cognitive psychology problem solving

Cognitive Behavioral Therapy

Solving problems the cognitive-behavioral way, problem solving is another part of behavioral therapy..

Posted February 2, 2022 | Reviewed by Ekua Hagan

• What Is Cognitive Behavioral Therapy?
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• Find a therapist who practices CBT
• Problem-solving is one technique used on the behavioral side of cognitive-behavioral therapy.
• The problem-solving technique is an iterative, five-step process that requires one to identify the problem and test different solutions.
• The technique differs from ad-hoc problem-solving in its suspension of judgment and evaluation of each solution.

As I have mentioned in previous posts, cognitive behavioral therapy is more than challenging negative, automatic thoughts. There is a whole behavioral piece of this therapy that focuses on what people do and how to change their actions to support their mental health. In this post, I’ll talk about the problem-solving technique from cognitive behavioral therapy and what makes it unique.

The problem-solving technique

While there are many different variations of this technique, I am going to describe the version I typically use, and which includes the main components of the technique:

The first step is to clearly define the problem. Sometimes, this includes answering a series of questions to make sure the problem is described in detail. Sometimes, the client is able to define the problem pretty clearly on their own. Sometimes, a discussion is needed to clearly outline the problem.

The next step is generating solutions without judgment. The "without judgment" part is crucial: Often when people are solving problems on their own, they will reject each potential solution as soon as they or someone else suggests it. This can lead to feeling helpless and also discarding solutions that would work.

The third step is evaluating the advantages and disadvantages of each solution. This is the step where judgment comes back.

Fourth, the client picks the most feasible solution that is most likely to work and they try it out.

The fifth step is evaluating whether the chosen solution worked, and if not, going back to step two or three to find another option. For step five, enough time has to pass for the solution to have made a difference.

This process is iterative, meaning the client and therapist always go back to the beginning to make sure the problem is resolved and if not, identify what needs to change.

Advantages of the problem-solving technique

The problem-solving technique might differ from ad hoc problem-solving in several ways. The most obvious is the suspension of judgment when coming up with solutions. We sometimes need to withhold judgment and see the solution (or problem) from a different perspective. Deliberately deciding not to judge solutions until later can help trigger that mindset change.

Another difference is the explicit evaluation of whether the solution worked. When people usually try to solve problems, they don’t go back and check whether the solution worked. It’s only if something goes very wrong that they try again. The problem-solving technique specifically includes evaluating the solution.

Lastly, the problem-solving technique starts with a specific definition of the problem instead of just jumping to solutions. To figure out where you are going, you have to know where you are.

One benefit of the cognitive behavioral therapy approach is the behavioral side. The behavioral part of therapy is a wide umbrella that includes problem-solving techniques among other techniques. Accessing multiple techniques means one is more likely to address the client’s main concern.

Salene M. W. Jones, Ph.D., is a clinical psychologist in Washington State.

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What Is Cognitive Psychology?

The Science of How We Think

Topics in Cognitive Psychology

• Current Research
• Cognitive Approach in Practice

Careers in Cognitive Psychology

How cognitive psychology differs from other branches of psychology, frequently asked questions.

Cognitive psychology is the study of internal mental processes—all of the workings inside your brain, including perception, thinking, memory, attention, language, problem-solving, and learning. Learning about how people think and process information helps researchers and psychologists understand the human brain and assist people with psychological difficulties.

This article discusses what cognitive psychology is—its history, current trends, practical applications, and career paths.

Findings from cognitive psychology help us understand how people think, including how they acquire and store memories. By knowing more about how these processes work, psychologists can develop new ways of helping people with cognitive problems.

Cognitive psychologists explore a wide variety of topics related to thinking processes. Some of these include: 

• Attention --our ability to process information in the environment while tuning out irrelevant details
• Choice-based behavior --actions driven by a choice among other possibilities
• Decision-making
• Information processing
• Language acquisition --how we learn to read, write, and express ourselves
• Problem-solving
• Speech perception -how we process what others are saying
• Visual perception --how we see the physical world around us

History of Cognitive Psychology

Although it is a relatively young branch of psychology , it has quickly grown to become one of the most popular subfields. Cognitive psychology grew into prominence between the 1950s and 1970s.

Prior to this time, behaviorism was the dominant perspective in psychology. This theory holds that we learn all our behaviors from interacting with our environment. It focuses strictly on observable behavior, not thought and emotion. Then, researchers became more interested in the internal processes that affect behavior instead of just the behavior itself. 

This shift is often referred to as the cognitive revolution in psychology. During this time, a great deal of research on topics including memory, attention, and language acquisition began to emerge. 

In 1967, the psychologist Ulric Neisser introduced the term cognitive psychology, which he defined as the study of the processes behind the perception, transformation, storage, and recovery of information.

Cognitive psychology became more prominent after the 1950s as a result of the cognitive revolution.

Current Research in Cognitive Psychology

The field of cognitive psychology is both broad and diverse. It touches on many aspects of daily life. There are numerous practical applications for this research, such as providing help coping with memory disorders, making better decisions , recovering from brain injury, treating learning disorders, and structuring educational curricula to enhance learning.

Current research on cognitive psychology helps play a role in how professionals approach the treatment of mental illness, traumatic brain injury, and degenerative brain diseases.

Thanks to the work of cognitive psychologists, we can better pinpoint ways to measure human intellectual abilities, develop new strategies to combat memory problems, and decode the workings of the human brain—all of which ultimately have a powerful impact on how we treat cognitive disorders.

The field of cognitive psychology is a rapidly growing area that continues to add to our understanding of the many influences that mental processes have on our health and daily lives.

From understanding how cognitive processes change as a child develops to looking at how the brain transforms sensory inputs into perceptions, cognitive psychology has helped us gain a deeper and richer understanding of the many mental events that contribute to our daily existence and overall well-being.

The Cognitive Approach in Practice

In addition to adding to our understanding of how the human mind works, the field of cognitive psychology has also had an impact on approaches to mental health. Before the 1970s, many mental health treatments were focused more on psychoanalytic , behavioral , and humanistic approaches.

The so-called "cognitive revolution" put a greater emphasis on understanding the way people process information and how thinking patterns might contribute to psychological distress. Thanks to research in this area, new approaches to treatment were developed to help treat depression, anxiety, phobias, and other psychological disorders .

Cognitive behavioral therapy and rational emotive behavior therapy are two methods in which clients and therapists focus on the underlying cognitions, or thoughts, that contribute to psychological distress.

What Is Cognitive Behavioral Therapy?

Cognitive behavioral therapy (CBT) is an approach that helps clients identify irrational beliefs and other cognitive distortions that are in conflict with reality and then aid them in replacing such thoughts with more realistic, healthy beliefs.

If you are experiencing symptoms of a psychological disorder that would benefit from the use of cognitive approaches, you might see a psychologist who has specific training in these cognitive treatment methods.

These professionals frequently go by titles other than cognitive psychologists, such as psychiatrists, clinical psychologists , or counseling psychologists , but many of the strategies they use are rooted in the cognitive tradition.

Many cognitive psychologists specialize in research with universities or government agencies. Others take a clinical focus and work directly with people who are experiencing challenges related to mental processes. They work in hospitals, mental health clinics, and private practices.

Research psychologists in this area often concentrate on a particular topic, such as memory. Others work directly on health concerns related to cognition, such as degenerative brain disorders and brain injuries.

Treatments rooted in cognitive research focus on helping people replace negative thought patterns with more positive, realistic ones. With the help of cognitive psychologists, people are often able to find ways to cope and even overcome such difficulties.

Reasons to Consult a Cognitive Psychologist

• Alzheimer's disease, dementia, or memory loss
• Brain trauma treatment
• Cognitive therapy for a mental health condition
• Interventions for learning disabilities
• Perceptual or sensory issues
• Therapy for a speech or language disorder

Whereas behavioral and some other realms of psychology focus on actions--which are external and observable--cognitive psychology is instead concerned with the thought processes behind the behavior. Cognitive psychologists see the mind as if it were a computer, taking in and processing information, and seek to understand the various factors involved.

A Word From Verywell

Cognitive psychology plays an important role in understanding the processes of memory, attention, and learning. It can also provide insights into cognitive conditions that may affect how people function.

Being diagnosed with a brain or cognitive health problem can be daunting, but it is important to remember that you are not alone. Together with a healthcare provider, you can come up with an effective treatment plan to help address brain health and cognitive problems.

Your treatment may involve consulting with a cognitive psychologist who has a background in the specific area of concern that you are facing, or you may be referred to another mental health professional that has training and experience with your particular condition.

Ulric Neisser is considered the founder of cognitive psychology. He was the first to introduce the term and to define the field of cognitive psychology. His primary interests were in the areas of perception and memory, but he suggested that all aspects of human thought and behavior were relevant to the study of cognition.

A cognitive map refers to a mental representation of an environment. Such maps can be formed through observation as well as through trial and error. These cognitive maps allow people to orient themselves in their environment.

While they share some similarities, there are some important differences between cognitive neuroscience and cognitive psychology. While cognitive psychology focuses on thinking processes, cognitive neuroscience is focused on finding connections between thinking and specific brain activity. Cognitive neuroscience also looks at the underlying biology that influences how information is processed.

Cognitive psychology is a form of experimental psychology. Cognitive psychologists use experimental methods to study the internal mental processes that play a role in behavior.

Sternberg RJ, Sternberg K. Cognitive Psychology . Wadsworth/Cengage Learning. 

Krapfl JE. Behaviorism and society . Behav Anal. 2016;39(1):123-9. doi:10.1007/s40614-016-0063-8

Cutting JE. Ulric Neisser (1928-2012) . Am Psychol . 2012;67(6):492. doi:10.1037/a0029351

Ruggiero GM, Spada MM, Caselli G, Sassaroli S. A historical and theoretical review of cognitive behavioral therapies: from structural self-knowledge to functional processes .  J Ration Emot Cogn Behav Ther . 2018;36(4):378-403. doi:10.1007/s10942-018-0292-8

Parvin P. Ulric Neisser, cognitive psychology pioneer, dies . Emory News Center.

APA Dictionary of Psychology. Cognitive map . American Psychological Association.

Forstmann BU, Wagenmakers EJ, Eichele T, Brown S, Serences JT. Reciprocal relations between cognitive neuroscience and formal cognitive models: opposites attract? . Trends Cogn Sci . 2011;15(6):272-279. doi:10.1016/j.tics.2011.04.002

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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9 Chapter 9. Problem-Solving

CHAPTER 9: PROBLEM SOLVING  

How do we achieve our goals when the solution is not immediately obvious? What mental blocks are likely to get in our way, and how can we leverage our prior knowledge to solve novel problems?

CHAPTER 9 LICENSE AND ATTRIBUTION

Source: Multiple authors. Memory. In Cognitive Psychology and Cognitive Neuroscience. Wikibooks. Retrieved from https://en.wikibooks.org/wiki/ Cognitive_Psychology_and_Cognitive_Neuroscience

Wikibooks are licensed under the Creative Commons Attribution-ShareAlike License.

Cognitive Psychology and Cognitive Neuroscience is licensed under the GNU Free Documentation License.

Condensed from original version. American spellings used. Content added or changed to reflect American perspective and references. Context and transitions added throughout. Substantially edited, adapted, and (in some parts) rewritten for clarity and course relevance.

Cover photo by Pixabay on Pexels.

Knut is sitting at his desk, staring at a blank paper in front of him, and nervously playing with a pen in his right hand. Just a few hours left to hand in his essay and he has not written a word. All of a sudden he smashes his fist on the table and cries out: “I need a plan!”

Knut is confronted with something every one of us encounters in his daily life: he has a problem, and he does not know how to solve it. But what exactly is a problem? Are there strategies to solve problems? These are just a few of the questions we want to answer in this chapter.

We begin our chapter by giving a short description of what psychologists regard as a problem. Afterward we will discuss different approaches towards problem solving, starting with gestalt psychologists and ending with modern search strategies connected to artificial intelligence. In addition we will also consider how experts solve problems.

The most basic definition of a problem is any given situation that differs from a desired goal. This definition is very useful for discussing problem solving in terms of evolutionary adaptation, as it allows us to understand every aspect of (human or animal) life as a problem. This includes issues like finding food in harsh winters, remembering where you left your provisions, making decisions about which way to go, learning, repeating and varying all kinds of complex movements, and so on. Though all of these problems were of crucial importance during the human evolutionary process, they are by no means solved exclusively by humans. We find an amazing variety of different solutions for these problems in nature (just consider, for example, the way a bat hunts its prey compared to a spider). We will mainly focus on problems that are not solved by animals or evolution; we will instead focus on abstract problems, such as playing chess. Furthermore, we will not consider problems that have an obvious solution. For example, imagine Knut decides to take a sip of coffee from the mug next to his right hand. He does not even have to think about how to do this. This is not because the situation itself is trivial (a robot capable of recognizing the mug, deciding whether it is full, then grabbing it and moving it to Knut’s mouth would be a highly complex machine) but because in the context of all possible situations it is so trivial that it no longer is a problem our consciousness needs to be bothered with. The problems we will discuss in the following all need some conscious effort, though some seem to be solved without us being able to say how exactly we got to the solution. We will often find that the strategies we use to solve these problems are applicable to more basic problems, too.

Non-trivial, abstract problems can be divided into two groups: well-defined problems and ill- defined problems.

WELL-DEFINED PROBLEMS

For many abstract problems, it is possible to find an algorithmic solution. We call problems well-defined if they can be properly formalized, which involves the following properties:

•        The problem has a clearly defined given state. This might be the line-up of a chess game, a given formula you have to solve, or the set-up of the towers of Hanoi game (which we will discuss later).

•        There is a finite set of operators, that is, rules you may apply to the given state. For the chess game, e.g., these would be the rules that tell you which piece you may move to which position.

•        Finally, the problem has a clear goal state: The equations is resolved to x, all discs are moved to the right stack, or the other player is in checkmate.

A problem that fulfils these requirements can be implemented algorithmically. Therefore many well-defined problems can be very effectively solved by computers, like playing chess.

ILL-DEFINED PROBLEMS

Though many problems can be properly formalized, there are still others where this is not the case. Good examples for this are all kinds of tasks that involve creativity, and, generally speaking, all problems for which it is not possible to clearly define a given state and a goal state. Formalizing a problem such as “Please paint a beautiful picture” may be impossible.

Still, this is a problem most people would be able to approach in one way or the other, even if the result may be totally different from person to person. And while Knut might judge that picture X is gorgeous, you might completely disagree.

The line between well-defined and ill-defined problems is not always neat: ill-defined problems often involve sub-problems that can be perfectly well-defined. On the other hand, many everyday problems that seem to be completely well-defined involve — when examined in detail — a great amount of creativity and ambiguity. Consider Knut’s fairly ill-defined task of writing an essay: he will not be able to complete this task without first understanding the text he has to write about. This step is the first subgoal Knut has to solve. In this example, an ill-defined problem involves a well-defined sub-problem

RESTRUCTURING: THE GESTALTIST APPROACH

One dominant approach to problem solving originated from Gestalt psychologists in the 1920s. Their understanding of problem solving emphasizes behavior in situations requiring relatively novel means of attaining goals and suggests that problem solving involves a process called restructuring. With a Gestalt approach, two main questions have to be considered to understand the process of problem solving: 1) How is a problem represented in a person’s mind?, and 2) How does solving this problem involve a reorganization or restructuring of this representation?

HOW IS A PROBLEM REPRESENTED IN THE MIND?

In current research internal and external representations are distinguished: an internal representation is one held in memory, and which has to be retrieved by cognitive processes, while an external representation exists in the environment, such like physical objects or symbols whose information can be picked up and processed by the perceptual system.

Generally speaking, problem representations are models of the situation as experienced by the solver. Representing a problem means to analyze it and split it into separate components, including objects, predicates, state space, operators, and selection criteria.

The efficiency of problem solving depends on the underlying representations in a person’s mind, which usually also involves personal aspects. Re-analyzing the problem along different dimensions, or changing from one representation to another, can result in arriving at a new understanding of a problem. This is called restructuring . The following example illustrates this:

Two boys of different ages are playing badminton. The older one is a more skilled player, and therefore the outcome of matches between the two becomes predictable. After repeated defeats the younger boy finally loses interest in playing. The older boy now faces a problem, namely that he has no one to play with anymore. The usual options, according to M. Wertheimer (1945/82), range from “offering candy” and “playing a different game” to “not playing at full ability” and “shaming the younger boy into playing.” All of these strategies aim at making the younger boy stay.

The older boy instead comes up with a different solution: He proposes that they should try to keep the birdie in play as long as possible. Thus, they change from a game of competition to one of cooperation. The proposal is happily accepted, and the game is on again. The key in this story is that the older boy restructured the problem, having found that his attitude toward the game made it difficult to keep the younger boy playing. With the new type of game the problem is solved: the older boy is not bored, and the younger boy is not frustrated. In some cases, new representations can make a problem more difficult or much easier to solve. In the latter case insight – the sudden realization of a problem’s solution – may be the key to finding a solution.

There are two very different ways of approaching a goal-oriented situation . In one case an organism readily reproduces the response to the given problem from past experience. This is called reproductive thinking .

The second way requires something new and di fferent to achieve the goal—prior learning is of little help here. Such productive thinking is sometimes argued to involve insight . Gestalt psychologists state that insight problems are a separate category of problems in their own right.

Tasks that might involve insight usually have certain features: they require something new and non-obvious to be done, and in most cases they are difficult enough to predict that the initial solution attempt will be unsuccessful. When you solve a problem of this kind you often have a so called “aha” experience: the solution pops into mind all of a sudden. In one moment you have no idea how to answer the problem, and you feel you are not making any progress trying out different ideas, but in the next moment the problem is solved.

For readers who would like to experience such an effect, here is an example of an insight problem: Knut is given four pieces of a chain; each made up of three links. The task is to link it all up to a closed loop. To open a link costs 2 cents, and to close a link costs 3 cents. Knut has 15 cents to spend. What should Knut do?

If you want to know the correct solution, turn to the next page.

To show that solving insight problems involves restructuring , psychologists have created a number of problems that are more difficult to solve for participants with previous experiences, since it is harder for them to change the representation of the given situation.

For non-insight problems the opposite is the case. Solving arithmetical problems, for instance, requires schemas, through which one can get to the solution step by step.

Sometimes, previous experience or familiarity can even make problem solving more difficult. This is the case whenever habitual directions get in the way of finding new directions – an effect called fixation .

FUNCTIONAL FIXEDNESS

Functional fixedness concerns the solution of object use problems . The basic idea is that when the usual function an object is emphasized, it will be far more difficult for a person to use that object in a novel manner. An example for this effect is the candle problem : Imagine you are given a box of matches, some candles and tacks. On the wall of the room there is a cork-board. Your task is to fix the candle to the cork-board in such a way that no wax will drop on the floor when the candle is lit. Got an idea?

Here’s a clue: when people are confronted with a problem and given certain objects to solve it, it is difficult for them to figure out that they could use the objects in a different way. In this example, the box has to be recognized as a support rather than as a container— tack the matchbox to the wall, and place the candle upright in the box. The box will catch the falling wax.

A further example is the two-string problem : Knut is left in a room with a pair of pliers and given the task to bind two strings together that are hanging from the ceiling. The problem he faces is that he can never reach both strings at a time because they are just too far away from each other. What can Knut do?

Solution: Knut has to recognize he can use the pliers in a novel function: as weight for a pendulum. He can tie them to one of the strings, push it away, hold the other string and wait for the first one to swing toward him.

MENTAL FIXEDNESS

Functional fixedness as involved in the examples above illustrates a mental set: a person’s tendency to respond to a given task in a manner based on past experience. Because Knut maps an object to a particular function he has difficulty varying the way of use (i.e., pliers as pendulum’s weight).

One approach to studying fixation was to study wrong-answer verbal insight problems . In these probems, people tend to give an incorrect answer when failing to solve a problem rather than to give no answer at all.

A typical example: People are told that on a lake the area covered by water lilies doubles every 24 hours and that it takes 60 days to cover the whole lake. Then they are asked how many days it takes to cover half the lake. The typical response is “30 days” (whereas 59 days is correct).

These wrong solutions are due to an inaccurate interpretation , or representation , of the problem. This can happen because of sloppiness (a quick shallow reading of the problem and/or weak monitoring of their efforts made to come to a solution). In this case error feedback should help people to reconsider the problem features, note the inadequacy of their first answer, and find the correct solution. If, however, people are truly fixated on their incorrect representation, being told the answer is wrong does not help. In a study by P.I. Dallop and

R.L. Dominowski in 1992 these two possibilities were investigated. In approximately one third of the cases error feedback led to right answers, so only approximately one third of the wrong answers were due to inadequate monitoring.

Another approach is the study of examples with and without a preceding analogous task. In cases such like the water-jug task, analogous thinking indeed leads to a correct solution, but to take a different way might make the case much simpler:

Imagine Knut again, this time he is given three jugs with different capacities and is asked to measure the required amount of water. He is not allowed to use anything except the jugs and as much water as he likes. In the first case the sizes are: 127 cups, 21 cups and 3 cups. His goal is to measure 100 cups of water.

In the second case Knut is asked to measure 18 cups from jugs of 39, 15 and 3 cups capacity.

Participants who are given the 100 cup task first choose a complicated way to solve the second task. Participants who did not know about that complex task solved the 18 cup case by just adding three cups to 15.

SOLVING PROBLEMS BY ANALOGY

One special kind of restructuring is analogical problem solving. Here, to find a solution to one problem (i.e., the target problem) an analogous solution to another problem (i.e., the base problem) is presented.

An example for this kind of strategy is the radiation problem posed by K. Duncker in 1945:

As a doctor you have to treat a patient with a malignant, inoperable tumor, buried deep inside the body. There exists a special kind of ray which is harmless at a low intensity, but at sufficiently high intensity is able to destroy the tumor. At such high intensity, however, the ray will also destroy the healthy tissue it passes through on the way to the tumor. What can be done to destroy the tumor while preserving the healthy tissue?

