M 175T Sp 09
GUIDELINES AND SUGGESTIONS FOR PREPARING AND PRESENTING PROOFS
First, work out the details of the complete proof yourself. Things to pay attention to:
• What can
you assume and what needs to deduced from the assumptions? For example,
if you assume one angle of a right triangle has measure α, then
the fact that the other acute angle has measure 90° - α is
something deduced (proved) from your assumption; it is not another
assumption.
• Do you have a logical reason for each step?
(that is, an explanation of how each step follows from the assumptions,
previously established statements, and mathematical theorems that are
reasonable to assume that the class knows.) If not, you need to figure
out what the reasons are; you may need to break down your proof into
further steps. It is a good idea to check with me what it is reasonable
to assume the class knows.
Next, think about how best to present the proof in class. Take into account the following:
- You
should try to maximize class participation as possible. So be sure to
think of good questions to ask the class to guide them in the right
direction.
- Think about what method of presentation
(blackboard, overhead, power point, physical models, etc.) works best
for the particular proof. In some cases, a combination works best.
- Also think about what questions students might ask, and how best to respond to them.
Come to class prepared with any materials you need (class handouts,
transparencies, paper, colored chalk, transparency pens, models, etc.)
• Check
with me enough in advance to see what I can supply (e.g., colored
chalk, transparency pens, transparencies; occasionally other things),
and please remind me by email if I need to bring something to class for
you.