This brief fabricated sample of student writing was used in class to model peer critique (two instructors act as students, one of whom is critiquing the writing of the other). The sample addresses the question of whether there are “gaps” in the rational numbers. Written by Joel Lewis with modifications by Peter Speh and Mohammed Abouzaid.

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The article “Maximum Overhang” by Mike Paterson, Yuval Peres, Mikkel Thorup, Peter Winkler, and Uri Zwick won the 2011 David P. Robbins Prize, an MAA Writing Award. This pdf of the article is annotated to point out to students how to write a mathematics paper. The annotations address the structure and content of an introduction, how to integrate equations, text, and figures, how to guide the audience through the content, how to cite, etc. The article addresses the question of how far a stack of blocks can extend from the edge of a table. It was published in the American

Read more →These slides are for a workshop on how to write a math paper. They provide successive examples of good and better writing. In the class, students are asked to read each sample and assess how well it achieves the stated goals for the paper.

Read more →This (fabricated) draft student paper is designed to start a class discussion about when conceptual explanations are needed in mathematical writing. The paper is about an algorithm for finding square roots. The first proof shows that the algorithm is correct, but the point of the second proof is never clearly stated (it shows that the algorithm is efficient). Written by Joel Lewis for M.I.T.’s communication-intensive offering of Real Analysis, based on Rudin’s Exercise 16 in Chapter 3.

Read more →This lesson plan and handout are for an 80-minute workshop to prepare students to write their term papers. During the workshop, an instructor provides guidance for choosing an appropriate focus for the paper (counterexample: “Everything I know about the Island of Corsica”); students talk with classmates to focus their topics; and the class discusses rhetorical differences among papers, presentations, and psets; the writing in two versions of the same paragraph; the structure of a paper; LaTeX; and acknowledging sources. From Mia Minnes’ Undergraduate Seminar in Logic.

Read more →These drafts of an article by Mark McLean illustrate how a proof can be improved by pulling out a lemma. Although the article is on an analysis topic beyond the understanding of Real Analysis students, Mohammed Abouzaid has drawn attention to the structure of the article by highlighting relevant guiding text, so the improvement caused by pulling out a lemma is clear.

Read more →This handout for a workshop on writing a math paper presents three versions of the same paragraph. The writing samples are designed to illustrate how ordering information within sentences can strengthen connectivity between sentences, thus creating flow and making the logic easier to follow. From Pedro Reis’ Undergraduate Seminar in Applied Physical Mathematics at MIT.

Read more →The following presentations can be used as a basis for discussion about good presentation technique: Videos are available from some conferences, including the 2006 International Congress of Mathematicians. An example of a good slide talk is Oded Schramm’s Random, Conformally Invariant Scaling Limits in 2 Dimensions from the 11th session. Steven Strogatz gave a series of three Simons Lectures at M.I.T. in the spring of 2011. Coupled oscillators that synchronize themselves Social networks that balance themselves Blogging about math for the New York Times [This presentation is about writing math for a general audience.] Many undergraduate math lectures are available

Read more →[The following notes are about Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry, in which the students give the lectures.] This spring of 2010, I tried something new: in-class critiques. They worked out very well, far better than I ever expected. When the students arrived for class, I gave them each a standard sheet of blank paper. During each student’s lecture, the others then wrote a critique, describing what was done well and what needed improvement, so as to reinforce good practices and suggest opportunities for growth. The critiques are marvelous — friendly and constructive, addressed

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