When this question was asked to participants in an experiment, most of them couldn’t come up with the appropriate answer to the problem. Then they were told a story that went something like this:

A general wanted to capture his enemy’s fortress. He gathered a large army to launch a full- scale direct attack, but then learned that all the roads leading directly towards the fortress were blocked by landmines. These roadblocks were designed in such a way that it was possible for small groups of the fortress-owner’s men to pass over them safely, but a large group of men would set them off. The general devised the following plan: He divided his troops into several smaller groups and ordered each of them to march down a different road, timed in such a way that the entire army would reunite exactly when reaching the fortress and could hit with full strength.

Here, the story about the general is the source problem, and the radiation problem is the target problem. The fortress is analogous to the tumor and the big army corresponds to the highly intensive ray. Likewise, a small group of soldiers represents a ray at low intensity. The s olution to the problem is to split the ray up, as the general did with his army, and send the now harmless rays towards the tumor from different angles in such a way that they all meet when reaching it. No healthy tissue is damaged but the tumor itself gets destroyed by the ray at its full intensity.

M. Gick and K. Holyoak presented Duncker’s radiation problem to a group of participants in 1980 and 1983. 10 percent of participants were able to solve the problem right away, but 30 percent could solve it when they read the story of the general before. After being given an additional hint — to use the story as help — 75 percent of them solved the problem.

Following these results, Gick and Holyoak concluded that analogical problem solving consists of three steps:

1.  Recognizing that an analogical connection exists between the source and the base problem.

2. Mapping corresponding parts of the two problems onto each other (fortress ® tumour, army ® ray, etc.)

3. Applying the mapping to generate a parallel solution to the target problem (using little groups of soldiers approaching from different directions ® sending several weaker rays from different directions)

Next, Gick and Holyoak started looking for factors that could help the recognizing and mapping processes.

The abstract concept that links the target problem with the base problem is called the problem schema. Gick and Holyoak facilitated the activation of a schema with their participants by giving them two stories and asking them to compare and summarize them. This activation of problem schemas is called “schema induction“.

The experimenters had participants read stories that presented problems and their solutions. One story was the above story about the general, and other stories required the same problem schema (i.e., if a heavy force coming from one direction is not suitable, use multiple smaller forces that simultaneously converge on the target). The experimenters manipulated how many of these stories the participants read before the participants were asked to solve the radiation problem. The experiment showed that in order to solve the target problem, reading two stories with analogical problems is more helpful than reading only one story. This evidence suggests that schema induction can be achieved by exposing people to multiple problems with the same problem schema.

HOW DO EXPERTS SOLVE PROBLEMS?

An expert is someone who devotes large amounts of their time and energy to one specific field of interest in which they, subsequently, reach a certain level of mastery. It should not be a surprise that experts tend to be better at solving problems in their field than novices (i.e., people who are beginners or not as well-trained in a field as experts) are. Experts are faster at coming up with solutions and have a higher rate of correct solutions. But what is the difference between the way experts and non-experts solve problems? Research on the nature of expertise has come up with the following conclusions:

1.       Experts know more about their field,

2.      their knowledge is organized differently, and

3.      they spend more time analyzing the problem.

Expertise is domain specific— when it comes to problems that are outside the experts’ domain of expertise, their performance often does not differ from that of novices.

Knowledge: An experiment by Chase and Simon (1973) dealt with the question of how well experts and novices are able to reproduce positions of chess pieces on chess boards after a brief presentation. The results showed that experts were far better at reproducing actual game positions, but that their performance was comparable with that of novices when the chess pieces were arranged randomly on the board. Chase and Simon concluded that the superior performance on actual game positions was due to the ability to recognize familiar patterns: A chess expert has up to 50,000 patterns stored in his memory. In comparison, a good player might know about 1,000 patterns by heart and a novice only few to none at all. This very detailed knowledge is of crucial help when an expert is confronted with a new problem in his field. Still, it is not only the amount of knowledge that makes an expert more successful. Experts also organize their knowledge differently from novices.

Organization: In 1981 M. Chi and her co-workers took a set of 24 physics problems and presented them to a group of physics professors as well as to a group of students with only one semester of physics. The task was to group the problems based on their similarities. The students tended to group the problems based on their surface structure (i.e., similarities of objects used in the problem, such as sketches illustrating the problem), whereas the professors used their deep structure (i.e., the general physical principles that underlie the problems) as criteria. By recognizing the actual structure of a problem experts are able to connect the given task to the relevant knowledge they already have (e.g., another problem they solved earlier which required the same strategy).

Analysis: Experts often spend more time analyzing a problem before actually trying to solve it. This way of approaching a problem may often result in what appears to be a slow start, but in the long run this strategy is much more effective. A novice, on the other hand, might start working on the problem right away, but often reach dead ends as they chose a wrong path in the very beginning.

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Chase, W. G., & Simon, H. A. (1973). Perception in chess. Cognitive psychology, 4(1), 55-81.

Chi, M. T., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive science, 5(2), 121-152.

Duncker, K., & Lees, L. S. (1945). On problem-solving. Psychological monographs, 58(5).

Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive psychology, 12(3), 306-355. Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive psychology, 15(1), 1-38.

Goldstein, E.B. (2005). Cogntive Psychology. Connecting Mind, Research, and Everyday Experience. Belmont: Thomson Wadsworth.

R.L. Dominowski and P. Dallob, Insight and Problem Solving. In The Nature of Insight, R.J. Sternberg & J.E. Davidson (Eds). MIT Press: USA, pp.33-62 (1995).

Wertheimer, M., (1945). Productive thinking. New York: Harper.

ESSENTIALS OF COGNITIVE PSYCHOLOGY Copyright © 2023 by Christopher Klein is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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In This Article Expand or collapse the "in this article" section Problem Solving and Decision Making

Introduction.

• General Approaches to Problem Solving
• Representational Accounts
• Problem Space and Search
• Working Memory and Problem Solving
• Domain-Specific Problem Solving
• The Rational Approach
• Prospect Theory
• Dual-Process Theory
• Cognitive Heuristics and Biases

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Problem Solving and Decision Making by Emily G. Nielsen , John Paul Minda LAST REVIEWED: 26 June 2019 LAST MODIFIED: 26 June 2019 DOI: 10.1093/obo/9780199828340-0246

Problem solving and decision making are both examples of complex, higher-order thinking. Both involve the assessment of the environment, the involvement of working memory or short-term memory, reliance on long term memory, effects of knowledge, and the application of heuristics to complete a behavior. A problem can be defined as an impasse or gap between a current state and a desired goal state. Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal. Problems can vary in complexity, abstraction, and how well defined (or not) the initial state and the goal state are. Research has generally approached problem solving by examining the behaviors and cognitive processes involved, and some work has examined problem solving using computational processes as well. Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions that deviate from rationality. The current bibliography first outlines some general resources on the psychology of problem solving and decision making before examining each of these topics in detail. Specifically, this review covers cognitive, neuroscientific, and computational approaches to problem solving, as well as decision making models and cognitive heuristics and biases.

General Overviews

Current research in the area of problem solving and decision making is published in both general and specialized scientific journals. Theoretical and scholarly work is often summarized and developed in full-length books and chapter. These may focus on the subfields of problem solving and decision making or the larger field of thinking and higher-order cognition.

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The Process of Problem Solving

• Editor's Choice
• Experimental Psychology
• Problem Solving

In a 2013 article published in the Journal of Cognitive Psychology , Ngar Yin Louis Lee (Chinese University of Hong Kong) and APS William James Fellow Philip N. Johnson-Laird (Princeton University) examined the ways people develop strategies to solve related problems. In a series of three experiments, the researchers asked participants to solve series of matchstick problems.

In matchstick problems, participants are presented with an array of joined squares. Each square in the array is comprised of separate pieces. Participants are asked to remove a certain number of pieces from the array while still maintaining a specific number of intact squares. Matchstick problems are considered to be fairly sophisticated, as there is generally more than one solution, several different tactics can be used to complete the task, and the types of tactics that are appropriate can change depending on the configuration of the array.

Louis Lee and Johnson-Laird began by examining what influences the tactics people use when they are first confronted with the matchstick problem. They found that initial problem-solving tactics were constrained by perceptual features of the array, with participants solving symmetrical problems and problems with salient solutions faster. Participants frequently used tactics that involved symmetry and salience even when other solutions that did not involve these features existed.

To examine how problem solving develops over time, the researchers had participants solve a series of matchstick problems while verbalizing their problem-solving thought process. The findings from this second experiment showed that people tend to go through two different stages when solving a series of problems.

People begin their problem-solving process in a generative manner during which they explore various tactics — some successful and some not. Then they use their experience to narrow down their choices of tactics, focusing on those that are the most successful. The point at which people begin to rely on this newfound tactical knowledge to create their strategic moves indicates a shift into a more evaluative stage of problem solving.

In the third and last experiment, participants completed a set of matchstick problems that could be solved using similar tactics and then solved several problems that required the use of novel tactics.  The researchers found that participants often had trouble leaving their set of successful tactics behind and shifting to new strategies.

From the three studies, the researchers concluded that when people tackle a problem, their initial moves may be constrained by perceptual components of the problem. As they try out different tactics, they hone in and settle on the ones that are most efficient; however, this deduced knowledge can in turn come to constrain players’ generation of moves — something that can make it difficult to switch to new tactics when required.

These findings help expand our understanding of the role of reasoning and deduction in problem solving and of the processes involved in the shift from less to more effective problem-solving strategies.

Reference Louis Lee, N. Y., Johnson-Laird, P. N. (2013). Strategic changes in problem solving. Journal of Cognitive Psychology, 25 , 165–173. doi: 10.1080/20445911.2012.719021

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Careers Up Close: Joel Anderson on Gender and Sexual Prejudices, the Freedoms of Academic Research, and the Importance of Collaboration

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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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Cognitive Approach in Psychology

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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Cognitive psychology is the scientific study of the mind as an information processor. It concerns how we take in information from the outside world, and how we make sense of that information.

Cognitive psychology studies mental processes, including how people perceive, think, remember, learn, solve problems, and make decisions.

Cognitive psychologists try to build cognitive models of the information processing that occurs inside people’s minds, including perception, attention, language, memory, thinking, and consciousness.

Cognitive psychology became of great importance in the mid-1950s. Several factors were important in this:

• Dissatisfaction with the behaviorist approach in its simple emphasis on external behavior rather than internal processes.
• The development of better experimental methods.
• Comparison between human and computer processing of information . Using computers allowed psychologists to try to understand the complexities of human cognition by comparing it with computers and artificial intelligence.

The emphasis of psychology shifted away from the study of conditioned behavior and psychoanalytical notions about the study of the mind, towards the understanding of human information processing using strict and rigorous laboratory investigation.

Summary Table

Theoretical Assumptions

Mediational processes occur between stimulus and response:

The behaviorist approach only studies external observable (stimulus and response) behavior that can be objectively measured.

They believe that internal behavior cannot be studied because we cannot see what happens in a person’s mind (and therefore cannot objectively measure it).

However, cognitive psychologists consider it essential to examine an organism’s mental processes and how these influence behavior.

Cognitive psychology assumes a mediational process occurs between stimulus/input and response/output. 

These are mediational processes because they mediate (i.e., go-between) between the stimulus and the response. They come after the stimulus and before the response.

Instead of the simple stimulus-response links proposed by behaviorism, the mediational processes of the organism are essential to understand.

Without this understanding, psychologists cannot have a complete understanding of behavior.

The mediational (i.e., mental) event could be memory , perception , attention or problem-solving, etc. 

• Perception : how we process and interpret sensory information.
• Attention : how we selectively focus on certain aspects of our environment.
• Memory : how we encode, store, and retrieve information.
• Language : how we acquire, comprehend, and produce language.
• Problem-solving and decision-making : how we reason, make judgments, and solve problems.
• Schemas : Cognitive psychologists assume that people’s prior knowledge, beliefs, and experiences shape their mental processes. 

For example, the cognitive approach suggests that problem gambling results from maladaptive thinking and faulty cognitions, which both result in illogical errors.

Gamblers misjudge the amount of skill involved with ‘chance’ games, so they are likely to participate with the mindset that the odds are in their favour and that they may have a good chance of winning.

Therefore, cognitive psychologists say that if you want to understand behavior, you must understand these mediational processes.

Psychology should be seen as a science:

This assumption is based on the idea that although not directly observable, the mind can be investigated using objective and rigorous methods, similar to how other sciences study natural phenomena. 

Controlled experiments

The cognitive approach believes that internal mental behavior can be scientifically studied using controlled experiments . It uses the results of its investigations to make inferences about mental processes.  Cognitive psychology uses highly controlled laboratory experiments to avoid the influence of extraneous variables . This allows the researcher to establish a causal relationship between the independent and dependent variables. These controlled experiments are replicable, and the data obtained is objective (not influenced by an individual’s judgment or opinion) and measurable. This gives psychology more credibility.

Operational definitions

Cognitive psychologists develop operational definitions to study mental processes scientifically. These definitions specify how abstract concepts, such as attention or memory, can be measured and quantified (e.g., verbal protocols of thinking aloud). This allows for reliable and replicable research findings.

Falsifiability

Falsifiability in psychology refers to the ability to disprove a theory or hypothesis through empirical observation or experimentation. If a claim is not falsifiable, it is considered unscientific.

Cognitive psychologists aim to develop falsifiable theories and models, meaning they can be tested and potentially disproven by empirical evidence.

This commitment to falsifiability helps to distinguish scientific theories from pseudoscientific or unfalsifiable claims.

Empirical evidence

Cognitive psychologists rely on empirical evidence to support their theories and models. They collect data through various methods, such as experiments, observations, and questionnaires, to test hypotheses and draw conclusions about mental processes.

Cognitive psychologists assume that mental processes are not random but are organized and structured in specific ways. They seek to identify the underlying cognitive structures and processes that enable people to perceive, remember, and think.

Cognitive psychologists have made significant contributions to our understanding of mental processes and have developed various theories and models, such as the multi-store model of memory , the working memory model , and the dual-process theory of thinking.

Humans are information processors:

The idea of information processing was adopted by cognitive psychologists as a model of how human thought works.

The information processing approach is based on several assumptions, including:

• Information is processed by a series of systems : The information processing approach proposes that a series of cognitive systems, such as attention, perception, and memory, process information from the environment. Each system plays a specific role in processing the information and passing it along to the next stage.
• Processing systems transform information : As information passes through these cognitive systems, it is transformed or modified in systematic ways. For example, incoming sensory information may be filtered by attention, encoded into memory, or used to update existing knowledge structures.
• Research aims to specify underlying processes and structures : The primary goal of research within the information processing approach is to identify, describe, and understand the specific cognitive processes and mental structures that underlie various aspects of cognitive performance, such as learning, problem-solving, and decision-making.
• Human information processing resembles computer processing : The information processing approach draws an analogy between human cognition and computer processing. Just as computers take in information, process it according to specific algorithms, and produce outputs, the human mind is thought to engage in similar processes of input, processing, and output.

Computer-Mind Analogy

The computer-brain metaphor, or the information processing approach, is a significant concept in cognitive psychology that likens the human brain’s functioning to that of a computer.

This metaphor suggests that the brain, like a computer, processes information through a series of linear steps, including input, storage, processing, and output.

According to this assumption, when we interact with the environment, we take in information through our senses (input).

This information is then processed by various cognitive systems, such as perception, attention, and memory. These systems work together to make sense of the input, organize it, and store it for later use.

During the processing stage, the mind performs operations on the information, such as encoding, transforming, and combining it with previously stored knowledge. This processing can involve various cognitive processes, such as thinking, reasoning, problem-solving, and decision-making.

The processed information can then be used to generate outputs, such as actions, decisions, or new ideas. These outputs are based on the information that has been processed and the individual’s goals and motivations.

This has led to models showing information flowing through the cognitive system, such as the multi-store memory model.

The information processing approach also assumes that the mind has a limited capacity for processing information, similar to a computer’s memory and processing limitations.

This means that humans can only attend to and process a certain amount of information at a given time, and that cognitive processes can be slowed down or impaired when the mind is overloaded.

The Role of Schemas

A schema is a “packet of information” or cognitive framework that helps us organize and interpret information. It is based on previous experience.

Cognitive psychologists assume that people’s prior knowledge, beliefs, and experiences shape their mental processes. They investigate how these factors influence perception, attention, memory, and thinking.

Schemas help us interpret incoming information quickly and effectively, preventing us from being overwhelmed by the vast amount of information we perceive in our environment.

Schemas can often affect cognitive processing (a mental framework of beliefs and expectations developed from experience). As people age, they become more detailed and sophisticated.

However, it can also lead to distortion of this information as we select and interpret environmental stimuli using schemas that might not be relevant.

This could be the cause of inaccuracies in areas such as eyewitness testimony. It can also explain some errors we make when perceiving optical illusions.

1. Behaviorist Critique

B.F. Skinner criticizes the cognitive approach. He believes that only external stimulus-response behavior should be studied, as this can be scientifically measured.

Therefore, mediation processes (between stimulus and response) do not exist as they cannot be seen and measured.

Behaviorism assumes that people are born a blank slate (tabula rasa) and are not born with cognitive functions like schemas , memory or perception .

Due to its subjective and unscientific nature, Skinner continues to find problems with cognitive research methods, namely introspection (as used by Wilhelm Wundt).

2. Complexity of mental experiences

Mental processes are highly complex and multifaceted, involving a wide range of cognitive, affective, and motivational factors that interact in intricate ways.

The complexity of mental experiences makes it difficult to isolate and study specific mental processes in a controlled manner.

Mental processes are often influenced by individual differences, such as personality, culture, and past experiences, which can introduce variability and confounds in research .

3. Experimental Methods 

While controlled experiments are the gold standard in cognitive psychology research, they may not always capture real-world mental processes’ complexity and ecological validity.

Some mental processes, such as creativity or decision-making in complex situations, may be difficult to study in laboratory settings.

Humanistic psychologist Carl Rogers believes that using laboratory experiments by cognitive psychology has low ecological validity and creates an artificial environment due to the control over variables .

Rogers emphasizes a more holistic approach to understanding behavior.

The cognitive approach uses a very scientific method that is controlled and replicable, so the results are reliable.

However, experiments lack ecological validity because of the artificiality of the tasks and environment, so they might not reflect the way people process information in their everyday lives.

For example, Baddeley (1966) used lists of words to find out the encoding used by LTM.

However, these words had no meaning to the participants, so the way they used their memory in this task was probably very different from what they would have done if the words had meaning for them.

This is a weakness, as the theories might not explain how memory works outside the laboratory.

4. Computer Analogy

The information processing paradigm of cognitive psychology views the minds in terms of a computer when processing information.

However, although there are similarities between the human mind and the operations of a computer (inputs and outputs, storage systems, and the use of a central processor), the computer analogy has been criticized.

For example, the human mind is characterized by consciousness, subjective experience, and self-awareness , which are not present in computers.

Computers do not have feelings, emotions, or a sense of self, which play crucial roles in human cognition and behavior.

The brain-computer metaphor is often used implicitly in neuroscience literature through terms like “sensory computation,” “algorithms,” and “neural codes.” However, it is difficult to identify these concepts in the actual brain.

5. Reductionist

The cognitive approach is reductionist as it does not consider emotions and motivation, which influence the processing of information and memory. For example, according to the Yerkes-Dodson law , anxiety can influence our memory.

Such machine reductionism (simplicity) ignores the influence of human emotion and motivation on the cognitive system and how this may affect our ability to process information.

Early theories of cognitive approach did not always recognize physical ( biological psychology ) and environmental (behaviorist approach) factors in determining behavior.

However, it’s important to note that modern cognitive psychology has evolved to incorporate a more holistic understanding of human cognition and behavior.

1. Importance of cognitive factors versus external events

Cognitive psychology emphasizes the role of internal cognitive processes in shaping emotional experiences, rather than solely focusing on external events.

Beck’s cognitive theory suggests that it is not the external events themselves that lead to depression, but rather the way an individual interprets and processes those events through their negative schemas.

This highlights the importance of addressing cognitive factors in the treatment of depression and other mental health issues.

Social exchange theory (Thibaut & Kelly, 1959) emphasizes that relationships are formed through internal mental processes, such as decision-making, rather than solely based on external factors.

The computer analogy can be applied to this concept, where individuals observe behaviors (input), process the costs and benefits (processing), and then make a decision about the relationship (output).

2. Interdisciplinary approach

While early cognitive psychology may have neglected physical and environmental factors, contemporary cognitive psychology has increasingly integrated insights from other approaches.

Cognitive psychology draws on methods and findings from other scientific disciplines, such as neuroscience , computer science, and linguistics, to inform their understanding of mental processes.

This interdisciplinary approach strengthens the scientific basis of cognitive psychology.

Cognitive psychology has influenced and integrated with many other approaches and areas of study to produce, for example, social learning theory , cognitive neuropsychology, and artificial intelligence (AI).

3. Real World Applications

Another strength is that the research conducted in this area of psychology very often has applications in the real world.

By highlighting the importance of cognitive processing, the cognitive approach can explain mental disorders such as depression.

Beck’s cognitive theory of depression argues that negative schemas about the self, the world, and the future are central to the development and maintenance of depression.

These negative schemas lead to biased processing of information, selective attention to negative aspects of experience, and distorted interpretations of events, which perpetuate the depressive state.

By identifying the role of cognitive processes in mental disorders, cognitive psychology has informed the development of targeted interventions.

Cognitive behavioral therapy aims to modify the maladaptive thought patterns and beliefs that underlie emotional distress, helping individuals to develop more balanced and adaptive ways of thinking.

CBT’s basis is to change how people process their thoughts to make them more rational or positive.

Through techniques such as cognitive restructuring, behavioral experiments, and guided discovery, CBT helps individuals to challenge and change their negative schemas, leading to improvements in mood and functioning.

