how to write math essay

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Course info, instructors.

• Prof. Haynes Miller
• Dr. Nat Stapleton
• Saul Glasman

Departments

• Mathematics

As Taught In

Learning resource types, project laboratory in mathematics.

Next: Revision and Feedback »

In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for good mathematical writing and the components of the writing workshop .

A central goal of the course is to teach students how to write effective, journal-style mathematics papers. Papers are a key way in which mathematicians share research findings and learn about others’ work. For each research project, each student group writes and revises a paper in the style of a professional mathematics journal paper. These research projects are perfect for helping students to learn to write as mathematicians because the students write about the new mathematics that they discover. They own it, they are committed to it, and they put a lot of effort into writing well.

Criteria for Good Writing

In the course, we help students learn to write papers that communicate clearly, follow the conventions of mathematics papers, and are mathematically engaging.

Communicating clearly is challenging for students because doing so requires writing precisely and correctly as well as anticipating readers’ needs. Although students have read textbooks and watched lectures that are worded precisely, they are often unaware of the care with which each word or piece of notation was chosen. So when students must choose the words and notation themselves, the task can be surprisingly challenging. Writing precisely is even more challenging when students write about insights they’re still developing. Even students who do a good job of writing precisely may have a different difficulty: providing sufficient groundwork for readers. When students are deeply focused on the details of their research, it can be hard for them to imagine what the reading experience may be like for someone new to that research. We can help students to communicate clearly by pointing out places within the draft at which readers may be confused by imprecise wording or by missing context.

For most students, the conventions of mathematics papers are unfamiliar because they have not read—much less written—mathematics journal papers before. The students’ first drafts often build upon their knowledge of more familiar genres: humanities papers and mathematics textbooks and lecture notes. So the text is often more verbose or explanatory than a typical paper in a mathematics journal. To help students learn the conventions of journal papers, including appropriate concision, we provide samples and individualized feedback.

Finally, a common student preconception is that mathematical writing is dry and formal, so we encourage students to write in a way that is mathematically engaging. In Spring 2013, for example, one student had to be persuaded that he did not have to use the passive voice. In reality, effective mathematics writing should be efficient and correct, but it should also provide motivation, communicate intuition, and stimulate interest.

To summarize, instruction and feedback in the course address many different aspects of successful writing:

• Precision and correctness: e.g., mathematical terminology and notation should be used correctly.
• Audience awareness: e.g., ideas should be introduced with appropriate preparation and motivation.
• Genre conventions: e.g., in most mathematics papers, the paper’s conclusion is stated in the introduction rather than in a final section titled “Conclusion.”
• Style: e.g., writing should stimulate interest.
• Other aspects of effective writing, as needed.

To help students learn to write effective mathematics papers, we provide various resources, a writing workshop, and individualized feedback on drafts.

Writing Resources

Various resources are provided to help students learn effective mathematical writing.

The following prize-winning journal article was annotated to point out various conventions and strategies of mathematical writing. (Courtesy of Mathematical Association of America. Courtesy of a Creative Commons BY-NC-SA license.)

An Annotated Journal Article (PDF)

This document introduces the structure of a paper and provides a miscellany of common mistakes to avoid.

Notes on Writing Mathematics (PDF)

LaTeX Resources

The following PDF, TeX, and Beamer samples guide students to present their work using LaTeX, a high-quality typesetting system designed for the production of technical and scientific documentation. The content in the PDF and TeX documents highlights the structure of a generic student paper.

Sample PDF Document created by pdfLaTeX (PDF)

Sample TeX Document (TEX)

Beamer template (TEX)

The following resources are provided to help students learn and use LaTeX.

LaTeX-Project. “ Obtaining LaTeX .” August 28, 2009.

Downes, Michael. “Short Math Guide for LaTeX.” (PDF) American Mathematical Society . Version 1.09. March 22, 2002.

Oetiker, Tobias, Hubert Partl, et al. “The Not So Short Introduction to LaTeX 2ε.” (PDF) Version 5.01. April 06, 2011.

Reckdahl, Keith. “Using Imported Graphics in LaTeX and pdfLaTeX.” (PDF) Version 3.0.1. January 12, 2006.

Writing Workshop

Each semester there is a writing workshop, led by the lead instructor, which features examples to stimulate discussion about how to write well. In Spring 2013, Haynes ran this workshop during the third class session and used the following slide deck, which was developed by Prof. Paul Seidel and modified with the help of Prof. Tom Mrowka and Prof. Richard Stanley.

The 18.821 Project Report (PDF)

This workshop was held before students had begun to think about the writing component of the course, and it seemed as if the students had to be reminded of the lessons of the workshop when they actually wrote their papers. In future semesters, we plan to offer the writing workshop closer to the time that students are drafting their first paper. We may also focus the examples used in the workshop on the few most important points rather than a broad coverage.

• Download video

This video features the writing workshop from Spring 2013 and includes instruction from Haynes as well as excerpts of the class discussion.

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Math Essay Writing Guide

It is often met that students feel wondered when they are asked to write essays in math classes. Actually, the tasks of math essay writing want to make students demonstrate their knowledge and understanding of mathematical concepts and ideas.

This kind of essay is what students of both college and high school students can be asked to create. Yes, this type of writing is quite special, and having its own tricks and demands. Still, guides for writing a math essay is mostly the same as for those of other subjects.

If you think you do not have enough time or skill to complete a math essay on your own, remember about the possibility to ask for essay help online .

Set Up Your Topic

Just like any other essay, math writing is to be started from choosing a topic. Here are several possible ways to go. First one wants you to choose any mathematical concept that seems to be interesting for you, like one of those you discussed with a teacher and classmates and want to investigate it a bit deeper. Another way is, you can choose any math problem you have solved in the past.

For this type of writing, you show up a problem, and then show your way towards solving it and getting the right answer. Whatever the type of essay is, you need to provide a brainstorm and find the topic worrying your mind the most, as to write about something you need to research it seriously. For instance think about any particular concept or equation of mathematics you would like to spend a bit more time to investigate, and then note your thoughts on a paper.

Consider the Audience

Thinking about the audience that is going to read your essay is a must for any essay, same thing goes for math paper writing. Mathematician P. R. Halmos offers the way to think about the particular person while writing an essay, in the text of his article “How to Write Mathematics”.

