how to write maths assignment in style

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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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A Comprehensive Guide to Math Writing Strategies

Math writing? Is that even possible? Perhaps, this topic currently raises some eyebrows. It’s even possible that you are hearing this term for the first time. So, to get this question out of the way, math writing is real. But what does it mean? Personally, math writing isn’t about making math; it is about making mathematical reasoning. Some mathematicians are said to be “mathematicians of the hands” because of their ability to apply mathematical reasoning to different objects.

Mathematical reasoning is an area that requires not only mathematical knowledge but also the application of that knowledge. Without mathematical reasoning then maths, itself, is worthless. But how do we note that reasoning that encapsulates our intelligence and capabilities? This is where math writing comes into play. Math writing helps us to record ideas, thoughts, and observations to gain insights and develop conjectures.

Why Isn’t Math Writing Common In Schools?

Teaching math writing in schools is difficult for a variety of reasons, including the fact that students have varied ways of processing and articulating information. Some of them go to great lengths to find the best website to get essay written in a bid to aid study. Even at that, they receive minimal guidance from their educators on what type of mathematical writing to incorporate.

Part of the issue originates from tutors’ lack of knowledge about the best methods for teaching math writing to their students. As a result, they completely disregard it, confining these students to standard instructional techniques that focus on computation and procedural competence. For example, there is a difference between knowing that 2 plus 2 is 4, and understanding why it is 4.

Most students are confined to knowing, but not understanding - these are two different concepts. Hence, they work out mathematical calculations effortlessly but can’t understand or communicate mathematically. Unfortunately, some tutors are helpless in bridging this gap as they were once students who weren’t privileged to learn math writing. This situation makes it difficult for them to teach this topic to their students. Besides, you cannot give what you don’t have.

Math writing obstacles come with feasible practical solutions that benefit both teachers and students.

Strategies that Promote Math Writing

Students who incorporate “cramming” into mathematical problems may have a hard time understanding the underlying factors that make maths relevant. Even though they know that 12 divided by 3 is 4, they don’t understand what makes it so. In such situations, learning becomes more of “what I was told,” rather than “what I understood.” However, the following strategies can improve mathematical learning and understanding when applied by tutors.

Modelling Writing Technique

This math writing technique focuses on constructing grammatical structures, sequencing ideas logically, justifying mathematical thoughts, using simple to complex vocabularies, among other strategies. With this process, tutors communicate their mathematical thoughts aloud while putting them into writing. Not only do the students grasp the teacher’s modelled writing style, but they connect with the tutor’s thoughts as well. Learning becomes visual and mental.

How can this technique work effectively? The modelling writing technique, also known as the think-aloud technique, comprises three segments: the writing process and the revision process.

Writing Process

This writing process helps students to understand how to put their mathematical thoughts on paper. The ideal timeframe for this phase should be between 5 to 10 minutes, and here is how it works:

• Find a learning need in the students concerning a maths topic and create a think-aloud lesson

• Explain to the students the purpose of this technique, targeted audience, benefits, and resources to be used

• Record your writing using an interactive board or paper chart, communicating your thoughts aloud as you proceed

• Be concise in writing these thoughts to prevent boredom and distraction

• Once done, communicate conclusive thoughts on the technique

• Ask the students to share their experience, questions, and lessons learnt during the process

Revision Process

Tutors and students should revise previous documentation to improve learning. But in what way? Revision inculcates the habit of rereading previously written documents. So, here is how it works:

• Dedicate time with the students to revise previous modelling-based documentations

• Explain to them the benefits of revision, including ways to improve on previous works

• Display the document and encourage group reading

• Put revisions into writing to aid learning

Mathematical Writing Conference

This math writing technique involves one-on-one learning communication between a tutor and a student. This time around, the students share their thoughts and ideas on their mathematical documentation with their tutors. With the information gathered, the teacher can provide the students with more insights on how to make their works better. This technique comprises four working parts:

• Researching the students’ mathematical thought and writing process

• Identifying the students’ actual instructional and learning needs

• Delivering a teaching point that addresses mathematical learning and writing needs

• Linking current learning process to the students’ future writing skills

The mathematical writing conference technique pushes the student to do better as there is a feedback mechanism on the teacher’s part. Students use highly focused teaching guidelines from their tutors to improve their math writing skills. Ideally, this technique should not last beyond five minutes. Conferences should be conversational, but brief as well.

Feedback should be concise, brief, and within the students’ capabilities. It should also come after a genuine compliment, celebrating their works.

Minilessons

Minilessons can focus on a smaller group or the entire class. Such learning sessions are concise and intensely focused, as students are assigned independent writing strategies to improve their math writing skills. These lessons span a maximum of 10 minutes. During this period, the tutor delivers a teaching point, after which the student put the lesson into practice, mostly in the class. By doing so, the teacher can engage them actively.

In summary, the teacher makes a connection, deliver a teaching point, engage the students, and link the lesson taught to future math writing works.

