Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

Planning the term

Here are some suggestions to consider as you design a math class that includes communication.

Learning to communicate math vs. communicating to learn math

As you plan the term, first ask yourself why you want to include communication in your math class. Do you want students to

Your answer will shape your assignments as well as the instruction and feedback you provide.

Helping students to give good presentations

  • Students are used to homework assignments, in which they are expected simply to demonstrate that they understand the material. So emphasize that the purpose of presenting is not to demonstrate that they know the material, but rather to help the other students to understand the material.
  • Practice presentations Watch at least one practice presentation for each student, and encourage students to do practice presentations with each other.
  • Class discussion Hold a class discussion about how to give a good presentation. Perhaps use one of your own presentations as a seed for discussion. (For example, if you will be giving a talk in a different context, you may invite the students to give you feedback on a practice presentation.) The class discussion is likely to be most helpful to the students if it happens after each student has had the experience of giving a presentation.
  • Feedback Give students constructive feedback on their in-class presentations.
  • Peer review/reflection Have students give each other feedback on their in-class presentations. Also encourage students to make notes for themselves about things they want to do (or avoid) in their own presentations.

Helping students to write well

  • Encourage student to read (critically). Students may learn the genres/discourse of mathematics best by reading diverse papers. Since not all mathematics is written well, it may help to discuss advantages/disadvantages of various papers.
  • Start with short writing assignments Before assigning a long paper, assign shorter papers so students can focus on smaller-scale writing issues before having to also juggle the challenges of structure and development inherent to a long paper. One option is to have students write in their own words a proof from one of the sources they’ll use for their longer paper. Doing so provides an opportunity to teach reading strategies as well as citation and appropriate source use.
  • Choice of topics Help students to choose appropriate, carefully focused topics. Even the best writers have difficulty writing well when the topic of the paper is unfocused.
  • Class discussion Hold a class discussion about how to write well. You could perhaps use a draft and revision of a paper you have written as a seed for discussion.
  • Peer review Have students give each other feedback on each other’s papers. The assigned audience for undergraduate seminar papers is usually peers, so peers can effectively identify which parts of a paper need clarification.
  • Feedback Give each student feedback on a draft of the paper (perhaps a later draft than that reviewed by peers).
  • Encourage sufficient time for revision When students are busy at the end of the semester, it can be very tempting to relax the deadline for the paper draft; but for students to write well, they need feedback and sufficient time for revision. To avoid the end of term crunch, schedule the draft(s) as early in the term as is reasonable.

Be aware of the regulations and of your department and institution

  • To ensure that students can plan their work and are not overworked at the end of the term, your institution may have rules about when assignments must be announced and how many and what types of assignments may be due at the end of the term.
  • If your institution has a communication requirement, be aware of how it affects your class and what resources are available to you.
  • If you are new to your department, check that you are aware of all relevant departmental guidelines and rules. For example, M.I.T. offers several undergraduate seminars so the department provides guidelines for undergraduate seminars.

General resources for planning a communication-intensive course

The following resources are not specific to mathematics.

  • The webpage Integrating Writing and Speaking Into Your Subject, provided by MIT’s Writing Across the Curriculum, addresses such topics as why and how to integrate communication with the content in a mathematics course, designing assignments, and assessing communication.
  • Resources for Teachers: Creating Writing Assignments, from MIT’s Comparative Media Studies Writing and Communication Center, contains information on how to create, check and sequence effective creative writing assignments of different formats.
  • Lave, Jean, and Etienne Wenger, Situated Learning: Legitimate Peripheral Participation, 1991, Cambridge University Press. pp. 33, 29, 40. Provides a theoretical context for designing courses that use situated learning to introduce students to the communities of practice of mathematicians (e.g., mathematics laboratories, capstones).
  • This AMS blog post provides some advice for creating a motivating syllabus for mathematics classes.
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