Halmos says it is good to think about someone who has math ways that “can stand mending”. To say in other words, when writing an essay, do not try jumping above your head and write the text for the audience that has the same skill in math as you do. Yes, you write a math essay in order to present the idea or to explain a problem solution. But still, you want to prove your method to be the best one. Try convincing the reader in that, and the essay is guaranteed to be interesting.

Concept Essay in Math

In case of math, concept essays look similar to those for other classes. In fact, you need to write a regular expository essay to complete your task. To do that, you research a certain math concept, analyze it, then form and develop your upcoming theoretical ideas basing on the experience and knowledge you could get when providing the investigation, and then claim it as a usual thesis statement.

Start writing your essay with the intro, importing the topic through it. include your claim about the theory there. The, you need to develop your claim in the further text, and to present reliable evidences you found during the research to prove your viewpoint. Write a conclusion, tie up any loose ends and readdress your theoretical info according to the way how it was provided before.

Math Equation Essay

To complete an equation essay successfully, you should show up the problem and solution at once, in the essay intro. Then, explain the problem significance and factors that made you choose your certain way towards the solution. Both significance and rationale are the same with a thesis statement, they serve as the base ground for your argumentation here.

Compose a paragraph that clearly shows the reader how to solve the problem according to your vision, make a “how-to” user guide for the chosen problem. If the problem is complex, set up a helpful graph that could demonstrate your equation result. Explain what can be seen on that graph. Same thing: define variables carefully and precisely with sentences like “Let’s think n is any real number.” Show up your problem solving methodical, guide the reader through the used formulas and explain why you used exactly those ones.

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How mathematical practices can improve your writing

Writing is similar to three specific mathematical practices: modelling, problem-solving and proving, writes Caroline Yoon. Here, she gives some tips on how to use these to improve academic writing

Caroline Yoon

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I feel for my students when I hand them their first essay assignment. Many are mathematicians, students and teachers who chose to study mathematics partly to avoid writing. But in my mathematics education courses, and in the discipline more generally, academic writing is part of our routine practice.

Mathematicians face some challenging stereotypes when it comes to writing. Writing is seen as ephemeral, subjective and context-dependent, whereas mathematics is seen as enduring, universal and context-free. Writing reflects self, but mathematics transcends it: they are distinct from each other.

This is a false dichotomy that can discourage mathematicians from writing. It suggests writing is outside the natural skill set of the mathematician, and that one’s mathematics training not only neglects one’s development as a writer but actively prevents it. Rather than capitulate to this false dichotomy, I propose we turn it around to examine how writing is similar to three specific mathematical practices: modelling, problem-solving and proving.

Three mathematical practices that can improve your writing

Mathematical modelling.

Let us consider a hypothetical mathematics education student who has spent weeks thinking, reading and talking about her essay topic, but only starts writing it the night before it is due. She writes one draft only – the one she hands in – and is disappointed with the low grade her essay receives.

She wishes she had started earlier but she was still trying to figure out what she wanted to say up until the moment she started writing. It was only the pressure of the deadline that forced her to start; without it, she would have spent even more time thinking and reading to develop her ideas. After all, she reasons, there is no point writing when you do not know what to write about!

This “think first, write after” approach, sometimes known as the “writing up” model is a dangerous trap many students fall into, and is at odds with the way writing works. The approach allows no room for imperfect drafts that are a necessary part of the writing process . Writing experts trade on the generative power of imperfect writing; they encourage writers to turn off their internal critics and allow themselves to write badly as a way of overcoming writing inertia and discovering new ideas. The “shitty first draft” is an ideal (and achievable) first goal in the writing process. Anyone can produce a sketchy first draft that generates material that can be worked on, improved and eventually rewritten into a more sharable form.

Mathematical modelling offers a compelling metaphor for the generative power of imperfect writing. Like polished writing, polished mathematical models are seldom produced in the first attempt. A modeller typically begins with some understanding of the real situation to be modelled. The modeller considers variables and relationships from his or her understanding of the real situation and writes them into an initial mathematical model.

The model is his or her mathematical description of the situation, written in mathematical notation, and the modeller who publishes a mathematical model has typically created and discarded multiple drafts along the way, just as the writer who publishes a piece of writing has typically written and discarded multiple drafts along the way.

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Problem-solving

Writing an original essay is like trying to solve a mathematics problem. There is no script to follow; it must be created by simultaneously determining one’s goals and figuring out how to achieve them. In both essay writing and mathematical problem-solving, getting stuck is natural and expected. It is even a special kind of thrill.

This observation might come as a surprise to mathematicians who do not think of their problem-solving activity as writing. But doing mathematics, the ordinary everyday act of manipulating mathematical relationships and objects to notice new levels of structure and pattern, involves scratching out symbols and marks, and moving ideas around the page or board.

Why do I care that mathematicians acknowledge their natural language of symbols and signs as writing? Quite frankly because they are good at it. They have spent years honing their ability to use writing to restructure their thoughts, to dissect their ideas, identify new arguments. They possess an analytic discipline that most writers struggle with.

Yet few of my mathematics education students take advantage of this in their academic writing. They want their writing to come out in consecutive, polished sentences and become discouraged when it does not. They do not use their writing to analyse and probe their arguments as they do when they are stuck on mathematical problems. By viewing writing only as a medium for communicating perfectly formed thoughts, they deny themselves their own laboratories, their own thinking tools.

I am not suggesting that one’s success in solving mathematical problems automatically translates into successful essay writing. But the metaphor of writing as problem-solving might encourage a mathematics education student not to give up too easily when she finds herself stuck in her writing.

Our hypothetical student now has a good draft that she is happy with. She is satisfied it represents her knowledge of the subject matter and has read extensively to check the accuracy of its content. A friend reads the draft and remarks that it is difficult to understand. Our student is unperturbed. She puts it down to her friend’s limited knowledge of the subject and is confident her more knowledgeable teacher will understand her essay.

But the essay is not an inert record judged on the number of correct facts it contains. It is also a rhetorical act that seeks to engage the public. It addresses an audience, it tries to persuade, to inspire some response or action.

Mathematical proofs are like expository essays in this regard; they must convince an audience. When undergraduate mathematics students learn to construct proofs of their own, a common piece of advice is to test them on different audiences. The phrase “Convince yourself, convince a friend, convince an enemy” becomes relevant in this respect.