In Conclusion

Math writing is designed to help students test their abilities to observe and write down math problems in English. Students who need help with complex math problems can undertake math writing . By using this technique, tutors can also provide individual instructional learning that enhances the students’ level of understanding. As such, schools should promote this technique more.

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Top-Rated Tips From Experts For Writing A Maths Assignment

Mathematics Mastery: Trust Our Experts for Impeccable Assignment Writing, Ensuring Precision and Academic Excellence.

Writing a mathematics assignment is rewarding yet challenging, requiring precision, clarity, and a deep understanding of mathematical concepts. Navigating this academic challenge successfully can be exhaustive for students. Under this circumstance, consider the insights and tips our expert professionals share. These tips enhance your approach to creating high-quality and accurate math assignments.

From effective problem-solving strategies to the importance of clear communication, these expert-recommended guidelines offer a comprehensive framework for achieving excellence in math homework. Whether you're a student looking to improve your assignment skills or an educator guiding others through the process, incorporating these tips can elevate the quality and impact of your math assignments.

Mastering Math Assignments: Strategies for Success

Embracing the world of mathematics can be enjoyable and intellectually stimulating when approached with the right mindset. Here are some valuable tips to enhance your ability to solve math assignments efficiently.

Eliminate Distractions: Dedicate focused time to complete your math assignments, as they often involve multi-step problem-solving. Minimize distractions by putting away your phone and notifying others of your study plans. Seeking assistance from math assignment help services can provide expert guidance and support you require for math assignments.

Utilize Mathematical Tricks: Learn and apply quick mathematical tricks from your professors for calculations. You can also opt for assistance from a math assignment helper to ace different techniques. Familiarity with these tricks can significantly expedite the problem-solving of math writing assignment.

Thoroughly Read and Follow Instructions: Carefully read the instructions provided by your instructor before diving into the assignment. Use a notepad to jot down essential information and create an outline for a better understanding. Clearly articulate your problem-solving process, ensuring you address all aspects mentioned in the instructions.

Start with Challenging Problems: Prioritize your math problems based on difficulty and importance. Tackle the most challenging problems first and gradually work your way down. This approach ensures efficient utilization of your energy and time.

Take Regular, Short Breaks: Maintain concentration by taking short breaks to alleviate stress and prevent burnout. Breaks of 15 to 20 minutes allow you to recharge without losing focus on your assignments.

Study with a Friend: Collaborating with a study companion can provide motivation and a fresh perspective. Explaining concepts to each other enhances understanding and promotes effective learning.

Seek Expert Assistance: Don't hesitate to ask for help from experts at any stage of your assignment. Technology facilitates instant access to professionals who can assist with complex problems, ensuring academic success.

Practice Regularly: Building a strong foundation in mathematics requires consistent practice. Regular practice eases complex computations and explores various methods. It also helps you to analyze shortcuts for rapid problem-solving.

Common Worries About Math Assignments:

Understanding why students may struggle with math assignments is essential. Common reasons include:

Problems in Math Concept Understanding

Difficulty in understanding math arises from a combination of factors.

Some learners find the abstract nature of mathematical concepts challenging. Others face problems due to confusion from previously perceived knowledge. Most students acknowledged they often find it hard to visualize and relate math problems to real-world scenarios. Foundational knowledge gaps hinder comprehension. Effective math understanding requires a supportive learning environment, including several techniques that we have explained in the visual. These steps emphasize building a solid foundation for understanding and solving mathematical problems.

Challenges Due to Teaching

Students face diverse study challenges due to teaching methodologies. One of them is the lack of effective communication between educators and students. If teachers fail to articulate concepts clearly, students may struggle to grasp subject materials. Inadequate teacher-student interaction can hinder the resolution of doubts or concept clarification. Outdated teaching methods fail to engage students, resulting in a lack of interest and motivation to study. Effective teaching involves adapting to the diverse needs of students. It fosters a positive and interactive study environment for a better learning experience.

Inconsistency in Practice:

Inconsistency in practice poses a significant challenge in various contexts, ranging from skill development to routine tasks. Irregular practice can impede progress. Inconsistency in practicing new skills or habits can hinder the cultivation of expertise or the formation of positive routines. The key to overcoming this challenge is establishing and adhering to a consistent, structured practice regimen. By doing so, individuals can enhance their learning, skill acquisition, and personal growth, fostering a more sustainable and effective path toward mastery and success.

Quick Tips for Improved Math Skills

Enhance your arithmetic abilities and speed up problem-solving with these additional tips:

Master the Basics:

Proficiency in fundamental operations is crucial for tackling more advanced topics. It ensures a solid foundation by mastering the core principles of arithmetic.

Understand Concepts, Don't Memorize:

Focus on understanding the underlying concepts rather than memorizing procedures. It enables flexible problem-solving and a deeper grasp of mathematical principles.

Use Online Resources:

Explore online platforms offering interactive math exercises and tutorials. Math assignment help websites provide valuable resources for offering academic assistance.

