 Wiggins & McTighe’s Six Facets of Understanding
• 2.1.1.1.1 Structure Of The Classroom
• 2.2.1.1 Instructional Implications
• 2.2.2.1 Instructional Implications
• 2.3.1 Mind set
• 2.3.2.1.1 Instructional Implications
• 2.4 Novice Versus Expert In Problem Solving
• 2.5.1 An overview of Cognitive Tutor
• 2.5.2.1 ACT-R theory
• 2.5.2.2 Production rules
• 2.5.2.3 Cognitive model and model tracing
• 2.5.2.4 Knowledge tracing
• 2.5.3.1 Cognitive Tutor® Geometry
• 2.5.3.2 Genetics Cognitive Tutor
• 2.6.1 Theorizing Solutions for Real World Problems
• 2.6.2 Experience is the Foundation of Learning
• 2.6.3 Self-Motivation Furthers Student Learning
• 2.6.4 Educators Find Challenges in Project Based Learning Implementation
• 2.6.5 Learner Need for Authentic Results through Critical Thought
• 2.7.1 Using the Process of Practical Design for Real-World Solutions
• 2.7.2 Critical Thought on Design in the Artificial World
• 2.7.3 Critical Thinking as Disruptive Achievement
• 2.7.4 Designers are Not Scientific?
• 2.7.5 21st Century Learners and the Need for Divergent Thinking
• 3.1 Educators Find Challenges in Project Based Learning Implementation
• 3.2 Learner Need for Authentic Results through Critical Thought
• 3.3 Critical Thinking as Disruptive Achievement
• 3.4.1 Argumentation Stages
• 3.5 The Impact of Argumentation on Learning
• 4.1.1 Production, Analysis, and Evaluation
• 4.2 How Argumentation Improves Critical Thinking
• 5.1 Teaching Tactics
• 5.2.1 The CoRT Thinking Materials
• 5.2.2 The Feuerstein Instrumental Enrichment Program (FIE)
• 5.2.3 The Productive Thinking Program
• 5.2.4 The IDEAL Problem Solver
• 5.3.1 Dialogue and Argumentation
• 5.3.2 Science and Argumentation
• 5.3.3.1 Historical Thinking - The Big Six
• 5.4 Instructing through Academic Controversy
• 7.1 External links
• 8 References

Critical thinking [ edit | edit source ]

Critical thinking is an extremely valuable aspect of education. The ability to think critically often increases over the lifespan as knowledge and experience is acquired, but it is crucial to begin the process of this development as early on as possible. Research has indicated that critical thinking skills are correlated with better transfer of knowledge, while a lack of critical thinking skills has been associated with biased reasoning [1] . Before children even begin formal schooling, they develop critical thinking skills at home because of interactions with parents and caregivers [2] . As well, critical thinking appears to improve with explicit instruction [3] . Being able to engage in critical thought is what allows us to make informed decisions in situations like elections, in which candidates present skewed views of themselves and other candidates. Without critical thinking, people would fall prey to fallacious information and biased reasoning. It is therefore important that students are introduced to critical thought and are encouraged to utilize critical thinking skills as they face problems.

Defining critical thinking [ edit | edit source ]

In general, critical thinking can be defined as the process of evaluating arguments and evidence to reach a conclusion that is the most appropriate and valid among other possible conclusions. Critical thinking is a dynamic and reflective process, and it is primarily evidence-based [4] . Thinking critically involves being able to criticize information objectively and explore opposing views, eventually leading to a conclusion based on evidence and careful thought. Critical thinkers are skeptical of information given to them, actively seek out evidence, and are not hesitant to take on decision-making and complex problem solving tasks [5] . Asking questions, debating topics, and critiquing the credibility of sources are all activities that involve thinking critically. As outlined by Glaser (1941), critical thinking involves three main components: a disposition for critical thought, knowledge of critical thinking strategies, and some ability to apply the strategies [6] . Having a disposition for critical thought is necessary for applying known strategies.

Critical thinking, which includes cognitive processes such as weighing and evaluating information, leads to more thorough understanding of an issue or problem. As a type of reflection, critical thinking also promotes an awareness of one's own perceptions, intentions, feelings and actions. [7]

Critical thinking as a western construct [ edit | edit source ]

In modern education, critical thinking is taken for granted as something that people universally need and should acquire, especially at a higher educational level [8] [9] . However, critical thinking is a human construct [10] - not a scientific fact - that is tied to Ancient Greek philosophy and beliefs [11] .

The link to Ancient Greece relates both to Ancient Greek priorities of logic over emotion [11] , as well as its democratic principles. Various authors, including Elder & Paul [12] , Moon [8] , and Stanlick & Strawser [13] share the view that critical thinking questioning back to the time of Socrates . Likewise, Morgan & Saxton (2006) associate critical thinking with a fundamental requirement of all democratic citizens [14] .

An additional connection with Ancient Greece involves the Socratic Method. The Socratic Method involves a conversation between two or more people in which they ask and answer questions to challenge each other’s theses using logic and reason [15] . Such debates are subject to the issue of objective/subjective dualism in that the purpose of debate is the belief that there is a ‘right answer’, yet the ability to conduct such a debate demonstrates the subjectivity of any thesis [15] .

Because of this strong connection to Ancient Greece, critical thinking is generally considered to be a western construct. This is further amplified another western construct called Bloom’s Taxonomy , which is considered to be the essence of critical thinking in modern education [16] .

Since critical thinking is a human construct, notions of what constitutes critical thinking vary considerably from person to person. Moon (2007) lists 21 common notions of critical thinking provided by people from her workshops, and then provides her own 2-page definition of the term [8] . One view of critical thinking is that it involves a set of skills that enables one to reach defensible conclusions and make decisions in a domain or context in which one has some prior knowledge [10] . Another view is that critical thinking involves the use of systematic logic and reasoning, which while not necessarily producing empirical answers nevertheless uses a rational and scientific approach [17] . Ultimately, Moon concludes that there is no right or wrong definition [8] .

Critical thinking in other parts of the world [ edit | edit source ]

Scholars argue that while the critical thinking construct is linked to western, democratic nations, that does not mean that other non-western cultures do not possess or use similar constructs that involve critical thinking [18] . Instead, “there are different ways or forms of reasoning” [19] ; for example, Asian approaches to debates involve finding connections between conflictive arguments in order for such ideas to coexist [18] . This is due to eastern values regarding face-saving [8] . In contrast, western approaches are often viewed as being competitive: attacking the views of others while defending one's own position. Despite this dichotomous generalisation, eastern and western approaches have more similarities than they would first seem. With regards to the diplomatic Asian approach to debating, western approaches also involve compromise and negotiation for the very reason that ideas are often complex and that there can be many ‘right’ answers [14] . Similarly, the extent to which other cultures adopt western notions of critical thinking is determined by cultural values. In Muslim cultures, for example, the value of critical thinking is link to views on the appropriateness of voicing one’s views [20] .

Disposition and critical thinking [ edit | edit source ]

It has been suggested that critical thinking skills alone are not sufficient for the application of critical thinking – a disposition for critical thinking is also necessary [5] . A disposition for critical thought differs from cognitive skills. A disposition is better explained as the ability to consciously choose a skill, rather than just the ability to execute the skill [4] . Having a disposition for critical thinking can include such things as genuine interest and ability in intellectual activities. Perkins et al. (2000) expand on the idea of the necessity for a critical thinking disposition, and indicate three aspects involved in critical thinking disposition: an inclination for engaging in intellectual behaviours; a sensitivity to opportunities, in which such behaviours may be engaged; and a general ability for engaging in critical thought [5] . Halpern (1998) suggests that this critical thinking disposition must include a willingness to continue with tasks that seem difficult, openmindedness, and a habit of planning [5] . In fact, in a cognitive skills study conducted by Clifford et al. (2004), they discovered that a disposition for critical thinking was associated with better overall critical thinking skills [4] .

These are characteristics of one's attitude or personality that facilitate the process of developing CT skills:

• Inquisitive
• Truthseeking
• Open-minded
• Confidence in reasoning

There are many factors that can influence one's disposition towards CT; the first of these is culture [5] . There are many aspects of culture that can impact the ability for people to think critically. For instance, religion can negatively impact the development of CT [5] . Many religions are founded upon faith, which often requires wholehearted belief without evidence or support. The nature of organized religion counters the very premise of CT, which is to evaluate the validity and credibility of any claim. Growing up in an environment such as this can be detrimental to the development of CT skills. This kind of environment can dampen dispositions that question religious views or examine the validity of religion. Another cultural factor that can be detrimental to a CT disposition is that of authority [5] . When a child is raised under the conditions of an authoritarian parenting style, it can be detrimental to many aspects of their lives, but especially to their CT skills, as they are taught not to question the credibility of authority and often receive punishment if they do. This is also applicable in the classroom [5] . Classroom environments that foster a disposition for critical thinking in which teachers who do not foster an atmosphere of openness or allow students to question what they are taught can impact CT development as well. Classrooms where questions are rejected or home environments in which there is a high level of parental power and control can all affect the ability of students to think critically. What is more, students will have been conditioned not to think this way for their entire lives [5] . However, despite these cultural limitations, there are ways in which a disposition for CT can be fostered in both the home and the classroom.

Classroom structure is a primary way in which CT dispositions can be highlighted. Fostering a classroom structure in which students are a part of the decision making process of what they are studying can be very helpful in creating CT dispositions [5] . Such structures help students become invested in what they are learning as well as promote a classroom atmosphere in which students may feel free to question the teacher, as well as other students' opinions and beliefs about different subjects. Allowing the freedom to scrutinize and evaluate information that has been given to students is an effective way of creating a classroom environment that can encourage students to develop CT dispositions. This freedom allows for the students to remain individuals within the larger classroom context, and gives them the power to evaluate and make decisions on their own. Allowing the students to share power in the classroom can be extremely beneficial in helping the students stay motivated and analytical of classroom teachings [5] . Teachers can also employ a variety of techniques that can help students become autonomous in the classroom. Giving students the opportunity to take on different roles can be effective in creating CT dispositions, such as making predictions and contemplating problems [5] . Allowing students to engage with problems that are presented, instead of just teaching them what the teacher or textbook believes to be true, is essential for students to develop their own opinions and individual, though. In addition to this, gathering data and information on the subject is an important part of developing CT dispositions. Doing so allows for students to go out and find resources that they themselves can analyze and come to conclusions on their own [5] . Using these aspects of CT students can most effectively relate to the predictions that were first made and critique the validity of the findings [5] .

Self-regulation and critical thinking [ edit | edit source ]

In conjunction with instructing CT, teachers also need to keep in mind the self-regulation of their students. Students need to be able to maintain motivation and have a proactive attitude towards their own learning when learning a new skill. In an article by Phan (2010), he argues that self-regulated students that have better goal setting have more personal responsibility for their learning, can maintain their motivation, are more cognitively flexible, and hence are more inclined to utilize CT. Since CT skills are highly reflective, they help in self-regulated learning (SRL), and in turn, self-regulatory strategies aid in developing CT skills. These two cognitive practices are assets to students’ growth and development [7] .

Self-Regulation provides students with the basic meta-cognitive awareness required for proactive learning. This pro-activity allows students to engage in the cognitive processes of CT, such as evaluation, reflection and inference. Through one’s meta-cognitive ability to assess one’s own thoughts, one develops the capability to become autonomous in one’s learning [7] . Instead of having a supervisor overlook every task, the learner can progress at their own pace while monitoring their performance, thereby engaging in SRL. Part of this process would include periodic reflection upon the strategies that one uses when completing a task. This reflection can facilitate the student’s learning by using CT to evaluate which strategies best suit their own learning based on their cognitive needs.

The complex nature of CT suggests that it requires a long developmental process requiring guidance, practice and reinforcement. To facilitate this process, self-monitoring as a first step to self-regulation can jump-start reflective thought through assessing one’s own educational performance. This assessment promotes self-efficacy through generating motivational beliefs about one’s academic capabilities [7] . From there, through practice, students can extend their CT skills beyond themselves and into their educational contexts. With practice, students use their meta-cognitive strategies as a basis for developing CT in the long run.

Critical thinking strategies [ edit | edit source ]

Psychologists and educators have discovered many different strategies for the development of critical thinking. Among these strategies are some that may be very familiar, such as concept maps or Venn diagrams , as well as some that may be less familiar, such as appeal-question stimuli strategies [21] . Concept mapping is particularly useful for illustrating the relationships between ideas and concepts, while Venn diagrams are often used to represent contrasting ideas [21] .

Venn Diagrams [ edit | edit source ]

Venn diagrams are used frequently in elementary grade levels and continue to be used as a contrast/compare tool throughout secondary school. An example of a situation in which a Venn diagram activity may be appropriate is during a science class. Instructors may direct students to develop a Venn diagram comparing and contrasting different plants or animals. Concept maps may be introduced in elementary grades, although they are most often used in the secondary and post-secondary levels. Concept maps are an interactive and versatile way to encourage students to engage with the course material. A key aspect of concept mapping is how it requires students to reflect on previously learned information and make connections. In elementary grades, concept maps can be introduced as a project, while later, possibly in college or university, students may use them as a study strategy. At the elementary level, students can use concept maps to make connections about the characters, settings, or plot in a story they have read. When introducing concept maps, teachers may provide students with a list of words or phrases and instruct the students to illustrate the connections between them in the form of a concept map. Asking questions can also be a simple and engaging way to develop critical thought. Teachers may begin by asking the students questions about the material, and then encouraging students to come up with their own questions. In secondary and post-secondary education, students may use questions as a way to assess the credibility of a source. At the elementary school level, questions can be used to assess students' understanding of the material, while also encouraging them to engage in critical thought by questioning the actions of characters in a story or the validity of an experiment. Appeal-question stimuli, founded by Svobodová, involves a process of students asking questions regarding their reading comprehension [21] .

Discussions [ edit | edit source ]

Using discussions as a way to develop students’ critical thinking skills can be a particularly valuable strategy for teachers. Peer interactions provide a basis for developing particular critical thinking skills, such as perspective taking and cooperation, which may not be as easily taught through instruction. A large part of discussions, of course, is language. Klooster (2002) suggested that critical thinking begins with asking questions [21] . Similarly, Vygotsky has claimed that language skills can be a crucial precursor for higher level thought processes [2] . As children develop larger vocabularies, they are better able to understand reading material and can then begin to think abstractly about the material and engage in thoughtful discussions with peers about what they understood [2] .

