his lesson plan outlines a workshop on giving seminar presentations. The workshop was conducted in Mia Minnes’ Undergraduate Seminar in Logic at M.I.T. after each student had presented to the class once. The workshop included a discussion of the students’ experiences presenting, two sample presentations given by the instructor to illustrate common pitfalls and how to avoid them, a discussion of the rhetorical differences between seminar presentations and class lectures, as well as the advantages and disadvantages of various forms of presentation (slides, board, overhead).

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This one-page reading assignment presents questions for students to consider as they read a draft of one of their instructor’s published papers. This assignment precedes a workshop on how to write a paper, in which the students discuss the draft and a revised version of the paper as well as writing process. From Pedro Reis’ Undergraduate Seminar in Physical Applied Mathematics at MIT.

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 one-page outline summarizes a workshop on how to give a mathematics presentation. The instructor begins by giving a practice run of a real talk he will be presenting shortly in another context, students critique the talk in pairs and then the class as a whole discusses the highest priorities for improving the talk. This workshop occurs at the beginning of the term before students have begun giving their own presentations, so the instructor concludes the workshop with some “veteran advice” for how to prepare a presentation. Links are included to handouts for critiquing a presentation and for preparing a

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 →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

Read more →When during the term should the lecture or workshop be held? Students tend to have more concrete ideas and questions about presentations after they’ve presented in front of the class, so if students will present multiple times during the term, a particularly good time to discuss presentation skills is after each student has presented once. Spark discussion with a sample presentation A sample presentation can help to spark good class discussion. You could give a practice presentation of your own and ask for feedback. Doing so helps to create a collegial atmosphere within the class. Example: In M.I.T.’s Seminar in

Read more →Context: This workshop from MIT’s Project Laboratory in Mathematics prepares students to collaborate in teams of three to research mathematics, write papers, and give presentations. The purpose of this workshop is to give students tools they can use to help their teams function productively. The most important part of the workshop is the discussion that follows the team activity. Authors: This workshop was developed primarily by Susan Ruff; the activity (not reported here) is from Google, via Robin Shostack Student preparation: Before the workshop, students watch the video Overcoming Unconscious Bias from the Global Communication Center at Carnegie Mellon University. This

Read more →To illustrate the value of a particular presentation strategy, consider giving the same short presentation twice: once without the strategy and once with it. Examples Sami Assaf’s Undergraduate Seminar in Discrete Mathematics at M.I.T. Sami gave two presentations on Young Tableaux. On the surface, the first presentation seemed to be an excellent presentation, but Young Tableaux and the preliminary concepts were presented only by their formal definitions. Sami carefully began with partitions, weight, etc, and gradually built up to Young Tableaux, but gave very little conceptual explanation of the definitions and did not provide a diagrammatic interpretation of the definitions.

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