Cognitive behavioral therapy (CBT) has been very effective in treating depression (Hollon & Beck, 1994), and moderately effective for anxiety problems (Beck, 1993). 

Issues and Debates

Free will vs. determinism.

The cognitive approach’s position is unclear. It argues that cognitive processes are influenced by experiences and schemas, which implies a degree of determinism.

On the other hand, cognitive-behavioral therapy (CBT) operates on the premise that individuals can change their thought patterns, suggesting a capacity for free will.

Nature vs. Nurture

The cognitive approach takes an interactionist view of the debate, acknowledging the influence of both nature and nurture on cognitive processes.

It recognizes that while some cognitive abilities, such as language acquisition, may have an innate component (nature), experiences and learning (nurture) also shape the way information is processed.

Holism vs. Reductionism

The cognitive approach tends to be reductionist in its methodology, as it often studies cognitive processes in isolation.

For example, researchers may focus on memory processes without considering the influence of other cognitive functions or environmental factors.

While this approach allows for more controlled study, it may lack ecological validity, as in real life, cognitive processes typically interact and function simultaneously.

Idiographic vs. Nomothetic

The cognitive approach is primarily nomothetic, as it seeks to establish general principles and theories of information processing that apply to all individuals.

It aims to identify universal patterns and mechanisms of cognition rather than focusing on individual differences.

History of Cognitive Psychology

• Wolfgang Köhler (1925) – Köhler’s book “The Mentality of Apes” challenged the behaviorist view by suggesting that animals could display insightful behavior, leading to the development of Gestalt psychology.
• Norbert Wiener (1948) – Wiener’s book “Cybernetics” introduced concepts such as input and output, which influenced the development of information processing models in cognitive psychology.
• Edward Tolman (1948) – Tolman’s work on cognitive maps in rats demonstrated that animals have an internal representation of their environment, challenging the behaviorist view.
• George Miller (1956) – Miller’s paper “The Magical Number 7 Plus or Minus 2” proposed that short-term memory has a limited capacity of around seven chunks of information, which became a foundational concept in cognitive psychology.
• Allen Newell and Herbert A. Simon (1972) – Newell and Simon developed the General Problem Solver, a computer program that simulated human problem-solving, contributing to the growth of artificial intelligence and cognitive modeling.
• George Miller and Jerome Bruner (1960) – Miller and Bruner established the Center for Cognitive Studies at Harvard, which played a significant role in the development of cognitive psychology as a distinct field.
• Ulric Neisser (1967) – Neisser’s book “Cognitive Psychology” formally established cognitive psychology as a separate area of study, focusing on mental processes such as perception, memory, and thinking.
• Richard Atkinson and Richard Shiffrin (1968) – Atkinson and Shiffrin proposed the Multi-Store Model of memory, which divided memory into sensory, short-term, and long-term stores, becoming a key model in the study of memory.
• Eleanor Rosch’s (1970s) research on natural categories and prototypes, which influenced the study of concept formation and categorization.
• Endel Tulving’s (1972) distinction between episodic and semantic memory, which further developed the understanding of long-term memory.
• Baddeley and Hitch’s (1974) proposal of the Working Memory Model, which expanded on the concept of short-term memory and introduced the idea of a central executive.
• Marvin Minsky’s (1975) framework of frames in artificial intelligence, which influenced the understanding of knowledge representation in cognitive psychology.
• David Rumelhart and Andrew Ortony’s (1977) work on schema theory, which described how knowledge is organized and used for understanding and remembering information.
• Amos Tversky and Daniel Kahneman’s (1970s-80s) research on heuristics and biases in decision making, which led to the development of behavioral economics and the study of judgment and decision-making.
• David Marr’s (1982) computational theory of vision, which provided a framework for understanding visual perception and influenced the field of computational cognitive science.
• The development of connectionism and parallel distributed processing (PDP) models in the 1980s, which provided an alternative to traditional symbolic models of cognitive processes.
• Noam Chomsky’s (1980s) theory of Universal Grammar and the language acquisition device, which influenced the study of language and cognitive development.
• The emergence of cognitive neuroscience in the 1990s, which combined techniques from cognitive psychology, neuroscience, and computer science to study the neural basis of cognitive processes.

Atkinson, R. C., & Shiffrin, R. M. (1968). Chapter: Human memory: A proposed system and its control processes. In Spence, K. W., & Spence, J. T. The psychology of learning and motivation (Volume 2). New York: Academic Press. pp. 89–195.

Baddeley, A. D., & Hitch, G. (1974). Working memory. In G. H. Bower (Ed.), The Psychology of Learning and Motivation: Advances in Research and Theory (Vol. 8, pp. 47-89). Academic Press.

Beck, A. T, & Steer, R. A. (1993). Beck Anxiety Inventory Manual. San Antonio: Harcourt Brace and Company.

Chomsky, N. (1986). Knowledge of Language: Its Nature, Origin, and Use . Praeger.

Gazzaniga, M. S. (Ed.). (1995). The Cognitive Neurosciences. MIT Press.

Hollon, S. D., & Beck, A. T. (1994). Cognitive and cognitive-behavioral therapies. In A. E. Bergin & S.L. Garfield (Eds.), Handbook of psychotherapy and behavior change (pp. 428—466) . New York: Wiley.

Köhler, W. (1925). An aspect of Gestalt psychology. The Pedagogical Seminary and Journal of Genetic Psychology, 32(4) , 691-723.

Marr, D. (1982). Vision: A Computational Investigation into the Human Representation and Processing of Visual Information . W. H. Freeman.

Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review , 63 (2): 81–97.

Minsky, M. (1975). A framework for representing knowledge. In P. H. Winston (Ed.), The Psychology of Computer Vision (pp. 211-277). McGraw-Hill.

Neisser, U (1967). Cognitive psychology . Appleton-Century-Crofts: New York

Newell, A., & Simon, H. (1972). Human problem solving . Prentice-Hall.

Rosch, E. H. (1973). Natural categories. Cognitive Psychology, 4 (3), 328-350.

Rumelhart, D. E., & McClelland, J. L. (1986). Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Volume 1: Foundations. MIT Press.

Rumelhart, D. E., & Ortony, A. (1977). The representation of knowledge in memory. In R. C. Anderson, R. J. Spiro, & W. E. Montague (Eds.), Schooling and the Acquisition of Knowledge (pp. 99-135). Erlbaum.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185 (4157), 1124-1131.

Thibaut, J., & Kelley, H. H. (1959). The social psychology of groups . New York: Wiley.

Tolman, E. C., Hall, C. S., & Bretnall, E. P. (1932). A disproof of the law of effect and a substitution of the laws of emphasis, motivation and disruption. Journal of Experimental Psychology, 15(6) , 601.

Tolman E. C. (1948). Cognitive maps in rats and men . Psychological Review. 55, 189–208

Tulving, E. (1972). Episodic and semantic memory. In E. Tulving & W. Donaldson (Eds.), Organization of Memory (pp. 381-403). Academic Press.

Wiener, N. (1948). Cybernetics or control and communication in the animal and the machine . Paris, (Hermann & Cie) & Camb. Mass. (MIT Press).

Further Reading

• Why Your Brain is Not a Computer
• Cognitive Psychology Historial Development

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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What Is the Cognitive Psychology Approach? 12 Key Theories

Maintaining focus on the oncoming traffic is paramount, yet I am barely aware of the seagulls flying overhead.

These noisy birds only receive attention when I am safely walking up the other side of the road, their cries reminding me of childhood seaside vacations.

Cognitive psychology focuses on the internal mental processes needed to make sense of the environment and decide on the next appropriate action (Eysenck & Keane, 2015).

This article explores the cognitive psychology approach, its origins, and several theories and models involved in cognition.

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This Article Contains:

What is the cognitive psychology approach, a brief history of cognitive psychology, cognitive psychology vs behaviorism, 12 key theories, concepts, and models, fascinating research experiments, a look at positive cognitive psychology, interesting resources from positivepsychology.com, a take-home message.

The upsurge of research into the mysteries of the human brain and mind has been considerable in recent decades, with recognition of the importance of cognitive process in clinical psychology and social psychology (Eysenck & Keane, 2015).

As a result, cognitive psychology has profoundly affected the field of psychology and our understanding of what it is to be human.

Perhaps more surprisingly, it has had such an effect without clear boundaries, an integrated set of assumptions and concepts, or a recognizable spokesperson (Gross, 2020).

So, what exactly is the cognitive psychology approach?

Cognitive psychology attempts to understand human cognition by focusing on what appear to be cognitive tasks that require little effort (Goldstein, 2011).

Let’s return to our example of walking down the road. Imagine now that we are also taking a call. We’re now combining several concurrent cognitive tasks:

• Perceiving the environment Distinguishing cars from traffic signals and discerning their direction and speed on the road as well as the people ahead standing, talking, and blocking the sidewalk.
• Paying attention Attending to what our partner is asking us on the phone, above the traffic noise.
• Visualizing Forming a mental image of items in the house, responding to the question, “Where did you leave your car keys?”
• Comprehending and producing language Understanding the real question (“I need to take the car. Where are your keys?”) from what is said and formulating a suitable reply.
• Problem-solving Working out how to get to the next appointment without the car.
• Decision-making Concluding that the timing of one meeting will not work and choosing to push it to another day.

While cognitive psychologists initially focused firmly on an analogy comparing the mind to a computer, their understanding has moved on.

There are currently four approaches, often overlapping and frequently combined, that science uses to understand human cognition (Eysenck & Keane, 2015):

• Cognitive psychology The attempt to “understand human cognition by using behavioral evidence” (Eysenck & Keane, 2015, p. 2).
• Cognitive neuropsychology Understanding ‘normal’ cognition through the study of patients living with a brain injury.
• Cognitive neuroscience Combining evidence from the brain with behavior to form a more complete picture of cognition.
• Computational cognitive science Using computational models to understand and test our understanding of human cognition.

Cognitive psychology plays a massive and essential role in understanding human cognition and is stronger because of its close relationships and interdependencies with other academic disciplines (Eysenck & Keane, 2015).

In 1868, a Dutch physiologist, Franciscus Donders, began to measure reaction time – something we would now see as an experiment in cognitive psychology (Goldstein, 2011).

Donders recognized that mental responses could not be measured directly but could be inferred from behavior. Not long after, Hermann Ebbinghaus began examining the nature and inner workings of human memory using nonsense syllables (Goldstein, 2011).

By the late 1800s, Wilhelm Wundt had set up the first laboratory dedicated to studying the mind scientifically. His approach became known as structuralism . His bold aim was to build a periodic table of the mind , containing all the sensations involved in creating any experience (Goldstein, 2011).

However, the use of analytical introspection to uncover hidden mental processes was gradually dropped when John Watson proposed a new psychological approach that became known as behaviorism (Goldstein, 2011).

Watson rejected the introspective approach and instead focused on observable behavior. His idea of classical conditioning – the connection of a new stimulus with a previously neutral one – was later surpassed by B. F. Skinner’s idea of operant conditioning , which focused on positive reinforcement (Goldstein, 2011).

Both theories sought to understand the relationship between stimulus and response rather than the mind’s inner workings (Goldstein, 2011).

Prompted by a scathing attack by linguist and cognitive scientist Noam Chomsky, by the 1950s behaviorism as the dominant psychological discipline was in decline. The introduction of the digital computer led to the information-processing approach , inspiring psychologists to think of the mind in terms of a sequence of processing stages (Goldstein, 2011).

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Moore (1996) recognized the tensions of the paradigm shift from behaviorism to cognitive psychology.

While research into cognitive psychology, cognitive neuropsychology, cognitive neuroscience, and computational cognitive science is now widely accepted as the driving force behind understanding mental processes (such as memory, perception, problem-solving, and attention), this was not always the case (Gross, 2020).

Moore (1996) highlighted the relationship between behaviorism and the relatively new field of cognitive psychology, and the sometimes mistaken assumptions regarding the nature of the former approach:

• Behaviorism is typically only associated with studying publicly observable behavior. Unlike behaviorism, cognitive psychology is viewed as free of the restrictions of logical positivism, which rely on verification through observation.

Since then, modern cognitive psychology has incorporated findings from many other disciplines, including evolutionary psychology, computer science, artificial intelligence , and neuroscience (Eysenck & Keane, 2015).

• Unlike behaviorism, cognitive psychology is theoretical and explanatory. Behaviorism is often considered merely descriptive, while cognitive psychology is seen as being able to explain what is behind behavior.

Particular ongoing advances in cognitive psychology include perception, language comprehension and production, and problem-solving (Eysenck & Keane, 2015).

• Behaviorism cannot incorporate theoretical terms. While challenged by some behaviorists at the time, it was argued that behaviorism could not incorporate theoretical terms unless related to directly observable behavior.

At the time, cognitive psychologists also argued that it was wrong of behaviorists to interpret mental states in terms of brain states.

Neuroscience advances, such as new imaging techniques like functional MRI, continue to offer fresh insights into the relationship between the brain and mental states (Eysenck & Keane, 2015).

Clearly, the relationship between behaviorism and the developing field of cognitive psychology has been complex. However, cognitive psychology has grown into a school of thought that has led to significant advances in understanding cognition, especially when teamed up with other developments in computing and neuroscience.

This may not have been possible without the shift in the dominant schools of thought in psychology (Gross, 2020; Goldstein, 2011; Eysenck & Keane, 2015).

And while it is beyond the scope of this article to cover the full breadth or depth of the areas of research, we list several of the most important and fascinating specialties and theories below.

It is hardly possible to imagine a world in which attention doesn’t play an essential role in how we interact with the environment, and yet, we rarely give it a thought.

According to cognitive psychology, attention is most active when driven by an individual’s expectations or goals, known as top-down processing . On the other hand, it is more passive when controlled by external stimuli, such as a loud noise, referred to as bottom-up processing (Eysenck & Keane, 2015).

A further distinction exists between focused attention (selective) and divided attention . Research into the former explores how we are able to focus on one item (noise, image, etc.) when there are several. In contrast, the latter looks at how we can maintain attention on two or more stimuli simultaneously.

Donald Broadbent proposed the bottleneck model to explain how we can attend to just one message when several are presented, for example, in dichotic listening experiments, where different auditory stimuli are presented to each ear. Broadbent’s model suggests multiple processing stages, each one progressively restricting the information flow (Goldstein, 2011).

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As with all other areas of cognition, perception is far more complicated than we might first imagine. Take, for example, vision. While a great deal of research has “involved presenting a visual stimulus and assessing aspects of its processing,” there is also the time aspect to consider (Eysenck & Keane, 2015, p. 121).

We need to not only perceive objects, but also make sense of their movement and detect changes in the visual environment over time (Eysenck & Keane, 2015).

Research suggests perception, like attention, combines bottom-up and top-down processing. Bottom-up processing involves neurons that fire in response to specific elements of an image – perhaps aspects of a face, nose, eyebrows, jawline, etc. Top-down processing considers how the knowledge someone brings with them affects their perception.

Bottom-down processing helps explain why two people, presented with the same stimuli, experience different perceptions as a result of their expectations and prior knowledge (Goldstein, 2011).

Combining bottom-up and top-down processing also enables the individual to make sense of both static and moving images when limited information is available; we can track a person walking through a crowd or a plane disappearing in and out of clouds (Eysenck & Keane, 2015).

The mirror neuron system is incredibly fascinating and is proving valuable in our attempts to understand biological motion. Observing actions activates similar areas of the brain as performing them. The model appears to explain how we can imitate the actions of another person – crucial to learning (Eysenck & Keane, 2015).

Language comprehension

Whether written or spoken, understanding language involves a high degree of multi-level processing (Eysenck & Keane, 2015).

Comprehension begins with an initial analysis of sentence structure (larger language units require additional processing). Beyond processing syntax (the rules for building and analyzing sentences), analysis of sentence meaning ( semantics ) is necessary to understand if the interpretation should be literal or involve irony, metaphor, or sarcasm (Eysenck & Keane, 2015).

Pragmatics examines intended meaning. For example, shouting, “That’s the doorbell!” is not likely to be a simple observation, but rather a request to answer the door (Eysenck & Keane, 2015).

Several models have been proposed to understand the analysis and comprehension of sentences, known as parsing , including (Eysenck & Keane, 2015):

• Garden-path model This model attempts to explain why some sentences are ambiguous (such as, “The horse raced past the barn fell.”). It suggests they are challenging to comprehend because the analysis is performed on each individual unit of the sentence with little feedback, and correction is inhibited.
• Constraint-based model The interpretations of a sentence may be limited by several constraints, including syntactic, semantic, and general world knowledge.
• Unrestricted race model This model combines the garden-path and constraint-based model, and suggests all sources of information inform syntactic structure. One such interpretation is selected until it is discarded, with good reason, for another.
• Good-enough representation This model proposes that parsing provides a ‘good-enough’ interpretation rather than something detailed, accurate, and complete.

The research and theories above hint at the vast complexity of human cognition and explain why so many models and concepts attempt to answer what happens when it works and, equally important, when it doesn’t.

A level of psychology: the cognitive approach – Atomi

There are many research experiments in cognitive psychology that highlight the successes and failings of human cognition. Each of the following three offers insight into the mental processes behind our thinking and behavior.

Cocktail party phenomenon

Selective attention – or in this case, selective listening – is often exemplified by what has become known as the cocktail party phenomenon  (Eysenck & Keane, 2015).

Even in a busy room and possibly mid-conversation, we can often hear if someone else mentions our name. It seems we can filter out surrounding noise by combining bottom-up and top-down processing to create a “winner takes it all” situation where the processing of one high-value auditory input suppresses the brain activity of all others (Goldstein, 2011).

While people may believe that the speed of hand movement allows magicians to trick us, research suggests the main factor is misdirection (Eysenck & Keane, 2015).

A 2010 study of a trick involving the disappearance of a lighter identified that when the lighter was dropped (to hide it from a later hand-opening finale), it was masked by directing attention from the fixation point – known as covert attention – with surprising effectiveness.

However, subjects were able to identify the drop when their attention was directed to the fixation point – known as overt attention (Kuhn & Findlay, 2010).

In a thought-provoking study exploring freewill, participants were asked to consciously decide whether to move their finger left or right while a functional MRI scanner monitored their prefrontal cortex and parietal cortex (Soon, Brass, Heinze, & Haynes, 2008).

Brain activity predicted the direction of movement a full seven seconds before they consciously became aware of their decision. While follow-up research has challenged some of the findings, it appears that brain activity may come before conscious thinking (Eysenck & Keane, 2015).

Associations have been found between positive emotions, creative thinking, and overall wellbeing, suggesting environmental changes that may benefit staff productivity and innovation in the workplace (Yuan, 2015).

Factors explored include creating climates geared toward creativity, boosting challenge, trust, freedom, risk taking, low conflict, and even the beneficial effects of humor.

Undoubtedly, further innovation will be seen from marrying the two powerful and compelling new fields of positive psychology and cognitive psychology.

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• Creating Savoring Rituals It’s possible to increase positive emotions by sharpening our sensory perceptions via savoring.

Learning to focus can help.

Step one – Identify everyday activities that bring you pleasure. Step two – Focus on experiencing pleasure as it happens when doing these activities.

At the end of the week, take some time to record your reflections on creating savoring rituals.

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Cognitive psychology is crucial in our search for understanding how we interact with and make sense of a constantly changing and potentially harmful environment.

Not only that, it offers insight into what happens when things go wrong and the likely impact on our wellbeing and ability to cope with life events.

Cognitive psychology’s strength is its willingness to embrace research findings from many other disciplines, combining them with existing psychological theory to create new models of cognition.

The tasks we appear to carry out unconsciously are a great deal more complex than they might first appear. Perception, attention, problem-solving, language comprehension and production, and decision-making often happen without intentional thought and yet have enormous consequences on our lives.

Use this article as a starting point to explore the many and diverse aspects of cognitive psychology. Consider their relationships with associated research fields and reflect on the importance of understanding cognition in helping clients overcome complex events or circumstances.

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

• Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
• Goldstein, E. B. (2011). Cognitive psychology . Wadsworth, Cengage Learning.
• Gross, R. D. (2020). Psychology: The science of mind and behaviour . Hodder and Stoughton.
• Kuhn, G., & Findlay, J. M. (2010). Misdirection, attention and awareness: Inattentional blindness reveals temporal relationship between eye movements and visual awareness. The Quarterly Journal of Experimental Psychology , 63 (1), 136–146.
• Moore, J. (1996). On the relation between behaviorism and cognitive psychology. Journal of Mind and Behavior , 17 (4), 345–367
• Soon, C. S., Brass, M., Heinze, H., & Haynes, J. (2008). Unconscious determinants of free decisions in the human brain. Nature Neuroscience , 11 (5), 543–545.
• Yuan, L. (2015). The happier one is, the more creative one becomes: An investigation on inspirational positive emotions from both subjective well-being and satisfaction at work. Psychology , 6 , 201–209.

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What our readers think.

As a widowed Mother and Grandmother, whom was recently told by an adult child that maybe I should have “cognitive” testing done, I found this article to be very informative and refreshing. Having the ability to read and and learn about cognitive psychology is interesting as their are so many ways our brains are affected from the time we are born until the time we reach each and every stage in life. I have spent time with my grandchildren who are from age 19 months, through 15 years old , and spend time with children who are 35, 34, and 32, and my parents who are 88 and 84. I appreciate your article and your time in writing it. Sincerely,

Cognitive Psychology creates & build human capacity to push physical and mental limits. My concept of cognition in human behavior was judged by the most time I met my lawyer or the doctor. Most of the time while listening a pause, oh I see and it is perpetual transition to see. Cognition emergence is very vital support as we see & perceive. My practices in engineering solution are base on my cognitive sensibilities.You article provokes the same perceptions. Thank you

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Cognitive psychologists study how people acquire, perceive, process and store information. This work can range from exploring how we learn language to understanding the interplay between cognition and emotion.

