PROFESSOR: So I usually start out
by handing out a sheet of usually three to five questions
that I give to everybody.
These are questions that I'm eventually
going to answer in the course of the lecture,
but I give the questions out at the beginning
because I want people to have something to think about
while I'm talking, especially when-- it's not
uncommon for people to go off into a daze,
and it's good for them to have something to think about.
And also, ideally, they answer the question themselves
before I get to the answer.
Then we proceed to--
depending on the day--
in a day when we're doing lectures,
I'll proceed to present material, ask questions,
and then, when I get to an appropriate breakpoint,
try to give people a chance to solve the problems that I've
handed out, and occasionally have people come up
to the boards, and give their solutions on the board.
Sometimes I'll bring in materials.
Like if we're doing polytopes, I might
bring in an icosahedron, or a dodecahedron,
or some more sophisticated shapes.
Or we might be working with tiles or various other pieces
we might be using to investigate combinatorial problems.
And then on some of the days-- of least
two or three days of the course are devoted to nothing
more than problem solving, so I don't do any talking
during those days at all other than to answer questions
that people may have.
And people work either individually
or in groups on solving problems.
And then the last day of the course, we actually
had a contest, where the students had an opportunity
to pit their brains against some of the more challenging
problems that are out there.
And actually I should mention, a lot of the students who
take the course are very interested in mathematics,
and one of their motivations for doing the course
is to better prepare themselves for some of the math
contests that are out there-- contests like the AMC,
the AIME, and the US Math Olympiad.
And I think a lot of kids find the combinatorics questions
on those tests to be some of the most challenging,
whereas my attitude is always when
I look at those tests, about half the problems,
I have no idea how I would solve them.
But when I look at the combinatorics problems,
they're gimmes.
And my hope is that by the end of the course,
the kids who take the course think the same thing,
but the nice thing about the existence of these contests
is it gives me a wonderful source of problems
to throw at the kids.