Mathematicians do not have to see themselves as starting from nothing when they engage in academic writing. Rather, they can use mathematical principles they have already honed in their training, but which they might not have formerly recognised as tools for improving their academic writing.

Practical tips for productive writing beliefs and behaviours

• Writing can generate ideas. Free writing is a good way to start. Set a timer and write continuously for 10 minutes without editing. These early drafts will be clumsy, but there will also be some gold that can be mined and developed.
• Writing can be used to analyse and organise ideas. When stuck, try to restructure your ideas. Identify the main point in each paragraph and play around with organising their flow. 
• Writing is a dialogue with the public. Seek out readers’ interpretations of your writing and listen to their impressions. Read your writing out loud to yourself: you will hear it differently!

Caroline Yoon is an associate professor of mathematics at the University of Auckland.

This is an edited version of the journal article “The writing mathematician” by Caroline Yoon, published in For the Learning of Mathematics  and collected in The Best Writing on Mathematics , edited by  Mircea Pitici  (Princeton University Press).

If you would like advice and insight from academics and university staff delivered direct to your inbox each week,  sign up for the Campus newsletter .

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Extended Essay: Group 5: Mathematics

• General Timeline
• Group 1: English Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts
• Interdisciplinary essays
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• Brainstorming
• Pre-Writing
• Research Techniques
• The Research Question
• Paraphrasing, Summarising and Quotations
• Writing an EE Introduction
• Writing the main body of your EE
• Writing your EE Conclusion
• Sources: Finding, Organising and Evaluating Them
• Conducting Interviews and Surveys
• Citing and Referencing
• Check-in Sessions
• First Formal Reflection
• Second Formal Reflection
• Final Reflection (Viva Voce)
• Researcher's Reflection Space (RRS) Examples
• Information for Supervisors
• How is the EE Graded?
• EE Online Resources
• Stavanger Public Library
• Exemplar Essays
• Extended Essay Presentations
• ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics—eg geometry or fractal theory
• the elegance of mathematics in the proving of theorems—eg number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
• the effect of technology on mathematics:
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE . 

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. 

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

• The EE is a more substantial piece of work that requires formal research
• The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

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• Last Updated: May 17, 2024 8:11 AM
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How to Apply a Mathematical Approach to Essay Writing

The use of mathematical strategies has long gone beyond solving complex levels and problems, making it easier and faster to complete tasks from other disciplines. One example of an academic task where the math approach will come into handy is writing an essay. With various techniques, your academic grades will increase, and your writing style will prosper.

Beneficial Impact on Your Writing

As a queen of science, mathematics promotes the development of various skills applicable to solving diverse problems and the formation of true-and-tried strategies for completing multiple academic assignments. With accuracy, objectivity, and logical rigor as a few fundamental principles, it provides students with a powerful tool to optimize many learning processes.

Not the least of them is writing essays that combine diverse techniques and approaches, the alternation of which will allow students to pump a range of skills from different angles. Using various mathematical models contributes to a more in-depth understanding of multiple cases and concepts while delegating tasks to professionals will save time to develop extra skills, requiring to visit ScamFighter for honest reviews preliminarily to avoid making a mistake in the choice.

Regular application of mathematical techniques, accompanied by developing strategies based on your experience and specific secrets, helps significantly expand the list of abilities and enhance those you already have. Among them are:

• logical reasoning;
• analytical abilities;
• mathematical literacy;
• visualization skills;
• critical thinking;

Many of the above may be helpful to you outside of academics, boosting personal and professional growth. These include activities such as communication strengthened through developed argumentation skills, deep understanding of concepts, etc.

Subsequently, you will quickly and qualitatively analyze large volumes of complex materials, making informed conclusions. It will help you figure out is MyAssignmentHelp.com safe and answer similar issues to see through suspicious companies in the shortest possible time, eliminating the risk of twisting you around someone’s finger by contacting only trusted services.

Where It Will Come in Very Handy

The mathematical approach can become the core of many strategies for writing academic papers in multiple fields of knowledge. Narrowing the latter’s focus, we can highlight economics in studying complex processes and concepts that mathematical methods can help with. In addition to in-depth analysis of large volumes of data, they will help you predict the further development of economic processes and identify key trends.

It also applies to essays studying scientific and high-tech phenomena where math strategies will cost modeling and interpretation. In addition, the use of mathematical approaches when writing essays on philosophy strengthens the argumentation and evidence provided. The well-known approaches of deduction and induction will allow you to shape the paper’s logical sequence while maintaining the structure’s integrity.

Specialists with many years of experience are always ready to help you with any topic, regardless of academic discipline, while the paperhelp.org promo codes on reddit and other available gifts enhance your experience.

Math Techniques to Apply in Writing Papers

Many ways to make your academic paper better and more detailed while at the same time infusing your writing style with new skills are based on multiple math approaches. Among them is a statistical method that strengthens your arguments and thoughts by involving various facts, surveys, and analyses. Another way to improve your paper would be to conduct a unique survey and then implement the results and processed information.

The use of math models, which facilitate the study of complex concepts and phenomena, will be no less valuable. Its beneficial effect lies in predicting trends, making effective comparisons, and identifying correlations between several concepts. Boosting visualization with graphs, figures, and diagrams will help achieve the latter. Probability theory can help analyze and assess the probability of a particular event. It will be especially effective if your essay topic explores random phenomena and considers potential risks.

Beyond academic writing, climate change approaches help develop valuable skills for solving various problems. You will not notice how you start reading your favorite book, article, or EssayBot review with increased attention to detail and in-depth analysis of multiple statements.

A Few More Things to Consider

Writing an essay using mathematical approaches can make your paper richer, making it easier to complete various tasks at specific workflow stages and presenting the materials you have mastered in the best light. However, it is necessary to remember some nuances to avoid the opposite effect, which manifests in various shortcomings that worsen the quality of the essay and confuse readers.

One of the primary reasons for the latter is an overabundance of formal vocabulary, turning your paper into a treasure trove of mathematical concepts. It makes it necessary to maintain maximum clarity, providing all relevant information where required. The same goes for introducing a variety of visual components, moving the tracking of their relevance to the top of your to-do list.

