Reading Mathematics Textbooks

Below is an annotated list of references on the subject of encouraging and teaching students to read mathematics textbooks. Physics professor Eric Mazur of Harvard University talks about the roles of transfer and assimilation of knowledge as components of student learning that can occur in or out of the class. Having students read their textbooks in meaningful ways enables the transfer phase to happen outside of class, providing more time in class for the more difficult phase, the assimilation phase.

See also this list of tips for reading your textbook that I assembled for a workshop on study tips for calculus students at Harvard.

Articles

  • Math Class: Have You Seen the Preview?

    In this Mathematical Association of America (MAA) article, Louise Amick of Washington College discusses her use of "previews" -- exploratory worksheets students complete before class in groups. Lectures are brief, and class time is used to discuss the preview problems and work on further problems.

  • Teaching Students to Read Technical Material: The Use of Reading Outlines

    In this Joint Mathematics Meetings presentation, Janet Andersen of Hope College discusses her use of "reading outlines" -- questions (basic, concept, and application) to be answered by students before class based on the reading. She spends almost all of her class time in discussion.

  • How We Get Our Students to Read the Text Before Class

    In this MAA article, Matt Boelkins of Grand Valley State University and Tommy Ratliff of Wheaton College discuss their use of email-based pre-class reading assignments. These are used to motivate students to read their textbooks, and responses from these assignments help shape each day's lecture.

  • Teaching and Testing Mathematics Reading [PDF 145KB]

    In this American Mathematical Monthly article, Carl Cowen of Indiana University Purdue University Indianapolis gives advice for helping students learn to read mathematics by guided discussion in class. He also describes his method of assessing students' reading skills on exams.

  • Requiring Student Questions on the Text

    In this MAA article, Bonnie Gold of Monmouth University describes her pre-class reading assignments. Students are to generate three questions (either answered or unanswered by their reading) based on the reading assignment. She uses these questions to guide her in-class discussions and responds to individual student questions outside of class. She also describes the "Content, Form, and Function Outlines" classroom assessment technique from Angelo and Cross' book, Classroom Assessment Techniques (Jossey Bass, 1993).

  • How to Survive Your College Math Class (and Take Home Something of Value)

    Matthew Saltzman and Marie Coffin of Clemson University have posted a study guide for basic math courses that includes a well-written section of advice on reading math texts. They make some good points about the low utility of highlighting math texts (since they are already so well organized in general) and about making the most of class time by not taking notes on material available on the textbook. Also, they give guidelines for interpreting mathematical equations.

Books

  • Matt Delong and Dale Winter, Learning to Teach and Teaching to Learn Mathematics, Mathematical Association of America, 2002.

    Delong and Winter's book provides a wealth of resources for training and mentoring beginning mathematics instructors. Chapter 5, "Getting Students to Read the Textbook," has several good ideas. Several of the online references listed above are from this book.

  • Wilbert McKeachie, McKeachie's Teaching Tips: Strategies, Research, and Theory for College and University Teachers, 10th ed., Houghton Mifflin Co., 1999.

    McKeachie's book would make a nice reference manual on teaching for beginning instructors in any discipline. However, Chapter 11, "Teaching Students How to Learn More from Textbooks and Other Reading," summarizes research on students' textbook reading. One study showed that students learn difficult material better via reading than via lectures. Other studies showed that questions given to guide students' reading that were designed to produce more thoughtful, integrative study were more effective than questions of fact. Another study showed that similar questions focusing on material at the top of the organizational structure facilitated learning, especially for the less able students.

Survey Tool

  • TextRev

    In 2000 two professors in the Department of Chemistry and Biochemistry at the University of Notre Dame began surveying their students to determine how they used their chemistry textbooks and related resources. This investigation eventually led to TextRev, a free survey tool for instructors, providing customizable surveys on textbooks and remote keypads (also known as personal response systems and classroom communication systems). They also provide summaries of survey results on certain physics and chemistry textbooks.

Page maintained by Derek Bruff (derek.bruff [at] vanderbilt.edu).

Last updated December 3, 2005.

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