Break Down Complex Problems:

Break down complex problems into smaller, manageable steps. This approach makes problem-solving more approachable and helps prevent feeling overwhelmed.

Teach Others:

Teaching a concept to someone else is an effective way to solidify your understanding. This process forces you to articulate ideas and reinforces your knowledge.

Seek Help When Needed:

Don't hesitate to ask for help when you encounter difficulties. Teachers, classmates, or online communities can provide valuable insights and clarification.

Review and Reflect:

Regularly review previously learned material and reflect on your progress. Identify areas of weakness and focus on reinforcing those concepts.

Utilize Educational Apps and Games:

Explore educational apps and games that make learning math enjoyable. These approaches can add an element of fun to your practice sessions.

In conclusion, assignments are integral to academic growth, and mastering math is a journey that requires dedication and effective time management. Seek assistance when needed, and you'll develop strong math skills with consistent practice.

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APA 7th edition manual

Apa 7 citation examples, missing elements - apa 7, apa 7 paper formatting basics, apa 7 document templates, more apa 7th ed. resources.

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This guide will introduce you to APA 7 citations, both for the References page of your paper and in-text citations. It is offered in multiple file formats below. 

• Citation Examples - APA 7 - Word Document
• Citation Examples - APA 7 - PDF

This guide will tell you exactly what to do if your resource is missing a citation element. Can't find the author, publication date, page numbers, or something else? Use this guide to find out what to do! This guide is offered in multiple formats below. ​​​​​​​

• Missing Elements - APA 7 - Word Document
• Missing Elements - APA 7 - PDF
• Typed, double-spaced paragraphs.
• 1" margins on all sides.
• Align text to the left.
• Choose one of these fonts: 11-point Calibri, 11-points Arial, 10-point Lucida Sans Unicode, 12-point Times New Roman, 11-point Georgia, 10-point Computer Modern.
• Include a page header (also known as the "running head") at the top of every page with the page number.
• APA papers are broken up into sections. Check with your instructor for their expectations.
• In general, headings and title are centered.

APA 7th edition recognizes two kinds of paper formats - student papers (undergraduate students) and professional research papers (graduate students and professionals). At Clackamas CC, you will use the student paper formatting conventions.

You don't have to format a paper from scratch! Download this APA-formatted document template as a Word document or Google document. Save it, erase the existing text, and type your text right into the template. Learn how to format a paper in APA format by reading the contents of the template. The References page has been formatted with hanging indents.

• Download & edit: APA Word document template Microsoft Word document template to save a copy of and type into. To edit it, save a copy to your desktop or Clackamas Office 365 account. Includes tips on how to format a paper in APA. Last updated Feb. 2020.
• Download & edit: Pages document template If you need this template in Pages, email [email protected]
• View Only: Sample APA student paper (7th ed.) This sample student paper includes descriptions of indentations, margins, headers, and other formatting conventions (APA, 2020).
• APA Style (APA.org) APA's site answers all the basic questions about APA 7th edition and gives sample "student" and "professional" papers. This will help you with document format, in-text citations, the References list, and various stylistics.
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• URL: https://libguides.clackamas.edu/math

Writing to learn: using writing to help students learn math

Editor’s-choice resources, non-math resources and research reviews (editor’s choice), research on writing to learn mathematics, additional resources, using communication to help reduce math anxiety.

Much of this site is primarily about “learning to write” math; this page is about “writing to learn” math. In other words, students may improve their understanding of math by writing about it.

The following resources describe or illustrate how writing about math can help students to learn math. Please feel free to contribute to this page. Particularly helpful would be a literature review, a structured, annotated bibliography, or a comprehensive bibliography (even if not current). Many of the resources below were found by undergraduate researcher Artur Araujo.

