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.

Sample presentations: examples & cautions

Page Contents
  1. Examples
  2. Cautions

To illustrate the value of a particular presentation strategy, consider giving the same short presentation twice: once without the strategy and once with it.


  • 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. She then asked the students to do a short in-class assignment: three questions to test their understanding of Young Tableaux. The students understandably had a hard time with the questions. In the second presentation, she covered the same concepts in the same order, but defined the concepts by example rather than with formal definitions (for one or two of the most important concepts, she formalized the concept after giving the example). The difference was like night and day: the second talk was so much easier to understand that the two talks provided a powerful illustration of the value of using examples and conceptual explanations to build understanding.The two sample talks were followed by a class discussion in which the class generated a set of guidelines for themselves for giving good presentations.
  • M.I.T.’s Project Lab in Mathematics
    Joel Lewis gave two presentations about knots.


  • Caution 1 Giving a sample presentation for students to deconstruct may work best at the beginning of the semester. Later in the term, it may be difficult to construct a sample talk that doesn’t seem to be singling out particular students’ weaknesses.
  • Caution 2 If you give two sample presentations for comparison, it is tempting and easy to have one of them be a bad presentation (illegible handwriting, mumbling, etc.). Although such presentations can be amusing, students don’t learn much because the problems are too obvious. It’s more effective to choose a non-obvious presentation principle you want to emphasize (e.g. choosing good examples, providing conceptual explanations, making connections) and then show the difference between a good presentation that doesn’t follow the principle and the same presentation improved by following the principle.
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