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Brain science and cognitive psychology is one of the most versatile psychological specialty areas today — and one of the most in demand. All professions have a compelling interest in how the brain works. Educators, curriculum designers, engineers, scientists, judges, public health and safety officials, architects and graphic designers all want to know more about how the brain processes information. Their research and its resulting applications have become an integral part of how organizations, schools and businesses function and succeed. In clinical settings, cognitive psychologists seek to treat issues related to human mental processes, including Alzheimer’s disease, speech issues, memory loss and sensory or perception difficulties.

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Analysing Complex Problem-Solving Strategies from a Cognitive Perspective: The Role of Thinking Skills

1 MTA-SZTE Digital Learning Technologies Research Group, Center for Learning and Instruction, University of Szeged, 6722 Szeged, Hungary

Gyöngyvér Molnár

2 MTA-SZTE Digital Learning Technologies Research Group, Institute of Education, University of Szeged, 6722 Szeged, Hungary; uh.degezs-u.yspde@ranlomyg

Associated Data

The data used to support the findings cannot be shared at this time as it also forms part of an ongoing study.

Complex problem solving (CPS) is considered to be one of the most important skills for successful learning. In an effort to explore the nature of CPS, this study aims to investigate the role of inductive reasoning (IR) and combinatorial reasoning (CR) in the problem-solving process of students using statistically distinguishable exploration strategies in the CPS environment. The sample was drawn from a group of university students (N = 1343). The tests were delivered via the eDia online assessment platform. Latent class analyses were employed to seek students whose problem-solving strategies showed similar patterns. Four qualitatively different class profiles were identified: (1) 84.3% of the students were proficient strategy users, (2) 6.2% were rapid learners, (3) 3.1% were non-persistent explorers, and (4) 6.5% were non-performing explorers. Better exploration strategy users showed greater development in thinking skills, and the roles of IR and CR in the CPS process were varied for each type of strategy user. To sum up, the analysis identified students’ problem-solving behaviours in respect of exploration strategy in the CPS environment and detected a number of remarkable differences in terms of the use of thinking skills between students with different exploration strategies.

1. Introduction

Problem solving is part and parcel of our daily activities, for instance, in determining what to wear in the morning, how to use our new electronic devices, how to reach a restaurant by public transport, how to arrange our schedule to achieve the greatest work efficiency and how to communicate with people in a foreign country. In most cases, it is essential to solve the problems that recur in our study, work and daily lives. These situations require problem solving. Generally, problem solving is the thinking that occurs if we want “to overcome barriers between a given state and a desired goal state by means of behavioural and/or cognitive, multistep activities” ( Frensch and Funke 1995, p. 18 ). It has also been considered as one of the most important skills for successful learning in the 21st century. This study focuses on one specific kind of problem solving, complex problem solving (CPS). (Numerous other terms are also used ( Funke et al. 2018 ), such as interactive problem solving ( Greiff et al. 2013 ; Wu and Molnár 2018 ), and creative problem solving ( OECD 2010 ), etc.).

CPS is a transversal skill ( Greiff et al. 2014 ), operating several mental activities and thinking skills (see Molnár et al. 2013 ). In order to explore the nature of CPS, some studies have focused on detecting its component skills ( Wu and Molnár 2018 ), whereas others have analysed students’ behaviour during the problem-solving process ( Greiff et al. 2018 ; Wu and Molnár 2021 ). This study aims to link these two fields by investigating the role of thinking skills in learning by examining students’ use of statistically distinguishable exploration strategies in the CPS environment.

1.1. Complex Problem Solving: Definition, Assessment and Relations to Intelligence

According to a widely accepted definition proposed by Buchner ( 1995 ), CPS is “the successful interaction with task environments that are dynamic (i.e., change as a function of users’ intervention and/or as a function of time) and in which some, if not all, of the environment’s regularities can only be revealed by successful exploration and integration of the information gained in that process” ( Buchner 1995, p. 14 ). A CPS process is split into two phases, knowledge acquisition and knowledge application. In the knowledge acquisition (KAC) phase of CPS, the problem solver understands the problem itself and stores the acquired information ( Funke 2001 ; Novick and Bassok 2005 ). In the knowledge application (KAP) phase, the problem solver applies the acquired knowledge to bring about the transition from a given state to a goal state ( Novick and Bassok 2005 ).

Problem solving, especially CPS, has frequently been compared or linked to intelligence in previous studies (e.g., Beckmann and Guthke 1995 ; Stadler et al. 2015 ; Wenke et al. 2005 ). Lotz et al. ( 2017 ) observed that “intelligence and [CPS] are two strongly overlapping constructs” (p. 98). There are many similarities and commonalities that can be detected between CPS and intelligence. For instance, CPS and intelligence share some of the same key features, such as the integration of information ( Stadler et al. 2015 ). Furthermore, Wenke et al. ( 2005 ) stated that “the ability to solve problems has featured prominently in virtually every definition of human intelligence” (p. 9); meanwhile, from the opposite perspective, intelligence has also been considered as one of the most important predictors of the ability to solve problems ( Wenke et al. 2005 ). Moreover, the relation between CPS and intelligence has also been discussed from an empirical perspective. A meta-analysis conducted by Stadler et al. ( 2015 ) selected 47 empirical studies (total sample size N = 13,740) which focused on the correlation between CPS and intelligence. The results of their analysis confirmed that a correlation between CPS and intelligence exists with a moderate effect size of M(g) = 0.43.

Due to the strong link between CPS and intelligence, assessments of these two domains have been connected and have overlapped to a certain extent. For instance, Beckmann and Guthke ( 1995 ) observed that some of the intelligence tests “capture something akin to an individual’s general ability to solve problems (e.g., Sternberg 1982 )” (p. 184). Nowadays, some widely used CPS assessment methods are related to intelligence but still constitute a distinct construct ( Schweizer et al. 2013 ), such as the MicroDYN approach ( Greiff and Funke 2009 ; Greiff et al. 2012 ; Schweizer et al. 2013 ). This approach uses the minimal complex system to simulate simplistic, artificial but still complex problems following certain construction rules ( Greiff and Funke 2009 ; Greiff et al. 2012 ).

The MicroDYN approach has been widely employed to measure problem solving in a well-defined problem context (i.e., “problems have a clear set of means for reaching a precisely described goal state”, Dörner and Funke 2017, p. 1 ). To complete a task based on the MicroDYN approach, the problem solver engages in dynamic interaction with the task to acquire relevant knowledge. It is not possible to create this kind of test environment with the traditional paper-and-pencil-based method. Therefore, it is currently only possible to conduct a MicroDYN-based CPS assessment within the computer-based assessment framework. In the context of computer-based assessment, the problem-solvers’ operations were recorded and logged by the assessment platform. Thus, except for regular achievement-focused result data, logfile data are also available for analysis. This provides the option of exploring and monitoring problem solvers’ behaviour and thinking processes, specifically, their exploration strategies, during the problem-solving process (see, e.g., Chen et al. 2019 ; Greiff et al. 2015a ; Molnár and Csapó 2018 ; Molnár et al. 2022 ; Wu and Molnár 2021 ).

Problem solving, in the context of an ill-defined problem (i.e., “problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear”, Dörner and Funke 2017, p. 1), involved a different cognitive process than that in the context of a well-defined problem ( Funke 2010 ; Schraw et al. 1995 ), and it cannot be measured with the MicroDYN approach. The nature of ill-defined problem solving has been explored and discussed in numerous studies (e.g., Dörner and Funke 2017 ; Hołda et al. 2020 ; Schraw et al. 1995 ; Welter et al. 2017 ). This will not be discussed here as this study focuses on well-defined problem solving.

1.2. Inductive and Combinatorial Reasoning as Component Skills of Complex Problem Solving

Frensch and Funke ( 1995 ) constructed a theoretical framework that summarizes the basic components of CPS and the interrelations among the components. The framework contains three separate components: problem solver, task and environment. The impact of the problem solver is mainly relevant to three main categories, which are memory contents, dynamic information processing and non-cognitive variables. Some thinking skills have been reported to play an important role in dynamic information processing. We can thus describe them as component skills of CPS. Inductive reasoning (IR) and combinatorial reasoning (CR) are the two thinking skills that have been most frequently discussed as component skills of CPS.

IR is the reasoning skill that has been covered most commonly in the literature. Currently, there is no universally accepted definition. Molnár et al. ( 2013 ) described it as the cognitive process of acquiring general regularities by generalizing single and specific observations and experiences, whereas Klauer ( 1990 ) defined it as the discovery of regularities that relies upon the detection of similarities and/or dissimilarities as concerns attributes of or relations to or between objects. Sandberg and McCullough ( 2010 ) provided a general conclusion of the definitions of IR: it is the process of moving from the specific to the general.

Csapó ( 1997 ) pointed out that IR is a basic component of thinking and that it forms a central aspect of intellectual functioning. Some studies have also discussed the role of IR in a problem-solving environment. For instance, Mayer ( 1998 ) stated that IR will be applied in information processing during the process of solving general problems. Gilhooly ( 1982 ) also pointed out that IR plays a key role in some activities in the problem-solving process, such as hypothesis generation and hypothesis testing. Moreover, the influence of IR on both KAC and KAP has been analysed and demonstrated in previous studies ( Molnár et al. 2013 ).

Empirical studies have also provided evidence that IR and CPS are related. Based on the results of a large-scale assessment (N = 2769), Molnár et al. ( 2013 ) showed that IR significantly correlated with 9–17-year-old students’ domain-general problem-solving achievement (r = 0.44–0.52). Greiff et al. ( 2015b ) conducted a large-scale assessment project (N = 2021) in Finland to explore the links between fluid reasoning skills and domain-general CPS. The study measured fluid reasoning as a two-dimensional model which consisted of deductive reasoning and scientific reasoning and included inductive thinking processes ( Greiff et al. 2015b ). The results drawing on structural equation modelling indicated that fluid reasoning which was partly based on IR had significant and strong predictive effects on both KAC (β = 0.51) and KAP (β = 0.55), the two phases of problem solving. Such studies have suggested that IR is one of the component skills of CPS.

According to Adey and Csapó ’s ( 2012 ) definition, CR is the process of creating complex constructions out of a set of given elements that satisfy the conditions explicitly given in or inferred from the situation. In this process, some cognitive operations, such as combinations, arrangements, permutations, notations and formulae, will be employed ( English 2005 ). CR is one of the basic components of formal thinking ( Batanero et al. 1997 ). The relationship between CR and CPS has frequently been discussed. English ( 2005 ) demonstrated that CR has an essential meaning in several types of problem situations, such as problems requiring the systematic testing of alternative solutions. Moreover, Newell ( 1993 ) pointed out that CR is applied in some key activities of problem-solving information processing, such as strategy generation and application. Its functions include, but are not limited to, helping problem solvers to discover relationships between certain elements and concepts, promoting their fluency of thinking when they are considering different strategies ( Csapó 1999 ) and identifying all possible alternatives ( OECD 2014 ). Moreover, Wu and Molnár ’s ( 2018 ) empirical study drew on a sample (N = 187) of 11–13-year-old primary school students in China. Their study built a structural equation model between CPS, IR and CR, and the result indicated that CR showed a strong and statistically significant predictive power for CPS (β = 0.55). Thus, the results of the empirical study also support the argument that CR is one of the component skills of CPS.

1.3. Behaviours and Strategies in a Complex Problem-Solving Environment

Wüstenberg et al. ( 2012 ) stated that the creation and implementation of strategic exploration are core actions of the problem-solving task. Exploring and generating effective information are key to successfully solving a problem. Wittmann and Hattrup ( 2004 ) illustrated that “riskier strategies [create] a learning environment with greater opportunities to discover and master the rules and boundaries [of a problem]” (p. 406). Thus, when gathering information about a complex problem, there may be differences between exploration strategies in terms of efficacy. The MicroDYN scenarios, a simplification and simulation of the real-world problem-solving context, will also be influenced by the adoption and implementation of exploration strategies.

The effectiveness of the isolated variation strategy (or “Vary-One-Thing-At-A-Time” strategy—VOTAT; Vollmeyer et al. 1996 ) in a CPS environment has been hotly debated ( Chen et al. 2019 ; Greiff et al. 2018 ; Molnár and Csapó 2018 ; Molnár et al. 2022 ; Wu and Molnár 2021 ; Wüstenberg et al. 2014 ). To use the VOTAT strategy, a problem solver “systematically varies only one input variable, whereas the others remain unchanged. This way, the effect of the variable that has just been changed can be observed directly by monitoring the changes in the output variables” ( Molnár and Csapó 2018, p. 2 ). Understanding and using VOTAT effectively is the foundation for developing more complex strategies for coordinating multiple variables and the basis for some phases of scientific thinking (i.e., inquiry, analysis, inference and argument; Kuhn 2010 ; Kuhn et al. 1995 ).

Some previous studies have indicated that students who are able to apply VOTAT are more likely to achieve higher performance in a CPS assessment ( Greiff et al. 2018 ), especially if the problem is a well-defined minimal complex system (such as MicroDYN) ( Fischer et al. 2012 ; Molnár and Csapó 2018 ; Wu and Molnár 2021 ). For instance, Molnár and Csapó ( 2018 ) conducted an empirical study to explore how students’ exploration strategies influence their performance in an interactive problem-solving environment. They measured a group (N = 4371) of 3rd- to 12th-grade (aged 9–18) Hungarian students’ problem-solving achievement and modelled students’ exploration strategies. This result confirmed that students’ exploration strategies influence their problem-solving performance. For example, conscious VOTAT strategy users proved to be the best problem-solvers. Furthermore, other empirical studies (e.g., Molnár et al. 2022 ; Wu and Molnár 2021 ) achieved similar results, thus confirming the importance of VOTAT in a MicroDYN-based CPS environment.

Lotz et al. ( 2017 ) illustrated that effective use of VOTAT is associated with higher levels of intelligence. Their study also pointed out that intelligence has the potential to facilitate successful exploration behaviour. Reasoning skills are an important component of general intelligence. Based on Lotz et al. ’s ( 2017 ) statements, the roles IR and CR play in the CPS process might vary due to students’ different strategy usage patterns. However, there is still a lack of empirical studies in this regard.

2. Research Aims and Questions

Numerous studies have explored the nature of CPS, some of them discussing and analysing it from behavioural or cognitive perspectives. However, there have barely been any that have merged these two perspectives. From the cognitive perspective, this study explores the role of thinking skills (including IR and CR) in the cognition process of CPS. From the behavioural perspective, the study focuses on students’ behaviour (i.e., their exploration strategy) in the CPS assessment process. More specifically, the research aims to fill this gap and examine students’ use of statistically distinguishable exploration strategies in CPS environments and to detect the connection between the level of students’ thinking skills and their behaviour strategies in the CPS environment. The following research questions were thus formed.

• (RQ1) What exploration strategy profiles characterise the various problem-solvers at the university level?
• (RQ2) Can developmental differences in CPS, IR and CR be detected among students with different exploration strategy profiles?
• (RQ3) What are the similarities and differences in the roles IR and CR play in the CPS process as well as in the two phases of CPS (i.e., KAC and KAP) among students with different exploration strategy profiles?

3.1. Participants and Procedure

The sample was drawn from one of the largest universities in Hungary. Participation was voluntary, but students were able to earn one course credit for taking part in the assessment. The participants were students who had just started their studies there (N = 1671). 43.4% of the first-year students took part in the assessment. 50.9% of the participants were female, and 49.1% were male. We filtered the sample and excluded those who had more than 80% missing data on any of the tests. After the data were cleaned, data from 1343 students were available for analysis. The test was designed and delivered via the eDia online assessment system ( Csapó and Molnár 2019 ). The assessment was held in the university ICT room and divided into two sessions. The first session involved the CPS test, whereas the second session entailed the IR and CR tests. Each session lasted 45 min. The language of the tests was Hungarian, the mother tongue of the students.

3.2. Instruments

3.2.1. complex problem solving (cps).

The CPS assessment instrument adopted the MicroDYN approach. It contains a total of twelve scenarios, and each scenario consisted of two items (one item in the KAC phase and one item in the KAP phase in each problem scenario). Twelve KAC items and twelve KAP items were therefore delivered on the CPS test for a total of twenty-four items. Each scenario has a fictional cover story. For instance, students found a sick cat in front of their house, and they were expected to feed the cat with two different kinds of cat food to help it recover.

Each item contains up to three input and three output variables. The relations between the input and output variables were formulated with linear structural equations ( Funke 2001 ). Figure 1 shows a MicroDYN sample structure containing three input variables (A, B and C), three output variables (X, Y and Z) and a number of possible relations between the variables. The complexity of the item was defined by the number of input and output variables, and the number of relations between the variables. The test began with the item with the lowest complexity. The complexity of each item gradually increased as the test progressed.

A typical MicroDYN structure with three input variables and three output variables ( Greiff and Funke 2009 ).

The interface of each item displays the value of each variable in both numerical and figural forms (See Figure 2 ). Each of the input variables has a controller, which makes it possible to vary and set the value between +2 (+ +) and −2 (− −). To operate the system, students need to click the “+” or “−” button or use the slider directly to select the value they want to be added to or subtracted from the current value of the input variable. After clicking the “Apply” button in the interface, the input variables will add or subtract the selected value, and the output variables will show the corresponding changes. The history of the values for the input and output variables within the same problem scenario is displayed on screen. If students want to withdraw all the changes and set all the variables to their original status, they can click the “Reset” button.

Screenshot of the MicroDYN item Cat—first phase (knowledge acquisition). (The items were administered in Hungarian.)

In the first phase of the problem-solving process, the KAC phase, students are asked to interact with the system by changing the value of the input variables and observing and analysing the corresponding changes in the output variables. They are then expected to determine the relationship between the input and output variables and draw it in the form of (an) arrow(s) on the concept map at the bottom of the interface. To avoid item dependence in the second phase of the problem-solving process, the students are provided with a concept map during the KAP phase (see Figure 3 ), which shows the correct connections between the input and output variables. The students are expected to interact with the system by manipulating the input variables to make the output variables reach the given target values in four steps or less. That is, they cannot click on the “Apply” button more than four times. The first phase had a 180 s time limit, whereas the second had a 90 s time limit.

Screenshot of the MicroDYN item Cat—second phase (knowledge application). (The items were administered in Hungarian).

3.2.2. Inductive Reasoning (IR)

The IR instrument (see Figure 4 ) was originally designed and developed in Hungary ( Csapó 1997 ). In the last 25 years, the instrument has been further developed and scaled for a wide age range ( Molnár and Csapó 2011 ). In addition, figural items have been added, and the assessment method has evolved from paper-and-pencil to computer-based ( Pásztor 2016 ). Currently, the instrument is widely employed in a number of countries (see, e.g., Mousa and Molnár 2020 ; Pásztor et al. 2018 ; Wu et al. 2022 ; Wu and Molnár 2018 ). In the present study, four types of items were included after test adaptation: figural series, figural analogies, number analogies and number series. Students were expected to ascertain the correct relationship between the given figures and numbers and select a suitable figure or number as their answer. Students used the drag-and-drop operation to provide their answers. In total, 49 inductive reasoning items were delivered to the participating students.

Sample items for the IR test. (The items were administered in Hungarian.).

3.2.3. Combinatorial Reasoning (CR)

The CR instrument (see Figure 5 ) was originally designed by Csapó ( 1988 ). The instrument was first developed in paper-and-pencil format and then modified for computer use ( Pásztor and Csapó 2014 ). Each item contained figural or verbal elements and a clear requirement for combing through the elements. Students were asked to list every single combination based on a given rule they could find. For the figural items, students provided their answers using the drag-and-drop operation; for the verbal items, they were asked to type their answers in a text box provided on screen. The test consisted of eight combinatorial reasoning items in total.

Sample item for the CR test. (The items were administered in Hungarian).

3.3. Scoring

Students’ performance was automatically scored via the eDia platform. Items on the CPS and IR tests were scored dichotomously. In the first phase (KAC) of the CPS test, if a student drew all the correct relations on the concept map provided on screen within the given timeframe, his/her performance was assigned a score of 1 or otherwise a score of 0. In the second phase (KAP) of the CPS test, if the student successfully reached the given target values of the output variables by manipulating the level of the input variables within no more than four steps and the given timeframe, then his/her performance earned a score of 1 or otherwise a score of 0. On the IR test items, if a student selected the correct figure or number as his/her answer, then he or she received a score of 1; otherwise, the score was 0.

Students’ performance on the CR test items was scored according to a special J index, which was developed by Csapó ( 1988 ). The J index ranges from 0 to 1, where 1 means that the student provided all the correct combinations without any redundant combinations on the task. The formula for computing the J index is the following:

x stands for the number of correct combinations in the student’s answer,

T stands for the number of all possible correct combinations, and

y stands for the number of redundant combinations in the student’s answer.

Furthermore, according to Csapó ’s ( 1988 ) design, if y is higher than T, then the J index will be counted as 0.

3.4. Coding and Labelling the Logfile Data

Beyond concrete answer data, students’ interaction and manipulation behaviour were also logged in the assessment system. This made it possible to analyse students’ exploration behaviour in the first phase of the CPS process (KAC phase). Toward this aim, we adopted a labelling system developed by Molnár and Csapó ( 2018 ) to transfer the raw logfile data to structured data files for analysis. Based on the system, each trial (i.e., the sum of manipulations within the same problem scenario which was applied and tested by clicking the “Apply” button) was modelled as a single data entity. The sum of these trials within the same problem was defined as a strategy. In our study, we only consider the trials which were able to provide useful and new information for the problem-solvers, whereas the redundant or operations trials were excluded.