It is also necessary to familiarize yourself with the central requirements and extra recommendations to find a mathematical approach to develop your topic quickly. At the same time, answers to questions like is EssayBot legit will bring you closer to successfully writing a paper without unnecessary investments. Another mandatory task is carefully proofreading and checking the essay after finishing writing, eliminating all the shortcomings and unnecessary things.

Final Thoughts

Using mathematical approaches to write essays can be advantageous from different angles, contributing to the development of a wide range of skills. However, adhering to a few points is essential to achieve maximum effect and avoid obstacles.

by: Effortless Math Team about 4 weeks ago (category: Blog )

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25 Interesting Math Topics: How to Write a Good Math Essay

writing good math essay

Mathematics is a fascinating world of numbers, shapes, and patterns. 

Whether you are a student looking to grasp math concepts or someone who finds math intriguing, these topics will spark your curiosity and help you discover the beauty of mathematics straightforwardly and engagingly.

In this article, I will explore interesting math topics that make this subject not only understandable but also enjoyable.

Why Write About Mathematics

First, it helps demystify a subject that many find intimidating. By breaking down complex mathematical concepts into simple, understandable language, we can make math accessible to a wider audience, fostering greater understanding and appreciation.

Second, writing about mathematics allows us to showcase the practical applications of math in everyday life, from managing personal finances to solving real-world problems.

This helps readers recognize the relevance of math and its role in various fields and industries.

Additionally, writing about mathematics can inspire curiosity and a love for learning.

It encourages critical thinking and problem-solving skills, promoting intellectual growth and academic success.

Finally, mathematics is a universal language that transcends cultural and linguistic barriers.

After discussing math topics, we can connect with a global audience, fostering a sense of unity and collaboration in the pursuit of knowledge

 25 Interesting Math Topics to Write On

 Mathematics is a vast and intriguing field, offering a multitude of interesting topics to explore and write about.

Here are 25 such topics that promise to engage both math enthusiasts and those seeking a deeper understanding of this fascinating subject.

1. Fibonacci Sequence: Delve into the mesmerizing world of numbers with this sequence, where each number is the sum of the two preceding ones.

2. Golden Ratio: Explore the ubiquity of the golden ratio in art, architecture, and nature.

3. Prime Numbers: Investigate the mysterious properties of prime numbers and their role in cryptography.

4. Chaos Theory: Understand the unpredictability of chaotic systems and how small changes can lead to drastically different outcomes.

5. Game Theory: Examine the strategies and decision-making processes behind games and real-world situations.

6. Cryptography: Uncover the mathematical principles behind secure communication and encryption.

7. Fractals: Discover the self-replicating geometric patterns that occur in nature and mathematics.

8. Probability Theory: Dive into the world of uncertainty and randomness, where math helps us make informed predictions.

9. Number Theory: Explore the properties and relationships of integers, including divisibility and congruence.

10. Geometry of Art: Analyze how geometry and math principles influence art and design.

11. Topology: Study the properties of space that remain unchanged under continuous transformations, leading to the concept of “rubber-sheet geometry.”

12. Knot Theory: Investigate the mathematical study of knots and their applications in various fields.

13. Number Systems: Learn about different number bases, such as binary and hexadecimal, and their significance in computer science.

14. Graph Theory: Explore networks, relationships, and the mathematics of connections.

15. The Monty Hall Problem: Delight in this famous probability puzzle based on a game show scenario.

16. Calculus: Examine the principles of differentiation and integration that underlie a wide range of scientific and engineering applications.

17. The Riemann Hypothesis: Consider one of the most famous unsolved problems in mathematics involving the distribution of prime numbers.

18. Euler’s Identity: Marvel at the beauty of Euler’s equation, often described as the most elegant mathematical formula.

19. The Four-Color Theorem: Uncover the fascinating problem of coloring maps with only four colors without adjacent regions sharing the same color.

20. P vs. NP Problem: Delve into one of the most critical unsolved problems in computer science, addressing the efficiency of algorithms.

21. The Bridges of Konigsberg: Explore a classic problem in graph theory that inspired the development of topology.

22. The Birthday Paradox: Understand the surprising likelihood of shared birthdays in a group.

23. Non-Euclidean Geometry: Step into the world of geometries where Euclid’s parallel postulate doesn’t hold, leading to intriguing alternatives like hyperbolic and elliptic geometry.

24. Perfect Numbers: Learn about the properties of numbers that are the sum of their proper divisors.

25. Zero: The History of Nothing: Trace the historical and mathematical significance of the number zero and its role in the development of mathematics.

How to Write a Good Math Essay

Mathematics essays , though often perceived as daunting, can be a rewarding way to delve into the world of mathematical concepts, problem-solving, and critical thinking.

Whether you are a student assigned to write a math essay or someone who wants to explore math topics in-depth, this guide will provide you with the key steps to write a good math essay that is clear, concise, and engaging.

1. Understanding the Essay Prompt

Before you begin writing, it’s crucial to understand the essay prompt or question.

Analyze the specific topic, the scope of the essay, and any guidelines or requirements provided by your instructor.

Mostly, this initial step sets the direction for your essay and ensures you stay on topic.

2. Research and Gather Information

You need to gather relevant information and resources to write a strong math essay. This includes textbooks, academic papers, and reputable websites.

Make sure to cite your sources properly using a recognized citation style such as APA, MLA, or Chicago.

3. Structuring Your Math Essay

Start with a clear introduction that provides an overview of the topic and the main thesis or argument of your essay. This section should capture the reader’s attention and present a roadmap for what to expect.

The body of your essay is where you present your arguments, explanations, and evidence. Use clear subheadings to organize your ideas. Ensure that your arguments are logical and well-structured.

Begin by defining any important mathematical concepts or terms necessary to understand your topic.

Clearly state your main arguments or theorems. Please support them with evidence, equations, diagrams, or examples.

Explain the logical steps or mathematical reasoning behind your arguments. This can include proofs, derivations, or calculations.

Ensure your writing is clear and free from jargon that might confuse the reader. Explain complex ideas in a way that’s accessible to a broader audience.

Whenever applicable, include diagrams, graphs, or visual aids to illustrate your points. Visual representations can enhance the clarity of your essay.

Summarize your main arguments, restate your thesis, and offer a concise conclusion. Address the significance of your findings and the implications of your research or discussion.