• J. Meier and T. Rishel, Writing in the Teaching & Learning of Mathematics , MAA Notes No 48, 1998. This book includes sound advice for designing small and large assignments, a summary of ideas from related fields (writing and cognitive science), and a rationale for using writing to help students learn math.
• Using Writing to Teach Mathematics , Andrew Sterrett, Ed., MAA Notes No. 16 This collection contains 31 articles by educators who use writing to teach math. From the preface: “The writers describe their experiences with Writing Across the Curriculum, with journals and other forms of expressive writing, and with specific courses. They offer specific advice on getting started with writing programs and on routine matters such as grading, correcting grammar, and the importance of rewriting. Several essays describe student reaction to writing in the mathematics classes and how to involve students in reading and grading the work of others.”
• B. Russek, “ Writing to Learn Mathematics ,”  the WAC Journal: A National Journal for Writing Across the Curriculum , Vol 9, August 1998 This article describes examples of writing-to-learn assignments in classes throughout the undergraduate math curriculum. Includes some sample student writing.
• P. Connolly and T. Vilardi, eds., Writing to Learn Mathematics & Science Teachers College Press, 1989. This is a collection of 23 articles, at least half of which are specific to mathematics.
• Countryman, J., Writing to Learn Mathematics: Strategies that Work, K-12 , Heinemann, 1992. For K-12, this book addresses writing to learn, getting started, autobiography, journals, word problems, words in mathematics, formal writing, assessment, etc.
• Herrera, T., “Reading and Writing Mathematics” MSP: MiddleSchoolPortal Accessed Feb 25, 2012. This clickable, annotated bibliography for middle school educators addresses reading, writing, and visual communication. Linked resources include webinars, online chapters, materials for students, lesson plans, and “virtual manipulatives.”
• C. L. Patterson and P. V. Prasad, “ Beyond Grades: Feedback to Stimulate Rethinking and Intellectual Growth ” On Teaching and Learning Mathematics AMS Blogs, American Mathematical Society, August 6, 2018. Patterson and Prasad use feedback and revision instead of grades to increase student learning from writing assignments.
• What is Writing to Learn? The WAC Clearinghouse These pages define writing to learn, provide examples of writing to learn activities and alternatives for evaluating these activities, etc.
• Reynolds, J., at al., “ Writing-to-Learn in Undergraduate Science Education: A Community-Based, Conceptually Driven Approach ,” CBE Life Sciences Education , 2012 Spring; 11 (1) : 17–25. A heuristic review of STEM writing-to-learn research since Rivard’s 1994 review. Contains a framework for future research. The database of articles reviewed is available here: Writing to Learn in STEM database
• Rivard, LP., “A review of writing to learn in science—implications for practice and research,” Journal of Research in Science Teaching , 1994; 31 :969–983.
• Porter, M. K. and Masingila, J. O., “Examining the Effects of Writing on Conceptual and Procedural Knowledge in Calculus,” Educational Studies in Mathematics, Vol 42, pp. 165–177, 2000. This study compares students’ errors in two calculus sections; one section uses writing to learn while the other uses comparable activities that do not involve writing. Both sections use discussion (talking to learn). Results show no statistically significant difference between the two sections, suggesting that non-writing activities + discussion are as effective as writing to learn + discussion.

If you are aware of additional research on writing to learn mathematics, please contact us .

• Schmidt, D, “ Writing in Math Class ,” Chapter 7 of Gere, Anne Ruggles. (2012). Roots in the Sawdust: Writing to Learn Across the Disciplines . WAC Clearinghouse Landmark Publications in Writing Studies. Originally Published in Print, 1985, by National Council of Teachers of English, Urbana, Illinois. This book chapter describes and includes example of how writing is used to open lines of communication between middle school students and their math teacher, to help the students to learn mathematics, and to give the students an opportunity to succeed in math class by writing book reports. The math teacher writes, “For me it is a way to get to know more about those varied and wonderful people who are my students.”
• Burns, M., “ Writing in Math ,” Educational Leadership , v62 n2 p30 Oct 2004 This 4-page article describes strategies for including writing in the elementary classroom. Assignment types include “keeping journals or logs, solving math problems, explaining mathematical ideas, and writing about learning processes.”

The following references and quotes are taken from the literature reviews in “Improving Writing and Speaking Skills using Mathematical Language” by Kimberly Hackett and Theresa Wilson. (Masters thesis, Saint Xavier University & IRI/Skylight Field-Based Master’s Program, 1995)

• Borasi, R. & Rose, B. J. (1989). Journal writing and mathematics instruction. Educational Studies in Mathematics, 20, p. 347-365. “the more students use their journals to write as a place where they can think on paper, not just report already formed ideas, the more they will take advantage of the potential of writing as a tool for learning and growth.”
• Abel, J. P. & Abel, F. J. (1989) Writing in the Mathematics classroom. The Clearing House, 62. p. 155-158. “The journal does not have to be collected but must be read and responded to”
• Artzt, A. F. (1994). Integrating writing and cooperative learning in the mathematics class. Mathematics Teacher, 87. p. 80-85. “Students enjoy discussing mathematics with other students and they benefit from their interaction with other students as well as with the teacher”
• Johnson, M. L. (1983). Writing in mathematics classes: A valuable tool for learning. Mathematics Teacher. 76. 117-119. “If students can write clearly about mathematical ideas, then it is clear that they understand those ideas. Students who write in mathematics must do considerable thinking and organizing of their thoughts to crystallize in their minds what they have studied”
• Keith, S. Z. (1988). Explorative writing and learning mathematics. Mathematics Teacher, 81. 714-719.
• LeGere, A. (1991). Collaboration and writing in the mathematics classroom. Mathematics Teacher, 84, 166-171. “Speaking and writing about mathematics problems can contribute significantly to understanding”
• McIntosh, M. E. (1991). No time for writing in your class? Mathematics Teacher, 82, 423-433. “learning logs should be used on a daily basis. Teachers can develop three different types of logs for students to use: ‘how-to’s’, ‘definitions’, and ‘troubleshooting’ “The benefits of using journals are: enhanced learning, awareness of students learning, and knowledge of what students are thinking.”
• Miller, L. D. (1991) Writing to learn mathematics. Mathematics Teacher, 84, 516-521. “the five types of writing categories…include: direct use of language, linguistic translation, summarizing/interpreting, applied use of language and creative use of language”
• Miller, L. D. & England, D. A. (1989). Writing to learn Algebra. School Science and Mathematics, 89. p. 299-312 “Writing can cause students to analyze, compare facts, and synthesize relevant material…These types of writing can be kept in a mathematics journal or mathematics log.”
• Nahrgang, C. L. & Peterson, B. T. (1986). Using writing to learn mathematics. Mathematics Teacher, 79, p. 461-465. “The journal has basically two functions: 1) it allows students to go at their own rate to understand mathematical concepts in terms of their own experiences, and 2) it also functions as a diagnostic tool, which can reveal confusion or show misunderstandings students have”
• Schmidtt, D. (1985). Writing in Math Class. In A. R. Gere (Eds.) Roots in the Sawdust: Writing to Learn Across the Disciplines. P. 104-116.