In this study, we analysed students’ trials to determine the extent to which they used the VOTAT strategy: fully, partially or not at all. This strategy is the most successful exploration strategy for such problems; it is the easiest to interpret and provides direct information about the given variable without any mediation effects ( Fischer et al. 2012 ; Greiff et al. 2018 ; Molnár and Csapó 2018 ; Wüstenberg et al. 2014 ; Wu and Molnár 2021 ). Based on the definition of VOTAT noted in Section 1.3 , we checked students’ trials to ascertain if they systematically varied one input variable while keeping the others unchanged, or applied a different, less successful strategy. We considered the following three types of trials:

• “Only one single input variable was manipulated, whose relationship to the output variables was unknown (we considered a relationship unknown if its effect cannot be known from previous settings), while the other variables were set at a neutral value like zero […]
• One single input variable was changed, whose relationship to the output variables was unknown. The others were not at zero, but at a setting used earlier. […]
• One single input variable was changed, whose relationship to the output variables was unknown, and the others were not at zero; however, the effect of the other input variable(s) was known from earlier settings. Even so, this combination was not attempted earlier” ( Molnár and Csapó 2018, p. 8 )

We used the numbers 0, 1 and 2 to distinguish the level of students’ use of the most effective exploration strategy (i.e., VOTAT). If a student applied one or more of the above trials for every input variable within the same scenario, we considered that they had used the full VOTAT strategy and labelled this behaviour 2. If a student had only employed VOTAT on some but not all of the input variables, we concluded that they had used a partial VOTAT strategy for that problem scenario and labelled it 1. If a student had used none of the trials noted above in their problem exploration, then we determined that they had not used VOTAT at all and thus gave them a label of 0.

3.5. Data Analysis Plan

We used LCA (latent class analysis) to explore students’ exploration strategy profiles. LCA is a latent variable modelling approach that can be used to identify unmeasured (latent) classes of samples with similarly observed variables. LCA has been widely used in analysing logfile data for CPS assessment and in exploring students’ behaviour patterns (see, e.g., Gnaldi et al. 2020 ; Greiff et al. 2018 ; Molnár et al. 2022 ; Molnár and Csapó 2018 ; Mustafić et al. 2019 ; Wu and Molnár 2021 ). The scores for the use of VOTAT in the KAC phase (0, 1, 2; see Section 3.4 ) were used for the LCA analysis. We used Mplus ( Muthén and Muthén 2010 ) to run the LCA analysis. Several indices were used to measure the model fit: AIC (Akaike information criterion), BIC (Bayesian information criterion) and aBIC (adjusted Bayesian information criterion). With these three indicators, lower values indicate a better model fit. Entropy (ranging from 0 to 1, with values close to 1 indicating high certainty in the classification). The Lo–Mendell–Rubin adjusted likelihood ratio was used to compare the model containing n latent classes with the model containing n − 1 latent classes, and the p value was the indicator for whether a significant difference could be detected ( Lo et al. 2001 ). The results of the Lo–Mendell–Rubin adjusted likelihood ratio analysis were used to decide the correct number of latent classes in LCA models.

ANOVA was used to analyse the performance differences for CPS, IR and CR across the students from the different class profiles. The analysis was run using SPSS. A path analysis (PA) was employed in the structural equation modelling (SEM) framework to investigate the roles of CR and IR in CPS and the similarities and differences across the students from the different exploration strategy profiles. The PA models were carried out with Mplus. The Tucker–Lewis index (TLI), the comparative fit index (CFI) and the root-mean-square error of approximation (RMSEA) were used as indicators for the model fit. A TLI and CFI larger than 0.90 paired with a RMSEA less than 0.08 are commonly considered as an acceptable model fit ( van de Schoot et al. 2012 ).

4.1. Descriptive Results

All three tests showed good reliability (Cronbach’s α: CPS: 0.89; IR: 0.87; CR: 0.79). Furthermore, the two sub-dimensions of the CPS test, KAC and KAP, also showed satisfactory reliability (Cronbach’s α: KAC: 0.86; KAP: 0.78). The tests thus proved to be reliable. The means and standard deviations of students’ performance (in percentage) on each test are provided in Table 1 .

The means and standard deviations of students’ performance on each test.

4.2. Four Qualitatively Different Exploration Strategy Profiles Can Be Distinguished in CPS

Based on the labelled logfile data for CPS, we applied latent class analyses to identify the behaviour patterns of the students in the exploration phase of the problem-solving process. The model fits for the LCA analysis are listed in Table 2 . Compared with the 2 or 3 latent class models, the 4 latent class model has a lower AIC, BIC and aBIC, and the likelihood ratio statistical test (the Lo–Mendell–Rubin adjusted likelihood ratio test) confirmed it has a significantly better model fit. The 5 and 6 latent class models did not show a better model fit than the 4 latent class model. Therefore, based on the results, four qualitatively different exploration strategy profiles can be distinguished, which covered 96% of the students.

Fit indices for latent class analyses.

The patterns for the four qualitatively different exploration strategy profiles are shown in Figure 6 . In total, 84.3% of the students were proficient exploration strategy users, who were able to use VOTAT in each problem scenario independent of its difficulty level (represented by the red line in Figure 5 ). In total, 6.2% of the students were rapid learners. They were not able to apply VOTAT at the beginning of the test on the easiest problems but managed to learn quickly, and, after a rapid learning curve by the end of the test, they reached the level of proficient exploration strategy users, even though the problems became much more complex (represented by the blue line). In total, 3.1% of the students proved to be non-persistent explorers, and they employed VOTAT on the easiest problems but did not transfer this knowledge to the more complex problems. Finally, they were no longer able to apply VOTAT when the complexity of the problems increased (represented by the green line). In total, 6.5% of the students were non-performing explorers; they barely used any VOTAT strategy during the whole test (represented by the pink line) independent of problem complexity.

Four qualitatively different exploration strategy profiles.

4.3. Better Exploration Strategy Users Showed Better Performance in Reasoning Skills

Students with different exploration strategy profiles showed different kinds of performance in each reasoning skill under investigation. Results (see Table 3 ) showed that more proficient strategy users tended to have higher achievement in all the domains assessed as well as in the two sub-dimensions in CPS (i.e., KAC and KAP; ANOVA: CPS: F(3, 1339) = 187.28, p < 0.001; KAC: F(3, 1339) = 237.15, p < 0.001; KAP: F(3, 1339) = 74.91, p < 0.001; IR: F(3, 1339) = 48.10, p < 0.001; CR: F(3, 1339) = 28.72, p < 0.001); specifically, students identified as “proficient exploration strategy users” achieved the highest level on the reasoning skills tests independent of the domains. On average, they were followed by rapid learners, non-persistent explorers and, finally, non-performing explorers. Tukey’s post hoc tests revealed more details on the performance differences of students with different exploration profiles in each of the domains being measured. Proficient strategy users proved to be significantly more skilled in each of the reasoning domains. They were followed by rapid learners, who outperformed non-persistent explorers and non-performing explorers in CPS. In the domains of IR and CR, there were no achievement differences between rapid learners and non-persistent explorers, who significantly outperformed non-performing strategy explorers.

Students’ performance on each test—grouped according to the different exploration strategy profiles.

4.4. The Roles of IR and CR in CPS and Its Processes Were Different for Each Type of Exploration Strategy User

Path analysis was used to explore the predictive power of IR and CR for CPS and its processes, knowledge acquisition and knowledge application, for each group of students with different exploration strategy profiles. That is, four path analysis models were built to indicate the predictive power of IR and CR for CPS (see Figure 7 ), and another four path analyses models were developed to monitor the predictive power of IR and CR for the two empirically distinguishable phases of CPS (i.e., KAC and KAP) (see Figure 8 ). All eight models had good model fits, the fit indices TLI and CFI were above 0.90, and RMSEA was less than 0.08.

Path analysis models (with CPS, IR and CR) for each type of strategy user; * significant at 0.05 ( p   <  0.05); ** significant at 0.01 ( p   <  0.01); N.S.: no significant effect can be found.

Path analysis models (with KAC, KAP, IR and CR) for each type of strategy user; * significant at 0.05 ( p  <  0.05); ** significant at 0.01 ( p  <  0.01); N.S.: no significant effect can be found.

Students’ level of IR significantly predicted their level of CPS in all four path analysis models independent of their exploration strategy profile ( Figure 7 ; proficient strategy users: β = 0.432, p < 0.01; rapid learners: β = 0.350, p < 0.01; non-persistent explorers: β = 0.309, p < 0.05; and non-performing explorers: β = 0.386, p < 0.01). This was not the case for CR, which only proved to have predictive power for CPS among proficient strategy users (β = 0.104, p < 0.01). IR and CR were significantly correlated in all four models.

After examining the roles of IR and CR in the CPS process, we went further to explore the roles of these two reasoning skills in the distinguishable phases of CPS. The path analysis models ( Figure 8 ) showed that the predictive power of IR and CR for KAC and KAP was varied in each group. Levels of IR and CR among non-persistent explorers and non-performing explorers failed to predict their achievement in the KAC phase of the CPS process. Moreover, rapid learners’ level of IR significantly predicted their achievement in the KAC phase (β = 0.327, p < 0.01), but their level of CR did not have the same predictive power. Furthermore, the proficient strategy users’ levels of both reasoning skills had significant predictive power for KAC (IR: β = 0.363, p < 0.01; CR: β = 0.132, p < 0.01). In addition, in the KAP phase of the CPS problems, IR played a significant role for all types of strategy users, although with different power (proficient strategy users: β = 0.408, p < 0.01; rapid learners: β = 0.339, p < 0.01; non-persistent explorers: β = 0.361, p < 0.01; and non-performing explorers: β = 0.447, p < 0.01); by contrast, CR did not have significant predictive power for the KAP phase in any of the models.

5. Discussion

The study aims to investigate the role of IR and CR in CPS and its phases among students using statistically distinguishable exploration strategies in different CPS environments. We examined 1343 Hungarian university students and assessed their CPS, IR and CR skills. Both achievement data and logfile data were used in the analysis. The traditional achievement indicators formed the foundation for analysing the students’ CPS, CR and IR performance, whereas process data extracted from logfile data were used to explore students’ exploration behaviour in various CPS environments.

Four qualitatively different exploration strategy profiles were distinguished: proficient strategy users, rapid learners, non-persistent explorers and non-performing explorers (RQ1). The four profiles were consistent with the result of another study conducted at university level (see Molnár et al. 2022 ), and the frequencies of these four profiles in these two studies were very similar. The two studies therefore corroborate and validate each other’s results. The majority of the participants were identified as proficient strategy users. More than 80% of the university students were able to employ effective exploration strategies in various CPS environments. Of the remaining students, some performed poorly in exploration strategy use in the early part of the test (rapid learners), some in the last part (non-persistent explorers) and some throughout the test (non-performing explorers). However, students with these three exploration strategy profiles only constituted small portions of the total sample (with proportions ranging from 3.1% to 6.5%). The university students therefore exhibited generally good performance in terms of exploration strategy use in a CPS environment, especially compared with previous results among younger students (e.g., primary school students, see Greiff et al. 2018 ; Wu and Molnár 2021 ; primary to secondary students, see Molnár and Csapó 2018 ).

The results have indicated that better exploration strategy users achieved higher CPS performance and had better development levels of IR and CR (RQ2). First, the results have confirmed the importance of VOTAT in a CPS environment. This finding is consistent with previous studies (e.g., Greiff et al. 2015a ; Molnár and Csapó 2018 ; Mustafić et al. 2019 ; Wu and Molnár 2021 ). Second, the results have confirmed that effective use of VOTAT is strongly tied to the level of IR and CR development. Reasoning forms an important component of human intelligence, and the level of development in reasoning was an indicator of the level of intelligence ( Klauer et al. 2002 ; Sternberg and Kaufman 2011 ). Therefore, this finding has supplemented empirical evidence for the argument that effective use of VOTAT is associated with levels of intelligence to a certain extent.

The roles of IR and CR proved to be varied for each type of exploration strategy user (RQ3). For instance, the level of CPS among the best exploration strategy users (i.e., the proficient strategy users) was predicted by both the levels of IR and CR, but this was not the case for students with other profiles. In addition, the results have indicated that IR played important roles in both the KAC and KAP phases for the students with relatively good exploration strategy profiles (i.e., proficient strategy users and rapid learners) but only in the KAP phase for the rest of the students (non-persistent explorers and non-performing explorers); moreover, the predictive power of CR can only be detected in the KAC phase of the proficient strategy users. To sum up, the results suggest a general trend of IR and CR playing more important roles in the CPS process among better exploration strategy users.

Combining the answers to RQ2 and RQ3, we can gain further insights into students’ exploration strategy use in a CPS environment. Our results have confirmed that the use of VOTAT is associated with the level of IR and CR development and that the importance of IR and CR increases with proficiency in exploration strategy use. Based on these findings, we can make a reasonable argument that IR and CR are essential skills for using VOTAT and that underdeveloped IR and CR will prevent students from using effective strategies in a CPS environment. Therefore, if we want to encourage students to become better exploration strategy users, it is important to first enhance their IR and CR skills. Previous studies have suggested that establishing explicit training in using effective strategies in a CPS environment is important for students’ CPS development ( Molnár et al. 2022 ). Our findings have identified the importance of IR and CR in exploration strategy use, which has important implications for designing training programmes.

The results have also provided a basis for further studies. Future studies have been suggested to further link the behavioural and cognitive perspectives in CPS research. For instance, IR and CR were considered as component skills of CPS (see Section 1.2 ). The results of the study have indicated the possibility of not only discussing the roles of IR and CR in the cognitive process of CPS, but also exploration behaviour in a CPS environment. The results have thus provided a new perspective for exploring the component skills of CPS.

6. Limitations

There are some limitations in the study. All the tests were low stake; therefore, students might not be sufficiently motivated to do their best. This feature might have produced the missing values detected in the sample. In addition, some students’ exploration behaviour shown in this study might theoretically be below their true level. However, considering that data cleaning was adopted in this study (see Section 3.1 ), we believe this phenomenon will not have a remarkable influence on the results. Moreover, the CPS test in this study was based on the MicroDYN approach, which is a well-established and widely used artificial model with a limited number of variables and relations. However, it does not have the power to cover all kinds of complex and dynamic problems in real life. For instance, the MicroDYN approach cannot measure ill-defined problem solving. Thus, this study can only demonstrate the influence of IR and CR on problem solving in well-defined MicroDYN-simulated problems. Furthermore, VOTAT is helpful with minimally complex problems under well-defined laboratory conditions, but it may not be that helpful with real-world, ill-defined complex problems ( Dörner and Funke 2017 ; Funke 2021 ). Therefore, the generalizability of the findings is limited.

7. Conclusions

In general, the results have shed new light on students’ problem-solving behaviours in respect of exploration strategy in a CPS environment and explored differences in terms of the use of thinking skills between students with different exploration strategies. Most studies discuss students’ problem-solving strategies from a behavioural perspective. By contrast, this paper discusses them from both behavioural and cognitive perspectives, thus expanding our understanding in this area. As for educational implications, the study contributes to designing and revising training methods for CPS by identifying the importance of IR and CR in exploration behaviour in a CPS environment. To sum up, the study has investigated the nature of CPS from a fresh angle and provided a sound basis for future studies.

Funding Statement

This study has been conducted with support provided by the National Research, Development and Innovation Fund of Hungary, financed under the OTKA K135727 funding scheme and supported by the Research Programme for Public Education Development, Hungarian Academy of Sciences (KOZOKT2021-16).

Author Contributions

Conceptualization, H.W. and G.M.; methodology, H.W. and G.M.; formal analysis, H.W.; writing—original draft preparation, H.W.; writing—review and editing, G.M.; project administration, G.M.; funding acquisition, G.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Ethical approval was not required for this study in accordance with the national and institutional guidelines. The assessments which provided data for this study were integrated parts of the educational processes of the participating university. The participation was voluntary.

Informed Consent Statement

All of the students in the assessment turned 18, that is, it was not required or possible to request and obtain written informed parental consent from the participants.

Data Availability Statement

Conflicts of interest.

Authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Define Cognitive Psychology: Meaning and Examples

Categories Cognition

Cognitive psychology is defined as the study of internal mental processes. Such processes include thinking, decision-making, problem-solving , language, attention, and memory. The cognitive approach in psychology is often considered part of the larger field of cognitive science. This branch of psychology is also related to several other disciplines, including neuroscience, philosophy, and linguistics.

To define cognitive psychology , it is important to understand the core focus of the cognitive approach, which is to psychology is on how people acquire, process, and store information. Cognitive psychologists are interested in studying what happens inside people’s minds.

Table of Contents

How Do We Define Cognitive Psychology?

While the cognitive approach to psychology is a popular branch of psychology today, it is actually a relatively young field of study. Until the 1950s, behaviorism was the dominant school of thought in psychology.

Between 1950 and 1970, the tide began to shift against behavioral psychology to focus on topics such as attention, memory, and problem-solving.

Often referred to as the cognitive revolution, this period generated considerable research on subjects, including processing models, cognitive research methods , and the first use of the term “cognitive psychology.”

The term “cognitive psychology” was first used in 1967 by American psychologist Ulric Neisser in his book Cognitive Psychology . Neisser went on to define cognitive psychology by saying that cognition involves “all processes by which the sensory input is transformed, reduced, elaborated, stored, recovered, and used.” Neisser also suggested that given such a broad and sweeping definition, cognition was involved in anything and everything that people do.

Essentially, all psychological events are cognitive events. Today, the American Psychological Association defines cognitive psychology as the “study of higher mental processes such as attention, language use, memory, perception, problem solving, and thinking.”

Understanding How We Define Cognitive Psychology

Some factors that contributed to the rise of the cognitive approach to psychology. These include:

• Dissatisfaction with the behaviorist approach : Behaviorism largely focused on looking at external influences on behavior. What the behavioral perspective failed to account for was the internal processes that influence human behavior. The cognitive approached emerged to fill this void.
• The increased use of computers : Scientists began comparing the way the human mind works to how a computer stores information on a hard drive. The information-processing model became popular as a result.

Thanks to these influences, the cognitive approach became an increasingly important branch of psychology. Behaviorism lost its hold as a dominant perspective, and psychologists began to look more intensely at memory, learning, language, and other internal processes.

Research Methods Used in Cognitive Psychology

Psychologists who use the cognitive approach rely on rigorous scientific methods to research the human mind. In many cases, this involves using experiments to determine if changes in an independent variable result in changes in the dependent variable.

Some of the main research methods used in the cognitive approach include:

Experimental Research

This involves conducting controlled experiments to manipulate variables and observe their effects on cognitive processes. Experiments are often conducted in laboratory settings to maintain control over extraneous variables.

For example, a memory experiment might involve randomly assigning participants to take a series of memory tests to determine if a certain change in conditions led to changes in memory abilities.

By using rigorous empirical methods, psychologists can accurately determine that it is the independent variable causing the changes rather than some other factor.

Cognitive Neuropsychology

This approach studies cognitive function by examining individuals with brain injuries or neurological disorders. By observing how damage to specific brain areas affects cognitive processes, researchers can infer the functions of those areas.

Neuroimaging Techniques

Cognitive neuroscientists use techniques to examine brain activity during cognitive tasks. Some of these neuroimaging tools include:

• Functional magnetic resonance imaging (fMRI)
• Positron emission tomography (PET)
• Electroencephalography (EEG)

Eye-Tracking Studies

Eye-tracking technology is used to study visual attention and perception by recording eye movements as participants view stimuli. This method provides insights into how people process visual information and allocate attention.

Areas of Study in the Cognitive Psychology

As mentioned previously, any mental event is considered a cognitive event. There are a number of larger topics that have held the interest of cognitive psychologists over the last few decades. These include:

Information-Processing

As you might imagine, studying what’s happening in a person’s thoughts is not always the easiest thing to do.

Very early in psychology’s history, Wilhelm Wundt attempted to use a process known as introspection to study what was happening inside a person’s mind. This involved training people to focus on their internal states and write down what they were feeling, thinking, or experiencing. This approach was extremely subjective, so it did not last long as a cognitive research tool.

Cognitive psychologists have developed different models of thinking to study the human mind. One of the most popular of these is the information-processing approach .

In this approach, the mind is thought of as a computer. Thoughts and memories are broken down into smaller units of knowledge. As information enters the mind through the senses, it is manipulated by the brain, which then determines what to do with it.

Some information triggers an immediate response. Other units of information are transferred into long-term memory for future use.

Units of Knowledge

Cognitive psychologists often break down the units of knowledge into three different types: concepts, prototypes, and schemas.

A concept is basically a larger category of knowledge. A broad category exists inside your mind for these concepts where similar items are grouped together. You have concepts for things that are concrete such as a dog or cat, as well as concepts for abstract ideas such as beauty, gravity, and love.

A prototype refers to the most recognizable example of a particular concept. For example, what comes to mind when you think of a chair. If a large, comfy recliner immediately springs to mind, that is your prototype for the concept of a chair. If a bench, office chair, or bar stool pops into your mind, then that would be your prototype for that concept.

A schema is a mental framework you utilize to make sense of the world around you. Concepts are essentially the building blocks that are used to construct schemas, which are mental models for what you expect from the world around you. You have schemas for a wide variety of objects, ideas, people, and situations.

So what happens when you come across information that does not fit into one of your existing schemas? In some cases, you might even encounter things in the world that challenges or completely upend the ideas you already hold.

When this happens, you can either assimilate or accommodate the information. Assimilating the information involves broadening your current schema or even creating a new one. Accommodating the information requires changing your previously held ideas altogether. This process allows you to learn new things and develop new and more complex schemas for the world around you.

The Cognitive Approach to Attention

Attention is another major topic studied in the field of cognitive psychology. Attention is a state of focused awareness of some aspect of the environment. This ability to focus your attention allows you to take in knowledge about relevant stimuli in the world around you while at the same time filtering out things that are not particularly important.

At any given moment in time, you are taking in an immense amount of information from your visual, auditory, olfactory, tactile, and taste senses. Because the human brain has a limited capacity for handling all of this information, attention is both limited and selective.

Your attentional processes allow you to focus on the things that are relevant and essential for your survival while filtering out extraneous details.

