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.

Giving a lecture or workshop on writing

The characteristics of good math writing are too many to address in a single writing lecture or workshop; for a small sample of these characteristics, see the pages about general principles of communicating math. So the instructor should choose characteristics on which to focus.

Examples of writing lectures and workshops

  • A brief mini-lecture could present handouts about guiding readers through the content, writing an introduction, and using sources. Students could also be pointed to other resources for writing and for learning LaTeX.
  • A longer (50-90 min) writing workshop could involve the students in some active learning. For example,
    • Pedro Reis used his own drafts as a springboard for discussion in M.I.T.’s undergraduate seminar Applied Physical Mathematics. Before the workshop, he asked the students to read early and later drafts of one of his papers, focusing their reading with questions that he supplied. These questions were then used to generate discussion during the workshop. The students were interested to hear about Pedro’s writing and revision process, and Pedro was able to use the writing samples to draw attention to writing issues he wanted to emphasize for the students.
    • In Peter Shor’s undergraduate seminar Information Theory at M.I.T., communication lecturer Susan Ruff teaches a class about how to help readers follow complicated logic (slides) by combining guiding text and known-to-new structure.
    • M.I.T.’s Paul Seidel created weak, good, and better writing samples to use as a springboard for class discussion in Project Lab in Mathematics. These samples do a good job of drawing students’ attention to common but non-obvious student writing mistakes; they also do a good job of illustrating how to avoid those mistakes.
    • Mia Minnes’ 90-minute writing workshop combined mini-lectures with pair work and class discussion in M.I.T.’s Seminar in Mathematical Logic. Students talked in pairs to discuss how to focus their papers, and the class discussed a writing sample taken from their textbook.
    • In M.I.T.’s communication-intensive offering of Real Analysis, writing recitations focus on various writing topics. For example, a 50-minute workshop on ordering information so content flows logically combines a mini-lecture with class discussion of two writing samples designed to illustrate how information can be ordered to improve connectivity.
    • Peter Shor asked students in M.I.T.’s undergraduate seminar 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.

    Note: The term “writing workshop” means different things to different people. For writing faculty, a “writing workshop” may mean a meeting of peers to discuss samples of each other’s writing, while for math faculty “writing workshop” may mean more broadly any class about writing that involves some discussion or active learning. We use the broader meaning here.

General resources (not specific to mathematics)

Research shows that lectures are a relatively ineffective method of teaching, so one of the interactive workshops described above may be more effective than giving a lecture about how to write. The first resource below is a TimeIdeas article (written for a general audience) that briefly summarizes and contains links to some of the research about the (in)effectiveness of lectures. The remaining resources below are for planning a class on writing.

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