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
- 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
- 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.