4. Proofreading and Editing

Once you’ve written your math essay, take the time to proofread and edit it. Pay attention to grammar, spelling, punctuation, and the overall flow of your writing.

Ensure that your essay is well-organized and free from errors.

Consider seeking feedback from peers or an instructor to gain a fresh perspective.

5. Presentation and Formatting

A well-presented essay is more likely to engage the reader. Follow these formatting guidelines:

• Use a legible font (e.g., Times New Roman or Arial) in a standard size (12-point).
• Double-space your essay and include page numbers if required.
• Create a title page with your name, essay title, course information, and date.
• Use section headings and subheadings for clarity.
• Include a reference page to cite your sources appropriately.

6. Mathematical Notation and Symbols

Mathematics relies heavily on notation and symbols. Ensure that you use mathematical notation correctly and consistently.

If you introduce new symbols or terminology, define them clearly for the reader’s understanding.

7. Seek Clarification

If you encounter difficulties or ambiguities in your math essay, don’t hesitate to seek clarification from your instructor or peers.

Discussing complex mathematical concepts with others can help you refine your understanding and improve your essay.

8. Practice and Feedback

Writing math essays, like any skill, improves with practice. The more you write and receive feedback, the better you’ll become.

Take your time with initial challenges. Instead, view them as opportunities for growth and learning.

With dedication and attention to detail, you can craft a math essay that not only conveys your mathematical knowledge but also engages and informs your readers.

Josh Jasen or JJ as we fondly call him, is a senior academic editor at Grade Bees in charge of the writing department. When not managing complex essays and academic writing tasks, Josh is busy advising students on how to pass assignments. In his spare time, he loves playing football or walking with his dog around the park.

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Essays About Math: Top 10 Examples and Writing Prompts 

Love it or hate it, an understanding of math is said to be crucial to success. So, if you are writing essays about math, read our top essay examples.  

Mathematics is the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them . It can be used for a variety of purposes, from calculating a business’s profit to estimating the mass of a black hole. However, it can be considered “controversial” to an extent.

Most students adore math or regard it as their least favorite. No other core subject has the same infamy as math for generating passionate reactions both for and against it. It has applications in every field, whether basic operations or complex calculus problems. Knowing the basics of math is necessary to do any work properly. 

If you are writing essays about Math, we have compiled some essay examples for you to get started. 

1. Mathematics: Problem Solving and Ideal Math Classroom by Darlene Gregory 

2. math essay by prasanna, 3. short essay on the importance of mathematics by jay prakash.

• 4.  Math Anxiety by Elias Wong

5. Why Math Isn’t as Useless as We Think by Murtaza Ali

1. mathematics – do you love or hate it, 2. why do many people despise math, 3. how does math prepare you for the future, 4. is mathematics an essential skill, 5. mathematics in the modern world.

“The trait of the teacher that is being strict is we know that will really help the students to change. But it will give a stress and pressure to students and that is one of the causes why students begin to dislike math. As a student I want a teacher that is not so much strict and giving considerations to his students. A teacher that is not giving loads of things to do and must know how to understand the reasons of his students.”

Gregory discusses the reasons for most students’ hatred of math and how teachers handle the subject in class. She says that math teachers do not explain the topics well, give too much work, and demand nothing less than perfection. To her, the ideal math class would involve teachers being more considerate and giving less work. 

You might also be interested in our ordinal number explainer.

“Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.”

In her essay, Prasanna gives readers a basic idea of what math is and its importance. She additionally lists down some of the many uses of mathematics in different career paths, namely managing finances, cooking, home modeling and construction, and traveling. Math may seem “useless” and “annoying” to many, but the essay gives readers a clear message: we need math to succeed. 

“In this modern age of Science and Technology, emphasis is given on Science such as Physics, Chemistry, Biology, Medicine and Engineering. Mathematics, which is a Science by any criterion, also is an efficient and necessary tool being employed by all these Sciences. As a matter of fact, all these Sciences progress only with the aid of Mathematics. So it is aptly remarked, ‘Mathematics is a Science of all Sciences and art of all arts.’”

As its title suggests, Prakash’s essay briefly explains why math is vital to human nature. As the world continues to advance and modernize, society emphasizes sciences such as medicine, chemistry, and physics. All sciences employ math; it cannot be studied without math. It also helps us better our reasoning skills and maximizes the human mind. It is not only necessary but beneficial to our everyday lives. 

4.   Math Anxiety by Elias Wong

“Math anxiety affects different not only students but also people in different ways. It’s important to be familiar with the thoughts you have about yourself and the situation when you encounter math. If you are aware of unrealistic or irrational thoughts you can work to replace those thoughts with more positive and realistic ones.”

Wong writes about the phenomenon known as “math anxiety.” This term is used to describe many people’s hatred or fear of math- they feel that they are incapable of doing it. This anxiety is caused mainly by students’ negative experiences in math class, which makes them believe they cannot do well. Wong explains that some people have brains geared towards math and others do not, but this should not stop people from trying to overcome their math anxiety. Through review and practice of basic mathematical skills, students can overcome them and even excel at math. 

“We see that math is not an obscure subject reserved for some pretentious intellectual nobility. Though we may not be aware of it, mathematics is embedded into many different aspects of our lives and our world — and by understanding it deeply, we may just gain a greater understanding of ourselves.”

Similar to some of the previous essays, Ali’s essay explains the importance of math. Interestingly, he tells a story of the life of a person name Kyle. He goes through the typical stages of life and enjoys typical human hobbies, including Rubik’s cube solving. Throughout this “Kyle’s” entire life, he performed the role of a mathematician in various ways. Ali explains that math is much more prevalent in our lives than we think, and by understanding it, we can better understand ourselves. 

Writing Prompts on Essays about Math

Math is a controversial subject that many people either passionately adore or despise. In this essay, reflect on your feelings towards math, and state your position on the topic. Then, give insights and reasons as to why you feel this way. Perhaps this subject comes easily to you, or perhaps it’s a subject that you find pretty challenging. For an insightful and compelling essay, you can include personal anecdotes to relate to your argument. 

It is well-known that many people despise math. In this essay, discuss why so many people do not enjoy maths and struggle with this subject in school. For a compelling essay, gather interview data and statistics to support your arguments. You could include different sections correlating to why people do not enjoy this subject.