Communication assignments are often used as part of a strategy to reduce math anxiety, thus indirectly improving learning of mathematics. See the page of resources and research about using communication to reduce math anxiety .

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How to Effectively Write a Mathematics Research Paper

Mathematics research papers are different from standard academic research papers in important ways, but not so different that they require an entirely separate set of guidelines. Mathematical papers rely heavily on logic and a specific type of language, including symbols and regimented notation. There are two basic structures of mathematical research papers: formal and informal exposition .

Structure and Style

Formal Exposition

The author must start with an outline that develops the logical structure of the paper. Each hypothesis and deduction should flow in an orderly and linear fashion using formal definitions and notation. The author should not repeat a proof or substitute words or phrases that differ from the definitions already established within the paper. The theorem-proof format, definitions, and logic fall under this style.

Informal Exposition

Informal exposition complements the formal exposition by providing the reasoning behind the theorems and proofs. Figures, proofs, equations, and mathematical sentences do not necessarily speak for themselves within a mathematics research paper . Authors will need to demonstrate why their hypotheses and deductions are valid and how they came to prove this. Analogies and examples fall under this style.

Conventions of Mathematics

Clarity is essential for writing an effective mathematics research paper. This means adhering to strong rules of logic, clear definitions, theorems and equations that are physically set apart from the surrounding text, and using math symbols and notation following the conventions of mathematical language. Each area incorporates detailed guidelines to assist the authors.

Related: Do you have questions on language, grammar, or manuscript drafting? Get personalized answers on the FREE Q&A Forum!

Logic is the framework upon which every good mathematics research paper is built. Each theorem or equation must flow logically.

Definitions

In order for the reader to understand the author’s work, definitions for terms and notations used throughout the paper must be set at the beginning of the paper. It is more effective to include this within the Introduction section of the paper rather than having a stand-alone section of definitions.

Theorems and Equations

Theorems and equations should be physically separated from the surrounding text. They will be used as reference points throughout, so they should have a well-defined beginning and end.

Math Symbols and Notations

Math symbols and notations are standardized within the mathematics literature. Deviation from these standards will cause confusion amongst readers. Therefore, the author should adhere to the guidelines for equations, units, and mathematical notation, available from various resources .

Protocols for mathematics writing get very specific – fonts, punctuation, examples, footnotes, sentences, paragraphs, and the title, all have detailed constraints and conventions applied to their usage. The American Mathematical Society is a good resource for additional guidelines.

LaTeX and Wolfram

Mathematical sentences contain equations, figures, and notations that are difficult to typeset using a typical word-processing program. Both LaTeX and Wolfram have expert typesetting capabilities to assist authors in writing.

LaTeX is highly recommended for researchers whose papers constitute mathematical figures and notation. It produces professional-looking documents and authentically represents mathematical language.

Wolfram Language & System Documentation Center’s Mathematica has sophisticated and convenient mathematical typesetting technology that produces professional-looking documents.

The main differences between the two systems are due to cost and accessibility. LaTeX is freely available, whereas Wolfram is not. In addition, any updates in Mathematica will come with an additional charge. LaTeX is an open-source system, but Mathematica is closed-source.

Good Writing and Logical Constructions

Regardless of the document preparation system selected, publication of a mathematics paper is similar to the publication of any academic research in that it requires good writing. Authors must apply a strict, logical construct when writing a mathematics research paper.

There are resources that provide very specific guidelines related to following sections to write and publish a mathematics research paper.

• Concept of a math paper
• Title, acknowledgment, and list of authors
• Introduction
• Body of the work
• Conclusion, appendix, and references
• Publication of a math paper
• Preprint archive
• Choice of the journal, submission
• Publication

The critical elements of a mathematics research paper are good writing and a logical construct that allows the reader to follow a clear path to the author’s conclusions.

Good advice. For me, writing an essay on mathematics was very difficult. I did not have enough time and knowledge to write a quality essay. I worked a lot in the library and read many articles on the Internet. I studied information about essay writing. But I couldn’t finish the essay in full. I had to look for professional writers on the subject of mathematics. He helped me finish a few paragraphs. The work was delivered on time and on an excellent assessment.

