### 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 Physical Mathematics, Pedro Reis gave a practice presentation for a real talk that he was going to give soon. After the practice presentation, students gave him feedback, discussing both what worked well and how the talk could be improved. During the discussion, the students’ comments about Pedro’s practice presentation were generalized to create a list of guidelines for the students to follow in their own presentations.

- Students may erroneously think that math presentations should be dry and unrelentingly formal. This misconception can be addressed by giving two short sample presentations, one of which appears to be quite good but is entirely “formal,” and the other of which communicates more effectively because it includes illustrations, conceptual explanations, etc. This same strategy (comparing two sample presentations) can also be used to emphasize other presentation techniques.
- Well-chosen online videos can also be used to spark discussion.
**Example**: In M.I.T.’s*Undergraduate Seminar in Discrete Mathematics*, Olivier Bernardi showed excerpts from two videos: the first 5 minutes of Oded Schramm’s*Random, Conformally Invariant Scaling Limits in 2 Dimensions*from the 11th session of the 2006 International Congress of Mathematicians, and the first 10 minutes of Alan Sokal’s Isaac Newton Institute web seminar giving an introduction to statistical mechanics for mathematicians, which illustrates good board work.- More online videos are linked from the page on examples of good math presentations.

### Discussion questions

Discussions with more than 30 educators from a variety of institutions has resulted in a list of characteristics of effective student writing and talks. The resulting list suggests some questions to fuel a discussion about effective presentations.

The following questions may also help spark discussion:

- What is the purpose of giving a presentation? (Students are in the habit of demonstrating that they know the content, so they may need to be told that demonstrating knowledge is insufficient for a presentation in which the goal is to help the audience understand.)
- What strategies are there for making a math presentation engaging for the audience?
- What are the reasons for including a proof in a presentation?
- What strategies can be used to convince the audience of the truth of a statement? Proof is an obvious answer, but what other strategies could be used?
- What are the different kinds of presentations one can give? How does the type of presentation affect the presenter’s choice of content, focus, level of detail, delivery, etc.?
- What about the presentations that you’ve seen has been most helpful to your learning?
- What advice do you have, for yourself and your classmates, for preparing good presentations?
- What was surprising to you about preparing and giving presentations?
- Be sure to discuss not only the characteristics of an effective presentation, but also the process of preparing an effective presentation. Your students may be particularly interested to hear the process you use to prepare an important presentation.
- If students have already presented once, beginning the class by asking students what they’d like to talk about may generate a list of questions that will occupy the entire class period.

### A useful trick for assessment

If you ask the class to generate a list of features of a good presentation, you can refer to this list when assessing later student presentations.

### Resources for students

The page of Resources for presentations has advice on presenting from Paul Halmos, Terry Tao, and others.

### 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 present. 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 presentations.

- Khan, S., “Why Long Lectures are Ineffective,”
*TimeIdeas Education*, Oct 2, 2012. - Patton, Martha. “Situated Writing Lessons: Putting Writing Advice in Disciplinary Context.”
*The Writing Instructor.*2004.

This article presents a template for constructing lessons on writing topics. Various examples are included in appendices. This template applies to creating lessons on any communication topic, not only writing.