Advice on Presentations

This is an informal summary of in-class discussions from a previous semester (Fall 2008).

Present information in an order that is logical and understandable. Identifying a good order is not trivial, and requires an understanding of your audience. Connect each new concept to a concept that is already familiar to the audience. Sometimes it helps to present a concept in a simplified form before presenting it in a more complicated form.

To make the content understandable, use forecasting: For example, before you present a lemma, say how the lemma will be used. Be sure it's always clear why you're doing what you're doing.

Help the audience to build an intuitive understanding of the material. One way to do so is to look at counterexamples.

Plan for wanderers: it's normal for people to stop listening for a while to think. Structure and deliver the talk carefully so that people can catch back up with you after they start listening again. Write enough on the board so they can look at the board to catch up, and verbally repeat important points.

Provide enough detail to be clear and convincing, but don't use too much detail (unnecessary detail can prevent understanding by obscuring the big picture).

Proofs are not always helpful in a presentation, so think carefully about whether one is necessary before you present one. Consider presenting a proof if

  • the proof is your main result
  • the proof is interesting, elegant, or pretty
  • the proof gives insight into the math
  • the proof illustrates the power of your result
  • the proof is needed in order to convince the audience

    • If none of the above apply, seriously consider not presenting the proof. There are other ways to convince your audience: data, examples, sketch proofs, diagrams.

    Speak to the audience rather than to the board. Not only will the audience be able to hear you better, but the presentation will be more engaging for the audience if they can see your facial expressions. Present with sufficient energy and enthusiasm: let the audience see that you're interested in the content. Use a varied tone that is neither too loud nor too quiet.

    Illustrate concepts with pictures. The pictures you show should help you make specific points, and you need to spend time explaining how they do so.

    Handle glitches well. The audience will take its cues from you: if you are flustered, the audience will be uncomfortable, but if you remain calm and in control, the audience will be less bothered by problems.

    Time yourself when you practice. Plan points during the presentation where you can adjust the presentation if you're running over (or under) time.

    Anticipate questions and be prepared to answer them. The audience is likely to ask questions about unclear points, weak spots in the research, alternate directions for research, etc. Practice in front of friends so they can point out likely questions.

    Be well prepared!