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Mathematics

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Mathematics Citation Formats

Reference management tools, help with scientific writing & presenting, writing for mathematicians, resources for scientific writing.

• Reference Sources

The primary reasons for citing sources in a research paper are to give credit to the authors whose work you have drawn upon and to allow readers to track down your sources, should they wish to explore further. Unlike many other disciplines, math does not have a single accepted way of citing resources. Ask your professor if they have a preferred bibliographic style before submitting a paper. Some faculty have no preference, as long as your sources are cited completely and correctly. Or you could mimic the citation style in one of the journals used by your professor. 

Many professors are now teaching math students to use variations of BibTeX, which automates managing references for use with LaTeX.

• Citation Help by Phil Schaller Last Updated Dec 1, 2023 568 views this year
• AMS Author Handbook American Mathematical Society journals use a LaTeX-based format.
• APA Style The National Council of Teachers of Mathematics and the Mathematical Association of America use APA Style.
• Mendeley A free reference manager and academic social network that can help you organize your research, collaborate with others online, and discover the latest research. You can automatically generate bibliographies, collaborate with other researchers online, import papers from other research software, find relevant papers based on what you’re reading, and access your papers from anywhere online.
• Zotero Zotero is a free citation management software that allows you to collect & manage citation information for articles, books, PDFs, and more.
• BibTex Created for use with LaTeX software, but now compatible with other software. Widely used in math, science and engineering. More help can be found in the Getting to Grips with LaTex

• Berry College Writing Center Writing Consultants are available to assist students with all stages of the writing process, from interpreting assignment guidelines and generating ideas for a new writing project to the difficult art of revision and putting the final touches on a polished draft.
• How to Write  a Paper in Scientific Journal  Style and Format From Bates College, how to write a paper in scientific journal style & format.
• Ten Simple Rules for Structuring Papers Focusing on how readers consume information, we present a set of ten simple rules to help you communicate the main idea of your paper. These rules are designed to make your paper more influential and the process of writing more efficient and pleasurable. more... less... citation: Mensh B, Kording K (2017) Ten simple rules for structuring papers. PLOS Computational Biology 13(9).
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Resources for My Subject

Mathematics: referencing guide.

• Moore Library
• Mathematics Collections
• Referencing Guide
• Study skills
• Research support

What is referencing?

Referencing is an important aspect of good academic practice. It demonstrates the breadth of your reading, indicates how you use the work of others to support your ideas and directs your reader to other useful information. It also helps to you to avoid any accusations of plagiarism and academic misconduct . This is taken very seriously at the University of Cambridge so it's important to take steps to get things right. 

Whatever stage of your academic career you are at you need to make sure that your work adheres to ethical standards. Part of this involves acknowledging the ideas of others where these have informed your work, for example to illustrate a point you are making. This is done by including a reference to the original creator/source of the work so that your readers can follow it up if needed. Adding references to the work of others helps to strengthen your own arguments and distinguish between your own ideas and existing work, showcasing the contribution you are making to the scholarly debate.  

How do I reference?

There are several different referencing styles and it's important to find out which one your department uses. Each style includes a variation of the same information which act as a map to point readers towards the original source. This might include elements such as the author, title, date of publication, title of journal publication and page numbers. These details help direct the reader straight to the original source so they can see the point being made in context and explore further.

You can see an example reference using the Harvard style below:

There are lots of different ways to incorporate existing materials into your own work. For more detail on how to include work through paraphrasing, quotation and summary you can view our online Moore Module on Avoiding Plagiaris m.

What do I need to reference?

The short answer is any material you use in your own work that you have not created yourself. This includes a range of materials from quotations and extracts of text through to images and audio recordings. You also need to remember that there may be restrictions on the amount of material you can include due to copyright restrictions.

There may be some circumstances where you include previously unpublished materials in your work such as letters, emails or notes from your lecturer. Even though a reader may not be able to access the original it is still important to include a reference and acknowledge the contribution of others. 

There are some things that you can include without the need to reference. You don't need to reference facts that are common knowledge (e.g. the sky is blue) or the generally accepted facts within your discipline. This will vary depending on the area you are working in so if in doubt check with your supervisor.

You also don't need to reference your own thoughts, observations or conclusions as these are your contribution to your work. The exception to this is if you have submitted the material in a previous assignment or for publication elsewhere. Including this material without a reference is known as self-plagiarism. For previously published material you need to include a reference as with any other published source and ensure that you stay within copyright guidelines. If you want to include work that you have previously submitted in an assignment then you should discuss this with your supervisor to determine the next steps. 

Self-plagiarism does not apply to drafts of your work. You are likely to create several drafts, some of which you may show to your tutors for comment. This is an acceptable academic practice and any revisions prior to submission are not self-plagiarism.