Studies have indicated that cross-age peer discussions may be particularly helpful in facilitating the development of critical thinking. Cross-age peer groups can be effective because of the motivation children tend to have when working with peers of different ages [2] . Younger children often look up to the older children as mentors and valuable sources of knowledge and experience, while older children feel a sense of maturity and a responsibility to share their knowledge and experience with younger students [2] . These cross-age peer discussions also provide students with the challenge of tailoring their use of language to the other group members in order to make their points understandable [2] . An example of cross-age peer groups that is relatively common in Canadian schools is the big buddy programs, where intermediate grade students are assigned a primary grade buddy to help over the course of the school year. Big buddies may help their little buddies with projects, advice, or school events. The big buddy/little buddy programs can be effective as younger students look up to their big buddies, and the big buddies feel a responsibility to help their little buddy. One important factor to be considered with cross-age peer discussions, as noted by Hattie (2006), is that these discussions should be highly structured activities facilitated by a teacher in order to ensure that students understand their group responsibilities [2] .

The classroom environment [ edit | edit source ]

Having an environment that is a safe place for students to ask questions and share ideas is extremely valuable for creating a classroom that encourages critical thinking. It has been suggested that students are more likely to develop a disposition for critical thinking when they are able to participate in the organization and planning of their classroom and class activities [5] . In these classrooms, students are legitimately encouraged by their teacher to engage in the decision making process regarding the functioning of the classroom [5] . It is also important for teachers to model the desired types of critical thought, by questioning themselves and other authorities in a respectful and appropriate manner [5] . Studies have indicated higher levels of cognitive engagement among students in classrooms with teachers who are enthusiastic and responsive [22] . Therefore, teachers should be encouraging and inclusive, and allow student engagement in classroom planning processes when possible.

Critical questions [ edit | edit source ]

Research is increasingly supporting the idea that critical thinking can be explicitly taught [23] . The use of critical questioning in education is of particular importance, because by teaching critical questioning, educators are actively modelling critical thinking processes. One of the key issues with teaching critical thinking in education is that students merely witness the product of critical thinking on the part of the teacher, i.e. they hear the conclusions that the teacher has reached through critical thinking [9] . Whereas an experienced critical thinker uses critical questions, these questions are implicit and not normally verbalised. However, for students to understand critical questioning and critical thinking strategies, the students must see the process of critical thinking. Modelling the formation and sequencing of critical questions explicitly demonstrates the thought process of how one can reach a logical conclusion.

There various methods of teaching critical questioning. The frameworks discussed below are among the most famous of these. All have their own strengths and weaknesses in terms of ease-of-use, complexity, and universality. Each of these methods approaches critical thinking with a specific definition of this human concept. As such, one’s own definition of critical thinking will likely affect one’s receptiveness to a specific critical questioning framework.

Socratic Method [ edit | edit source ]

One of the key features of western approaches to critical thinking involves the importance of critical questioning, which is linked to the Socratic Method from Ancient Greece traditions. Whether answering existing questions posed or creating new questions to be considered, critical thinking involves questions, whether explicitly / implicitly, consciously / unconsciously [13] . Browne & Keeley (2006) base their definition of critical thinking specifically on the involvement of critical questions [24] .

Answers to critical questions are not necessarily empirical. They may involve reasoning and be logical, but are nevertheless subject to alternative views from others, thus making all views both subjective and objective at the same time. Elder & Paul (2009) separate such critical questions into three categories [12] :

• Questions that have a correct answer, which can be determined using knowledge
• Questions that are open to subjective answers that cannot be judged
• Questions that produce objective answers that are judged based the quality of evidence and reasoning used

Books on critical questioning tend to be influenced heavily by the Socratic Method, and they make a distinction between ‘good’ and ‘bad’ questions. Good questions are those that are relevant to the topic at hand and that take a logical, systematic approach [14] [13] , while bad questions are those that are not relevant to the topic, are superficial, and are sequenced haphazardly. Elder & Paul (2009) argue that “[i]t is not possible to be a good thinker and a poor questioner.” [25] In other words, if a person cannot thinking of relevant and logical questions, they will be unable to reach any rational conclusions.

Additionally, as indicated above, critical thinking requires more than just asking the right questions. There is a direct relationship between critical thinking and knowledge [23] . One can possess knowledge, but not know how to apply it. Conversely, one can have good critical questioning skills, but lack the knowledge to judge the merits of an answer.

In terms of teaching critical questioning using the Socratic Method, it is essential to appreciate that there is no set of questions that one can follow, since the type of critical questions needed is based on the actual context. Consequently, the examples presented by different authors vary quite considerably. Nevertheless, there are specific guidelines one can follow [26] :

• Use critical questions to identify and understand the situation, issues, viewpoints and conclusions
• Use critical questions to search for assumptions, ambiguity, conflicts, or fallacies
• Use critical questions to evaluate the effects of the ideas

Part 1 of the Socratic Method is more of an information gathering stage, using questions to find out essential details, to clarify ideas or opinions, and to determine objectives. Part 2 uses the information from Part 1 and then uses questions to probe for underlying details that could provide reasons for critiquing the accuracy of the idea. Part 3 uses questions to reflect upon the consequences of such ideas.

Conklin (2012) separates the above three parts into six parts [27] :

• Using questions to understand
• Using questions to determine assumptions
• Using questions to discover reasons / evidence
• Using questions to determine perspectives
• Using questions to determine consequences
• Using questions to evaluate a given question

Here are some sample questions for each part [28] :

Questions for understanding:

• Why do you think that?
• What have you studied about this topic so far?
• How does this relate to what you are studying now?

Questions that determine assumptions

• How could you check that assumption?
• What else could be assumed?
• What are your views on that? Do you agree or disagree?

Questions that discover reasons / evidence

• How can you be sure?
• Why is this happening?
• What evidence do you have to back up your opinion?

Questions that determine perspectives

• How could you look at this argument another way?
• Which perspective is better?

Questions that determine consequences

• How does it affect you?
• What impact does that have?

Questions that evaluate a given question

• Why was I asked this question?
• Which questions led to the most interesting answers?
• What other questions should be asked?

Depending on the text, the Socratic Method can be extraordinarily elaborate, making it challenging for educators to apply. Conklin (2012) states that a teacher would need to spend time planning such questions in advance, rather than expect to produce them during a lesson [27] .

Bloom’s Taxonomy [ edit | edit source ]

Bloom’s Taxonomy was originally designed in 1956 to determine cognitive educational objectives and assess students’ higher-order thinking skills [29] . Since then, though, it has become adapted and used as a useful tool for promoting critical thinking skills, particularly through critical questioning [30] . These critical questions involve Bloom’s categories of understanding, applying, analysing, synthesising and evaluating. Such categories can be seen to relate to the Socratic Method promoted by other authors, i.e. the importance of questioning to understanding, analyse and evaluate. Moon (2007) believes that “‘evaluation’, ‘reflection’ and ‘understanding’” are key aspects of critical thinking [8] , which should therefore appear in any notion of critical thinking. At the same time, Bloom’s Taxonomy generates a natural set of questions that can be adapted to various contexts [31] .

In one example, a teacher uses a picture of a New York speakeasy bar. Using Bloom’s Taxonomy, the teacher could ask and model the following critical questions [14] :

• KNOWLEDGE: What do you see in the picture?
• COMPREHENSION: What do people do in places like that?
• ANALYSIS: Why are there so many policemen in the picture?
• APPLICATION: What similar situations do we see nowadays?
• SYNTHESIS: What if there were no laws prohibiting such behaviour?
• EVALUATION: How would you feel if you were one of these people? Why?

Norman Webb’s Depth of Knowledge [ edit | edit source ]

Webb’s Depth of Knowledge (DOK) taxonomy was produced in 2002 in response to Bloom’s Taxonomy [32] . In contrast with Bloom’s Taxonomy, Webb’s DOK focuses on considering thinking in terms of complexity of thinking rather than difficulty [32] .

Webb’s DOK has four levels:

• Recall & reproduction
• Working with skills & concepts
• Short-term strategic thinking
• Extended strategic thinking

Level 1 aligns with Bloom’s level of remembering and recalling information. Example critical questions in this level would include:

• What is the name of the protagonist?
• What did Oliver Twist ask Fagin?

Level 2 involves various skills, such as classifying, comparing, predicting, gathering, and displaying. Critical questions can be derived from these skill sets, including the following:

• How do these two ideas compare?
• How would you categorise these objects?
• How would you summarize the text?

Level 3 involves analysis and evaluation, once again aligning with Bloom’s Taxonomy.

• What conclusions can you reach?
• What theory can you generate to explain this?
• What is the best answer? Why?

At the same time, Level 3 of DOK shares similarities with the Socratic Method in that the individual must defend their views.

Level 4 is the most elaborate and challenging level. It involves making interdisciplinary connections and the creation of new ideas / solutions.

Since DOK becomes increasingly elaborate with levels and leads to the requirement to defend one’s position using logic and evidence, there are parallels with the Socratic Method. At the same time, because is used to develop standards in assessing critical thinking, it shares similarities with Bloom’s Taxonomy.

Williams Model [ edit | edit source ]

The Williams Model was designed by Frank Williams in the 1970s [27] . Unlike other methods, the Williams Model was designed specifically to promote creative thinking using critical questioning [27] . This model involves the following aspects:

• Flexibility
• Elaboration
• Originality
• Risk taking
• Imagination

Critical questions regarding fluency follow a sort of brainstorming approach in that the questions are designed to generates ideas and options [27] . For ‘flexibility’, the questions are designed to produce variations on existing ideas. ‘Elaboration’ questions are about building upon existing ideas and developing the level of detail. As the name suggests, critical questions for ‘originality’ are for promoting the development of new ideas. The ‘curiosity’ aspect of the Williams Model bears a similarity with that of the ‘Wonder’ stage of the Know Wonder Learn (KWL) system [33] . ‘Risk taking’ questions are designed to provoke experimentation. Although the name ‘complexity’ may sound similar to ‘elaboration’, it is instead about finding order among chaos, making connections, and filling in gaps of information. The final aspect is ‘Imagination’, which involves using questions to visualise.

Wiggins & McTighe’s Six Facets of Understanding [ edit | edit source ]

Wiggins & McTighe’s ‘Six Facets of Understanding’ are all based on deep understanding aspects of critical thinking [34] . The method is used for teachers to design questions for students to promote critical thinking [34] . The six facets are Explanation, Interpretation, Application, Perspective, Empathy, and Self-Knowledge [35] .

‘Why’ and ‘How’ questions dominate the ‘Explanation’ facet in developing theory and reasoning [36] :

• How did this happen? Why do you think this?
• How does this connect to the other theory?

Interpretation questions encourage reading between the lines, creating analogies or metaphors, and creating written or visual scenarios to illustrate the idea. Questions include:

• How would you explain this idea in other words?
• Why do you think that there is conflict between the two sides?
• Why is it important to know this?

Application questions are about getting students to use knowledge. Part of this comes from predicting what will happen based on prior experience. Another aspect involves learning from the past. Critical questions in this facet include:

• How might we prevent this happening again?
• What do you think will happen?
• How does this work?

Perspective questions involves not only looking at ideas from other people’s perspectives, but also determining what people’s points of views are. In comparison with Empathy questions, though, Perspective questions involve more of an analytical and critical examination [35] . Here are some example questions:

• What are the different points of view concerning this topic?
• Whose is speaking in the poem?
• Whose point of view is being expressed?
• How might this look from the other person’s perspective?

Empathy questions involve perspective-taking, including empathy, in order to show an open mind to considering what it would feel like to walk in another person’s shoes.

• How would you feel in the same situation?
• What would it be like to live in those conditions?
• How would you react if someone did that your family?

Self-knowledge questions are primarily designed to encourage self reflection and to develop greater self awareness [35] . In particular, Self-Knowledge questions reveal one’s biases, values, and prejudices and how they influence our judgment of others. Critical questions in this facet include:

• How has my life shaped my view on this topic?
• What do I really know about the lives of people in that community?
• What knowledge or experience do I lack?
• How do I know what I know? Where did that information / idea come from?

Questions within the Six Facets of Understanding all incorporate the following attributes [36] :

• They are open ended
• They require deep thought
• They require critical thinking
• They promote transfer of knowledge
• They are designed to lead to follow-up questions
• They require answers that are substantiated

For examples of critical questioning in action in a classroom environment, view the External Link section at the bottom of this page.

Problem Solving [ edit | edit source ]

In everyday life we are surrounded by a plethora of problems that require solutions and our attention to resolve them to reach our goals [37] . We may be confronted with problems such as: needing to determine the best route to get to work, what to wear for an interview, how to do well on an argumentative essay or needing to find the solution to a quadratic equation. A problem is present in situations where there is a desire to solve the problem, however the solution is not obvious to the solver [38] . Problem solving is the process of finding the solutions to these problems. [39] . Although they are related, critical thinking differs fundamentally from problem solving. Critical thought is actually a process that can be applied to problem solving. For example, students may find themselves engaging in critical thought when they encounter ill-defined problems that require them to consider many options or possible answers. In essence, those who are able to think critically are able to solve problems effectively [40] .

This chapter on problem solving will first differentiate between Well-defined Problems and Ill-defined Problems , then explain uses of conceptualizing and visually representing problems within the context of problem solving and finally we will discuss how mental set may impede successful problem solving.

Well-defined and Ill-defined Problems [ edit | edit source ]

Problems can be categorized into two types: ill-defined or well-defined [37] Cognitive Psychology and Instruction (5th Ed). New York: Pearson.</ref> to the problem at hand. An example of a well-defined problem is an algebraic problem (ex: 2x - 29 = 7) where one must find the value of x. Another example may be converting the weight of the turkey from kilograms to pounds. In both instances these represent well-defined problems as there is one correct solution and a clearly defined way of finding that solution.

In contrast, ill-defined problems represent those we may face in our daily lives, the goals are unclear and they have information that is conflicting, incomplete or inconclusive [41] . An example of an ill-defined problem may be “how do we solve climate change?” or “how should we resolve poverty” as there is no one right answer to these problems. These problems yield the possibility to many different solutions as there isn’t a universally agreed upon strategy for solving them. People approach these problems differently depending on their assumptions, application of theory or values that they use to inform their approach [42] . Furthermore, each solution to a problem has its own unique strengths and weaknesses. [42] .

Table 1. Summarizes the difference between well-defined and ill-defined problems.

Differences in Solving Ill-defined and Well-defined Problems [ edit | edit source ]

In earlier times, researchers assumed both types of problems were solved in similar ways [44] , more contemporary research highlights some distinct differences between processes behind finding a solution.

Kitchener (1983) proposed that well-defined problems did not involve assumptions regarding Epistemological Beliefs [37] because they have a clear and definite solution, while ill-defined problems require these beliefs due to not having a clear and particular solution [45] . In support of this idea, Schraw, Dunkle and Bendixen conducted an experiment with 200 participants, where they found that performance in well-defined problems is not predictive of one's performance on ill-defined problems, as ill-defined problems activated different beliefs about knowledge. [46]

Furthermore Shin, Jonassen and McGee (2003), [43] found that solving ill-defined problems brought forth different skills than those found in well-structured problems. In well-structured problems domain knowledge and justification skills highly predicted problem-solving scores, whereas scores on ill-structured tasks were predictive of argumentation, attitudes and metacognition in an astronomy simulation.

