Writing to learn: using writing to help students learn math

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.

Editor’s-choice resources

  • 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.”

Non-math resources and research reviews (editor’s choice)

Research on Writing to Learn Mathematics

  • 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.

 

Additional resources

  • 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.”
  • Moursund, D., and D. Ricketts, “Communicating in the Language of Mathematics,” from IAE-pedia (Information Age Education)
    This online essay written for pre-service math teachers addresses the learning of language, including the language of mathematics, and how knowledge of a language affects learning. Includes brief reviews of literature of writing to learn and of the relationship between language ability and mathematics learning.
  • Burchfield, P. et al., “Writing in the Mathematics Curriculum” from The Mathematics of Change, 1993 Woodrow Wilson Leadership Program in Mathematics
    This online resource for K-12 teachers provides ideas for including writing in the mathematics classroom (e.g., word webs, KWL activity, letter to a younger student, writing and following directions, tangrams, pair share, linking, learning logs, children’s storybook,  journals, portfolios, tests, and a poem called a cinquain). Sample prompts are included.
  • 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.

Using communication to help reduce math anxiety

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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CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)

What is Math Comm

MAA Mathematical Communication (mathcomm.org) is a developing collection of resources for engaging students in writing and speaking about mathematics. The site originated in the MIT Department of Mathematics and was expanded through support from an NSF grant.