The audience is most likely to be engaged if they have a reason to pay attention and if the presenter makes the presentation interesting. Giving the audience a reason to pay attention Homework and quizzes encourage students to pay attention to each other’s presentations. In student-taught classes, homework and quizzes may seem inappropriate because students are supposed to be self-motivated learners working together to learn the material. A possible middle ground in these classes is for the students to write questions for each other: Examples of strategies Student-supplied homework–Scott Carnahan Student-supplied quizzes–Sami Assaf Peer critique–Steven Kleiman Strategies for giving engaging

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Many of the following resources were found by undergraduate researcher Noor Doukmak: How to give an effective math talk Giving Good Talks by Satyan L. Devadoss From the Early Career Section of Notices of the American Mathematical Society, Nov 2019 10 Ancient Rules for Giving a Conference/Seminar/Research Talk in Mathematics, by A. Kercheval From the Early Career Section of Notices of the American Mathematical Society, Nov 2019 How to Talk Mathematics by Paul Halmos Touches on the issues of simplicity, details, proofs, problems, organization, preparation, brevity, techniques, flexibility, and short talks. Talks are not the same as papers by Terry

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 →It is extremely helpful for students to rehearse at least their first presentation with you. (drawback: significant time commitment from the instructor.) Mia Minnes writes of her experience using practice presentations in M.I.T.’s Seminar in Mathematical Logic, “I found that the rehearsals of presenations for my seminar last year were very beneficial to the students and drastically improved the experience (for the audience too!). Most of my students had never spoken in front of a group before, not to mention written on the blackboard, and the rehearsal with me brought to light things they needed to work on before their

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

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.

Read more →Encourage students to improve their presentations: otherwise presenting repeatedly may merely ingrain bad habits. Feedback can come from peers and from instructors. Range of instructor feedback Consider commenting on the following: Timing notes: an outline of the talk including the amount of time spent on each portion. Feedback on the presentation style: style of speech, use of visual aids (blackboard/ slides/ images), pacing, audience engagement. Feedback on mathematical content: correctness, connections of material to other parts of course or other parts of mathematics (this is a good way to pique students’ interest in the subject matter). Feedback on teaching strategy:

Read more →If one of your objectives is for students to learn to communicate as mathematicians, then consider creating a presentation context that is comparable to those encountered by mathematicians (e.g., conference talk, colloquium talk, poster presentation, lecture to students, informal presentation to collaborators). Short Talks Assigning short talks at the start of the term acts as an ice breaker and helps the class get to know each other gives you a quick way to assess which students will need the most help with presenting helps the students to start becoming more comfortable speaking in front of the class If students will

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