Aligned with these findings, Cho and Jonassen (2002) [47] found that groups solving ill-structured problems produced more argumentation and problem solving strategies due to the importance of considering a wide variety of solutions and perspectives. In contrast, the same argumentation technique distracted the participant's activities when they dealt with well-defined problems. This research highlights the potential differences in the processes behind solving ill-defined and well-defined problems.

Implications Of The Classroom Environment [ edit | edit source ]

The fundamental differences between well-structured and ill-structured problems implicate that solving ill-structured problems calls for different skills, strategies, and approaches than well-structured problems [43] . Meanwhile, most tasks in the educational setting are designed around engaging learners in solving well-structured problems that are found at the end of textbook chapters or on standardized tests. [48] . Unfortunately the strategies used for well-defined problems have little application to ill-defined problems that are likely to be encountered day to day [49] as simplified problem solving strategies used for the well-structured designs have been found to have almost no similarities to real-life problems [48]

This demonstrates the need to restructure classrooms in a way that facilitates the student problem solving of ill-structured problems. One way we may facilitate this is through asking students questions that exemplify the problems found in everyday life [50] . This type of approach is called problem based learning and this type of classroom structure students are given the opportunity to address questions by collecting and compiling evidence, data and information from a plethora of sources [51] . In doing so students learn to analyze the information,data and information, while taking into consideration the vast interpretations and perspectives in order to present and explain their findings [51] .

Structure Of The Classroom [ edit | edit source ]

In problem-based learning, students work in small groups to where they explore meaningful problems, identify the information needed to solve the given problem, and devise effective approaches for the solution [50] . Students utilize these strategies, analyze and consider their results to devise new strategies until they have come up with an effective solution [50] . The teacher’s role in this classroom structure is to guide the process, facilitate participation and pose questions to elicit reflections and critical thinking about their findings [50] . In addition teachers may also provide traditional lectures and explanations that are intended to support student inquiry [50] .

In support of the argument to implement a problem-based approach to problem solving, a meta-analysis conducted by Dochy, Segers, Van den Bossche, & Gijbels (2003), found problem-based learning to be superior to traditional styles of learning though in supporting flexible problem solving, application of knowledge, and hypothesis generation. [52] Furthermore, Williams, Hemstreet, Liu, and Smith (1998) found that this approach fostered greater gains in conceptual understanding in science [53] . Lastly Gallagher, Stepien, & Rosenthal (1992), found that in comparing traditional vs. project-based approaches students in problem-based learning demonstrate an ability to define problems. [54] These findings highlight the benefits of problem-based learning on understanding and defining problems in science. Given the positive effects of defining problems this education approach may also be applied to our next sub-topic of conceptualizing problems.

Steps to Problem Solving [ edit | edit source ]

There have been five stages consistently found within the literature of problem solving: (1) identifying the problem, (2) representing the problem, (3) choosing the appropriate strategy, (4) implementing the strategy, and (5) assessing the solutions [37] . This overview will focus on the first two stages of problem solving and examine how they influence problem solving.

Conceptualizing Problems [ edit | edit source ]

One of the most tedious and taxing aspects of problem solving is identifying the problem as it requires one to consider the problem through multiple lenses and perspectives without being attached to one particular solution to early on in the task [39] . In addition it is also important to spend time clearly identifying the problem due to the association between time spent "conceptualizing a particular problem and the quality of one's solutions". [37] For example consider the following problem:

Becka baked a chocolate cake in her oven for twenty five minutes. How long would it take her to bake three chocolate cakes?

Most people would jump to the conclusion to multiply twenty five by three, however if we place all three cakes in the oven at a time we find it would take the same time to bake three cakes as it would take to bake one. This example highlights the need to properly conceptualize the problem and look at it from different viewpoints, before rushing to solutions.

Taking this one step further, break down the five steps as the would be used to conceptualize the problem:

Stage 1 - Define the Problem

Stage 2 - Brainstorm Solutions

Stage 3 - Pick a Solution

Stage 4 - Implement the Solution

Stage 5 - Review the Result

Research also supports the importance of taking one's time to clearly identifying the problem before proceeding to other stages. In support of this argument, Getzel and Csikszentmihalyi found that artist students that spend more time identifying the problem when producing their art were rated as having more creative and original pieces than artists who spent less time at this stage [37] . These researchers postulated that in considering a wider scope of options during this initial stage they were able to come up with more original and dynamic solutions.

Furthermore, when comparing the approaches of experienced teachers and novice post-secondary students studying to be teachers, it was found that experienced teachers spent a greater amount of time lesson planning in comparison to post-secondary students when in a placed in a hypothetical classroom. [37] In addition these teachers offered significantly more solutions to problems posed in both ill-defined and well-defined problems. Therefore it is implicated that successful problem solving is associated with the time spent finding the correct problem and the consideration of multiple solutions.

Instructional Implications [ edit | edit source ]

One instructional implication we may draw from the literature that supports that the direct relationship between time spent on conceptualizing a problem and the quality of the solution, is that teachers should encourage students to spend as much time as possible at this stage [37] . In providing this knowledge and by monitoring student’s problem solving processes to ensure that they “linger” when conceptualizing problems, we may facilitate effective problem solving [37] .

Representing the Problem [ edit | edit source ]

Problem Representation refers to how the known information about a particular problem is organized [37] . In abstract representation of a problem, we merely think or speak about the problem without externally visually representing [37] . In representing a problem tangibly this is done by creating a visual representation on paper, computer, etc. of the data though graphs, stories, symbols, pictures or equations. These visual representations [37] may be helpful they can help us keep track of solutions and steps to a problem, which can particularly be useful when encountering complex problems.

For example if we look at Dunker's Buddhist Monk example [37]  :

In the morning a Buddhist monk walks outside at sunrise to climb up the mountain to get to the temple at the peak. He reaches the temple just prior to sunset. A couple days later, he departs from the temple at sunrise to climb back down the mountain, travelling quicker than he did during his ascent as he is going down the mountain. Can you show a location along the path that the monk would have passed on both at the exact time of the day? [37]

In solely using abstraction, this problem is seemingly impossible to solve due to the vast amount of information, how it is verbally presented and the amount of irrelevant information present in the question. In using a visual representation we are able to create a mental image of where the two points would intersect and are better able to come up with a solution [55] .

Research supports the benefits of visual representation when confronted with difficult problems. Martin and Schwartz [56] found greater usage of external representations when confronted with a difficult task and they had intermittent access to resources, which suggests that these representations are used as a tool when problems are too complex without external aids. Results found that while creating the initial visual representation itself took up time, those who created these visual representations solved tasks with greater efficiency and accuracy.

Another benefit is that these visual representations may foster problem solving abilities by enabling us to overcome our cognitive biases. In a study conducted by Chambers and Reisberg [57] , participants were asked to look at the image below then close their eyes and form a mental image. When asked to recall their mental image of the photo and see if there were any alternate possibilities of what the photo could be, none of the participants were able to do so. However when participants were given the visual representation of the photo they were quickly able to manipulate the position of the photo to come up with an alternate explanation of what the photo could be. This shows how visual representations may be used in education by learners to counteract mental sets, which will be discussed in the next section.

As shown above, relying on abstraction can often overload one’s cognitive resources due to short- term memory being limited to seven items of information at a time [37] . Many problems surpass these limits disabling us being able to hold all the relevant information needed to solve a problem in our working memory [37] . Therefore it is implicated that in posing problems teachers should represent them written or visually in order to reduce the cognitive load. Lastly another implication is that as teachers we may increase problem-solving skills through demonstrating to students different types of external representations that can be used to show the relevant information pertaining to the problem. These representations may include different types of graphs, charts and imagery, which all can serve as tools for students in coming up with an effective solution, representing relevant information and reducing cognitive load

Challenges of Problem Solving [ edit | edit source ]

As discussed above there are many techniques to facilitate the problem solving process, however there are factors that can also hinder this process. For example: one’s past experiences can often impede problem solving as they can provide a barrier in looking at novel solutions, approaches or ideas [58] .

Mind set [ edit | edit source ]

A mind set refers to one's tendency to be influenced by one's past experiences in approaching tasks. [58] Mental set refers to confining ourselves to using solutions that have worked in the past rather than seeking out alternative approaches. Mental sets can be functional in certain situation as in using strategies that have worked before we are quickly able to come up with solutions. However, they can also eliminate other potential and more effective solutions.

Functional Fixedness [ edit | edit source ]

Functional Fixedness is a type of mental set that refers to our tendency to focus on a specific function of an object (ie. what we traditionally use it for) while overlooking other potential novel functions of that object. [37]

A classic example of functional fixedness is the candle problem [59] . Consider you are at a table with a box full of tacks, one candle, and matches, you are then asked to mount the lit candle on the wall corkscrew board wall as quickly as possible, and make sure that this doesn't cause any wax to melt on the table. Due to functional fixedness you might first be inclined to pin the candle to the wall as that is what tacks are typically used for, similar to participants in this experiment. However, this is the incorrect solution as it would cause the wax to melt on the table.

The most effective solution requires you to view the box containing the tacks as a platform for the candle rather than it's traditional use as a receptacle. In emptying the box, we may use it as a platform for the candle and then use the tacks inside to attach the box to the wall. It is difficult to initially arrive at this solution as we tend to fixate on the function of the box of holding the tacks and have difficulty designating an alternate function to the box (ie. as a platform as opposed to a receptacle). This experiment demonstrates how prior knowledge can lead to fixation and can hinder problem solving.

Techniques to Overcome Functional Fixedness [ edit | edit source ]

As proposed by McCaffrey (2012), [60] one way to overcome functional fixedness is to break the object into parts. In doing so we may ask two fundamental questions “can it be broken down further” and “does my description of the part imply a use”. To explain this we can use McCaffrey’s steel ring figure-8 example. In this scenario the subject is given two steel rings, a candle and a match, they are asked to make the two steel rings into a figure 8. Looking at the tools provided to the subject they might decide that the wax from the candle could potentially hold the two pieces of steel together when heated up. However the wax would not be strong enough. It leaves them with a problem, how do they attach the two steel rings to make them a figure eight.

In being left with the wick as a tool, and labelling it as such we become fixated on seeing the primary function of the wick as giving off light, which hinders our ability to come up with a solution for creating a figure-8. In order to effectively solve problem we must break down our concept of the wick down further. In seeing a wick as just a waxed piece of string, we are able to get past functional fixedness and see the alternate functions of the string. In doing so we may come to the conclusion and see the waxed string as being able to be used to tie the two rings together. In showing the effectiveness of this approach McCaffrey (2012) found that people trained to use this technique solved 67% more problems than the control group [60] .

Given the effectiveness of this approach, it is implicated that one way we may promote Divergent Thinking is through teaching students to consider: "whether the object may be broken down further" [60] and "whether the description of the part imply a use" in doing so we may teach students to break down objects to their purest form and make salient the obscure features of a problem. This connects to the previously discussed idea of conceptualization where problem solving effectiveness can be increased through focusing time on defining the problem rather than jumping to conclusions based on our own preconceptions. In the following section we will discuss what strategies experts use when solving problems.

Novice Versus Expert In Problem Solving [ edit | edit source ]

Many researchers view effective problem solving as being dependent on two important variables: the amount of experience we have in trying to solve a particular category of problems [61] , which we addressed earlier by demonstrating that in practicing problem solving through engaging in a problem-based approach we may increase problem solving skills. However, the second factor to consider is the amount of domain-specific knowledge that we have to draw upon [61] . Experts possess a vast amount of domain knowledge, which allows them to efficiently apply their knowledge to relevant problems. Experts have a well-organized knowledge of their domain, which impacts they notice and how they arrange, represent and interpret information, this in turn enables them to better recall, reason and solve problems in comparison to novices. [62]

In comparing experts to novices in their problem strategies, experts are able to organize their knowledge around the deep structure in important ideas or concepts in their domain, such as what kind of solution strategy is required to solve the problem [63] . In contrast novices group problems based on surface structure of the problems, such as the objects that appear in the problem. [63]

Experts also spend more time than novices analyzing and identifying problems at the beginning of the problem-solving process. Experts take more time in thinking and planning before implementing solutions and use a limited set of strategies that are optimal in allowing them to richer and more effective solutions to the given problem. [64]

In addition experts will engage in deeper and more complete problem representation novices, in using external representations such as sketches and diagrams to represent information and solve problems. In doing so they are able to solve problems quicker and come up with better solutions. [65]

Given the literature above it is evident that problem solving and expertise overlap as the key strategies that experts utilize are also provided as effective problem solving strategies. Therefore, we may conclude that experts not only have a vast knowledge of their domain, they also know and implement the most effective strategies in order to solve problem more efficiently and effectively in comparison to novices. [65] In the next section we will discuss the connection between problem solving and critical thinking.

Cognitive Tutor for Problem Solving [ edit | edit source ]

Cognitive Tutor is a kind of Intelligent Tutoring Systems. [66] It can assign different problems to students according to their individual basis, trace users’ solution steps, provide just-in-time feedback and hint, and implement mastery learning criteria. [67]

According to Anderson and colleague, [67] the students who worked with LISP tutors completed the problems 30% faster and 43% outperformed than their peers with the help of teachers in mini-course. Also, college students who employed ACT Programming Tutor (APT) with the function of immediate feedback finished faster on a set of problems and 25% better on tests than the students who received the conventional instruction. [68] In addition, in high school geometry school settings, students who used Geometry Proof Tutor (GPT) for in- class problem solving had a letter grade scores higher than their peers who participated in traditional classroom problem-solving activities on a subsequent test. [69]

An overview of Cognitive Tutor [ edit | edit source ]

In 1985, Anderson, Boyle, and Reigser added the discipline of cognitive psychology to the Intelligent Tutoring Systems. Since then, the intelligent tutoring system adopted this approach to construct cognitive models for students to gain knowledge was named Cognitive Tutors. [67] The most widely used Cognitive Tutor is Cognitive Tutor® Algebra I. [69] Carnegie Learning, Inc., the trademark owner, is developing full- scale Cognitive Tutor®, including Algebra I, II, Bridge to Algebra, Geometry, and Integrated Math I, II, III. Cognitive Tutor® now includes Spanish Modules, as well.

