N J Wildberger


School of Maths UNSW Sydney 2052 Australia


Tel:61 (02) 9385 7098

Fax:61 (02) 9385 7123

Specific Mathematics Lecturing Skills...


At the university level, there are a wide range of different lecturing scenarios, from large first year service courses, perhaps with hundreds of students, to smaller specialized classes of higher year or graduate students, perhaps with only a few students. Obviously the skills required will vary accordingly, but what follows are some rules that are useful in most situations. This is of course a very personal choice, and is oriented to mathematics teaching.


  • Never speak longer than your allotted time (many otherwise excellent lectures are marred by the speaker extending his/her time by just two minutes!)
  • Speak clearly and deliberately, but avoid a monotone presentation by using variation in tone and emphasis.
  • Speak loudly enough that everyone can hear, and look directly at your audience as you speak. Try to look at every single student at least once during your lecture!
  • Speak more slowly than usual. Better to say less than more. Practice deliberately slowing down your speach if this is an issue for you (it probably is).
  • Smile, enjoy the privilege of having young people listen to you, but do not let your personality project too much into the situation.


Should you use the blackboard/whiteboard, or go for transparencies or Power Point? The general principle is that active is better than passive. However, it is also true that active is more difficult than passive. So sometimes a compromise is necessary.

  • If you can, try to give an active presentation. That means try to avoid prepared transparencies or Power Point presentations. This reinforces the idea that mathematics is an active discipline. The way you handle those inevitable mistakes will also teach your students a lot about how to do mathematics.
  • Make sure the board is completely clean before you start. Start from the top left and work your way to the bottom right, having first partitioned the available space into workable columns (at least in your mind).
  • Write/print clearly. If necessary, practise this important skill. There is no excuse for a professional teacher having hard-to-read writing. Do not erase material until most of the board is occupied. Try to leave everything on a minimum time (say 5 minutes). When you erase, do so thoroughly.
  • Use visual mediums (slides, computer presentations, transparencies) to augment your presentation, but do so sparingly.
  • If you are using transparencies, it is better to write on them actively rather than having prepared ones. This requires some practice, making sure you always allow a good view of the screen, use colour effectively, and write, or print clearly and large enough. If your writing is sloppy, or you don't know the material thoroughly, you are better off with prepared transparencies.


  • Make sure you have a good and realistic idea of the capabilities of your audience. If necessary, ask them questions. Try to gauge how well they are understanding the material. A lot of chatter, or dull vacant expressions, are clues that you have lost them. In this case, backtrack, review, recapitulate the main ideas.
  • Be attentive and respectful towards your audience. Dress neatly. The larger the class, the more important it is to maintain an element of formality along with some showmanship and if possible, humour.
  • There should be at most three main points in a mathematics lecture. Make sure you know what these are, and emphasize them, possibly repeatedly. There should be at least three main examples in a mathematics lecture. Make sure you have prepared and worked these out carefully.
  • Try to make personal contact with students, even in a large class. Ask a random student a question (taking care not to embarass them, and praising them if they get things somewhat right), or engage the entire class in a calculation. Five minutes of active work in an hour-long class is not unreasonable.
  • Be available for questions/feedback immediately after your lecture. This is the safest way of finding out how your class is going. If necessary, end your class a few minutes early so that students know you are available at this time for questions.