In this essay, begin by reading articles and essays about the importance of studying math. Then, write about the different ways that having proficient math skills can help you later in life. Next, use real-life examples of where maths is necessary, such as banking, shopping, planning holidays, and more! For an engaging essay, use some anecdotes from your experiences of using math in your daily life.

Many people have said that math is essential for the future and that you shouldn’t take a math class for granted. However, many also say that only a basic understanding of math is essential; the rest depends on one’s career. Is it essential to learn calculus and trigonometry? Choose your position and back up your claim with evidence. 

Prasanna’s essay lists down just a few applications math has in our daily lives. For this essay, you can choose any activity, whether running, painting, or playing video games, and explain how math is used there. Then, write about mathematical concepts related to your chosen activity and explain how they are used. Finally, be sure to link it back to the importance of math, as this is essentially the topic around which your essay is based. 

If you are interested in learning more, check out our essay writing tips !

For help with your essays, check out our round-up of the best essay checkers

Martin is an avid writer specializing in editing and proofreading. He also enjoys literary analysis and writing about food and travel.

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IB Math EE - Propel Your Mind To A 34/34

Unlock the secrets to acing your IB Math EE with a guaranteed 34/34 score! Propel your mind to success and make the most of your potential. 💯

Table of content

Extended essay & what is it❓, ib math ee vs math ia 🥊 , wth is an ib math extended essay 🌋, a brief about ib math ee 🩲, sexy pointers you can't-miss 🤤, 4 ways to find the right math ee topic ⭕, formulate your research question 🔎, planning your research & essay 📖, structuring your essay 🏗️, ib math ee reflection, what to do 🪞, ib math ee criteria 🧮, ib math ee examples 🛹.

It's time we address the elephant in the room.

IB Mathematics Extended Essay.

There, we said it.

If you've taken up IB Math EE, we're here to tell you that it isn't over, contrary to what you might have heard.

Researching, planning, and finally writing a good IB Math EE is no walk in the park, but rest assured that you'll feel different once you've gone through this valuable document.

Nail IB presents the only comprehensive guide you need to nail your IB Math EE.

Let's keep it accurate.

IB Math EE is a rigorous, independent, academic research essay that calls for,

• a keen interest in Mathematics,
• strong mathematical aptitude & reasoning,
• a focused and disciplined approach, and most importantly,
• essential tips, techniques, and quality guidance.

When one opts for IB Math EE, one should ensure a strong passion for Mathematics and a solid mathematical foundation. Not to mention being willing to devote their time and effort to this self-directed research.

Disclaimer -  If you have second thoughts, you should reconsider and re-evaluate your choice because it's no use aiming in the dark.

There needs to be more!

Invaluable tips and techniques are the last missing piece of the IB Math EE puzzle.

Given the panic and stigma around Math Extended Essay, what students need, is not some more panic; instead, expert guidance to keep them pumped to write their EE papers with skill, precision, and utmost zeal. And so, true to our word, we're here to help you.

Say it out loud for me - I got this!

Before diving any further, we are thrilled to share our premium IB Math resources. Check out the  IB Math AI SL  bundle and the  IB Math AI HL  bundle, including everything from comprehensive, up-to-date video lecture courses by Adam Nazha to curated IB Resource Libraries. All your IB DP Math queries are now answered!

While you're at it, check out our  IB Math AA SL  repository, where Patrick Jones (yep, you got that right, our very own  PatrickJMT  - the best Mathematics instructor in the world) will guide you with a brilliant video lecture course he has created to help you nail your concepts and exams alike! Happy learning!

Returning to our one-stop guide for all things IB Math EE, let us see what this article will cover.

• Extended Essay & What is it ❓
• IB Math EE Vs Math IA  🥊
• WTH Is An IB Math Extended Essay?  🌋
• A Brief About IB Math EE ?  🩲
• Sexy Pointers You Can't Miss  🤤
• 4 Ways To Find The Right Math EE topic  ⭕
• Formulate Your Research Question  🔎
• Planning Your Research and Essay  📖
• Structuring Your Essay  🏗️
• Writing Your Essay Writing Your Reflection  🪞
• IB Math EE Criteria  🧮
• IB Math EE Examples  🛹

First things first, let’s briefly discuss what an Extended Essay is.

As the IB defines it, the Extended Essay is a  4000-word in-depth  study, part of the IB Diploma Programme core mandatory for all students.

A  500-word  reflection component-inclusive of 3 reflections - is submitted with the academic writing.

This, of course, is done under the supervision of your IB advisor. The critical thing to note is that you can choose to write an Extended Essay on any subject offered by the IB in your session, though it is highly recommended you settle on a topic you are studying as a part of your IB curriculum.

The purpose of an Extended Essay is to motivate students to conduct formal research on a subject area of interest, independently work on the chosen research question and gain guidance from their respective IB mentors every step of the way.

The IB highlights the significance of the Extended Essay:

• Hands-on learning for undergraduate research
• An opportunity for students to research an area of interest relating to one of the 6 DP subjects opted for by the student.

The skills the Extended Essay aims to develop in students are:

• Coming up with a relevant Research Question
• Personally engaging with a topic of exploration
• A coherent communication of ideas
• Strong Argument building

For better understanding, go through  this document on Extended Essays   by the IB. It will make things more transparent.

Students often confuse their Internal Assessments with Extended Essays, which is a grave mistake. Gaining clarity on both these components of the IB DP core is essential. Let us understand the significant difference between the two.

• While Internal Assessments require students to investigate and explore an idea, Extended Essays are more formal. Students need to perform primary and secondary research on a research question they choose based on a diverse topic about the subject. Since EE is an independently researched essay, your mentor may only be able to give you some of the answers you wanted, unlike the IA.
• Students must write one Extended Essay on a subject of their choice for their IB Diploma Programme, but I must be prepared for all the topics.
• Internal Assessments are graded internally by the subject instructor and then moderated externally. Extended Essays are marked externally by examiners appointed by the IB. Your grade on your Extended Essay is combined with your Theory of Knowledge Essay/Exhibition score to assign you your overall score/points.

Word of caution:  Do not choose the same investigation topic/research question for your Internal Assessment and the Extended Essay.