Cognitive Tutors support the idea of learning by doing, an important part of human tutoring, which to provide students the performance opportunities to apply the objective skills or concepts and content related feedback. [69] To monitor students’ performance, Cognitive Tutors adopt two Algorithms , model tracing and knowledge tracing. Model tracing can provide immediate feedback, and give content-specific advice based on every step of the students’ performance trace. [67] Knowledge tracing can select appropriate tasks for every user to achieve mastery learning according to the calculation of one’s prior knowledge. [67] [69]

Cognitive Tutors can be created and applied to different curriculum or domains to help students learn, as well as being integrated into classroom learning as adaptive software. The curriculum and domains include mathematics in middle school and high school, [66] [68] [70] genetics in post-secondary institutions, [71] and programming. [67] [68] [72] [73]

Cognitive Tutors yielded huge impacts on the classroom, student motivation, and student achievement. [74] Regarding the effectiveness of Cognitive Tutors, research evidence supports more effectiveness of Cognitive Tutors than classroom instruction. [67] [75] [76] [68]

The Theoretical Background of Cognitive Tutor [ edit | edit source ]

Act-r theory [ edit | edit source ].

The theoretical background of Cognitive Tutors is ACT-R theory of learning and performance, which distinguishes between procedural knowledge and declarative knowledge. [67] According to the ACT-R theory, procedural knowledge cannot be directly absorbed into people’s heads, and it can be presented in the notation of if-then Production rules. The only way to acquire procedural knowledge is learning by doing.

Production rules [ edit | edit source ]

Production rules characterize how students, whether they beginning learners or advanced learners, think in a domain or subject. [67] Production rules can represent students' informal or intuitive thinking. [77] The informal or intuitive forms of thinking are usually different from what textbook taught, and students might gain such patterns of thinking outside from school. [78] Heuristic methods, such us providing a plan of actions for problem-solving instead of giving particular operation; [79] and non-traditional strategies, such as working with graphics rather than symbols when solving equation, [69] can be represented in production rules as well.

Cognitive model and model tracing [ edit | edit source ]


Cognitive model is constructed on both ACT-R theory and empirical studies of learners. [69] All the solutions and typical misconceptions of learners are represented in the production system of the cognitive model.

For example, there are three strategies of solving an algebra equation, 2(3+X)=10. Strategy 1 is multiplying 2 across the sum (3+X); Strategy 2 is dividing both sides of the equation by 2; Strategy 3 shows the misconception of failing to multiply 2 across the sum (3+X). Since there are various methods of each task, students can choose their way of solving problems.

Model tracing is an algorithm that can run forward along every student’s learning steps and provide instant context-specific feedback. If a student chooses the correct answer, for example, using strategy 1 or strategy 2 to solve the equation, the Cognitive Tutor® will accept the action and provide the student next task. If the student’s mistake match a common misconception, such as using strategy 3, the Cognitive Tutor will highlight this step as incorrect and provide a just-in- time feedback, such as you also need to multiply X by 2. If the student’s mistake does not match any of the production rule in the cognitive model, which means that the student does not use any of the strategies above, the Cognitive Tutor® will flag this step as an error in red and italicized. Students can ask for advice or hint any time when solving problems. According to Corbett, [68] there are three levels of advice. The first level is to accomplish a particular goal; the second level is to offer general ideas of achieving the goal, and the third level is to give students detailed advice on how to solve the problem in the current context.

Knowledge tracing [ edit | edit source ]

Knowledge tracing can monitor the growing number of production rules during the problem solving process. Every student can choose one production rule every step of his or her way of solving problems, and Cognitive Tutors can calculate an updated estimate of the probability of the student has learned the particular rule. [68] [69] The probability estimates of the rules are integrated into the interface and displayed in the skill-meter. Using probability estimates, the Cognitive Tutors can select appropriate tasks or problems according to students’ individual needs.

Effectiveness [ edit | edit source ]

Cognitive tutor® geometry [ edit | edit source ].

Aleven and Koedinger conducted two experiments to examine whether Cognitive Tutor® can scaffold self-explanation effectively in high school geometry class settings. [66] The findings suggested that “problem-solving practice with a Cognitive Tutor® is even more effective when the students explain their steps by providing references to problem-solving principles.” [80]

In geometry learning, it could happen when students have over-generalized production rules in their prior knowledge, and thus leading shallow encoding and learning. For instance, a student may choose the correct answer and go to next step base on the over-generalized production rule, if an angle looks equal to another, then it is , instead of real understanding. According to Aleven & Koedinger, self-explanation can promote more general encoding during problem-solving practice for it can push students to think more and reflect explicitly on the rules in the domain of geometry. [66]

All the geometry class in the experiments includes classroom discussion, small-group activities, lectures, and solving problems with Cognitive Tutor®. In both of the experiments, students are required to solve problems with the help of the Cognitive Tutor®. However, the Cognitive Tutor® were provided with two different versions, the new version can support self-explanation which is also called guided learning by doing and explaining, [66] and the other cannot. Theses additional features of the new version required students to justify each step by entering geometry principles or referring the principles to an online glossary of geometry knowledge, as well as providing explanations and solutions according to students’ individual choice. Also, the form of explanation in the new version is different from speech-based explanations mentioned in another experiment on self-explanation. The researchers found that students who use the new version of the Cognitive Tutor® were not only better able to give accurate explanation, but also able to deeper understand the domain rules. Thus, the students were able to transfer those learned rules to new situations better, avoiding shallow encoding and learning.

Genetics Cognitive Tutor [ edit | edit source ]

Corbett et al. (2010) conducted two evaluations of the Genetics Cognitive Tutor in seven different kinds of biology courses in 12 universities in America. The findings suggested the effectiveness of implementing Genetics Cognitive Tutor in post-secondary institution genetic problem-solving practice settings. [81]

In the first evaluation, the participants used the Genetics Cognitive Tutor with their class activities or homework assignments. The software has 16 modules with about 125 problems in five general genetic topics. Genetics Cognitive Tutor utilized the cognitive model of genetics problem solving knowledge to provide step-by-step help, and both model tracing and knowledge tracing. With the average correctness of pretest (43%) and post-test (61%), the average improvements of using Genetic Cognitive Tutors was 18%. In the second empirical evaluations, the researchers examined whether the knowledge tracing can correctly predict students’ knowledge. The finding suggested that the algorithm of knowledge tracing is capable of accurately estimating every student performance on the paper- and-pencil post-test.

Project Based Learning and Design Thinking [ edit | edit source ]

Theorizing solutions for real world problems [ edit | edit source ].

Project Based Learning is a concept that is meant to place the student at the center of learning. The learner is expected to take on an active role in their learning by responding to a complex challenge or question through an extended period of investigation. Project Based Learning is meant for students to acknowledge the curriculum of their class, but also access the knowledge that they already have to solve the problem challenge. At its roots, project-based learning is an activity in which students develop an understanding of a topic based on a real-life problem or issue and requires learners to have a degree of responsibility in designing their learning activity [82] . Blummenfeld et al. (1991) states that Project Based Learning allows students to be responsible for both their initial question, activities, and nature of their artifacts [83] .

Project based learning is based on five criteria [84]

Challenges are based on authentic, real-world problems that require learners to engage through an inquiry process and demonstrate understanding through active or experiential learning. An example would be elementary or secondary students being asked by their teacher to solve a school problem – such as how to deal with cafeteria compost. Students would be encouraged to work in groups to develop solutions for this problem within specific criteria for research, construction, and demonstration of their idea as learners are cognitively engaged with subject matter over an extended period of time keeping them motivated [83] . The result is complex learning that defines its success is more than as more than the sum of the parts [85] . Project Based Learning aims at learners coordinating skills of knowledge, collaboration, and a final project presentation. This type of schema construction allows learners to use concrete training to perform concrete results. The learner uses previous knowledge to connect with new information and elaborate on their revised perception of a topic [85] . In Project Based Learning this would constitute the process of information gathering and discussing this information within a team to decide on a final solution for the group-instructed problem.

Unlike Problem-Based Learning, experiential learning within a constructivist pedagogy, is the basis of Project Based Learning, and learners show their knowledge, or lack there of, by working towards a real solution through trial and error on a specific driving question. The philosophy of Experiential experiential learning education comes from the theories developed by John Dewey in his work Education and Experience. Dewey argues that experience is shown to be a continuous process of learning by arousing curiosity, strengthen initiative, and is a force in moving the learner towards further knowledge [86] . The experiential aspect of Project Based Learning through working towards solutions for real world problems ties learner’s solutions to practical constructs. Learners must make up the expected gap in their knowledge through research and working together in a collaborative group. The experiential learning through Project Based Learning is focused on a driving question usually presented by the teacher. It is this focus that students must respond to with a designed artifact to show acquired knowledge.

The constructivist methodology of Project Based Learning is invoked through the guided discovery process set forth by the instructor, unlike pure discovery which has been criticised for student having too much freedom [87] , Project Based Learning involves a specific question driven by the instructor to focus the process of investigation. This form of constructivist pedagogy has shown to promote cognitive processing that is most effective in this type of learning environment [87] . Project Based Learning provides a platform for learners to find their own solutions to the teacher driven question, but also have a system in which to discover, analyze, and present. Therefore, Project Based Learning delivers beneficial cognitive meaningful learning by selecting, organizing, and integrating knowledge [87] .

Experience is the Foundation of Learning [ edit | edit source ]

Project Based Learning is a branch of education theory that is based on the idea of learning through doing. John Dewey indicated that teachers and schools should help learners to achieve greater depth in correlation between theory and real-world through experiential and constructivist methods. Dewey stated that education should contain an experiential continuum and a democratization of education to promote a better quality of human experience [86] . These two elements are consistent with Project Based Learning through the application of authentic, real world problems and production of artifacts as solutions, and the learner finding their own solutions through a collaborative effort with in a group. Blumenfeld et al. mentions that the value in Project Based Learning comes from questions that students can relate to including personal health and welfare, community concerns, or current events [83] .

Project Based Learning has basis also in the work of Jean Piaget who surmised that the learner is best served to learn in a constructivist manner – using previous knowledge as a foundation for new learning and connections. The learner’s intelligence is progressed from the assimilation of things in the learner’s environment to alter their original schema by accommodating multiple new schema and assimilating all of this experienced knowledge [88] . Piaget believed in the learner discovering new knowledge for themselves, but that without collaboration the individual would not be able to coherently organize their solution [87] . Project Based Learning acknowledges Piaget’s beliefs on the need for collective communication and its use in assembling new knowledge for the learner.

Self-Motivation Furthers Student Learning [ edit | edit source ]

Project Based Learning is perceived as beneficial to learners in various ways including gained knowledge, communication, and creativity. While engaging on a single challenge, learners obtain a greater depth of knowledge. Moreover, abilities in communication, leadership, and inter-social skills are strengthened due to the collaborative nature of Project Based Learning. Students retain content longer and have a better understanding of what they are learning. There are at least four strands of cognitive research to support Project Based Learning [84] – motivation, expertise, contextual factors, and technology.

Motivation of students that is centred on the learning and mastery of subject matter are more inclined to have sustained engagement with their work [89] . Therefore, Project Based Learning discourages public competition in favour of cooperative goals to reduce the threat to individual students and increase focus on learning and mastery [84] . Project Based Learning is designed to allow students to reach goals together, without fear of reprisal or individual criticism. For instance, Helle, et al. completed a study of information system design students who were asked to work on a specific assignment over a seven-month timeline. Students were given questionnaires about their experience during this assignment to determine their motivation level. Helle, et al. examined the motivation of learners in project groups and found intrinsic motivation increased by 0.52 standard deviations, showing that Project Based learner groups used self-motivation more often to complete assignments. Further, the study implied intrinsic motivation increase substantially for those who were lowest in self-regulation [90] .

Learner metacognitive and self-regulation skills are lacking in many students and these are important to master in student development in domains [84] . In the Project Based Learning system the relationship between student and teacher allows the instructor to use scaffolding to introduce more advance forms of inquiry for students to model, thus middle school students and older are very capable of meaningful learning and sophisticated results [91] . Learners would then become experts over time of additional skills sets that they developed on their own within this system.

Contextually, situated cognition is best realized when the material to be used resembles real-life as much as possible [84] , therefore, Project Based Learning provides confidence in learners to succeed in similar tasks outside of school because they no longer associate subjects as artificial boundaries to knowledge transfer. Gorges and Goke (2015) investigated the relationship between student perception of their abilities in major high school subjects and their relating these skills to real-world problem application through an online survey. Learners showed confidence in problem-solving skills and how to apply their learning to real-life situations, as Gorges and Goke [92] report, and that students who used Project Based Learning style learning have increased self-efficacy and self-concepts of ability in math (SD .77), history (SD .72), etc. [92] . Therefore, students are more likely to use domain-specific knowledge outside of an academic setting through increased confidence. Further, a comparison between students immediately after finishing a course and 12 weeks to 2 years provided effect sizes that showed Project Based Learning helped retain much knowledge [92] .

Technology use allows learners to have a more authentic experience by providing users with an environment that includes data, expanded interaction and collaboration, and emulates the use of artifacts [84] . The learner, in accessing technology, can enhance the benefits of Project Based Learning by having more autonomy is finding knowledge and connecting with group members. Creativity is enhanced as students must find innovative solutions to their authentic problem challenges. For instance, using digital-story-telling techniques through Project Based Learning, as stated by Hung and Hwang [93] , to collect data (photos) in elementary class to help answer a specific project question on global warming in science provided a significant increase in tests results (SD 0.64). As well, in order to find answers, learners must access a broad range of knowledge, usually crossing over various disciplines. The end result is that projects are resolved by student groups that use their knowledge and access to additional knowledge (usually through technology) to build a solution to the specific problem.

Educators Find Challenges in Project Based Learning Implementation [ edit | edit source ]

One of the main arguments against this type of learning is that the project can become unfocused and not have the appropriate amount of classroom time to build solutions. Educators themselves marginalized Project Based Learning because they lack the training and background knowledge in its implementation. Further financial constraints to provide effective evaluation through technology dissuades teachers as well [94] . The information gained by students could be provided in a lecture-style instruction and can be just as effective according to critics. Further, the danger is in learners becoming off-task in their time spent in the classroom, and if they are not continually focused on the task and the learning content, then the project will not be successful. Educators with traditional backgrounds in teaching find Project Based Learning requires instructors to maintain student connection to content and management of their time – this is not necessarily a style that all teachers can accomplish [94] .Blumenfeld et al. (1998) state that real success from Project Based Learning begins and ends with a focused structure that allows teacher modelling, examples, suggested strategies, distributing guidelines, giving feedback during the activity, and allowing for revision of work [91] .