The Cognitive Approach to Memory

How people form, recall, and retain memories is another important focus in the cognitive approach. The two major types of memory that researchers tend to look at are known as short-term memory and long-term memory.

Short-Term Memory

Short-term memories are all the things that you are actively thinking about and aware of at any given moment. This type of memory is both limited and very brief.

Estimates suggest that you can probably hold anywhere from 5 to 9 items in short-term memory for approximately 20 to 30 seconds.

Long-Term Memory

If this information is actively rehearsed and attended to, it may be transferred to what is known as long-term memory. As the name suggests, this type of memory is much more durable. While these longer-lasting memories are still susceptible to forgetting , the information retained in your long-term memory can last anywhere from days to decades.

Cognitive psychologists are interested in the various processes that influence how memories are formed, stored, and later retrieved. They also look at things that might interfere with the formation and storage of memories as well as various factors that might lead to memory errors or even false memories.

The Cognitive Approach to Intelligence

Human intelligence is also a major topic of interest within cognitive psychology, but it is also one of the most hotly debated and sometimes controversial. Not only has there been considerable questioning over how intelligence is measured (or if it can even be measured), but experts also disagree on exactly how to define intelligence itself.

One survey of psychologists found that experts provided more than 70 different definitions of what made up intelligence. While exact definitions vary, many agree that two important themes include both the ability to learn and the capacity to adapt as a result of experience.

Researchers have found that more intelligent people tend to perform better on tasks that require working memory , problem-solving, selective attention , concept formation, and decision-making. When looking at intelligence, cognitive psychologists often focus on understanding the mental processes that underlie these critical abilities.

Cognitive Development

Cognitive development refers to the changes in cognitive abilities that occur over the lifespan, from infancy through old age. Cognitive psychologists study the development of perception, attention, memory, language, and reasoning skills.

Research in cognitive development explores factors that influence cognitive growth, such as genetics, environment, and social interactions.

Language is a complex cognitive ability that enables communication through the use of symbols and grammatical rules. Cognitive psychologists study the cognitive processes involved in language comprehension, production, and acquisition.

Research in language examines topics such as syntax, semantics, pragmatics, and the neurobiological basis of language processing.

Reasons to Study Cognitive Psychology

Because cognitive psychology touches on many other disciplines, this branch of psychology is frequently studied by people in different fields. Even if you are not a psychology student, learning some of the basics of cognitive psychology can be helpful.

The following are just a few of those who may benefit from studying cognitive psychology.

• Students interested in behavioral neuroscience, linguistics, industrial-organizational psychology, artificial intelligence, and other related areas.
• Teachers, curriculum designers, instructional developers, and other educators may find it helpful to learn more about how people process, learn, and remember information.
• Engineers, scientists, artists, architects, and designers can all benefit from understanding internal mental states and processes.

Key Points to Remember About Cognitive Approach

• The cognitive approach emerged during the 1960s and 70s and has become a major force in the field of psychology.
• Cognitive psychologists are interested in mental processes, including how people take in, store, and utilize information.
• The cognitive approach to psychology often relies on an information-processing model that likens the human mind to a computer.
• Findings from the field of cognitive psychology apply in many areas, including our understanding of learning, memory, moral development, attention, decision-making, problem-solving, perceptions, and therapy approaches such as cognitive-behavior therapy and rational emotive behavior therapy.

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Miller, G. A. (1956). The magical n u mber seven, plus or minus two: Some limits on our capacity for processing information .  Psychological Review, 63 (2), 81–97. https://doi.org/10.1037/h0043158

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Image: Julia Freeman-Woolpert / freeimages.com

How to Optimize Self-Assessment Accuracy in Cognitive Skill Acquisition When Learning from Worked Examples

• INTERVENTION STUDY
• Open access
• Published: 07 September 2024
• Volume 36 , article number  103 , ( 2024 )

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• Julia Waldeyer   ORCID: orcid.org/0000-0001-8116-9200 1   na1 ,
• Tino Endres 2   na1 ,
• Julian Roelle 1   na1 ,
• Martine Baars 3 &
• Alexander Renkl 2  

The present study was designed to understand and optimize self-assessment accuracy in cognitive skill acquisition through example-based learning. We focused on the initial problem-solving phase, which follows after studying worked examples. At the end of this phase, it is important that learners are aware whether they have already understood the solution procedure. In Experiment 1, we tested whether self-assessment accuracy depended on whether learners were prompted to infer their self-assessments from explanation-based cues (ability to explain the problems’ solutions) or from performance-based cues (problem-solving performance) and on whether learners were informed about the to-be-monitored cue before or only after the problem-solving phase. We found that performance-based cues resulted in better self-assessment accuracy and that informing learners about the to-be-monitored cue before problem-solving enhanced self-assessment accuracy. In Experiment 2, we again tested whether self-assessment accuracy depended on whether learners were prompted to infer their self-assessments from explanation- or performance-based cues. We furthermore varied whether learners received instruction on criteria for interpreting the cues and whether learners were prompted to self-explain during problem-solving. When learners received no further instructional support, like in Experiment 1, performance-based cues yielded better self-assessment accuracy. Only when learners who were prompted to infer their self-assessments from explanation-based cues received both cue criteria instruction and prompts to engage in self-explaining during problem-solving did they show similar self-assessment accuracy as learners who utilized performance-based cues. Overall, we conclude that it is more efficient to prompt learners to monitor performance-based rather than explanation-based cues in the initial problem-solving phase.

Avoid common mistakes on your manuscript.

The worked-example approach is a well-established method to foster initial cognitive skill acquisition (e.g., Sweller et al., 2019 ). This approach usually involves four stages (Renkl, 2014 ; see also van Gog et al., 2020 ). First, learners are provided with instructional explanations that communicate basic knowledge on new principles and concepts. In terms of models of cognitive skill acquisition (e.g., Anderson, 1982 ; VanLehn, 1996 ), this stage corresponds with the early phase , in which learners need to gain a basic understanding of the learning content. Second, learners receive multiple worked examples that illustrate how the principles and concepts can be used to solve problems and are engaged in self-explaining the examples. After they have studied and self-explained the worked examples, learners turn to problem-solving in the third stage. As does studying worked examples, initial problem-solving also serves the theoretical function of supporting learners in understanding the rationale of the solutions. Hence, both studying worked examples and initial problem-solving correspond with the intermediate phase of cognitive skill acquisition, which focuses on learning how the principles and concepts can be used to solve concrete problems (see Renkl, 2014 ). In the fourth stage, learners practice problem-solving extensively. This stage, which corresponds with the late phase of cognitive skill acquisition, is mainly focused on enhancing problem-solving speed and accuracy.

The transition from the third to the fourth stage is hence accompanied by a change in the main learning goal. It changes from understanding the rationale of solutions (Stage 1–3) to enhancing the accuracy and speed of problem-solving (Stage 4). Thus, at least when learners navigate through these stages in a self-regulated manner, it is crucial that learners accurately self-assess their level of understanding after the initial problem-solving, because they should proceed to Stage 4 only when their level of understanding is sufficient. There is evidence that learners use their initial problem-solving performance to diagnose their level of understanding (e.g., Foster et al., 2018 ). It is also found that learners decide to engage in further problem-solving (i.e., proceeding to Stage 4) too often (see Foster et al., 2018 ), which likely reflects the widespread finding that learners’ self-assessments tend to be inaccurate (for recent meta-analytical findings, see León et al., 2023 ).

The present study’s main goal was to investigate how self-assessment accuracy in the initial problem-solving phase of cognitive skill acquisition through learning from worked examples could be optimized. Specifically, we were interested to explore whether self-assessment accuracy increased when learners were prompted to infer their self-assessments from their ability to explain the rationale of the problems’ solutions (i.e., explanation-based cues ) rather than from their problem-solving performance (i.e., performance-based cues ). Furthermore, we tested whether informing learners about to-be-monitored cues already before the problem-solving phase enhanced self-assessment accuracy.

Cognitive Skill Acquisition Through the Worked-Example Approach

Based on the worked example effect (Sweller & Cooper, 1985 )―one of the first effects postulated by cognitive load theory (see Sweller et al., 1998 )―the worked-example approach has been developed and become one of the prominent and widely used procedures to foster cognitive skill acquisition (e.g., Atkinson, 2002 ; Foster et al., 2018 ; Hefter et al., 2014 ; Kölbach & Sumfleth, 2013 ; Rawson et al., 2020 ; Schworm & Renkl, 2007 ; van Gog et al., 2008 ; for an overview, see also Renkl, 2014 ). This approach usually involves four stages and relates to two important learning goals (see Fig.  1 ).

Cognitive skill acquisition through the worked-example approach of example-based learning

The first important learning goal is to understand the rationale of solutions for the problems to be solved with the respective cognitive skill. This goal is pursued in the first three stages―the present study focuses on these stages. In the first stage, learners receive instructional explanations that communicate basic knowledge concerning the principles and concepts on which the cognitive skill is based (see Wittwer & Renkl, 2010 ). For instance, when learners acquire the cognitive skill of solving mathematical urn model problems , which relate to the calculation of probabilities of combinations of random events (e.g., events in repeated dice rolling or drawing objects from a vessel such as an urn), instructional explanations could explain stochastic principles concerning the order of events (i.e., order is relevant or irrelevant) and concerning the replacement of events after they have been removed from the urn (i.e., with or without replacement). Hence, such explanations cover the four stochastic principles of order relevant/with replacement, order relevant/without replacement, order irrelevant/with replacement, and order irrelevant/without replacement (see Berthold & Renkl, 2009 ; Schalk et al., 2020 ). In terms of models of cognitive skill acquisition (e.g., VanLehn, 1996 ), this first stage can be mapped on the early phase , which relates to gaining a basic understanding of the content that is to be learned.

In the second stage, learners receive multiple worked examples that illustrate how the previously explained basic knowledge can be used to solve problems. This stage directly relates to supporting learners in understanding the rationale of the solution procedure. More specifically, in this step, learners engage in generative learning activities that are targeted at understanding how the basic knowledge acquired in the first stage can be used to explain or justify solution steps (e.g., Hefter et al., 2015 ; Nokes et al., 2011 ; Roelle et al., 2017 ). Unfortunately, learners often do not sufficiently engage in such self-explaining of worked examples on their own (e.g., Chi et al., 1989 ; Renkl, 1997 ). Consequently, worked examples are frequently provided together with self-explanation prompts that explicitly require learners to engage in relating the worked examples to the previously provided instructional explanations (e.g., Atkinson et al., 2003 ; Conati & VanLehn, 2000 ; Hefter et al., 2015 ; Schworm & Renkl, 2007 ). In the case of the cognitive skill of solving mathematical urn model problems , for example, such self-explanation prompts could require learners to explain which of the solution’s features reflect whether the sequence of events is relevant or irrelevant, and which features reflect whether events are replaced.

In the third stage, learners turn to problem-solving. Note that this initial problem-solving phase targets the same learning goal as the previous stage. That is, the theoretical function of the initial problem-solving is to support learners in deeply understanding the rationale of the solution procedures (see Renkl, 2014 ). Hence, both the second and third stages of the procedure relate to the intermediate phase of cognitive skill acquisition (see VanLehn, 1996 ), which focuses on learning how the basic principles and concepts can be used to solve concrete problems (Renkl, 2014 ). Other than the worked examples, however, the initial problem-solving likely serves a secondary function beyond the deepening of learners’ understanding by applying and refining the acquired schemata. Specifically, the early problem-solving may also serve the function of helping learners to self-assess their level of understanding of the to-be-learned solution rationales. If learners realize they have not understood how to solve the examples on their own, they can turn back to studying the worked examples (for a similar notion from research on learning from example-problem sequences, see van Gog et al., 2020 ).

In the fourth stage, like in the third stage, learners engage in problem-solving. Other than in Stage 3, however, the main learning goal is not to foster understanding the problem-solving procedure’s rationale. Rather, the main learning goal in Stage 4 is to enhance the speed and accuracy of problem-solving (see Renkl, 2014 ). That is, once learners have formed a quality problem-solving schema or multiple schemata through the first three stages, enhancing the efficiency of the schema(ta) is key. Accordingly, this stage corresponds with late phases of cognitive skill acquisition. Although to date it is generally unclear how many problems learners need to solve at what times to effectively consolidate the acquired schemata (e.g., Rawson et al., 2020 ; see also Rawson & Dunlosky, 2022 ), this stage is considered the end of the approach of learning from worked examples.

A wealth of previous research has dealt with optimizing this approach. These studies investigated instructional support measures that related to single stages as well as to transitions between the stages. In terms of support measures associated with single stages, previous research has, for example, investigated prompts to enhance deep processing of the basic instructional explanations (Stage 1; e.g., Roelle et al., 2017 ) or prompts to elicit self-explanations during processing the worked examples (i.e., Stage 2; e.g., Berthold et al., 2009 ). In terms of supporting the transitions between stages, previous research has, among other aspects, analyzed the degree and difficulty of required retrieval of previously processed principles and concepts from memory when learners transition from processing the instructional explanations to studying worked examples (i.e., Stage 1 → Stage 2; e.g., Roelle & Renkl, 2020 ; see also Hiller et al., 2020 ) or on fading worked examples to transition from worked examples to (initial) problem-solving (i.e., Stage 2 → Stage 3; e.g., Foster et al., 2018 ; Renkl et al., 2004 ).

Despite this wealth of research that contributed to optimizing learning from worked examples, however, there is still room for optimization. Such optimization potential lies, for example, in the initial problem-solving phase (i.e., Stage 3). At least when learners navigate the example-based sequence in a self-regulated manner, they need to self-assess their level of understanding of the solution procedure in this phase. (Accurate) self-assessment helps to decide whether to turn back to worked-example study (Stage 2) or proceed with more problem-solving (Stage 4). A study by Foster et al. ( 2018 ), however, found that learners tend to proceed to Stage 4 too early, which detrimentally affects learning outcomes. One potential explanation for this suboptimality is that in the initial problem-solving phase, learners infer their self-assessments from cues of relatively low diagnosticity.

The Role of Cue Utilization in Self-Assessment in the Initial Problem-Solving Phase

Inaccurate student self-assessment and its consequences have attracted a great deal of attention in recent years (e.g., Alexander, 2013 ; de Bruin & van Gog, 2012 ; de Bruin & van Merriënboer, 2017 ; León et al., 2023 ; Panadero et al., 2016 ; Waldeyer et al., 2023 ). One theoretical model explaining how learners form self-assessments and why they are often inaccurate is the cue-utilization framework (Koriat, 1997 ). According to this framework, learners infer their self-assessments from cues , which they can monitor during learning. For example, such cues could be the fluency with which learners solve certain problems, the degree to which they can retrieve previously studied information from memory, or their interest in the topic (e.g., Thiede et al., 2010 ). The accuracy of learners’ self-assessments is therefore thought to depend on the degree to which the utilized cues are diagnostic (i.e., predictive) in the respective context (see de Bruin et al., 2017 ). Hence, inaccurate self-assessments are assumed to result from cues of low diagnosticity, which is supported by a wealth of findings concerning learners’ cue utilization in different settings (e.g., in problem-solving, see, e.g., Ackerman et al., 2013 ; Baars et al., 2014a , b , 2017 ; Oudman et al., 2022 ; in learning from texts, see, e.g., de Bruin et al., 2017 ; Endres et al., 2023 ; van de Pol et al., 2021a ; Waldeyer & Roelle, 2023 ; for overviews, see Prinz et al., 2020 ; Thiede et al., 2010 ; van de Pol et al., 2021b ).

Findings by Foster et al. ( 2018 ) indicate that in the initial problem-solving phase of learning from worked examples, learners infer their self-assessments from their (perceived) problem-solving performance. At first glance, using this cue appears to be sensible, as this cue is highly salient and hence likely easy to monitor during problem-solving. If a learner has acquired a high level of understanding, this should be reflected in good problem-solving performance and hence the cue of problem-solving performance should be highly diagnostic. In support of this notion, Baars et al. ( 2014a , b ) found that self-assessments made by primary school students were more accurate when learners could monitor their performance on a practice problem after worked-example study when learning about addition and subtraction problems as compared to monitoring their performance after studying worked examples without subsequent problem-solving. However, at second glance, the diagnosticity of the cue of problem-solving performance might depend on how learners solved the problems. When learners have not yet reached a sufficient level of understanding, they search for solutions via shallow strategies, for example, a copy-and-adapt strategy (i.e., copying the solution procedure from a presumably similar problem and adapting just the numbers; VanLehn et al., 2016 ), a keyword strategy (i.e., selecting a solution procedure by a keyword in the cover story of a problem (Karp et al., 2019 ), or means-end analyses without schema construction efforts (Salden et al., 2010 ; see also Renkl, 2014 ). Such shallow problem-solving strategies often result in correct solutions (e.g., Karp et al., 2019 ), which, in turn, may lead to performance cues that might be misleading with respect to learning in the sense of understanding. Such shallow strategies are also very resource-intensive, and their effectiveness depends on variable features of the to-be-solved problems (e.g., on whether the to-be-solved problem is actually structurally similar to the one from which the solution is adapted). Hence, success on shallowly solved problems might not be a reliable predictor of future performance on isomorphic problems. Rather, the diagnosticity of the cue of problem-solving performance should be relatively low in this case. In support of this notion, Baars et al. ( 2014a , b ) found that providing learners with the correct solution to a problem as a standard for comparison improved learners’ self-assessments only for identical problems and not for isomorphic problems. These findings suggest that learners might have inferred their self-assessments from surface features of the problems they practiced instead of from structural features such as their understanding of the solution procedure.

On a more general level, the outlined line of reasoning concerning the potentially suboptimal diagnosticity of problem-solving performance as a cue is in line with desirable difficulties research (e.g., Soderstrom & Bjork, 2015 ). This research, the core of which relates to the counterintuitive finding that learning activities that slow down improvement or even hinder performance during learning often produce superior long-term learning, indicates that learners often mix up performance (e.g., problem-solving success) and learning (e.g., the level of understanding of the to-be-learned principles and concepts) when judging their progress in studying (Soderstrom & Bjork, 2015 ; see also Endres et al., 2024 ). For example, Rohrer and Taylor ( 2007 , Exp. 2) found in mathematics learning that learners who studied different problem types in a mixed (i.e., interleaved) sequence learned more than learners who studied blocked sequences, as indicated by a 1-week delayed posttest. The performance during learning, however, was higher on part of the learners with blocked sequences. Hence, like in the outlined case of shallow solution procedures in learning from worked examples, the diagnosticity of the cue of performance during learning would have been relatively low.

An alternative cue from which learners could infer the degree to which they have understood the to-be-learned knowledge or mastered the to-be-acquired cognitive skill at the end of Stage 3 of the worked-example sequence could be their ability to explain how the problems should be solved. There is evidence which suggests that the quality of self-explanations is predictive of learners’ level of understanding in example-based learning (e.g., Hefter et al., 2015 ; Otieno et al., 2011 ; Roelle & Renkl, 2020 ). However, like solving problems, explaining problem-solving procedures can be done in a shallow way as well. For example, when learners who used shallow strategies to solve problems are prompted to infer their self-assessments from the ability to explain how the problems should be solved, they might believe that explanations of their shallow strategies would suffice. Although this case might be relatively rare as learners likely know that their strategy is hardly aligned with how the problems should be solved ideally, explanation-based cues, like performance-based cues, might be of low diagnosticity as well in some cases.

In view of the outlined arguments concerning performance-based and explanation-based cues and the available empirical evidence, it is hard to predict with some certainty whether the one or other type of cue would result in better self-assessment accuracy in the initial problem-solving phase in learning from worked examples. Regardless of the type of cue from which the self-assessments are inferred, however, self-assessment accuracy should be higher when learners monitor the respective cue from the beginning of the problem-solving phase rather than reconstruct the cue only after problem-solving. A promising means to enhance self-assessment accuracy could hence be to inform learners about the to-be-monitored cue already at the beginning of the problem-solving phase. Surprisingly, however, to date, the effects of the point in time at which learners are informed about the cue from which they should infer their self-assessments have largely been ignored in research on self-assessment accuracy.

It is important to highlight that informing learners before the initial problem-solving phase about the cue to use for monitoring might entail not only beneficial effects but could have negative side effects as well. There is evidence that monitoring requires mental effort (e.g., Froese & Roelle, 2022 ; Panadero et al., 2016 ). When the task of problem-solving imposes high cognitive load, the additional mental effort required for monitoring could compromise learners’ performance in the initial problem-solving phase (e.g., Valcke, 2002 ; see also van Gog et al., 2011 ). This, in turn, could decrease the diagnosticity of the cue of problem-solving performance, as the low performance would be due to the requirement to attend to certain cues for monitoring and not to insufficient understanding. An alternative effect of too high cognitive load could be that learners disengage from monitoring the respective cue, which should also decrease self-assessment accuracy but not compromise problem-solving performance. A third potential consequence of high cognitive load could be that learners infer that they are not learning well. There is evidence that learners infer self-assessments from perceived mental effort such that self-assessments decrease as subjective mental effort increases (see Baars et al., 2020 ). If learners would lower their self-assessments because of high experienced mental effort and their problem-solving performance would be compromised by the high perceived mental effort as well, informing learners about the to-be-monitored cues before problem-solving could increase self-assessment accuracy, but for unintended reasons. In investigating effects of the point in time at which learners are informed about the to-be-monitored cues, it is hence crucial to also analyze effects on cognitive load (i.e., mental effort) and problem-solving performance and relations between cognitive load and self-assessments in order to test for such unintended mechanisms (see also the Effort Monitoring and Regulation (EMR) Framework by de Bruin et al., 2020 ).

Experiment 1

In Experiment 1, we addressed two main research questions with respect to understanding and optimizing self-assessment accuracy in cognitive skill acquisition by the approach of learning from worked examples.

