Tips on Math Oral Presentations

After attending a workshop on Project work oral presentation, I've summarised the main learning points and added a few that are related to oral presentations that involve mathematics.

Preparation for Oral Presentation (OP)

1. It is important to organise the content into an order that flows. It depends on what you're trying to present. For instance, for an OP on history of mathematics, one can organise the presentation in terms of chronological flow. For group presentations, ensure each speaker has an equal amount of content to deliver. Sometimes, the first speaker who introduces the subject is more interesting than the middle speakers. The last speaker who summarises the OP would also have a better job. Hence make sure each speaker has enough interesting points to deliver. The presentation will flow well when the transition between speakers is smooth. Try to lead the discussion on to the next speaker by giving a short prelude of how the next speaker will add on or continue with the topic at hand. This will allow the audience to anticipate what the next speaker will say, and hence makes the presentation clearer.
2. Once the presentation material is organised and allocated to each speaker, it is important for the group to rehearse. Rehearsals serve many purposes. Firstly, rehearsing helps the individual speakers learn their speech. Secondly, it provides an opportunity for practising speaker transition, powerpoint transitions and other forms of coordination among the group. For instance, a flip chart needs to be flipped at a particular instant when the speaker arrives at a point in his delivery.
3. For each individual, cue cards should be made. Cue cards are small cards that can be bought at any stationery shop. The latter is extremely useful for the speaker to state what he wants to say during the OP. Writing on the cue card itself provides a way for the speaker to organise his thoughts. Moreover, priority of points can also be made with a highlighter on the cue card. For example, the speaker can highlight all important points that he must deliver in yellow, and any other less important points in green. Orange highlighted points might mean miscellaneous that are saved for the Question and Answer (QnA) session.
4. In short, if you fail to plan, you plan to fail, especially when it comes to oral presentations.

Audio Visual Materials in OPs
Here are a few pointers when using AV materials during presentations.

1. Keep Powerpoint slides simple and sweet. Use concise words and avoid long and cluttered sentences. It is very hard to read and follow a speech when there are too many words on the screen. Try to be as concise as possible.
2. Use only pictures and animations that add value to the OP. Avoid using animations that serve no purpose but to decorate the slide. This may distract the audience and hence hamper them from paying attention to your delivery.
3. Coordinate font, font size, backgrounds and color combinations. Try to have a good contrast for words and background. For instance, if you have a dark background on you master slide, try to use light colors for the words. Otherwise the audience may not be able to see the words clearly on the screen. Always rehearse with powerslide done. What you see on your PC monitor may not turn out as well on the projector screen.
4. Limit videos and music files to 1- 2 minutes, unless it has a very important and direct impact to what you want to deliver. A video which is too long may bore the audience and cuts down on the time you have to speak. Remember, your delivery is the most important grading criteria, not your resources. Use MS moviemaker to crop clips down to the bare minimum.
5. Always test out all equipment such as PCs, projectors etc prior to the presentation. You might never know what might break down at the eleventh hour (Murphy's law).

Public Speaking Skills
When it comes to public speaking, the most important point to take note is to always practise. Practise makes perfect. There is no one who is born to be an effective speaker. One needs to learn and practise speaking in order to be a good oral presenter. In order to be a good speaker, one needs to engage the audience. Here are some pointers to note:

1. Understand the background of your audience. This should already been acknowledged when planning for the OP, since, for example, it is fruitless to explain in depth how to tune a viola to a group of students who have no prerequisite knowledge about string instruments. Hence the speaker must first bridge the gap with the introduction of what a viola is, its parts before moving into the body of his speech.
2. Interact and engage the audience. There are many techniques of doing this. Although I've mentioned that one can refer to cue cards during OPs, it is important to look up and make eye contact with the audience. Try to look at various people to ascertain whether they can understand what you're saying. If they are nodding to certain points, they are probably following. But if they are frowning or not paying attention, perhaps you are going too fast or they cannot follow your speech. There are other ways to engage the audience. Questions can be posed to the audience, a poll can be taken so that the audience can participate in your OP. A bit of humour can also liven up your speech. Also, one can move a bit around the room to exert your presence. However, do not stroll too much into the audiences' personal space, which would make them uncomfortable (e.g. breathing down their necks).
3. Speak in a varying tone. Practise on your intonation. Nothing makes a OP more boring than a speaker who speaks in a monotone, nonchalant way. Be enthusiastic and speak with suitable degrees of pitch, tone and volume. When rehearsing, get feedback from your group mates. Are you speaking at the right volume? Are you using repetitive words like "ok" or "basically" in the speech? Lastly, display the right body language. It gives the most impactful impression to your presentation. For instance, always stand straight and not one one leg. Use hand gestures if necessary.

A word on Mathematics Oral Presentations
Very often, students present long mathematical working during their short OPs. It is important for the speakers to understand that the audience cannot grasp all the mathematics in the short period of time. Personally, one should try to give clear outlines of the working and present main ideas of proof. It is not effective to list all the working down on slides either. Just present the main ideas of the proof. But more importantly, discuss the result and conclude on how the mathematical result has an impact to the topic being delivered. Start and end off with this in mind so that the audience can follow more easily. This applies to any math presentation, be it a noble prize lecture or a short classroom presentation.

In conclusion, I have briefly gone through three important aspects of OP. A good OP cannot be done without sufficient preparation. Practise the OP as many times as possible to ensure all elements are in place. Plan your audio visual materials in an effective way. Remember, powerpoint slides are used to enhance your OP, not to distract the audience or confuse them. Lastly, practise on effective public speaking skills. Engage the audience with your body language and voice tone.