Learner Need for Authentic Results through Critical Thought [ edit | edit source ]

Project Based Learning is applicable to a number of different disciplines since it has various applications in learning, and is specifically relevant with the 21st century redefinition of education (differentiated, technologically-focused, collaboration, cross-curricular). STEM (Science, Technology, Engineering, Mathematics) is one form of 21st century education that benefits from instructors using Project Based Learning since it natural bridges between domains. The focus of STEM is to prepare secondary students for the rigors of post-secondary education and being able to solve complex problems in teams as would be expected when performing these jobs in the real world after graduation. Many potential occupational areas could benefit from Project Based Learning including medical, engineering, computer design, and education. Project Based Learning allows secondary students the opportunity to broaden their knowledge and become successful in high-stakes situation [95] . Moreover, these same students then develop a depth in knowledge when it comes to reflecting upon their strengths and limitations [95] . The result would be a learner who has developed critical thinking and has had a chance to apply it to real situations. Further the construction of a finished product is a realistic expectation in presenting an authentic result from learning. The product result demands accountability, and learner adherent to instructor expectations as well as constraints for the project [95] .

The learner is disciplined to focus on specific outcomes, understand the parameters of the task, and demonstrate a viable artifact. The implication is that students will be ready to meet the challenges of a high-technology, fast-paced work world where innovation, collaboration, and results-driven product is essential for success. Technology is one area where Project Based Learning can be applied by developing skills in real-world application, thus cognitive tools aforded by new technology will be useful if perceived as essential for the project (as is the case in many real-world applications) [83] .. For example, designers of computer systems with prior knowledge may be able to know how to trouble-shoot an operating system, but they do not really understand how things fit or work together, and they have a false sense of security about their skills [96] .

Design-Thinking as a Sub-set of Project-Based Learning [ edit | edit source ]

Using the process of practical design for real-world solutions [ edit | edit source ].

Design Thinking is a pedagogical approach to teaching through a constructionist methodology of challenge-based problem solving branching off of Project Based learning. It should be understood as a combination of sub-disciplines having design as the subject of their cognitive interests [97] .

An example of design-thinking would be learners engaged with finding a solution to a real-world problem. However, unlike Project Based Learning, design-thinking asks the learner to create a practical solution within a scaffolding process (Figure 3) such as finding a method to deliver clean drinking water to a village. Designers would consider social, economic, and political considerations, but would deliver a final presentation of a working prototype that could be marketable. Hence a water system could be produced to deliver water to villagers, but within the limits of the materials, finances, and local policies in mind. It designates cores principles of empathy, define, ideate, prototype, and test to fulfill the challenges of design. Starting with a goal (solution) in mind, empathise is placed upon creative and practical decision making through design to achieve an improved future result. It draws upon a thinking that requires investigation into the details of a problem to find hidden parameters for a solution-based result. The achieved goal then becomes the launching point for further goal-setting and problem solving. [97]

This type of approach to education is based on the premise that the modern world is full of artificial constructs, and that our civilization historically has relied upon these artifacts to further our progress in technological advances. Herbert Simon, a founder of design-thinking, states that the world that students find themselves in today is much more man-made and artificial that it is a natural world [98] . The challenge of design-thinking is to foster innovation by enhancing student creative thinking abilities [99] . Design-thinking is a tool for scaffolding conventional educational projects into Project Based thinking. Van Merrienbroer (2004) views design-learning as a scaffolding for whole-task practice. It decreases intrinsic cognitive load while learners can practice on the simplest of worked-out examples [87] . Therefore, Design-thinking is currently becoming popular due to its ability to bridge between the justification of what the learner knows and what the learner discovers within the context of 21st century skills and learning. A further example of this process is the design of a product that children will use to increase their physical activity (see video on Design Thinking) and can be explained using the scaffold of Design Thinking:

Critical Thought on Design in the Artificial World [ edit | edit source ]

Design-thinking is can be traced back to a specific scholars including Herbert Simon, Donald Schon, and Nigel Cross. Simon published his findings on the gap he found in education of professions in 1969. He observed that techniques in the natural sciences and that just as science strove to show simplicity in the natural world of underlying complex systems, and Simon determined the it was the same for the artificial world as well [100] . Not only should this include the process behind the sciences, but the arts and humanities as well since music, for example involves formal patterns like mathematics (Simon, 136). Hence, the creative designs of everyone is based upon a common language and its application. While Schon builds upon the empathetic characteristics of design-thinking as a Ford Professor of Urban Planning and Education at MIT, referring to this process as an artistic and intuitive process for problem-solving [101] . Schon realized that part of the design process was also the reflection-in-action that must be involved during critical thinking and ideating. Moreover, the solutions for problems do not lie in text-books, but in the designer’s ability to frame their own understanding of the situation [100] . Cross fuses these earlier ideas into a pedagogy surrounding education stating that design-thinking should be part of the general education of both sciences and humanities [97] . He implies that students encouraged to use this style of thinking will improve cognitive development of non-verbal thought and communication [97] .

Critical Thinking as Disruptive Achievement [ edit | edit source ]

Design-thinking follows a specific flow from theoretical to practical. It relies upon guided learning to promote effective learner solutions and goes beyond inquiry which has been argued does not work because it goes beyond the limits of long-term memory [97] . Design-thinking requires the learner to have a meta-analysis of their process. Creativity (innovative thought) is evident in design thinking through studies in defocused and focused attention to stimuli in memory activation [97] . Hu et al. (2010) developed a process of disrupted thinking in elementary students by having them use logical methods of critical thought towards specific design projects, over a four-year period, through specific lesson techniques. The results show that these students had increased thinking ability (SD .78) and that these effects have a long-term transfer increasing student academic achievement [102] . This shows use of divergent and convergent thinking in the creative process, and both of these process of thought has been noted to be important in the process of creativity (Goldschmidt, 2016, p 2) and demonstrates the Higher Order Thinking that is associated with long-term memory. Design-thinking specifically demonstrates the capability of having learners develop

Designers are Not Scientific? [ edit | edit source ]

Design-thinking critics comment that design is in itself not a science or cognitive method of learning, and is a non-scientific activity due to the use of intuitive processes [97] . The learner is not truly involved within a cognitive practice (scientific process of reasoning). However, the belief of Cross is that design itself is a science to be studied, hence it can be investigated with systematic and reliable methods of investigation [97] . Further, Schon states that there is connection between theory and practice that in design thinking means that there is a loyalty to developing a theoretical idea into a real world prototype [101] . Design-thinking is a process of scientific cognitive practice that does constitute technical rationality [101] and using this practice to understand the limits of their design that includes a reflective practice and meta. Further, this pedagogy is the application for the natural gap between theory and practice for most ideas, by allowing the learner to step beyond normal instruction and practice to try something new and innovative to come up with a solution. Design-thinking rejects heuristically-derived responses based on client or expert appreciation to take on an unforeseen form [101] .

21st Century Learners and the Need for Divergent Thinking [ edit | edit source ]

Design-thinking is exceptionally positioned for use with 21st century skills based around technological literacy. Specifically, it is meant to assist the learner in developing creative and critical skills towards the application of technology. Designing is a distinct form of thinking that creates a qualitative relationship to satisfy a purpose [103] . Moreover, in a world that is rapidly becoming technologized, design-thinking the ability to make decisions based upon feel, be able to pay attention to nuances, and appraise the consequences of one’s actions [103] . The designer needs to be able to think outside the perceived acceptable solution and look to use current technology. Therefore, learners using design thinking are approaching all forms of technology as potential applications for a solution. Prototyping might include not just a hardware application, but also the use of software. Cutting-edge technologies such as Augmented Reality and Virtual Reality would be acceptable forms of solutions for design challenges. Specific application of design-thinking is, therefore applicable to areas of study that require technological adaptation and innovation. Specifically, the K-12 BC new curriculum (2016) has a specific focus on Applied Design, Skills, and Technologies that calls for all students to have knowledge of design-thinking throughout their entire education career and its application towards the advancement of technology. Therefore, Design Thinking is a relative and essential component to engaging student critical thought process.

Argumentation [ edit | edit source ]

Argumentation is the process of assembling and communicating reasons for or against an idea, that is, the act of making and presenting arguments. CT in addition to clear communication makes a good argument. It is the process through which one rationally solves problems, issues and disputes as well as resolving questions [104] .

The practice of argumentation consists of two dimensions: dialogue and structure [105] . The dialogue in argumentative discussions focus on specific speech acts – actions done through language (i.e. accept, reject, refute, etc.) – that help advance the speaker’s position. The structure of an argument helps distinguish the different perspectives in discussion and highlight positions for which speakers are arguing [105] .

One of the main arguments against this type of learning is that the project can become unfocused and not have the appropriate amount of classroom time to build solutions. Educators themselves marginalize PBL* because they lack the training and background knowledge in its implementation. Further financial constraints to provide effective evaluation through technology dissuades teachers as well (Efstratia, 2014, p 1258). The information gained by students could be provided in a lecture-style instruction and can be just as effective according to critics. Further, the danger is in learners becoming off-task in their time spent in the classroom, and if they are not continually focused on the task and the learning content, then the project will not be successful. Educators with traditional backgrounds in teaching find Project Based Learning requires instructors to maintain student connection to content and management of their time – this is not necessarily a style that all teachers can accomplish (Efstratia, 2014, p 1258).

Project Based Learning is applicable to a number of different disciplines since it has various applications in learning, and is specifically relevant with the 21st century redefinition of education (differentiated, technologically-focused, collaboration, cross-curricular). STEM (Science, Technology, Engineering, Mathematics) is one form of 21st century education that benefits from instructors using Project Based Learning since it natural bridges between domains. The focus of STEM is to prepare secondary students for the rigors of post-secondary education and being able to solve complex problems in teams as would be expected when performing these jobs in the real world after graduation. Many potential occupational areas could benefit from Project Based Learning including medical, engineering, computer design, and education.

Project Based Learning allows secondary students the opportunity to broaden their knowledge and become successful in high-stakes situation (Capraro, et al., 2013, p 2). Moreover, these same students then develop a depth in knowledge when it comes to reflecting upon their strengths and limitations (Capraro, et al., 2013, p 2). The result would be a learner who has developed critical thinking and has had a chance to apply it to real situations. Further the construction of a finished product is a realistic expectation in presenting an authentic result from learning. The product result demands accountability, and learner adherent to instructor expectations as well as constraints for the project (Capraro, et al., 2013, p 2). The learner is disciplined to focus on specific outcomes, understand the parameters of the task, and demonstrate a viable artifact. The implication is that students will be ready to meet the challenges of a high-technology, fast-paced work world where innovation, collaboration, and results-driven product is essential for success. Technology is one area where Project Based Learning can be applied by developing skills in real-world application. For example, designers of computer systems with prior knowledge may be able to know how to trouble-shoot an operating system, but they do not really understand how things fit or work together, and they have a false sense of security about their skills (Gary, 2013, p 1).

Design-thinking follows a specific flow from theoretical to practical. It relies upon guided learning to promote effective learner solutions and goes beyond inquiry which has been argued does not work because it goes beyond the limits of long-term memory (Lazonder and Harmsen, 2016, p 2). Design-thinking requires the learner to have a meta-analysis of their process. Creativity (innovative thought) is evident in design thinking through studies in defocused and focused attention to stimuli in memory activation (Goldschmidt, 2016, p 1). Hu et al. (2010) developed a process of disrupted thinking in elementary students by having them use logical methods of critical thought towards specific design projects, over a four-year period, through specific lesson techniques. The results show that these students had increased thinking ability (SD .78) and that these effects have a long-term transfer increasing student academic achievement (Hu, et al. 2010, p 554). This shows use of divergent and convergent thinking in the creative process, and both of these process of thought has been noted to be important in the process of creativity (Goldschmidt, 2016, p 2) and demonstrates the Higher Order Thinking that is associated with long-term memory. Design-thinking specifically demonstrates the capability of having learners develop.

The Process of Argumentation [ edit | edit source ]

Argumentation stages [ edit | edit source ].

The psychological process of argumentation that allows one the produce, analyze and evaluate arguments [106] . These stages will be discussed in more detail later in this chapter.

The Impact of Argumentation on Learning [ edit | edit source ]

Argumentation does not only impact the development of CT and vice versa, it affects many other aspects of learning as well. For instance, a study conducted in a junior high school science class showed that when students engaged in argumentation, they drew heavily on their prior knowledge and experiences [107] . Not only did argumentation enable the students to use their prior knowledge, it also helped them consolidate knowledge and elaborate on their understanding of the subject at a higher level [107] . These are just a few of the ways in which argumentation can be seen to impact aspects of learning other than the development of CT.

Video: Argumentation in Education: https://www.youtube.com/watch?v=YHm5xUZmCDg

The Relationship between Critical Thinking and Argumentation [ edit | edit source ]

Argumentation and CT appear to have a close relationship in instruction. Many studies have shown the impact that both of these elements can have on one another. Data suggests that when CT is infused into instruction it impacts the ability of students to argue [108] tasks that involve both critical thinking and creative thinking must be of an argumentative nature [109] , and that argument analysis and storytelling can improve CT [110] . In other words it would appear that both CT and argumentation impact the development of each other in students and that both impact other aspects of learning and cognition.

How Critical Thinking Improves Argumentation [ edit | edit source ]

CT facilitates the evaluation of the information necessary to make an argument. It aids in the judgement of the validity of each position. It is used to assess the credibility of sources and helps in approaching the issue from multiple points of view. The elements of CT and argumentation have many common features. For example, examining evidence and counter-evidence of a statement and the information that backs up these claims are both facets of creating a sound argument and thinking critically.

The impact of how CT explicitly impacts one’s ability to argue and reason with reference to the aforementioned four CT components will be examined in this section. First, there needs to be an examination of the aspects of CT and how they can be impacted by argumentation. The first component, knowledge, as stated by Bruning et. al (2011), actively shapes the way in which one resolves problems [111] . Therefore, it is essential that students have a solid foundation of knowledge of whatever it is that they are arguing. The ability to use well founded information in order to effectively analyze the credibility of new information is imperative for students who wish to increase their argumentative abilities. The second component of CT that is important for argumentation is inference . As Chesñevar and Simari (2007) discuss in their examination of how we develop arguments, inference and deduction are essential aspects of reaching new conclusions from knowledge that is already known or proven [112] .

In other words, the ability to reach conclusions from known information is pivotal in developing and elaborating an argument. As well, the use of induction , a part of the CT process, is important to argumentation. As Bruning et al. suggest, the ability to make a general conclusion from known information is an essential part of the CT process [111] . Ontañón and Plaza (2015) make the argument that induction can be used in argumentation through communication with one another. Moreover, making inductions of general conclusions using the complete information that every member of the group can provide shows how interaction can be helpful through the use of induction in argumentation [113] . Therefore, it can be seen how induction, an important part of CT, can have a significant impact on argumentation and collaboration. The final component of CT, that may be the most important in its relationship to argumentation, is evaluation . The components of Evaluation indicated by Bruning et al. are analyzing, judging and weighing. These are three essential aspects of creating a successful argument [111] . Hornikx and Hahn (2012) provide a framework for three key elements of argumentation that are heavily attached in these Bruning et al.'s three aspects of CT [106] .