Research Question 1: Does self-assessment accuracy at the end of the initial problem-solving phase (i.e., Stage 3), where learners need to be aware whether they have already understood the rationale behind the solution procedure, depend on whether learners were prompted to infer their self-assessments from explanation-based cues or from performance-based cues?

Research Question 2: Does informing learners about the type of to-be-monitored cues already before the problem-solving phase increase self-assessment accuracy as compared to informing learners only after the problem-solving phase?

We also addressed the outlined potential unintended effects of informing learners about the to-be-monitored cue already before the problem-solving phase. Specifically, in Research Question 3, we pursued the following questions:

Research Question 3: Does informing learners about the type of to-be-monitored cues already before the problem-solving phase affect mental effort and performance in the problem-solving phase? Do learners’ mental effort ratings und learners’ self-assessments correlate? Do these potential correlations differ between learners with and without up-front information about the to-be-monitored cue?

Sample and Design

As we were interested in effects relevant for educational practice, we used the lower limit of a medium effect size ( η p 2  = 0.06; further parameters: α  = 0.05, β  = 0.20) as the basis for our a priori power analysis. This power analysis, which was conducted with G*Power 3.1.9.3 (Faul et al., 2007 ), was fitted for a 2 × 2 between-subjects ANOVA and yielded a required sample size of N  = 128. Hence, we recruited N  = 135 university students from different universities in Germany (73.3% female; M Age  = 26.37 years, SD Age  = 7.25 years) majoring in various disciplines. We excluded one participant who reported being diagnosed with dyscalculia and five participants who achieved a score higher than 90% on the pretest. Our final sample comprised 129 university students (73.6% female; M Age  = 26.01 years, SD Age  = 6.66 years).

All learners were instructed on the cognitive skill of solving mathematical urn model problems , which relate to the calculation of probabilities of combinations of random events (e.g., events in repeated dice rolling), by means of learning from worked examples. Hence, all learners first received basic instructional explanations about stochastic principles (Stage 1) and were then given four worked examples together with self-explanation prompts (Stage 2). In the third stage, all learners were to solve four mathematical urn model problems (Stage 3) and then self-assess how well they understood the solution rationales. The experimental manipulation took place during this initial problem-solving phase. Specifically, we varied whether the learners were prompted to infer their self-assessments from performance-based cues or from explanation-based cues (i.e., factor of prompted cue type ). Furthermore, we varied whether learners were or were not informed about the to-be-monitored cue at the beginning of the problem-solving phase (i.e., factor of timing of cue prompt ). Hence, the experiment followed a 2 × 2 factorial between-subject design. The participants were randomly assigned to the conditions.

The participation was compensated with online vouchers worth 15€. The experiment was approved by the ethics committee of Ruhr University Bochum (No. EPE-2022–027). We collected written informed consent from all participants.

Stages 1 and 2: Introductory Instructional Explanations and Worked Examples

In the first stage of the example-based learning procedure, all participants were asked to carefully read basic instructional explanations that covered stochastic principles concerning mathematical urn models. Specifically, we used a slightly adapted version of the instructional explanations used by Berthold and Renkl ( 2009 ) and Schalk et al. ( 2020 ). The instructional explanations introduced the concepts of probability of (a) an event in a single-stage experiment, (b) a sequence of events in multistage experiments, and (c) multiple sequences of events in multistage experiments. Furthermore, the instructional explanations covered four stochastic principles capturing situations in which the order of an event is relevant or irrelevant and in which events are removed for the next experiment and are then either returned or kept outside of it (i.e., with/without replacement). At the end of this introduction, the participants were shown a table in which the four stochastic principles were listed and illustrated (see Fig.  2 ).

Screenshot of the table on the four stochastic principles (translated from German)

After reading the basic instructional explanations, that is, in the second stage, the participants were provided with four worked examples in which the four stochastic principles were embedded in different contexts. Each worked example contained a question, a colored diagram that illustrated the calculation path, and a mathematical calculation including the solution and answer. Self-explanation prompts accompanied the worked examples in order to scaffold deep processing (Chi & Bassok, 1989 ; Renkl, 2014 ; see Fig.  3 for a worked example illustrating the principle “order relevant/without replacement” and the self-explanation prompt). The worked examples were shown to all participants in the same order.

Illustration of a worked example with self-explanation prompt (translated from German)

Stage 3: Initial Problem-Solving Phase

In the third stage of the example-based learning procedure, the learners turned to problem-solving. Specifically, all participants were provided with four problems to be solved. Each problem was provided on an individual page and learners had access to a tool for calculations and a box in which they could write notes. Each problem dealt with one of the four stochastic principles studied beforehand (see Fig.  4 ). The problems were shown to all participants in the same order.

Screenshot of a problem-solving task (translated from German)

The experimental manipulations took place during this initial problem-solving phase. After having worked on all four problems, all participants were required to self-assess their level of understanding of the rationales of the four problems’ solutions. In view of the notion that the required level of understanding at the end of the initial problem-solving phase relates to both understanding of the abstract principles and understanding of how to solve concrete problems, learners were posed two questions. First, all learners were asked “how well did you understand the four types of combinations of random events?” (i.e., the four stochastic principles) with the answer scale ranging from 0% (not at all) to 100% (very good). Second, all learners were asked “how well can you solve problems about the four types of random-event combinations?” with the answer scale ranging from 0% (not at all) to 100% (very good). Depending on the prompted cue type , learners were asked to infer their self-assessments from “how well you were able to solve the four problems you just completed” (i.e., performance-based cues) or from “how well you could explain how the four problems you just completed are solved” (i.e., explanation-based cues).

The factor timing of cue prompt related to the instruction that was provided at the beginning of the problem-solving phase. The learners in the conditions who were informed about the prompted cue type already at the beginning of the problem-solving phase received the following instruction: “In the following, you are to solve four problems on the four types of stochastic principles on your own. In doing so, please pay attention to how well you can solve the problems” (i.e., performance-based cue condition), or “[…] how well you can explain how the problems are solved” (i.e., explanation-based cue condition). “You will need this information afterwards.” By contrast, the learners in the conditions who were informed about the prompted cue type only after problem-solving were simply told that “in the following, you are to solve four problems on the four types of stochastic principles on your own.”

Instruments and Measures

To assess the participants’ prior knowledge on stochastics, we used a pretest containing six questions. Two of these questions were multiple-choice-single-select questions and four required an open answer. The open answers were scored by two independent raters applying a scoring protocol. Interrater reliability as determined by the intraclass coefficient with measures of absolute agreement was very good, ICC > 0.85. The pretest score was obtained by calculating the ratio of the theoretical maximum number of points. These scores were then converted into percentage values (i.e., 0–100%). Internal consistency was acceptable, ω  = 0.72.

Performance in the Initial Problem-Solving Phase

The learners’ solutions to the four problems in the initial problem-solving phase (Stage 3) were scored by two independent raters using a scoring protocol. Interrater reliability as determined by the intraclass coefficient with measures of absolute agreement was very good (ICC > 0.85).

Self-Assessments

In learning from worked examples, the required level of understanding at the end of the initial problem-solving phase relates to both understanding of the abstract principles and to understanding of how to solve concrete problems (see Renkl, 2014 ). Accordingly, we asked learners to self-assess how well they thought they understood the four types of combinations of random events and how well they thought they could solve problems about the four types of random-event combinations (0% = not all to 100% = very good). These two self-assessments correlated strongly ( r  = 0.87, p  < 0.001). Hence, we aggregated them to determine the self-assessed level of understanding (0–100%).

To assess the participants’ level of actual understanding concerning the four types of stochastics problems, we designed a posttest containing ten questions. Four of these questions were problem-solving tasks that were isomorphic to the problems provided in the initial problem-solving phase. Of the further six questions, two related to transfer problems that went beyond the problems provided in the initial problem-solving phase and four were designed to assess the learners’ level of understanding on an abstract level (e.g., “You roll a dice three times in a row and aim to roll two sixes and a single one in random order. How would you characterize this problem in terms of ‘order relevance’ and ‘replacement’?”).

All questions were scored by two independent raters applying a scoring protocol. Interrater reliability was very good for all tasks (all ICCs > 0.85). The final posttest scores were obtained by averaging the scores of all ten questions (i.e., 0–100%; ω  = 0.83).

Self-Assessment Accuracy

We calculated absolute accuracy to determine the accuracy of learners’ self-assessments. Specifically, we used the formula proposed by Schraw ( 2009 ) and computed the squared deviation between learners’ self-assessments and their performance on the posttest. It is important to highlight that our original plan was to use the deviation between learners’ self-assessments and the overall posttest performance to determine absolute accuracy. A thoughtful comment of an anonymous reviewer, however, highlighted that as the learners’ self-assessments were explicitly related to the four types of problems (see above), the accuracy measure would only make sense when a posttest performance of 100% would reflect fully accurate performance on the four types of problems. For determining absolute accuracy, we hence used only the learners’ performance on the four problems that were isomorphic to the problems that were provided in the initial problem-solving phase. Scores closer to zero indicate better absolute accuracy (theoretical minimum, 0; theoretical maximum, 10,000).

Mental Effort

Subjective mental effort invested in the problem-solving phase was assessed by asking participants to judge the mental effort they invested in the problem-solving phase after each problem on a 9-point Likert scale (i.e., higher scores represent higher mental effort). The question’s wording was adapted from scales for assessing mental effort (see Paas, 1992 ; Paas et al., 2003 ). For the later analyses, the four ratings were averaged ( ω  = 0.95).

This experiment was conducted in an online learning environment on https://www.unipark.com , which participants accessed from their own devices. First, participants gave general information on gender, age, grade point average in high school (HSGPA), and dyscalculia, and then worked on the pretest. Afterwards, they went through the example-based learning sequence in a self-paced manner. The experimental manipulation took place during the initial problem-solving phase (i.e., Stage 3 of the sequence). That is, learners in the conditions who were informed about the prompted cue type before problem-solving were informed about the to-be-monitored cue type at the beginning of the problem-solving phase and, when they were to self-assess their level of understanding at the end of the phase, we varied whether learners were prompted to infer their self-assessments from performance-based or from explanation-based cues. Finally, all participants took the posttest.

The descriptive results are found in Table  1 .

Preliminary Analyses

In the first step, we tested whether the random assignment resulted in comparable groups. Applying Bayesian ANOVAs with a JZS prior, we were able to find strong evidence for non-existing differences (null hypothesis) between the groups concerning gender distribution, BF 01  = 16.66, and HSGPA, BF 01  = 21.71. We found anecdotal evidence for non-existing differences regarding prior knowledge, BF 01  = 2.52, and age, BF 01  = 1.31. Overall, these results indicate that the random assignment resulted in comparable groups.

In view of the notion that differences in self-assessment accuracy can simply result from effects of support measures on performance (e.g., when a support measure fosters performance, overestimation of performance becomes less likely, which can increase self-assessment accuracy, see Froese & Roelle, 2023 ), we also analyzed whether the groups differed concerning performance on the posttest. Bayesian ANOVAs showed substantial evidence for non-existing differences regarding the overall posttest score, BF 01  = 4.78, as well as regarding the performance on the four problems that were isomorphic to the problems that were provided in the initial problem-solving phase, BF 01  = 8.11. Hence, the effects on self-assessment accuracy found in the present study (see below) cannot be attributed to effects of the support measures on posttest performance.

Effects on Self-Assessment Accuracy

We tested whether prompting learners to infer their self-assessments from explanation-based cues or performance-based cues led to differences concerning self-assessment accuracy (Research Question 1). We addressed this research question by determining the main effect of prompted cue type in a 2 × 2 ANOVA with the factors prompted cue type and timing of cue prompt . We found a statistically significant main effect of prompted cue type, F (1, 125) = 6.45, p  = 0.012, η p 2  = 0.05. The groups that were prompted to utilize performance-based cues showed better self-assessment accuracy (i.e., values closer to zero).

In Research Question 2, we were interested in whether informing learners about the type of to-be-monitored cue already before the problem-solving phase would increase self-assessment accuracy as compared to informing learners only after the problem-solving phase. We addressed this research question by determining the main effect of timing of cue prompt . In support of our assumption, the 2 × 2 ANOVA revealed that the groups that were informed about the to-be-monitored cue already before the problem-solving phase showed better self-assessment accuracy, F (1, 125) = 4.09, p  = 0.046, η p 2  = 0.03.

For exploratory purposes, we also analyzed whether there was an interaction between the two factors concerning self-assessment accuracy. The ANOVA, however, did not reveal a statistically significant interaction effect, F (1, 125) = 0.10, p  = 0.758, η p 2  < 0.01.

Effects on Mental Effort and Performance During Problem-Solving

In Research Question 3, we tested whether the point in time when learners were informed about the to-be-monitored cue would affect mental effort and performance in the problem-solving phase. Furthermore, we determined the correlations between mental effort und learners’ self-assessments, which might indicate that learners used cognitive load as a cue in self-assessments and whether these correlations would differ between learners with and without up-front information about the to-be-monitored cue. We addressed the first part of this research question by determining the main effect of timing of cue prompt in a 2 × 2 ANOVA with the factors prompted cue type and timing of cue prompt . In terms of mental effort, the ANOVA did not reveal a statistically significant main effect of timing of cue prompt, F (1, 125) = 0.96, p  = 0.330, η p 2  < 0.01. We also examined the main effect of prompted cue type and the interaction between the two factors. However, none of these effects was statistically significant, F (1, 125) = 0.01, p  = 0.906, η p 2  < 0.01, and F (1, 125) < 0.01, p  = 0.958, η p 2  < 0.01, respectively.

In terms of problem-solving performance, we found a similar pattern of results. There was no main effect of timing of cue prompt, F (1, 125) = 1.03, p  = 0.311, η p 2  < 0.01, and also no main effect of prompted cue type and no interaction effect, F (1, 125) < 0.01, p  = 0.975, η p 2  < 0.01, and F (1, 125) = 0.56, p  = 0.457, η p 2  < 0.01.

To address the second part of Research Question 3, we determined the correlations between mental effort and self-assessments for the learners with and without information on the cue at the beginning of the problem-solving phase. For both learners with and without cue information before problem-solving, there was a statistically significant negative correlation between mental effort and self-assessments, r  =  − 0.29, p  = 0.012, and r  =  − 0.27, p  =  − 0.048. A Fisher’s z -test did not indicate a statistically significant difference between these correlations, z  = 0.17, p  = 0.431. This finding suggests that informing learners about the to-be-monitored cue in advance did not affect the degree to which learners inferred their self-assessments from the unspecific cue of cognitive load during problem-solving.

With regard to Research Question 1, we found that prompting learners to infer their self-assessments from performance-based cues fostered absolute accuracy (i.e., resulted in more accurate self-assessments) in comparison to prompting learners to infer their self-assessments from explanation-based cues. One explanation for this finding is as follows. Potentially, the learners who were prompted to utilize performance-based cues hardly accidentally solved the problems correctly by means of shallow strategies although they did not understand the solution rationale. Hence, problem-solving performance was a highly diagnostic cue. Moreover, utilizing the explanation-based cue might have been difficult. Specifically, unlike the learners who were prompted to monitor their problem-solving performance, which is highly salient during problem-solving and probably familiar to learners, the learners who were prompted to monitor their ability to explain the solution procedures during problem-solving potentially did not know what exactly they were supposed to monitor or what type of explanation would be of high quality. Hence, the learners may not have known how to utilize the explanation-based cue.

In terms of Research Question 2, we found that the learners who were informed about the cue they were to monitor already before the problem-solving phase showed better self-assessment accuracy than their counterparts. One explanation for this finding is that when learners were informed about the to-be-monitored cue in advance, they were attending to the cue already during problem-solving, which was less error-prone than having to remember or reconstruct the cue only after having finished the problem-solving phase. The finding that informing learners about the to-be-monitored cue already before the problem-solving phase fostered self-assessment accuracy furthermore indicates that the instruction to attend to performance-based or explanation-based cues during problem-solving did not overload learners. In line with this assumption, we did not find a significant effect of the timing of the cue prompt concerning mental effort or performance in the problem-solving phase (Research Question 3). Also, the timing of the cue prompt did not affect the correlation between mental effort and self-assessments. Given that the level of mental effort was generally relatively low (i.e., M  = 5.37 on a 9-point Likert scale), this pattern of results suggests that the learners were not overwhelmed by the requirement to monitor certain cues during problem-solving, even when the learners were informed in advance about the to-be-monitored cue.

Experiment 2

The main purpose of Experiment 2 was to understand why prompting learners to infer their self-assessments from explanation-based cues results in lower self-assessment accuracy than prompting learners to infer their self-assessments from performance-based as well as to investigate how learners could be supported to exploit the potential of explanation-based cues in learning from worked examples. As mentioned above, one explanation for the inferiority of explanation-based cues in Experiment 1 could be that learners lack knowledge about criteria for good or poor explanations of problem-solving procedures. In Experiment 2, we varied whether learners were provided with information that clarifies criteria for good or poor explanations or good or poor problem-solving performance, respectively (i.e., factor of cue criteria instruction ), as suggested by research on rubrics that transparently communicate assessment criteria to learners (for a recent overview, see Panadero et al., 2023 ; see also Panadero et al., 2024 ).

However, the beneficial effects of communicating assessment criteria to learners found in rubrics research were all found in settings in which learners were explicitly engaged in the task or activity whose quality they were to assess with the help of rubrics. In the initial problem-solving phase of example-based learning, however, it is reasonable to assume that learners hardly engage in explaining. Hence, learners may have not or only scarcely engaged in the activity whose quality they should assess with the help of rubrics. The guidance offered by rubrics, which communicate criteria for good or poor explanations, could thus be insufficient for improving the effects of explanation-based cues on self-assessment accuracy. Rather, to exploit the potential of explanation-based cues, learners might additionally need to be engaged in explanation activities during problem-solving. In Experiment 2, we hence also varied whether learners received self-explanation prompts in the problem-solving phase. Against this background, we addressed the following research questions in Experiment 2.

Research Question 1: Does the effect of the prompted cue type (performance-based vs. explanation-based) on self-assessment accuracy depend on whether learners are provided with criteria that help them interpret the cues and engaged in self-explanation activities during problem-solving?

In particular, we were interested in whether learners who are prompted to infer their self-assessments from explanation-based cues would exploit the potential of these cues and hence catch up or even outperform learners who are prompted to infer their self-assessments from performance-based cues only when they were both informed about criteria and engaged in self-explanation activities during problem-solving. Based on the findings of Experiment 1, we assumed that learners who are prompted to infer their self-assessments from performance-based cues would already be familiar with these cues and hence scarcely benefit from being informed about criteria for good problem-solving performance; they might even be hindered by being engaged in self-explanation activities, because it could distract them from monitoring their performance. We hence expected a three-way interaction between type of cue prompt , cue criteria instruction , and explanation prompts during problem-solving .

Like in Experiment 1, we were furthermore interested in whether the support measures that were implemented before or during the problem-solving phase affect mental effort and performance in the problem-solving phase.

Research Question 2: Does cue criteria instruction affect mental effort and performance in the problem-solving phase?

Research Question 3: Do self-explanation prompts affect mental effort and performance in the problem-solving phase?

The effect of prompted cue type was of small-to-medium size in Experiment 1 (i.e., η p 2  = 0.05). A power analysis using this effect size and an α -level of 0.05 and a β -level of 0.20 yielded a required sample size of N  = 152. This power analysis was fitted for detecting the main effects of the above-mentioned size in a 2 × 2 × 2 ANOVA, which corresponded with the design of Experiment 2 (see below). To increase statistical power, we decided to oversample and recruit N  = 268 German university students (72.4% female, 0.7% diverse; M Age  = 23.93 years, SD Age  = 4.03 years) majoring in various disciplines. We excluded one participant who reported having dyscalculia; 15 participants achieved a score higher than 90% in the pretest. Our final sample comprised 252 university students (72.6% female; M Age  = 23.90 years, SD Age  = 3.94 years). By this sample size, a power of 95% (i.e., β -level of 0.05) could be established in Experiment 2.

Like in Experiment 1, all learners were instructed on the cognitive skill of solving mathematical urn model problems . Again, the experimental manipulations took place during the initial problem-solving phase (i.e., Stage 3). As in Experiment 1, we varied whether the learners were prompted to infer their self-assessments from performance-based cues or from explanation-based cues (i.e., factor of prompted cue type ). Other than in Experiment 1, all learners were informed about the to-be-monitored cue already at the beginning of the problem-solving phase. We also varied (1) whether at the beginning of the problem-solving phase learners received instruction on criteria that should be met for a cue to indicate high quality (i.e., factor of cue criteria instruction ) and (2) whether learners were prompted to explain their solutions while problem-solving (i.e., factor of self-explanation prompts ). Hence, the experiment followed a 2 × 2 × 2 factorial between-subject design. Participants were randomly assigned to the conditions.

Written informed consent was obtained from all participants, and their voluntary participation was compensated with 20 Euros. The experiment was approved by the ethics committee of Ruhr University Bochum (No. EPE-2022–027).

Stage 1 and 2: Introductory Instructional Explanations and Worked Examples

The introductory instructional explanations and worked examples were the same as in Experiment 1.

All participants were provided with the same four stochastic problems as in Experiment 1. The experimental manipulations took place during this initial problem-solving phase. Once the participants had worked on all four problems, they were required to self-assess their level of understanding of the rationales of the problems’ solutions with the same two questions as in Experiment 1. Dependent on the factor of prompted cue type , learners were asked to infer their self-assessments from “how well you were able to solve the four problems you just completed” (i.e., performance-based cue) or from “how well you could explain how the four problems you just completed are solved” (i.e., explanation-based cue). All participants were informed about the to-be-monitored cue at the beginning of the initial problem-solving phase.