New AI tools such as ChatGPT have been in the news in recent months and you may have questions about how these could be used as part of your studies. The University of Cambridge has  clear guidelines  which class the use of ChatGPT and other AI tools a form of academic misconduct as they do not represent the work of the individual student. You should also be wary of any references supplied by AI tools as these may be  inaccurate or false .

Zotero is a free, open-source research tool which works with your web browser to automatically detect and store information about your sources. Some of the key benefits of Zotero are:

• Create automatic bibliographies and in-text citations.
• Save and annotate PDFs and other sources in application.
• Build an interactive timeline of your research.

You can find more information on installing and using Zotero in this online guide from Georgia State University (written by Jason Puckett). 

EndNote is a reference management tool provided by Clarivate. Although there is a charge for the full version current Cambridge staff and students can download a single use licence version using their Raven password . A free version is also available but this offers limited functionality. Some of the key benefits of EndNote are:

• Upgraded account available to current staff and students.
• Import citations from a range of databases.
• Online backup is available.

You can find out more information about installing and using EndNote in this online guid e from Cambridge University Libraries. 

BibTex is the recommended reference manager for Latex users. It allows references to be consistenly formatted by separating the information about an item and the format that it is presented in, in a way that will be familiar to LaTeX users. Some of the key benefits of BibTex are:

• Integration with Latex.
• Works well for mathematical writing.
• Can be used with other tools such as Overleaf for collaborative writing and publishing. 

You can find more information on installing and using BibTex in these online tutorials from Overleaf.

Mendeley is another reference management tool which offers similar functionality to others listed. Owned by Elsevier it provides a wide range of functions including the ability to create a researcher profile. Some of the key benefits of Mendeley are:

• Build an online profile for you and your research.
• Find relevant papers based on the research you are reading.
• Annotate and share papers.

You can find out more information on installing and using Zotero in this online guide from Cambridge University Libraries.

Cite Them Right

Referencing & Academic Integrity Resources

The Physical Sciences Research Support Team has also developed a range of resources on academic integrity, referencing and how to avoid plagiarism. You can find some highlights below of explore the full range on our Research Support Hub .

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‘registering’ math academic language: providing supports for english learners.

Posted May 30, 2024 by snp146

By Anita Sundrani and Asia Ellis

In recent years, there has been a significant shift in the way students are taught mathematics. Math is no longer just about basic computation and procedures. Students are tasked with solving real-world problems that require a high level of proficiency in academic language . Strong academic language skills allow students to build a deep conceptual understanding of the mathematics content and practices necessary for success in today’s classrooms.

In light of these shifts, we share an overview of academic language, with a focus on three related facets that connect to E4’s research priorities: 1) mathematics academic language, 2) challenges faced by English Learners in developing their academic language toolkit, and 3) strategies mathematics teachers can use to support English Learners’ academic language development.

What is academic language?

At its core, academic language is the form of communication used in schools and in classrooms, which differs from the language that is used at home and in other contexts.

Researchers have proposed many different frameworks that explain how students develop academic language. Some focus more on the individual student’s experiences (i.e., cognitive ), while others focus more on the surrounding environment (i.e., raciolinguistic , sociocultural , sociolinguistic ).

Our exploration of academic language takes a sociolinguistic and sociocultural approach. This perspective highlights the unique nature of social interactions in the classroom, and the ways they differ from everyday exchanges. In other words, they have their own register .

What is a Register?

In linguistics, a register is the way people use different types of language in different contexts – for example, a scientist needs to make specific language choices when engaging in a professional setting that may differ from their everyday language (See Moschkovich, 2015 ; Sarris & Chavez, 2020 ; Wilkinson, 2019 ). The term applies to both speaking and writing.

How does academic language fit in math?

Standards in mathematics, such as the Common Core State Standards require students to have a deep understanding of the language of mathematics to solve problems. Students should be able to demonstrate their understanding of a problem by listening to and reading descriptions of the problem and then discussing related concepts with peers and teachers. Underlying each of these expectations are the four equally important areas of language – vocabulary, syntax, semantics, and discourse.

• Academic Vocabulary
• Syntax and Semantics

Mathematics Academic Vocabulary

Mathematics academic vocabulary is the component of academic language that gets the most airtime and experts agree: the unique vocabulary associated with mathematics (e.g., diameter, vertex, ratio) supports overall language development. When targeting mathematics academic vocabulary in the classroom, educators need to define terms explicitly, giving examples in the relevant context to illustrate meaning.

The National Council of Teachers of Mathematics (NCTM) cautions against teaching mathematics (and vocabulary) without a context, instead encouraging the introduction of real-world connections once students have mastered the mathematics content procedurally. A more decontextualized approach makes it more difficult for students to engage in mathematical discourse when the time arrives. Instead, vocabulary should be integrated into everyday instruction through high-cognitive demand activities that balance both conceptual and procedural understandings of mathematics. Teachers should also engage students in opportunities to discuss what they’re learning orally and in writing (one such example is provided below).