Production, Analysis, and Evaluation [ edit | edit source ]

The three aspects of argumentation that Hornikx and Hahn focus on in their research is the production , analysis and evaluation of arguments [106] . Producing an argument uses the key aspects of CT; there must be evaluation, analysis, judgement and weighing of the argument that one wishes to make a stand on. Analysis of arguments and analysis in CT go hand in hand, there must be a critical analysis of information and viewpoints in order to create a successful and fully supported argument. As well, evaluation is used similarly in argumentation as it is derived from CT. Assessing the credibility of sources and information is an essential part in finding articles and papers that can assist someone in making an informed decision. The final aspect of evaluation in critical thinking is metacognition, thinking about thinking or monitoring one's own thoughts [111] . Monitoring one's own thoughts and taking time to understand the rationality of the decisions that one makes is also a significant part of argumentation. According to Pinto et al.’s research, there is a strong correlation between one's argumentation ability and metacognition. [114] In other words, the ability to think about one’s own thoughts and the validity of those thoughts correlates positively with the ability to formulate sound arguments. The transfer of thoughts into speech/argumentation shows that CT influences argumentation dramatically, however some research suggests that the two interact in different ways as well. It can clearly be seen through the research presented that argumentation is heavily influenced by CT skills, such as knowledge, inference, evaluation and metacognition. However there are also strong implications that instruction of CT in a curriculum can bolster argumentation. A study conducted by Bensley et. al (2010) suggests that when CT skills are directly infused into a course compared to groups that received no CT instruction, those who received CT instruction showed significant gains in their ability of argument analysis [115] . There can be many arguments made for the implication of specific CT skills to impact argumentation, but this research shows that explicit teaching of CT in general can increase the ability of students to more effectively analyze arguments as well. This should be taken into account that Skills Programs mentioned later in this chapter should be instituted if teachers wish to foster argumentation as well as CT in the classroom.

How Argumentation Improves Critical Thinking [ edit | edit source ]

Argumentation is a part of the CT process, it clarifies reasoning and the increases one's ability to assess viable information. It is a part of metacognition in the sense that one needs to evaluate their own ideas. CT skills such as induction and/or deduction are used to create a structured and clear argument.

Research by Glassner and Schwarz (2007) shows that argumentation lies at the intersection of critical and creative thinking. They argue that reasoning, which is both critical and creative, is done through argumentation in adolescents. They suggest that reasoning is constantly being influenced by other perspectives and information. The ability to think creatively as well as critically about new information is managed by argumentation [116] . The back and forth process of accommodating, evaluating, and being open minded to new information can be argued as critical and creative thinking working together. However, the way in which one reaches conclusions from information is created from the ability to weigh this information, and then to successfully draw a conclusion regarding the validity of the solution that students come to. There is also a clear correlation of how argumentation helps students to nurture CT skills as well.

It is clear that CT can directly impact argumentation, but this relationship can also be seen as bidirectional, with argumentation instruction developing the CT skills. A study by Gold et al. shows that CT skills can be fostered through the use of argument analysis and storytelling in instruction [117] . This research suggests that argumentation and argument analysis are not only be beneficial to students, but also to older adults. This study was conducted using mature adult managers as participants. The article outlines four skills of CT that can be impacted by the use of argument analysis and storytelling: critique of rhetoric, tradition, authority, and knowledge. These four skills of CT are somewhat deeper than many instructed in high schools and extremely important to develop. The ability of argumentation to impact CT in a way that enables a person to gain a better perspective on their view about these things is essential to developing personal values as well as being able to use argumentation and CT to critique those values when presented with new information. The ability of argumentation to influence the ability of individuals to analyze their own traditions and knowledge is important for all students as it can give them better insight into what they value.

Argumentation is beneficial to CT skills as well as creative thinking skills in high school students. Research done by Demir and İsleyen (2015) shows that argumentation based a science learning approach in 9th graders improves both of types of thinking [118] . The ability of students to use argumentation to foster CT as well as creative thinking can be seen as being very beneficial, as mentioned earlier creative and CT skills use argumentation as a means of reasoning to draw conclusions, it is therefore not surprising that argumentation in instruction also fosters both of these abilities. In summation, it can clearly be seen that there is a link between both argumentation and CT along with many skills in the subset of CT skills. Explicit instruction of both of these concepts seems to foster the growth of the other and can be seen as complementary. In the next sections of this chapter how these aspects can be beneficial if taught within the curriculum and how they go hand in hand in fostering sound reasoning as well as skills that will help students throughout their lives will be examined.

Instructional Application of Argumentation and Critical Thinking [ edit | edit source ]

Teaching Tactics [ edit | edit source ]

An effective method for structuring the instruction of CT is to organize the thinking skills into a clear and sequential steps. The order in which these steps aid in guiding the student towards internalizing those steps in order to apply them in their daily lives. By taking a deductive approach, starting from broader skills and narrowing them down to task-specific skills helps the student begin from what they know and generate something that they hadn't known before through CT. In the spirit of CT, a student's awareness of their own skills also plays an important role in their learning. In the classroom, they should be encouraged to reflect upon the process through which they completed a goal rather than just the result. Through the encouragement of reflection, students can become more aware of the necessary thinking skills necessary for tasks, such as Argumentation.

Instructing CT and Argumentation predisposes the instruction to using CT skills first. In designing a plan to teach CT, one must be able to critically evaluate and assess different methods and make an informed decision on which would work best for one's class. There are a variety of approaches towards instructing CT. Descriptive Models consist of explanations of how "good" thinking occurs. Specifically, it focuses on thinking strategies such as heuristics to assess information and how to make decisions. Prescriptive Models consist of explanations of what good thinking should be. In a sense, these models give a prototype, a "prescription", of what good thinking is. This approach is comparatively less applicable and sets a high standard of what is expected of higher order thinking. In addition to evaluating which approach would work best for them, prior to teaching CT, instructors need to carefully select the specific types of CT skills that they want students to learn. This process involves assessing factors such as age range, performance level as well as cognitive ability of one's class in order to create a program that can benefit most of, if not all, the students. A final aspect of instruction to consider as an educator is whether direct or indirect instruction will be used to teach CT. Direct Instruction refers to the explicit teaching of CT skills that emphasizes rules and steps for thinking. This is most effective when solutions to problems are limited or when the cognitive task is easy. In contrast, Indirect Instruction refers to a learner-oriented type of teaching that focuses on the student building their own understanding of thinking. This is most effective when problems are ambiguous, unclear or open to interpretation such as moral or ethical decisions [111] .

One example of indirect CT instruction is through the process of writing literature reviews. According to Chandler and Dedman, having the skills to collect, assess and write literature reviews as well as summarize results of studies requires CT. In a teaching note, they evaluated a BSW (Baccalaureate of Social Work) program that strived to improve CT in undergraduate students. Specifically, they assert that practical writing assignments, such as creating literature reviews, help students combine revision and reflection while expanding their thinking to evaluate multiple perspectives on a topic. They found that upon reframing the assignment as a tool to facilitate students in becoming critical reviewers, students viewed the literature review as a summation of course material in addition to an opportunity to improve critical reading and writing skills. Through questioning during discussions, students were guided to analyze the authority and credibility of their articles. The students actively sought for more evidence to support articles on their topics. They found that students successfully created well synthesized literature reviews at the end of the BSW program [119] . This program used implicit instruction of CT skills through dialogue between instructor and students as well as peer engagement. Instead of explicitly stating specific skills or steps to learn CT, the instructors lead the students to practice CT through an assignment. As students worked on the assignment, they needed to use reasoning, analysis and inferential skills in order to synthesize and draw conclusions around the evidence they found on their topics. Practical application of CT skills through an assignment helped students develop CT through indirect instruction.

Argument mapping is a way to visualize argumentation. The following are links to argument mapping software: https://www.rationaleonline.com/ http://www.argunet.org/editor/ http://debategraph.org/planet https://www.truthmapping.com/map/1021/#s7164

Skills Programs for CT [ edit | edit source ]

These programs aid in the formulation of critical thinking skills through alternative methods of instruction such as problem-solving. They are usually targeted towards special populations such as students with learning disabilities or cognitive deficits.

The CoRT Thinking Materials [ edit | edit source ]

The CoRT (Cognitive Research Trust) program is based on de Bono’s idea that thinking skills should be taught in school as a subject [120] . The Thinking Materials are geared towards the improvement of thinking skills. This skills program takes on a Gestalt approach and emphasizes the perceptual factor of problem solving. It usually spans over the course of 2 years and is suitable for a wide age range of children. The lessons strive to develop creative thinking, problem-solving as well as interpersonal skills. The materials are split into 6 units and cover topics such as planning, analyzing, comparing, selecting, evaluating and generating alternatives. A typical unit has leaflets covering a single topic, followed by examples using practice items. The leaflets are usually effective in group settings. The focus of these units are to practice thinking skills, therefore much of the instructional time is spent on practicing the topics brought up in the leaflets [111] .

Much of the empirical research on this stand-alone program revolves around the development of creative thinking, however, it is relatively more extensive in comparison to the other programs mentioned in this chapter. The CoRT program has been shown to improve creativity in gifted students. Al-Faoury and Khwaileh (2014) assessed the effectiveness of the CoRT on gifted students’ creative writing abilities. The students were given a pretest that evaluated the fluency, flexibility and originality in writing creative short stories [120] . Students in the experimental group were taught 20 CoRT lessons in total with 10 from CoRT 1 “Breadth” and 10 from CoRT 4 “Creativity” over the course of three months while the control group received traditional lessons on creative writing. The posttest followed the same parameters as the pretest and the results were analyzed by comparing pre and posttest scores. The researchers found a statistically significant effect of CoRT on the experimental group’s fluency, flexibility and originality scores. The mean scores of the experimental groups in all three elements were higher than the control group [120] . These findings suggest that the CoRT program aids gifted students in creative writing skills as indicated through the use of rhetorical devices (metaphor, analogy, etc.), developing characters through dialogue and the control of complex structures [120] . The flexibility and fluency of writing is also applicable to the practice of argumentation and CT. In developing the ability to articulate and modify ideas, students can transfer these skills from creative writing towards higher-order cognitive processes such as CT and argumentation.

The Feuerstein Instrumental Enrichment Program (FIE) [ edit | edit source ]

The FIE is a specialized program focused on mediated learning experiences that strives to develop critical thinking and problem solving skills. Mediation is learning through interaction between the student and the mediator. Similar to Vygotsky's scaffolding, mediation is student-oriented and hinges upon 4 parameters: Intentionality, Reciprocity, Transcendence and Meaning. [121] Intentionality emphasizes the differences between mediation and interaction where the student and mediator have a common goal in mind. Reciprocity involves the student-oriented mentality of mediation, the response of the student hold most importance over academic results. Transcendence focuses on the connectivity of the mediation, it encourages the formation of associations and applications that stretch beyond the scope of the immediate material. Lastly, Meaning in mediation is where the student and mediator explicitly identify "why" and "what for" which promotes dialogue between the two during mediation. [121] [122]

The "instruments" used to facilitate instruction are a series of paper and pencil exercises geared towards practicing internalizing higher order thinking strategies. The instruments cover domains such as analytic perception, spatial organization, categorization, comparison and many more. The implementation of this program varies across countries and is also dependent on the targeted population. A typical program contains 14 units with 3-4 sessions for a few hours every week administered by trained IE staff and teachers. [121]

The Productive Thinking Program [ edit | edit source ]

The Productive Thinking Program consists of the development of planning skills, generating and checking hypotheses as well as creating new ideas. This program is designed as a set of 15 lessons aimed at being completed over one semester. The target population of the program is upper-level elementary school students. The lessons are administered through the use of narrative booklets, often taking a detective-like approach to problem solving where the student is the detective solving a mystery. A structured sequence of steps guides the student to attain an objective specific to the lesson at hand. [123] Following the booklet or story, supplementary problems are given in order for students to apply and practice learned skills. [111]

The IDEAL Problem Solver [ edit | edit source ]

The IDEAL Problem Solver structures problem-solving as 5 steps using the acronym IDEAL. First, (I)dentify the problem, the solver needs to find out what the problem is. Second, (D)efine the problem involves having a clear picture of the entire problem before trying to solve it. Third, (E)xplore the alternatives, meaning that the solver needs to assess the potential solutions available. Fourth, (A)cting on a plan, that is, applying the solution and doing the act of solving. Lastly, (L)ooking at the effects which encompasses the evaluation of the consequences of the chosen solution. IDEAL is flexible in that it can be adapted to suit a wide age range and different levels of ability in its application. It can also be applied to different domains such as composition or physics. [111]

Instructing Argumentation [ edit | edit source ]

Research on argumentation is a comparatively new field of study for education, but has been noted to be of significant importance to almost all educational settings. Grade schools, high schools, and colleges now emphasize the use of argumentation in the classroom as it is seen as the best way for communication and debate in a both vocational and educational settings around the world. [124] A longitudinal study done by Crowell and Kuhn showed that an effective way to help students gain argumentative skills was through consistent and dense application of argumentation in the classroom and as homework. [124] During this longitudinal study, students were exposed to a variety of different methods from which they gained argumentative abilities. The activities employed such as peer collaboration, using computers, reflection activities, individual essays, and small group work all have implications for being valuable in teaching argumentation although it is not clear which ones are the most effective. [124] Data also showed that students all rose to a similar level of argumentative ability, no matter what they scored on argumentative tests before the study began. This shows that even students with seemingly no argumentative skills can be instructed to become as skilled or more skilled than their peers who tested higher than them at the beginning of the study. [124]

Dialogue and Argumentation [ edit | edit source ]

Research by Crowell and Kuhn (2011) highlights collaborative dialogical activities as practical interventions in the development of argumentative skills. The researchers implemented a longitudinal argumentative intervention that used topic cycles to structure a middle school philosophy class [125] . The students had class twice a week for 50 minutes each class over the span of three years. The intervention is as follows: first, students were split into small groups on the same side of the argument to generate ideas around the topic (“for” and “against” teams). Then individuals from either side argue with an opponent through an electronic medium. Finally, the students engage in a whole class debate. These three stages were termed Pregame, Game and Endgame, respectively. After the intervention, students were required to write individual essays regarding the topic through which their argumentative skills would be assessed [125] . The results showed an increased in the generation of dual perspective arguments in the intervention group. Such arguments require the arguer to assume the opposing stance to one’s own and reason its implications. This type of argument reflects a higher-order reasoning that requires critical assessment of multiple perspectives. These results did not begin to appear until year two and was only found statistically significant in year three suggesting that argumentative skills have a longer development trajectory than other lower-level cognitive skills [125] . Through this stand-alone intervention, the collaborative aspect of dialogical activities facilitates the development of intellectual dispositions necessary for good argumentation [125] .

