Reading mathematics

The following resources are about reading mathematics to understand it.

Resources for students

  • Terry Tao’s blog What’s New has a section On Writing with a subsection on reading writing.
  • Stewart, I., “How to Learn Math,” Letters to a Young Mathematician, Basic Books, 2006, pp. 62-70. (Book Review at MAA website)
    This letter is from a wonderful collection of letters from a mathematician to “Meg,” as she progresses from a high school student wondering whether higher levels of math are anything more than “bigger numbers and harder calculations,” to a tenured professor. The letters are unerringly encouraging while explaining myriad aspects of what it’s like to be a mathematician. The letter, “How to Learn Math,” is to Meg when she is a college student and explains what to do to get past sticking points when reading. The author also advises Meg to “read around the subject” to gain a sense of the larger picture within which any subject fits.
  • Gerver, R., “Reading and Keeping a Research Journal,” Writing Math Research Papers: A Guide for Students and Instructors Key Curriculum Press, 2004.
    This book chapter provides guidance for reading the literature relevant to a research project. Subsections include “Preparing to Read,” “Reading and Taking Notes,” and “Conquering Difficult Concepts.”
  • How to Read Mathematics” by Shai Simonson and Fernando Gouvea
    Provides advice such as “don’t miss the big picture” and “make the idea your own” and illustrates how this advice can be applied to an example of mathematical writing. From Rediscovering Mathematics by Shai Simonson.
  • Section 0.1 “Reading Mathematics” of Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by John H. Hubbard, Prentice Hall 2002 provides helpful, readable advice such as that it’s more important to understand a theorem statement than its proof, and it’s OK to skip ahead to examples.
  • Mark Tomforde, “Tips for reading your mathematics textbook” A two-page handout for undergraduates.
  • See also the resources for teachers below, some of which include resources for students.

Resources for college/university teachers

  • Ashley Reiter, “Helping Undergraduates Learn to Read Mathematics” MAA 1998
    This webpage about reading theorems and definitions provides guidance to students with commentary for teachers.
  • Peter Shor asked students in M.I.T.’s undergraduate Seminar in Information Theory to analyze a well-written key paper in the field to identify strategies the author used to help readers understand, convince readers, and interest readers. Here is the pre-workshop reading assignment, with questions to focus the reading.
  • In M.I.T.’s undergraduate Seminar in Theoretical Computer Science, which is taken primarily by juniors and seniors, students write a term paper on a topic of their choice. To do so, they must find and read sources, including mathematics research articles. Attached are a suggested reading strategy (student resource) and an in-class activity designed to introduce students to the reading strategy and to familiarize them with some of the common features of mathematics papers that facilitate the finding of information within the paper. By Susan Ruff and Zachary Remscrim.
  • Andersen, J., “Teaching Students to Read Technical Material: The Use of Reading OutlinesMath Forum – Orlando Presentation
    In this online essay, Janet Andersen describes how she structures her classes to encourage students to read the textbook. Given as a presentation at the 1996 Joint Mathematics Meetings in Orlando, Florida.

Resources for middle school and high school teachers

  • “Reading Math” a page of the website Middle School Math and Science hosted by The Ohio State University College of Education and Human Ecology
    This clickable, annotated bibliography for middle school educators includes links to resources such as classroom strategies and “A Maths Dictionary for Kids.”

If you know of other good resources for elementary, middle, or high school, please let us know.

Research

  • Shepherd, Mary D., and Carla C. van de Sande. “Reading mathematics for understanding—from novice to expert.” The Journal of Mathematical Behavior 35 (2014): 74-86.
  • Lara Alcock, “How do people read mathematics” In this blog post, Lara Alcock briefly summarizes and provides links to the research she has done with her collaborators into how experts and novices read mathematics, and the effectiveness of a pedagogical intervention designed to help novices become more expert at reading proofs.
  • Shepherd, Mary D., Annie Selden, and John Selden. “Difficulties First-Year University Mathematics Students Have in Reading Their Mathematics Textbook. Technical Report. No. 2009-1.” Online Submission (2009).
    The researchers find that first year students have a hard time successfully completing straightforward tasks based on a reading, despite being good at mathematics and good readers in general (per ACT scores and use of metacognitive reading strategies).

Encourage students to read critically: not all mathematics is written well. Students can learn much about how to write mathematics by noticing what does and doesn’t work well for them as readers.

If you know of other good resources related to reading mathematics, please let us know.

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