For a much better breakdown of the EE document, you must go through our article on the  IB Extended Essay . It contains an IB EE checklist you must attend to and a detailed overview of the structure and planning of the EE.

Now that we’ve got our basics to, let’s get down to business. The fear around IB Math Extended Essay makes the most confident students hesitate and doubt their choices. But we aren’t here to scare you. The myth about the horrors of the IB Math EE isn’t all false; it’s a caution. Because unless you’re prepared with ammunition, strategy, and the will to put in the effort, there’s a slim chance you can survive the Math Extended Essay battle.

If you’ve opted for Math Extended Essay, we assume you have a strong passion for Mathematics. When the going gets tough while working on one’s Extended Essay-which, which is usually the case-your only hope at the end of the tunnel is your drive for the subject you’ve chosen. Being a rigorous subject for writing one’s Extended Essay, Mathematics can be incredibly demanding. So unless you want to play it risky, we suggest you reassess your liking for Mathematics. Once you know for sure, that’s when it begins. Lots of research. Since it is an independently written document, you want to be doing your homework well.

We will further break down the IB Math Extended Essay, from planning to execution, so that you can organize your thoughts and make appropriate decisions.

The Math Extended Essay is an in-depth research document covering any topic with a mathematical focus, i.e., not limited to the mathematics theory (shouldn’t be entirely descriptive). IB has divided Math Extended Essays into six categories:

• the applicability of mathematics to solve both real and abstract problems
• The beauty of mathematics examples includes geometry or fractal theory.
• the application of mathematics in the proving of theorems, for example, number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• the effect of technology on mathematics
• in creating links between different branches of mathematics,
• Or in bringing about a new branch of mathematics or causing a particular unit to flourish.

Your Math EE topic should be an extension of your IB Maths syllabus or the practical application of the knowledge you’ve gained in class.

Before moving on to the planning and structure of the Math Extended Essay, here are some pointers you absolutely cannot afford to miss:

• Attempting a Math EE requires a decent amount of hard work. While conducting preliminary research, ensure you land on a topic you can personally engage with and are familiar with. Going for a complicated subject, you can’t comprehend and interpret futile.
• The mathematical work you put in will have to meet a certain level of sophistication, so avoid going for a topic that gives rise to a trivial research question. Your research question shouldn’t be too generic or broad on similar lines. Ensure you can sufficiently narrow down your area of investigation.
• Another thing to remember is that the topic you finally choose should have a good research foundation and room for a novel contribution.
• Incorporate Primary and Secondary research wherever appropriate.
• Proper Referencing should be done for the essay.
• For Reflection, emphasize the Planning, Research, and Writing Processes.

Spitball ideas -  You begin here. Write down any interesting ideas you can come up with. This is your brainstorming session.

Do your Research -  You could not, would not want to meddle with this step, let alone skip it. Research. Read reports, articles, and documentation. Keep jotting important points down simultaneously. The study will and must go on throughout your search for the right math EE topic.

Approach professors/professionals/experts -  Contact concerned lecturers, professors, and industry professionals. They can provide you with invaluable insights. It would be best if you also discussed ideas with your mentor.

Point to Note -  Your goal should be to find a topic you understand and contribute to. It is always recommended to refer to your Math syllabus; something there inspires you to get the ball rolling!

Your essay will be structured as a document answering the Research Question you’re working on. It should be focused, clear and arguable. You will build your essay around your Research Question; hence pay close attention to it.

All you will include in your essay must be mentioned in your Research Question. This means the focused area you will be exploring and the methods you will use to achieve a plausible outcome.

Honing your Research Question is a continuous process. If it appears relatively easy or complex, please rephrase it. Good Research Questions may start with: “How can we model…”, “To what extent…” etc.

Collect Primary and Secondary data and incorporate it wherever appropriate.

Primary sources for Math research include 

• Data-gathering
• Visualization
• Abstraction
• Conjecturing

A few sources to gather Secondary data include Google Scholar, textbooks, databases such as JSTOR, etc. For your essay, know your aims and devise a step-by-step plan to answer your research question while maintaining a mathematical focus.

• Though you can approach your essay in whichever way you like, there should be a consistent logical structure.
• The work done in your essay should develop to answer your research question.
• Subheadings will provide your work with much-needed coherence and viability.
• Describe your way of thinking
• Write definitions and Conjectures.
• Use symbols, theorems, graphs, and diagrams
• Justify your conclusions.
• Visual aids such as graphs and diagrams should be included in the body, while tables and computer programs should be mentioned in the footnotes or the appendix.
• Data must be analyzed appropriately using relevant techniques, correctly reasoned arguments, and adequate methodology to achieve a result.
• Provide the necessary explanation and commentary for all your work.
• Throughout the writing, you may need to re-evaluate the method, approach, and structure to fit the word count adequately.

Once you’re finished writing, you will have to reassess everything from scratch- the equations, the theory, etc., to ensure the coherence of your essay.

• The three reflections should highlight how the process of writing your essay changed in due course of work and what you’ve learned from it.
• The Reflection should emphasize the planning, research, and writing process.
• You should discuss your choices, the re-evaluations you had to make, the limitations of your work, and how you overcame them, if at all.
• The three reflections are written at the beginning, mid, and towards the end of your essay and should have a word limit of approximately 150, 150, and 200, respectively.

Extended Essays are assessed externally by IB-appointed examiners and are marked on a scale of 0 to 34. The score obtained by a student corresponds to a particular band. The bands are:

A -  refers to work of an excellent standard (Level 6)

B -  refers to the creation of a good standard (Level 6)

C -  refers to work of a satisfactory standard (Level-12)

D -  refers to the product of a mediocre standard (Level 4)

E -  refers to the design of an elementary average (Level 6)

Anything below D will be considered a failing grade, and the student will not be awarded the IB diploma.  As we said, your EE is not a component you can mess up.

The Extended Essay Rubric includes the following Assessment Criteria:

Criterion A -   Focus and Method (Covers the topic, research question, and methodology)

Criterion B -  Knowledge and Understanding (Covers context, subject-specific terminology, and concepts)

Criterion C -  Critical Thinking (Covers research, analysis, discussion, and evaluation)

Criterion D -  Presentation (Covers structure, layout)

Criterion E -  Engagement (Covers reflection on planning and progress)

Now that we’ve discovered and learned about the process of writing a Math EE, here are a couple of ideas to give you an idea about how your Math EE questions should be framed:

Topic -  Archimedes’ calculation of areas

Research Question -  What is the legacy of Archimedes’ calculations of circular and parabolic areas in today’s integration methods?