Further research suggests that teaching through the use of collaborative discussions and argumentative dialogue is an effective teaching strategy [105] . Through argumentation, students can acquire knowledge of concepts as well as the foundational ideas behind these concepts. In formulating arguments, students need to generate premises that provide structure to an argument through accepted definitions or claims. Argumentation helps students reveal and clarify misconceptions as well as elaborate on background knowledge. The two aforementioned dimensions of argumentation – dialogue and structure – are often used in assessing and measuring argumentative performance [105] . Specifically, through student-expert dialogue, the students can be guided to give certain arguments and counterarguments depending on the expert’s dialectical decisions [105] . This scaffolding helps the student engage in more critical evaluations that delve deeper into the topic in discussion.

In a study using content and functional coding schemes of argumentative behavior during peer-peer and peer-expert dialogue pairings, Macagno, Mayweg-Paus and Kuhn (2014) found that through student-expert dialogues, students were able to later formulate arguments that dealt with abstract concepts at the root of the issue at hand (i.e. ethical principles, conflict of values) in comparison to peer-peer dialogues [105] . The expert used more specific and sophisticated ways of attacking the student’s argument, such as suggesting an alternative solution to the problem at hand, which in turn enhanced the performance of the student in later meta-dialogues [105] . The results suggest that the practical application of argumentation through collaborate activities facilitates the development of argumentation skills. Similar to CT skills development, rather than teaching, implicit instruction through the practice of argumentation in interactive settings helps its development.

Science and Argumentation [ edit | edit source ]

Much of the literature surrounding the application of argumentation in the classroom revolves around the scientific domain. Argumentation is often used as a tool in scientific learning to enhance CT skills, improve class engagement and activate prior knowledge and beliefs around the subject [105] . In order to articulate and refine scientific theories and knowledge, scientists themselves utilize argumentation [104] . Jonassen and Kim (2010) assert that science educators often emphasize the role of argumentation more than other disciplines [126] . Argumentation supports the learning of how to solve well-structures problems as well as ill-structured ones in science, and from there by extension, in daily life. Specifically, the ill-structured ones reflect more practical everyday problems where goals and limitations are unclear and there are multiple solution pathways as well as multiple factors for evaluating possible solutions [104] .

Through argumentation, students learn to use sound reasoning and CT in order to assess and justify their solution to a problem. For example, a well-structured problem would be one posed in a physics class where concrete laws and formulas dictate the solution pathway to a problem or review questions found at the end textbook chapters which require the application of a finite set of concepts and theories. An ill-structured problem would be finding the cause of heart disease in an individual. Multiple developmental and lifestyle factors contribute to this one problem in addition to the various different forms of heart disease that need to be evaluated. This sort of problem requires the application of knowledge from other domains such as nutrition, emotional well-being and genetics. Since ill-structured problems do not have a definite answer, students are provided with an opportunity to formulate arguments that justify their solutions [104] . Through the practice of resolving problems in science, such as these, students can use CT to develop their argumentative ability.

One’s willingness to argue as well as one's ability to argue also play a significant role in learning science [127] . For one science is at its core, extremely argumentative.

If students have to ability to engage in argumentation at an early age then there knowledge of specific content such as science can grow immensely. The main reason for this is argumentative discourse, being able to disagree with others is extremely important because for adolescents they are at an age which is fundamentally social (ie junior to senior high) using this social ability is pivotal as students at this point may have the confidence to disagree with one another. When a student disagrees with another in argument in a classroom setting it gives them an opportunity to explain the way in which they think about the material. This verbalization of one’s own thoughts and ideas on a subject can help with learning the subject immensely [127] . It also allows for the student to reflect upon and expand their ideas as they have to present them to the class which helps with learning. This also provides the opportunity for the student to identify any misconceptions they have about the subject at hand as more than likely they will receive rebuttal arguments from others in their class [127] . All these factors are aspects of CT and contribute to the learning of the concept and conceptual change in the student which is what learning is all about. The nature of adolescent social behaviour could provide a window through which argumentation could benefit their learning in dramatic ways in learning science [127] .

Argumentation, Problem Solving and Critical Thinking in History Education [ edit | edit source ]

History education offers learners an abundant opportunity to develop their problem solving and critical thinking skills while broadening their perspective on the human condition. The study of history addresses a knowledge gap; specifically, it is the difference between our knowledge of present day and the “infinite, unorganized and unknowable everything that ever happened”. [128] It has long been understood that the study of history requires critical thought and analytical problem-solving skills. In order to become proficient at the study of history, learners must interpret and construct how we come to know about the past and navigate the connection between the past and the body of knowledge we call history. [129] Unfortunately, history education has been demoted to simply recalling factual information - via the overuse of rote memorization and multiple-choice testing - all of which is placed outside the context of present day. This approach does little to inspire a love of history nor does it support the learner’s ability to construct an understanding of how the past and present are connected.

On the other hand, the study of science and mathematics has for many years been centred around developing skills through problem-solving activities. Students learn basic skills and build upon these skills through a progression of increasingly complex problems in order to further their understanding of scientific theory and mathematical relationships. Specific to science education, learners are taught to think like scientists and approach problems using the scientific method. If this approach works well for science and math education, why should it not be utilized for the teaching of history? [128] . Therefore, to develop historical thinking skills it is necessary for instructors to teach the strategies and problem-solving approaches that are used by professional historians. However, unlike science and mathematics, the problems we solve in history are often ill-defined and may be unanswerable in a definitive sense making it more challenging for students to learn and transfer these skills. The following section will address these challenges and provide support for teaching historical thinking via The Big Six Historical Thinking Concepts (2013).

Historical Thinking - The Big Six [ edit | edit source ]

Based upon years of research and first-hand classroom experience, Seixas and Morton (2013) established a set of six competencies essential to the development of historical thinking skills. Much like science and mathematics education discussed above, the Big Six approach to history education allows the learner to progress from simplistic to advanced tasks. Moreover, the Big Six approach is intended to help the learner “move from depending on easily available, commonsense notions of the past to using the culture’s most powerful intellectual tools for understanding history”. (pg 1) [128] Additionally, the Big Six concepts reveal to the learner the difficulties we encounter while attempting to construct a history of the past. The Big Six competencies include the following: historical significance, evidence, continuity and change, cause and consequence, historical perspectives, and the ethical dimension.

Historical Significance

To develop a critical view of history the learner must recognize and define the qualities that makes something (e.g., person, event, social change) historically significant and why they should spend their time learning about this thing. Behaviourist approaches to history education, focusing on the textbook as the main source of information, have caused learners to become passive in their approach to learning about the past. The textbook becomes the authority on what they need to know. Moreover, the sole use of textbooks to teach national history may contribute to the creation of a “master narrative” that limits a student’s access to what is controversial about their country’s past. [130] By shifting the focus away from the textbook, learners may be able to further their critical thinking skills by following the steps historians take to study the past and constructing their own “reasoned decisions about historical significance”. [128] However, even if a learner is provided primary source evidence to construct a narrative of the past but is not taught to recognize the subjective side to historical thinking - why these pieces of evidence were selected, why this topic was selected, and why they are both historically significant - they may not recognize the impacts of human motivation on the construction of historic understanding. Unlike scientific inquiry that relies on a “positivistic definition of rationality”, historical thinking requires learners to acknowledge human motivation - their own motivation in studying the past, their instructors motivation for selecting certain topics of study, and the motivation of those living in the past [131]

Seixas & Morton (2013) cite two elements involved in constructing historical significance: “big, compelling concerns that exist in our lives today, such as environmental sustainability, justice, power, [and] welfare” and “particular events, objects, and people whose historical significance is in question” (pg 16) [128] The intersection between these two elements is where historical significance is found. It is useful here to add Freedman’s (2015), definition of critical historical reasoning . Critical historical reasoning requires us to recognize that the study of history is not objective. Historians “frame their investigations through the questions they pose and the theories they advance” and therefore, learners of history must analyze the “integrity of historical narratives and their pattern of emphasis and omission” (pg 360). [131] Critical historical reasoning aims towards “conscious awareness of the frame one has adopted and the affordances and constraints it imposes” (pg 360) [131] . Therefore, both historians and learners of history must recognize that historical significance is assigned and not an inherent feature of the past, and, importantly, is subject to change.

The second set of competencies described by Seixas and Morton (2013) are based on using evidence to address an inquiry about the past. In a study of the cognitive processes involved in evaluating source documents, Wineburg (1991) lists three heuristics: corroboration, sourcing, and contextualization. Corroboration refers to comparing one piece of evidence to another, sourcing is identifying the author(s) of the evidence prior to reading or viewing the material, and contextualization refers to situating evidence in a specific time and place (pg 77). [132]

This study utilized an expert/novice design to compare how historians and high school students make sense of historic documents. Wineburg (1991) argues that the historians were more successful in the task not because of the “schema-driven processing” common to science and mathematics, but by building a model of the [historic] event through the construction of “context-specific schema tailored to this specific event” (pg 83). [132] Additionally, historians demonstrated greater appreciation for the source of the historic documents compared to the students. This suggests that the students did not make the connection between a document's author and the reliability of the source. As Wineburg states, the historian understands “that there are no free-floating details, only details tied to witnesses, and if witnesses are suspect, so are their details” (pg. 84). [132] This study suggests the potential for historical understanding to be improved by teaching the cognitive strategies historians use to construct history.

Multiple narratives of the past exist as individuals bring their own values and experiences to their interpretations of historical evidence. Recognizing this may push learners beyond accepting historic accounts at face value and pull them towards a more critical approach to history. Inquiry-based guided discovery activities, such as Freedman’s (2015) Vietnam war narrative study, suggest that students may gain an awareness of the way they and others “frame” history through exploring primary source documents and comparing their accounts with standardized accounts (i.e. a textbook). [133] By allowing learners to view history as an interpretation of evidence rather than a fixed body of knowledge, we can promote critical thought through the learners’ creation of inferences based on evidence and construction of arguments to support their inferences.

Continuity and Change

Developing an understanding of continuity and change requires the learner to recognize that these two elements overlap over the chronology of history; some things are changing at the same time that other things remain the same. If students are able to recognize continuity and the processes of change in their own lives they should be able to transfer this understanding to their study of the past. [134] Students should be encouraged to describe and question the rate and depth of historic change as well as consider whether the change should be viewed as progress or decline. [134] The evaluation of historic change as positive or negative is, of course, dependent on the perspective taken by the viewer. An example of continuity through history is the development of cultural identity. Carretero and van Alphen (2014), explored this concept in their study of master narratives in Argentinian high school students. They suggest that identity can be useful to facilitate history education, but could also create misconceptions by the learner confounding past with present (or, presentism), as demonstrated when using “we” to discuss people involved in victorious battles or revolutions of the past which gave shape to a nation (pg 308-309). [130] It is useful, then to teach students to differentiate between periods of history. However, periodization of history, much like everything else in the knowledge domain, is based on interpretation and is dependent on the questions historians ask [134]

Educational technology such as interactive timelines, narrative history games, and online discussion groups may help learners make connections between the past and present. For example, the Museum of Civilization offers a teaching tool on the history of Canadian medicare ( http://www.museedelhistoire.ca/cmc/exhibitions/hist/medicare/medic01e.shtml ). Interactive timelines allow students to see connections between continuity, change, cause, and consequences by visually representing where these elements can be found over historic time. Also, guiding the learners’ exploration of interactive timelines by selecting strong inquiry questions may improve students understanding and facilitate the development of historical thinking. For example, an investigation into the European Renaissance could be framed by the following question: “Did everyone in Europe experience the Renaissance the same way?” Questions such as this are open-ended so as to not restrict where the students takes their inquiry but also suggest a relationship between the changes of the Renaissance and the continuity of European society. Other examples of educational technology that support historical thinking include the “Wold History for us All” ( http://worldhistoryforusall.sdsu.edu/ ) project. This website offers world history units separated into large-scale and local-scale topics and organized by historic period. The lesson plans and resources may allow the learner to making connections between local issues and the broader, global conditions affecting world history. Finally, a case study by Blackenship (2009) suggests that online discussion groups are a useful for developing critical thinking by allowing the teacher to view the students’ thought processes and thereby facilitating formative assessment and informing the type of instructional interventions required by the teacher. Blackenship (2009) cites additional research supporting the use of online discussion because it allows the learners to collect their thoughts before responding to a discussion prompt; they have more time to access prior knowledge and consider their own ideas. [135]

Cause and Consequence

The historical thinking competencies of cause and consequence require learners to become proficient at identifying direct and indirect causes of historic events as well as their immediate and long-term consequences. Effective understanding of the causes of historic change requires the recognition of both the actions of individuals as well as the prevailing conditions of the time. Historical thinking requires students to go beyond simplistic immediate causes and think of history as web of “interrelated causes and consequences, each with various influences” (pg 110). [134] In addition to improving understanding of the past, these competencies may help learners to better understand present-day conflicts and issues. Shreiner (2014) used the novice/expert format to evaluate how people utilize their knowledge of history to make reasoned conclusions about events of the present. Similar to the Wineburg (1991) study discussed above, Shreiner (2014) found the experts were better at contextualizing and using sourcing to critically analyze documents for reliability and utility in establishing a reasoned judgement. Additionally, the study found that while students would use narrative to construct meaning, they typically created schematic narrative templates - general statements about the past which lack specific details & events. [136] Seixas and Morton (2013) caution the use of overly-simplistic timelines of history because they could create a misconception that history is nothing more than a list of isolated events.The study indicates that historical narratives that follow periodization schemes and are characterized by cause-and-effect relationships, as well as change over time, are helpful for understanding contemporary issues. [134] Therefore, it is important that educators work to develop these competencies in students. Much like historic change, the consequences of certain actions in history can be viewed as positive and negative, depending on perspective. This will be discussed in further detail below.