The learners who were provided with further support on how to utilize the prompted cue received instruction on criteria of high-quality explanations/performance (i.e., cue criteria instruction ). Specifically, the participants who were prompted to infer their self-assessments from performance-based cues received the following cue criteria instruction: “A complete and therefore very good solution means that you are able to successfully perform all necessary steps to solve the specific problem. A very poor solution, on the other hand, means that you are unable to perform any of the steps needed to solve the specific problem.” By contrast, the learners who were prompted to infer their self-assessments from explanation-based cues received the following cue criteria instruction: “A very good explanation means that you are able to explain why the specific task could be characterized as relevant/irrelevant and with/without replacement. Furthermore, a very good explanation shows that you are able to explain for which aspects of the solution approach, the type of stochastic principles plays a role and for what reason. Furthermore, a crucial aspect of a good explanation is the ability to clearly identify and articulate the specific areas within the solution approach where stochastic principles apply and the underlying reasons for their significance. A very poor explanation, on the other hand, would mean that you are unable to explain these aspects.”

The participants who were prompted to engage in self-explaining while problem-solving received a self-explanation prompt in conjunction with each of the four to-be-solved problems. The prompts required learners to explain “In which aspects of the solution approach does the task type play a central role, and for what reasons?” The learners should write their responses to the self-explanation prompts into a text box.

To assess the participants’ prior knowledge on stochastics, we posed the same pretest questions and applied the same scoring protocol as in Experiment 1. Interrater reliability was very good (ICC > 0.85) and internal consistency was acceptable, ω  = 0.67.

The problem-solving performance was scored via the same scoring protocol as in Experiment 1. Interrater reliability was very good (all ICCs > 0.85).

To assess the participants’ level of understanding concerning the four types of stochastics problems, we used the same posttest and scoring protocol as in Experiment 1. Interrater reliability was very good (all ICCs > 0.85). Internal consistency was very good as well, ω  = 0.85.

Self-Assessments and Self-Assessment Accuracy

Self-assessments of learners’ level of understanding were assessed by the same two questions as in Experiment 1, which again correlated strongly ( r  = 0.86, p  < 0.001) and were thus aggregated. Absolute accuracy was determined the same way as in Experiment 1.

As in Experiment 1, we asked participants to judge their subjectively invested mental effort while problem-solving after each problem on a 9-point Likert scale (i.e., higher scores represent higher mental effort) and averaged the ratings for further analyses ( ω  = 0.95).

As Experiment 1, Experiment 2 was conducted in an online learning environment on https://www.unipark.com , which participants accessed from their own devices. Until learners entered the initial problem-solving phase, the procedure was identical to Experiment 1.

The experimental manipulations took place during the initial problem-solving phase (i.e., Stage 3 of the sequence). Here, the participants were prompted to focus on either performance-based cues or explanation-based cues and were or were not provided with cue criteria instruction. In the conditions with self-explanation prompts, participants were asked to generate self-explanations while problem-solving. Participants could work on each problem as long as they wanted but could not return to a problem once they had clicked a button to proceed. Participants answered the question on mental effort after each problem. They then self-assessed their level of understanding, whereby we varied whether learners were prompted to infer their self-assessments from performance-based or explanation-based cues. Finally, all participants took the posttest.

The descriptive results are found in Table  2 .

Applying Bayesian ANOVAs, we found strong evidence for non-existing differences (null hypothesis) between the groups with regard to gender distribution, BF 01  = 29.72, HSGPA, BF 01  = 13.30, and prior knowledge, BF 01  = 39.77. We observed moderate evidence for non-existing differences with regard to age, BF 01  = 6.43. Overall, these results indicate that the random assignment resulted in comparable groups.

As in Experiment 1, we also tested whether the groups differed in their posttest performance. Bayesian ANOVAs showed substantial evidence for non-existing differences regarding the overall posttest score, BF 01  = 12.57, as well as regarding learner performance on the posttest tasks that were isomorphic to the tasks in the initial problem-solving phase, BF 01  = 5950.11. Hence, the effects on self-assessment accuracy found in the present study (see below) cannot be attributed to effects of the support measures on posttest performance.

To address Research Question 1, we ran a 2 × 2 × 2 ANOVA with the factors prompted cue type , cue criteria instruction , and self-explanation prompts . Most importantly, there was a statistically significant three-way interaction, F (1, 244) = 7.41, p  = 0.007, η p 2  = 0.03 (all other effects of the ANOVA were not statistically significant, all p  > 0.076). To explore the interaction pattern, in the first step, we analyzed the effects of prompted cue type and cue criteria instruction separately for the learners with and without self-explanation prompts.

For the learners without self-explanation prompts, a 2 × 2 ANOVA revealed a statistically significant main effect of prompted cue type, F (1, 118) = 4.01, p  = 0.048, η p 2  = 0.03. The learners who were prompted to use performance-based cues showed better absolute accuracy (i.e., values closer to zero). There was no statistically significant main effect of cue criteria instruction and also no statistically significant interaction, F (1, 118) = 0.14, p  = 0.705, η p 2  < 0.01, and F (1, 118) = 1.13, p  = 0.291, η p 2  = 0.01. For the learners with self-explanation prompts, by contrast, a 2 × 2 ANOVA did not yield a statistically significant main effect for prompted cue type, F (1, 126) = 0.17, p  = 0.678, η p 2  < 0.01. There was also no statistically significant main effect for cue criteria instruction, F (1, 126) = 0.31, p  = 0.579, η p 2  < 0.01. However, there was a statistically significant interaction effect, F (1, 126) = 8.37, p  = 0.005, η p 2  = 0.06 (for an illustration of the pattern of results, see Fig.  5 ).

Illustration of the effects of prompted cue type and cue criteria instruction for the learners with and without self-explanation prompts

In the next step, we explored the interaction effect between prompted cue type and cue criteria instruction for the learners with self-explanation prompts. We found that for the learners without cue instruction, performance-based cues yielded better absolute accuracy than explanation-based cues ( p  = 0.028, η p 2  = 0.08), whereas for the learners with cue instruction, explanation-based cues yielded better accuracy than performance-based cues ( p  = 0.044, η p 2  = 0.06).

In Research Questions 2 and 3, we were interested in whether cue criteria instruction and self-explanation prompts would affect mental effort and performance in the initial problem-solving phase. We addressed this research question by determining the main effects of these factors in a 2 × 2 × 2 ANOVA with the factors prompted cue type , cue criteria instruction , and self-explanation prompts . In terms of mental effort, the ANOVA revealed neither a statistically significant main effect of cue criteria instruction, F (1, 244) = 0.82, p  = 0.368, η p 2  < 0.01, nor a statistically significant main effect of self-explanation prompts, F (1, 244) = 1.94, p  = 0.165, η p 2  = 0.01. The only statistically significant effect yielded by this ANOVA was a statistically significant interaction between cue criteria instruction and self-explanation prompts, F (1, 244) = 4.70, p  = 0.031, η p 2  = 0.02. Self-explanation prompts increased mental effort for learners without cue instruction ( p  = 0.016, η p 2  = 0.05) but did not significantly affect mental effort for learners with cue instruction ( p  = 0.572, η p 2  < 0.01).

In terms of problem-solving performance, the ANOVA revealed neither a statistically significant main effect of cue criteria instruction, F (1, 244) = 1.92, p  = 0.167, η p 2  = 0.01, nor a statistically significant main effect of self-explanation prompts, F (1, 244) = 2.90, p  = 0.090, η p 2  = 0.01. In addition, none of the interactions effects was statistically significant, all p  > 0.064.

In terms of Research Question 1, we found that only when learners were provided with criteria that helped them to interpret the to-be-monitored cues and were engaged in self-explaining during problem-solving did the learners who were prompted to infer their self-assessments from explanation-based cues outperform their counterparts who were prompted to infer their self-assessments from performance-based cues in terms of self-assessment accuracy. When the learners who were prompted to infer their self-assessments from explanation-based cues received none or only one of these support measures, like in Experiment 1, prompting learners to use performance-based cues yielded higher self-assessment accuracy. One explanation for this pattern of results is that learners lack knowledge on how to interpret explanation-based cues and that learners scarcely engage in explaining during problem-solving on their own accord. Consequently, the learners who were prompted to monitor the highly salient cue of problem-solving performance, which likely was familiar to learners and hence easy to interpret, showed better accuracy when learners did not receive the supplementary support measures of cue criteria instruction and self-explanation prompts. Notably, even when the explanation-based learners received both support measures, their superiority over the performance-based learners in terms of self-assessment accuracy at least in part resulted from the fact that the self-explanation prompts appeared to hinder the learners who were prompted to monitor performance-based cues (see Fig.  5 ). Furthermore, two of the groups who were prompted to infer their self-assessments from performance-based cues, at least on a descriptive level, still showed lower absolute accuracy scores (i.e., better self-assessment accuracy) than the best-supported explanation-based group (see Table  2 ). Jointly, these results provide insight into how learners can be supported to exploit the potential of explanation-based cues in learning from worked examples and show that focusing learners on performance-based cues might be most efficient and effective.

General Discussion

The present study’s main goal was to investigate how self-assessment accuracy in the initial problem-solving phase of cognitive skill acquisition through learning from worked examples can be optimized. In particular, we were interested (a) in whether self-assessment accuracy would depend on whether learners were prompted to infer their self-assessments from explanation-based or performance-based cues and (b) in whether informing learners about the cue already before the problem-solving phase would matter. In view of Experiment 1’s results, we were furthermore interested (c) in whether learners can be supported in exploiting the potential of explanation-based cues through instruction on criteria for interpreting the cue and through prompting them to engage in self-explaining during problem-solving.

At least when learners did not receive further instructional support measures that helped them to monitor and utilize the cues, we found in both experiments evidence that prompting learners to infer their self-assessments from performance-based cues yields better self-assessment accuracy at the end of the initial problem-solving phase of learning from worked examples. From a theoretical view, we assumed that an advantage of performance-based cues would be that it is highly salient and that learners are familiar with this cue and that a disadvantage could be that learners could in some cases solve problems correctly although they did not understand the solution rationale (i.e., based on shallow problem-solving strategies), which would result in low diagnosticity. In terms of explanation-based cues, we assumed that they could be advantageous because self-explanation quality has been found to be a reliable predictor of learning outcomes in example-based learning and that a disadvantage could be that learners would believe that shallow explanations (e.g., explanations of shallow problem-solving strategies) could suffice. Across both experiments, we found clear evidence that prompting learners to infer their self-assessments from performance-based cues has the greatest net benefit regarding self-assessment accuracy. Furthermore, in Experiment 2, we found that the inferiority of explanation-based cues mainly stems from the facts that learners do not know when an explanation is of poor or good quality and that learners scarcely engage in explaining during problem-solving. Accordingly, the rubric-like information when an explanation is of high quality alone did not increase self-assessment accuracy. It is important to highlight, however, that this finding does not contradict the widespread finding that rubrics are helpful in student self-assessment (e.g., Krebs et al., 2022 ; Panadero et al., 2023 ). Rather, they highlight that when learners have not or only scarcely engaged in an activity or task, informing them about assessment criteria for the respective activity or task scarcely affects self-assessment accuracy. Importantly, our findings also highlight that engaging learners in an activity that is not aligned with the cues that are to be monitored detrimentally affects self-assessment accuracy. Evidently, at least when they also received cue criteria instruction, the learners who were to monitor performance-based cues were even hindered by the requirement to engage in self-explanation activities during problem-solving.

Jointly, these results indicate that, dependent on the presence of further support measures, prompting learners to infer their self-assessments from performance-based cues and prompting learners to infer their self-assessments from explanation-based cues can result in similar levels of self-assessment accuracy. However, in terms of efficiency, focusing learners on performance-based cues seems to be preferable. Unlike explanation-based cues, at least university students can readily utilize performance-based cues in forming self-assessments. Explanation-based cues, by contrast, require at least some further instructional support to result in similar levels of self-assessment accuracy.

The original motivation of the present study was to optimize self-assessment accuracy in learning from worked examples. Specifically, based on findings by Foster and colleagues (Foster et al. 2018 ), which suggested that learners spontaneously use their initial problem-solving performance to diagnose their level of understanding in the initial problem-solving phase of learning from worked examples and that learners decide to engage in further problem-solving (i.e., proceeding to Stage 4) too often, we intended to investigate whether prompting learners to infer their self-assessments from explanation-based cues could be a fruitful remedy. In view of the findings of our two experiments, we can clearly state that explanation-based cues are not the cure we had hoped for. By contrast, informing learners about the to-be-monitored cue already before the problem-solving phase did function in the expected manner. Although the effect was only of small-to-medium size, we can hence recommend that, at least when it comes to utilizing performance-based or explanation-based cues, informing learners that they need to monitor the cue already before they engage in problem-solving is beneficial. An obvious explanation for this effect is that when learners are informed about the to-be-monitored cues already before problem-solving, they do not or only to a lower degree need to reconstruct the cue afterwards, which might be less error-prone. As it does not seem to affect mental effort during problem-solving and thus does not increase the risk of cognitive overload, up-front information concerning to-be-monitored cues hence beneficially affects self-assessment accuracy in learning from worked examples.

Relating the Present Findings to Effort Monitoring and Self-Regulation

This article is part of a special issue on cognitive load and self-regulation, with a special eye on the research questions outlined in the EMR framework by de Bruin et al. ( 2020 ). We discuss the contributions of the present findings to these research questions.

A basic tenet of the EMR framework by de Bruin et al. ( 2020 ) is that mental effort is a cue that is frequently used by learners in forming self-assessments and that there is typically a negative relation between mental effort and judgments of learning. This assumption was supported by the meta-analysis of Baars et al. ( 2020 ), which was inspired by this framework. We have found negative relations between mental effort and self-assessments (Exp. 1), which is in line with the assumption of de Bruin et al. ( 2020 ) that mental effort plays a role in forming self-assessments.

De Bruin et al. ( 2020 ) also stated that in text learning, students might better refer to their ability to explain the text rather than judging their reading fluency when monitoring their learning (see RQ1 by de Bruin et al., 2020 ). We tested in our experiments whether an analogue assumption can be made also in the case of example-based skill acquisition: It might be better in terms of self-assessment accuracy to use the ability to explain problem solutions than to refer to the ability (or fluency) to solve problems. However, we could not support this assumption as performance-based cues were overall superior. A tentative conclusion relevant to the EMR framework is that it might depend on the learning method and/or the type of learning goals (declarative knowledge by learning from text; cognitive skill acquisition by example-based learning) which types of cue are especially useful for accurate self-assessment.

De Bruin et al. ( 2020 ) claimed that research should investigate which design aspects influence students’ monitoring and self-assessment (see RQ1 by de Bruin et al., 2020 ). Such findings are relevant in two respects: Understanding context effects and informing about possible support procedures for accurate self-assessment. Our results are revealing in at least two respects in this regard. First, we found that it makes a difference for self-assessment accuracy whether the learners are provided (or not) with both instruction on cue interpretation and self-explanation prompts when using explanation-based cues. Such support is not a necessary condition for the productive use of performance-based cues, that is, the usefulness of performance-based cues does not depend on such design factors. An interesting general, though, tentative conclusion is that such context or design factors may not generally be relevant for cue use but their relevance may depend on the specific type of cues to be used. Admittedly, further research has to test this claim. Second, a support factor that may be of general relevance for assessment accuracy is the timing of instruction on monitoring. We found that informing the learner before a learning phase to use specific cues in monitoring their learning fostered self-assessment accuracy, irrespective of the type of cue to be used. A specific advantage of this metacognitive support procedure is that it is easy to implement. In addition, this procedure did not induce additional effort or cognitive load, which might have been a potential negative side effect. The latter finding is also relevant to de Bruin et al.’s ( 2020 ) question for further research whether students should be made aware about issues of monitoring (see RQ3 by de Bruin et al., 2020 ). Our findings suggest “yes,” at least when it is done by the procedure used in our studies.

Limitations and Directions for Future Research

The present study has some limitations and raises important open questions to be addressed in future research. First, it is an open question whether the effects of utilizing explanation-based cues increase over time. As outlined above, our learners were probably very familiar with performance-based cues, but not with explanation-based cues. Although additional instructional support in the form of cue criteria instruction and self-explanation prompts enhanced the benefits of prompting learners to infer their self-assessments from explanation-based cues, those cues were likely nevertheless still new for the learners. Once learners have familiarized themselves with explanation-based cues and are potentially given feedback on the accuracy of their self-assessments, the benefits of these cues might potentially increase. This notion aligns with findings in strategy training literature, which indicate that longer interventions are usually required to overcome a utilization deficiency (e.g., Endres et al., 2021 ; Nückles et al., 2020 ; see also Abel et al., 2024 ; Trentepohl et al., 2022 ), meaning that even in principle effective strategies need to be trained and partly automated before they show positive effects. Hence, the lacking superiority of explanation-based cues even in the best-supported group in Experiment 2 does not need to be the end of research on the benefits of explanation-based cues.

Another issue that could be addressed in future research concerns the fact that in the present study, the initial problem-solving phase followed immediately after the worked-examples phase and that the posttest followed immediately after the initial problem-solving phase. Hence, it is an open question whether the pattern of results between the performance-based and explanation-based cues would depend on the delay between the phases. For example, the explanation-based cues might result in overconfident self-assessments when the delay between the worked-examples phase and the initial problem-solving phase is very short, because at this time, learners likely remember the principles and concepts and solution rationales that were previously explained very well. However, in view of the relatively high forgetting rates even after short delays (e.g., Karpicke, 2017 ; Rowland, 2014 ; see also Roelle et al., 2022 , 2023 ), such high rates of correct retrieval from memory might not reflect learners’ actual level of the to-be-learned content. As in authentic learning settings (e.g., in classroom lessons at high school), these phases are likely frequently separated by one or even several days (e.g., because learners need to engage in initial problem-solving for homework after some worked examples have been explained in the previous lesson); it would hence be fruitful to address the role of the delays between these phases for the effects found in the present study.

A third issue is how we formulated the self-assessment questions. They did not explicitly ask learners to predict how many of the given number of tasks they would be able to solve correctly. More concrete item formulations have been recommended by some researchers (e.g., Ackermann & Thompson, 2017 ) to help enable more valid self-assessments. In the present study, we admittedly do not know whether learners who said that they understood the solution rationales “very well” would expect to solve all problems correctly, which is why the absolute numbers of the self-assessment accuracy measure need to be interpreted cautiously. A further potential point of criticism with respect to how we measured the self-assessments is that we did not require learners to self-assess their level of understanding for each of the four types of problems separately. Consequently, we cannot rule out that, for instance, a student who assigned herself a score of 50% because she thought she understood the problems without replacement but not the problems with replacement actually correctly solved the problems with replacement but not the problems without replacement on the posttest. In this case, the student would be considered fully accurate in the present study although her self-assessments were actually inaccurate. A remedy for this potential validity threat would be to assess separate self-assessments for each type of problem in future research. Furthermore, like the above-mentioned limitation with respect to the formulation of the self-assessment items, this limitation casts doubt on the absolute numbers of the self-assessment measure. However, this limitation should be less relevant to the effects between groups we found in the present experiments. As it applied to all groups in a similar manner, this limitation cannot explain why some groups (e.g., the ones who were prompted to infer their self-assessments from performance-based cues) showed more accurate self-assessments in both experiments.

The limitations concerning the self-assessment measure relate to another open question in the present study. As we did not implement the fourth stage of the worked-example approach of example-based learning, we do not know whether the improvement in self-assessment through the different cues and support measures would actually matter, as it affects the effectiveness and efficiency of learners’ decision whether to return to studying a worked example or to begin intensive problem-solving. Future studies could hence implement the fourth phase as well as give learners the opportunity to flexibly switch between stages so as to explore cue instruction’s effects on both self-assessment and on learning from worked examples.

The present study contributes the following main points to understanding and optimizing self-assessment accuracy in the initial problem-solving phase of cognitive skill acquisition through learning from worked examples. First, prompting learners to infer their self-assessments from performance-based cues and explanation-based cues can lead to similar levels of self-assessment accuracy. However, learners might be more readily prepared to utilize performance-based cues, which is why we consider prompting learners to utilize this cue more efficient. Second, both information on assessment criteria and actual engagement in self-explaining seems to be necessary to exploit the potential of explanation-based cues. It is an open question whether learners would become better and better in utilizing explanation-based cues over time; in this case, the effects on self-assessment accuracy would increase and the required support would decrease on future occasions. Future research on this topic could be very fruitful. Third, informing learners about the to-be-monitored cue already before the initial problem-solving phase is an effective and easy to implement means to enhance self-assessment accuracy in example-based learning. Hence, to reduce learners’ tendency to prematurely proceed to Stage 4 and hence engage in further problem-solving too early, regardless of whether learners are prompted to infer their self-assessments from performance-based or explanation-based cues, learners should be informed about the to-be-monitored cues in advance.

Data Availability

Data will be made available on request.

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Waldeyer, J., Endres, T., Roelle, J. et al. How to Optimize Self-Assessment Accuracy in Cognitive Skill Acquisition When Learning from Worked Examples. Educ Psychol Rev 36 , 103 (2024). https://doi.org/10.1007/s10648-024-09944-4

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Title: cognidual framework: self-training large language models within a dual-system theoretical framework for improving cognitive tasks.

Abstract: Cognitive psychology investigates perception, attention, memory, language, problem-solving, decision-making, and reasoning. Kahneman's dual-system theory elucidates the human decision-making process, distinguishing between the rapid, intuitive System 1 and the deliberative, rational System 2. Recent advancements have positioned large language Models (LLMs) as formidable tools nearing human-level proficiency in various cognitive tasks. Nonetheless, the presence of a dual-system framework analogous to human cognition in LLMs remains unexplored. This study introduces the \textbf{CogniDual Framework for LLMs} (CFLLMs), designed to assess whether LLMs can, through self-training, evolve from deliberate deduction to intuitive responses, thereby emulating the human process of acquiring and mastering new information. Our findings reveal the cognitive mechanisms behind LLMs' response generation, enhancing our understanding of their capabilities in cognitive psychology. Practically, self-trained models can provide faster responses to certain queries, reducing computational demands during inference.

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