Topic -  Approximation of irrational numbers by rational numbers

Research Question -  How well can π, e, √2, and other irrationals be approximated by rational numbers?

Topic -   The geometry of navigation

Research Question -  What was the role of mathematics and geometry in navigation when we relied on the stars? Does it still play a part now we have manufactured satellites?

You should also check out this  sample band, A Math EE, published by the IB . This will give you an honest insight into making a band-A essay. Also, go through  band B, C, and D extended essays  to understand the loopholes to avoid.

And that’s a wrap!

We hope this comprehensive IB Math EE guide answers your queries regarding the EE. We also suggest you go through  this IB Extended Essay guide  to clarify the Extended Essay component of your IB DP curriculum. You should also try Nail IB’s Extended Essay guide; check it out  here !

At Nail IB, we’re committed to delivering A-quality guidance so that your IB DP journey is smooth and successful. You can explore  our take-test  series here and access   premium guides  here.

Happy learning!

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Reflecting on My Own Math Experiences

Hi thank you so much for being here..

Welcome! I am so glad you have come across this post! My name is Julia Park and I am a senior at Millersville University! I am an Early Childhood Education major and I have learned so much so far! If you have a moment, feel free to check out my previous blog posts!

In my last post, I shared information about learning centers in math class! In this post, I will be reflecting on my mathematical journey. My experiences in math have really shaped the way I teach my students.

My Early Math Memories

I believe that early math experiences can really shape a child’s mindset towards mathematics. It has definitely shaped mine. Unfortunately, it has been a long journey of growing my interest in math, and I am still working on it! 

When I was in elementary school, even up until my time at Millersville, math has been a huge struggle for me. I have grown up with the incredibly damaging misconception that you have to be a “math person” to excel in math.  A lot of my peers had the same mindset, which made it even harder to let go of those limiting thoughts. 

I discussed this in my growth mindset blog post , but “math people” do not exist! I have my own reasons as to why I thought there were math people, but children’s experiences often vary. I think my fixed mindset was formed from experiences with not-so-nice teachers, the pressure of time limits and the need for accuracy in class, and a lack of hands-on learning. Those are just a few ideas of why I think I have had a tough time with math and I will be discussing more ideas later in this post!

Although it was hard to get through math class sometimes, I am really grateful that I have had these experiences because I can learn from them and relate to my own students. I want my students to feel comfortable with asking for help and to know that it is possible to learn and grow in many ways!

What I Have Learned From Past Teachers

Through my time as a student in math class, I have had many different experiences with a variety of teachers. I want to share the good and the bad of what I have gone through because I think it is beneficial for teachers to reflect on all experiences related to learning. We can take what we learn to inform our own teaching practices. 

Positive approaches I have learned from teachers:

• Providing assistance outside of class
• Using a hands-on learning approach
• Giving time to practice skills in class
• Utilizing interactive math games
• Facilitating class discussions 
• Being kind and encouraging when a student is struggling 

Approaches of teachers that were difficult for me: 

• Focusing on accuracy only and not effort
• Putting pressure on students to turn in extensive assignments with a limited amount of time
• Teaching new concepts too fast
• Using too many lectures and PowerPoint presentations
• Not having time to reflect on concepts in class
• Being intimidating when a student is struggling 

Every student learns differently. These experiences are unique to me and not everyone will be able to relate to what I have taken from my past math classes. However, I think it is important to recognize that although one strategy might work for one student, it might not work for another student.  This notion emphasizes the need for differentiation. I will be discussing differentiation more in the next section. 

Strategies I Want to Use to Teach Math

As I finish this semester at Millersville University, I am leaving with so many new ways of teaching math that I was not even aware of previously. I have a new passion for making math class fun and interesting for my students. The following are some examples of strategies I would love to incorporate in my future math class: 

• My math instruction will be differentiated based on my students’ needs. I will monitor their progress through various assessments and observations to modify or individualize my instruction when needed.
• Hands-on learning will be included to increase the engagement and participation of my students. I want to make math fun and exciting!!
• Class discussions will be a huge part of my mathematics instruction. Discussions in math class promote a deeper understanding of mathematical concepts in children.  
• I would love to try to use interactive notebooks to organize my students’ learning and create engaging experiences. I had not heard of these notebooks until this year and I love them!
• Technology , manipulatives , and children’s literature are just a few tools I plan on using to enhance mathematics instruction for my students. 
• Parent involvement is very important for a child’s education and I will consistently keep in contact with families to increase this involvement. 
• I am very passionate about modeling a growth mindset for my students. I want my students to believe in themselves and in their ability to grow.
• I will strive to create a safe and welcoming environment for my students. I want them to be comfortable with sharing their ideas and to not fear making mistakes. To do this, I will value effort just as much as accuracy. 

Mistakes Are Learning Opportunities!

One of the biggest lessons I have learned throughout my time at Millersville is that making mistakes is okay. I used to put so much pressure on myself to be perfect and know everything, but that is not healthy. Teachers are not robots made to feed information to students. Instead, we have a purpose to learn alongside our students and to welcome mistakes as learning opportunities.

I am much more comfortable now being honest with my students in moments of uncertainty. I would rather figure something out with them than provide them with the wrong information. It’s really fun to explore ideas with students and work together toward a common goal. These experiences with students are valuable and strengthen the student-teacher relationship. When children trust their teachers, they are more engaged, motivated, and feel an increased amount of comfort when reaching out for help and sharing their thoughts with others. 

Check out my blog post about growth mindset to learn more about the importance of making mistakes and the value of having a positive mindset in math class!

Thank you so much for reading!

I had a blast sharing my mathematical experiences with you all! I have grown so much through the years and I can’t wait to keep growing as I gain more experience. I hope you learned about some ways you can teach mathematics in your own classroom! Thank you for reading. I sincerely appreciate it!

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Hi! I am Julia Park and I'm a junior at Millersville University. I am currently studying Early Childhood Education. I am so excited to share my journey through my new blog! View all posts by Julia Park