Historical Perspectives and Ethics

The final two historical thinking competencies proposed by Seixas and Morton are historical perspectives and ethics. Historical perspectives refers to analyzing the historical context for conditions that would influence a historic figure to view an event or act in a particular way. This could include religious beliefs, social status, geographic location, time period, prevailing economic and political conditions, and social/cultural conditions. This again requires some interpretation of evidence as oftentimes we do not have evidence that explicitly describes a historic figure’s attitudes and reasons for acting. Primary source documents, such as letters and journals can provide insight but still require the historian to use inference to make sense of the documents and connect the information to a wider historical narrative or biographical sketch of an individual. Additionally, “[h]ard statistics, such as birth and death rates, ages of marriage, literacy rates, and family size... can all help us make inferences about people's experiences, thoughts, and feelings” (pg 143). [134] There are, of course, limitations to how much we can infer about the past; however, Seixas and Morton (2013) suggest that acknowledging the limitations of what we can know about the past is part of “healthy historical thinking” (pg 143). [134] Learners can develop their understanding of historical perspective by observing the contrast between past and present ways of life and worldviews, identifying universal human traits that transcend time periods (e.g., love for a child), and avoiding presentism and anachronism . [134] A greater understanding of historical perspective will be useful for students when encountering conflicting historical accounts as they will be able to see where the historical actors are “coming from” and therefore better understand their actions. Historical perspective and ethics are related. Seixas and Morton (2013) argue that “the ethical dimension of historical thinking helps to imbue the study of history with meaning” (pg 170). [134] To understand the moral reasons for an individual's actions we need to understand the influence of historical, geographical, and cultural context. Additionally, to understand ethical consequences of the past we make moral judgments which require “empathetic understanding[;] an understanding of the differences between our moral universe and theirs” (Seixas and Peck, 2004, pg 113). [137] People with little experience with historical thinking have difficulty separating the moral standards of today’s society with the societies of the past. Additionally, students tend to judge other cultures more critically than their own; oftentimes defending or justifying actions of their own nations. [138] Therefore, Lopez, Carretero and Rodriguez-Moneo (2014) suggest using national narratives of nations different from the learner’s own nation to more effectively develop critical historical thinking. As the learner becomes proficient at analyzing the ethical decisions of the past, they can translate these skills to analyzing present-day ethical questions. Role playing is a useful instructional strategy for teaching historical perspective. Traditional, face-to-face classrooms allow for dramatic role play activities, debates, and mock trials where students can take on the role of an individual or social group from history. Additionally, educational games and websites allow for the integration of technology while using the role play strategy. Whitworth and Berson (2003) found that, in the 1990-2000s, technology in the social studies classroom was focused mostly on using the internet as a digital version of material that would have otherwise been presented in the classroom. They suggest that alternative uses of technology - such as inquiry-based webquests, simulations, and collaborative working environments - promote interaction and critical thinking skills. [139] One example of a learning object that promotes critical thinking through role playing is the Musee-Mccord’s online game collection ( http://www.mccord-museum.qc.ca/en/keys/games/ ). Specifically, the Victorian Period and the Roaring Twenties games allow the learner to progress through the time period and make decisions appropriate to the historic context of the period. These games are paired with relevant resources from the museum collections which can enhance the learner’s depth of understanding of the period. In terms of teaching strategies for the ethical component of history can be explored through historical narratives, debating ethical positions on historic events, and evaluating and critiquing secondary sources of information for ethical judgements.

To summarize, introducing professional historians’ strategies for studying history is widely regarded as a way to improve historical thinking in students. Professional historian’s cognitive processes of corroborating accounts, critically analyzing sources, and establishing historic context are reflected well by Seixas and Morton’s Big Six Historical Thinking Concepts (2013). Historical thinking gives students the skills to problem solve within the context of history and make sense of the past and connect it to the present in order to broaden the learner’s perspective, understand prevailing social conditions, and influence how they interact with the world. See the Historical Thinking Project’s webpage ( http://historicalthinking.ca/lessons ) for instructional ideas for all the historical competencies.

Instructing through Academic Controversy [ edit | edit source ]

Using the technique of Academic Controversy could be an effective way of teaching both argumentation and CT skills to students. Academic controversy involves dividing a cooperative group of four in two pairs of students and assigning them opposing positions of an argument or issue, after which the two pairs each argue for their position. The groups then switch their positions and argue again, finally the group of four is asked to come up with an all-around solution to the problem [140] . This activity can be effective in instructing both aspects of argumentation and CT, though it may be a bit dated. The activity is argumentative by nature, making students come up with reasons and claims for two sets of arguments. This equilibrium is important to the argumentative process because provides the students with an opportunity to evaluate the key points of their argument and the opposition's which could be beneficial in any debate. As well, this activity is geared to engage students in a few aspects of CT such as evaluation, since the students must assess each side of the argument. It also engages metacognitive processes as the students must come up with a synthesized conclusion with their peers of their own arguments, a process which requires them to be both analytical and open minded. This activity is a good way of increasing both CT skills and argumentation as it requires students to be open-minded, but also engage in analytical debate.

Glossary [ edit | edit source ]

Suggested readings [ edit | edit source ].

• Abrami, P.C., Bernard, R.M., Borokhovski, E., Wade, A., Surkes, M.A., Tamim, R., & Zhang, D. (2008). Instructional Interventions Affecting Critical Thinking Skills and Dispositions: A Stage 1 Meta-Analysis. Review of Educational Research, 78(4). 1102-1134. DOI: 10.3102/0034654308326084.
• Phan, H.P. (2010). Critical thinking as a self-regulatory process component in teaching and learning. Psicothema, 22(2). 284-292.
• Kozulin, A. & Presseisen, B.Z. (1995). Mediated Learning Experience and Psychological Tools: Vygotsky’s and Feuerstein’s Perspective in a Study of Student Learning. Educational Psychologist, 30(2), 67-75.
• Crowell, A., & Kuhn, D. (2011). Dialogic Argumentation as a Vehicle for Developing Young Adolescents’ Thinking. Psychological Science, 22(4), 545-552. DOI: 10.1177/0956797611402512.

External links [ edit | edit source ]

• Critical Thinking: How Children Can Start Thinking Deeply, Part 1
• Critical Thinking for Kids In Action, Part 2
• Critical Thinking for Kids In Action, Part 3
• Critical Thinking for Kids In Action, Part 4
• Critical Thinking Exercises for Kids

References [ edit | edit source ]

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• ↑ a b Joseph Krajcik , Phyllis C. Blumenfeld , Ronald W. Marx , Kristin M. Bass , Jennifer Fredricks & Elliot Soloway (1998) Inquiry in Project-Based Science Classrooms: Initial Attempts by Middle School Students, Journal of the Learning Sciences, 7:3-4, 313-350, DOI: 10.1080/10508406.1998.9672057
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• ↑ a b Efstratia, Douladeli. (2014). Experiential education through project based learning. Procedia – Social and Behavioral Sciences . 152, 1256-1260.
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• ↑ Gary, Kevin. (2013), Project-Based Learning. Computer. (Vol 48:9). Tempe: Arizona State. 
• ↑ a b c d e f g h Cross, N. (2007). Designerly ways of knowing . Basel, Switzerland: Birkha¨user.
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• ↑ Aflatoony, Leila & Ron Wakkary, (2015). Thoughtful Thinkers: Secondary Schooler’s Learning about Design Thinking. Simon Fraser University: Surrey, BC.
• ↑ a b Koh, Joyce Hwee Ling, Chin Sing Chai, Benjamin Wong, & Huang-Yao Hong. (2015) Design Thinking for Education. Singapore: Springer Science + Business Media.
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• ↑ a b Wells, Alastair. (2013). The importance of design thinking for technological literacy: a phenomenological perspective . International Journal Technol Des Educ. (23:623-636). DOI 10.1007/s10798-012-9207-7.
• ↑ a b c d Jonassen, D.H., & Kim, B. (2010). Arguing to learn ad learning to argue: design justifications and guidelines. Education Technology & Research Development, 58(4), 439-457. DOI 10.1007/s11423-009-9143-8.
• ↑ a b c d e f g h Macagno, F., Mayweg-Paus, W., & Kuhn, D. (2014). Argumentation theory in Education Studies: Coding and Improving Students’ Argumentative Strategies. Topoi, 34, 523-537.
• ↑ a b c Hornikx, J., & Hahn, U. (2012). Reasoning and argumentation: Towards an integrated psychology of argumentation. Thinking & Reasoning, 18(3), 225-243. DOI: 10.1080/13546783.2012.674715.
• ↑ a b Aufschnaiter, C., Erduran, S., Osborne, J., & Simon, S. (2008). Arguing to learn and learning to argue: Case studies of how students' argumentation relates to their scientific knowledge. Journal of Research in Science Teaching, 45(1), 101-131. doi:10.1002/tea.20213
• ↑ Bensley, A., Crowe, D., Bernhardt, P., Buckner, C., & Allman, A. (2010). Teaching and assessing CT skills for argument analysis in psychology. Teaching of Psychology, 37(2), 91-96. doi:10.1080/00986281003626656
• ↑ Glassner, A., & Schwarz, B. B. (2007). What stands and develops between creative and critical thinking? argumentation?. Thinking Skills and Creativity, 2(1), 10-18. doi:10.1016/j.tsc.2006.10.001
• ↑ Gold J., Holman D., & Thorpe R. (2002). The role of argument analysis and story telling in facilitating critical thinking. Management Learning, 33(3), 371-388. doi:10.1177/1350507602333005
• ↑ a b c d e f g h Bruning, R. H., Schraw, G. J., & Norby, M. M. (2011). Cognitive psychology and instruction (5th ed.) Pearson.
• ↑ Chesñevar, I., & Simari, G. (2007). Modelling inference in argumentation through labelled deduction: Formalization and logical properties. Logica Universalis, 2007, Volume 1, Number 1, Page 93, 1(1), 93-124. doi:10.1007/s11787-006-0005-4
• ↑ Ontañón, S., & Plaza, E. (2015). Coordinated inductive learning using argumentation-based communication. Autonomous Agents and Multi-Agent Systems, 29(2), 266-304. doi:10.1007/s10458-014-9256-2
• ↑ Pinto, M., Iliceto, P., & Melagno, S. (2012). Argumentative abilities in metacognition and in metalinguistics: A study on university students. European Journal of Psychology of Education, 27(1), 35-58. doi:10.1007/s10212-011-0064-7
• ↑ Bensley, A., Crowe, D., Bernhardt, P., Buckner, C., & Allman, A. (2010). Teaching and assessing critical thinking skills for argument analysis in psychology. Teaching of Psychology, 37(2), 91-96. doi:10.1080/00986281003626656
• ↑ Demir, B., & İsleyen, T. (2015). The effects of argumentation based science learning approach on creative thinking skills of students. Educational Research Quarterly, 39(1), 49-82.
• ↑ Chandler, S. & Dedman, D.E. (2012). Writing a Literature Review: An Essential Component of Critical Thinking. The Journal of Baccalaureate Social Work, 17. 160-165.
• ↑ a b c d Al-Faoury, O.H., & Khwaileh, F. (2014). The Effect of Teaching CoRT Program No. (4) Entitles “Creativity” on the Gifted Learners’ Writing in Ein El-Basha Center for Gifted Students. Theory and Practice in Language Studies, 4(11), 2249-2257. doi:10.4304/tpls.4.11.2249-2257.
• ↑ a b c Kozulin, A. & Presseisen, B.Z. (1995). Mediated Learning Experience and Psychological Tools: Vygotsky’s and Feuerstein’s Perspective in a Study of Student Learning. Educational Psychologist, 30(2), 67-75.
• ↑ Presseisen, B.Z. & Kozulin, A. (1992). Mediated Learning – The Contributions of Vygotsky and Feuerstein in Theory and Practice.
• ↑ Schuler, G. (1974). The Effectiveness of the Productive Thinking Program. Paper presented at the Annual Meeting of the American Educational Research Association. Retrieved from: http://www.eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED103479 .
• ↑ a b c d Crowell, A., & Kuhn, D. (2014). Developing dialogic argumentation skills: A 3-year intervention study. Journal of Cognition and Development, 15(2), 363-381. doi:10.1080/15248372.2012.725187
• ↑ a b c d Crowell, A., & Kuhn, D. (2011). Dialogic Argumentation as a Vehicle for Developing Young Adolescents’ Thinking. Psychological Science, 22(4), 545-552. DOI: 10.1177/0956797611402512.
• ↑ Jonassen, D.H., & Kim, B. (2010). Arguing to learn ad learning to argue: design justifications and guidelines. Education Technology & Research Development, 58(4), 439-457. DOI 10.1007/s11423-009-9143-8.
• ↑ a b c d Bathgate, M., Crowell, A., Schunn, C., Cannady, M., & Dorph, R. (2015). The learning benefits of being willing and able to engage in scientific argumentation. International Journal of Science Education, 37(10), 1590-1612. doi:10.1080/09500693.2015.1045958
• ↑ a b c d e Seixas, P., Morton, T., Colyer, J., & Fornazzari, S. (2013). The Big Six: Historical thinking Concepts. Toronto: Nelson Education.
• ↑ Osborne, K. (2013). Forward. Seixas, P., Morton, T., Colyer, J., & Fornazzari, S. The Big Six: Historical thinking Concepts. Toronto: Nelson Education.
• ↑ a b Carretero, M., & van Alphen, F. (2014). Do Master Narratives Change Among High School Students? A Characterization of How National History Is Represented. Cognition and Instruction, 32(3), 290–312. http://doi.org/10.1080/07370008.2014.919298
• ↑ a b c Freedman, E. B. (2015). “What Happened Needs to Be Told”: Fostering Critical Historical Reasoning in the Classroom. Cognition and Instruction, 33(4), 357–398. http://doi.org/10.1080/07370008.2015.1101465
• ↑ a b c Wineburg, S. S. (1991). Historical problem solving: A study of the cognitive processes used in the evaluation of documentary and pictorial evidence. Journal of Educational Psychology, 83(1), 73–87. http://doi.org/10.1037/0022-0663.83.1.73
• ↑ Freedman, E. B. (2015). “What Happened Needs to Be Told”: Fostering Critical Historical Reasoning in the Classroom. Cognition and Instruction, 33(4), 357–398. http://doi.org/10.1080/07370008.2015.1101465
• ↑ a b c d e f g h i Seixas, P., Morton, T., Colyer, J., & Fornazzari, S. (2013). The Big Six: Historical thinking Concepts. Toronto: Nelson Education.
• ↑ Blackenship, W. (2009). Making connections: Using online discussion forums to engage students in historical inquiry. Social Education, 73(3), 127-130.
• ↑ Shreiner, T. L. (2014). Using Historical Knowledge to Reason About Contemporary Political Issues: An Expert–Novice Study. Cognition and Instruction, 32(4), 313–352. http://doi.org/10.1080/07370008.2014.948680
• ↑ Seixas, P., & Peck, C. (2004). Teaching Historical Thinking. Challenges and Prospects for Canadian Social Studies, 109–117.
• ↑ Lopez, C., Carretero, M., & Rodriguez-Moneo, M. (2014). Telling a national narrative that is not your own. Does it enable critical historical consumption? Culture & Psychology , 20 (4 ), 547–571. http://doi.org/10.1177/1354067X14554156
• ↑ Whitworth, S. A., & Berson, M. J. (2003). Computer technology in the social studies: An examination of the effectiveness literature (1996-2001). Contemporary Issues in Technology and Teacher Education [Online serial], 2(4). Retrieved from http://www.citejournal.org/volume-2/issue-4-02/social-studies/computer-technology-in-the-social-studies-an-examination-of-the-effectiveness-literature-1996-2001
• ↑ Johnson, D. W., & Johnson, R. T. (1993). Creative and critical thinking through academic controversy. The American Behavioral Scientist, 37(1), 40-53. Retrieved from https://www.proquest.com/docview/1306753602

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35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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