Mathematics Syntax and Semantics

Semantics references the overall meaning of a statement in context. For example , “in a mathematical word problem, four plus seven times a certain number is 20; what is the number , students must infer that a certain number and the number are actually the same number.” This applied use of the mathematics register takes time for students to master, so it is important that students have multiple opportunities to make sense of word problems and symbols.

Syntax focuses on the structure of statements. For instance , students need to understand the relationship between words, such as “greater than” or “the same as” in order to work with equations and inequalities. Taken together, students begin to learn how to speak and write as mathematicians and understand what is being asked of them in the mathematics classroom. Despite the language-rich underpinnings of the mathematics register, teachers may be hesitant to include literacy instructional practices in their teaching, believing that language learning is outside of their expertise and focus as math teachers.

Mathematics Discourse

Though most scholars agree that discourse is an integral component of language acquisition, they disagree on how it should be introduced. Some believe that students must first master vocabulary and mathematics procedures prior to engaging in discussion, while others believe that all aspects of mathematics academic language can be developed simultaneously through purposeful mathematics discourse. Expert Judit Moschkovich explains that mathematics discourse “involves not only written text, but also multiple modes, representations (gestures, objects, drawings, tables, graphs, symbols, etc.), and registers.” This means that math instruction should focus on conceptual understanding of math content and engage students in explaining, reasoning, and justifying their mathematical ideas with their peers, teachers, and in writing .

How does mathematics academic language affect English Learners’ success in math?

Due to the instructional shift toward conceptual understanding and real-world applications, English Learners (ELs) face unique challenges while learning mathematics. In particular, learning in a nonprimary language requires a heavier mental load to move from one register to another, a process more commonly known as “code-switching.” Code-switching (also known as translanguaging) can lead to more oral and written errors because the learner has to constantly switch between their primary language and nonprimary language where the syntax may be different .

There is also the added challenge of technical” and “subtechnical” vocabulary words . “Technical” vocabulary words that have a mathematical definition (e.g., circle) and “subtechnical” words that may have both a mathematical definition and colloquial one (e.g., “yard” is a unit of measurement and can also refer to an area outside a home).

This culmination of challenges, along with the misconception that mathematics should be separate from language instruction, may lead teachers to underestimate the true mathematical abilities of ELs compared with their English monolingual peers. Because of this, teachers may unnecessarily assign ELs more content below grade level than their English-only classmates, leading to widening gaps in mathematics performance (see here and here ).

Mathematics Instructional Strategies for English Learners It is more appropriate to provide ELs with high-quality tools that are responsive to their mathematical strengths and primary language to better enable them to access on-grade-level material. These strategies should emphasize:

• a balance between conceptual and procedural understanding,
• high cognitive demand,
• positive beliefs about mathematics, and
• the eight Common Core mathematical practices.

Potential strategies include:

Introducing els to mathematics vocabulary in context with brief mathematics language lessons..

For example, Ellevation, an organization designed to both serve ELs and teachers of ELs, offers math primers to support Els in math. Math primers are quick five-minute lessons that introduce students to a mathematical term and present a real-world application of the term, aided by a mathematics representation as a visual anchor. Their goal is to use a contextualized approach to mathematics vocabulary to help ELs engage in rich discourse with their peers, and in turn, access grade-level material at any level of proficiency. A recent investigation found that implementing this strategy in isolation sporadically during the academic year does not have an impact on ELs’ mathematics knowledge. This finding supports Moschkovich’s assertion that mathematics academic language development should be a holistic endeavor that should combine language development and mathematics proficiency through mathematical discourse.

Focusing on students’ mathematical reasoning in their argument, as opposed to precise language usage.

This approach puts the emphasis on students’ understanding of concepts, instead of the register, which then allows students to gradually become accustomed to the register through repeated oral and written practice. Also, listening for students’ mathematical ideas frames them as knowledgeable about mathematics, and avoids a deficit mindset about ELs .

Acknowledging the complexity of language and the different ways it takes place in the classroom.

Students are expected to speak, read, and write in the mathematics register, recognize multiple representations (e.g., tables, graphs, pictures, symbols), understand different forms of text (e.g., textbook explanations of concepts, word problems), and to communicate with different audiences. Therefore, teachers should provide ELs, as well as their peers, plenty of opportunities to engage in the complexity of language through different modalities and sequence them in ways that support comprehension (see related work on this topic by Moschkovich (2012) , Peng and colleagues (2020) , and Sarris and Chávez (2020) ).

Academic language is complicated and nuanced, as each subject area requires instruction to be responsive to its specific register. Although there are commonalities across subjects–including a focus on vocabulary, syntax, semantics, and discourse–the strategies to develop these language components are distinct. Within mathematics education, language instruction is often overlooked as math is viewed as the subject of numbers. This forces English learners to simultaneously learn English and the mathematics register. However, there are numerous strategies that frame ELs as doers of mathematics while they learn both. When teachers recognize and build upon ELs mathematical strengths and knowledge, these students are better situated to grow and thrive as learners across the board.

Categories: Author: Anita Sundrani , Author: Asia Ellis , Research Brief