Caleb Cheek

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					Teaching Statement                Caleb Cheek                          November 2010

Most of the teaching that I have done thus far has taken the form of informal training
sessions for peers, either coworkers or senior citizens in the community. This expe-
rience has greatly influenced my perspective on the teaching process, and I find it
useful to keep in mind how my teaching would be received by this sort of audience.
My students, after all, are the ones who decide whether my course has accomplished
anything. Comparing how I teach a lecture hall of somewhat anonymous students
mathematics to how I would teach something non-mathematical to someone I know
and respect lets me get away with less: I can’t disguise a lack of adequate motivation
with the conviction that mathematics is a deep and difficult subject, because they’ll
admit they don’t care. I can’t complain about my coworkers’ lack of suitable prepara-
tion and unwillingness to work (not for very long, at least), so I don’t complain about
my calculus students. The main point that has been emphasized by my experience is
that to be worth anything as an instructor, I need to have respect for my students.

Part of this is recognizing that having an inflexible set of expectations just doesn’t
work. My students are in the course for a variety of reasons, and all have different
ideas of what they want to get out of it. Being a successful instructor means taking
into account their different learning goals, and understanding the best way to get
each type of student motivated. They all have other things going on in their lives,
as well as several other courses. If I haven’t given my students sufficient motivation
to put effort into learning the material, there’s no reason they should spend time on
my course rather than something else. I am careful to avoid alienating my students
by overstressing motivation that doesn’t work for them; they aren’t motivated by the
things I am, or even the things I was when I took calculus. Very rarely do calculus
students want to become young mathematicians, so I don’t demand that they treat
mathematics as a thing of beauty. For the students in disciplines that make heavy use
of math, like the natural sciences and economics, I motivate concepts by borrowing
ideas from a broad range of these subjects. In this way, I seek to expose students to
the utility of mathematics.

Something I consider essential to my teaching is that I make every effort to teach to
the students I have, not the ones I think I should have. I try to throw all notions of
’ideal’ students out the window; my ideal students are the ones who happen to be in
my course. In particular, this means making sure that every student in my course
will get something out of it, regardless of the grade they get in the course or whether
they’ll directly use the material they learn again. What I expect out of an individ-

Teaching Statement                Caleb Cheek                          November 2010

ual student is tailored to what they want to achieve by taking my course, but as a
base goal, I expect that every student will spend some time thinking mathematically,
which is a somewhat strange thing to do. Accomplishing this goal means I have to
make myself approachable, and make the material as entertaining as it can be. An
effective way to do this can be through short tangents about math in popular culture
at the start of class; that everyone knows the torus because it’s the thing Asteroids
is played on is a particular favourite.

To accommodate the development of mathematical thinking, I believe that carefully
chosen homework questions together with frequent and constructive feedback can
change routine exercises into a valuable learning experience. The instantaneous feed-
back provided by dynamic web content for courses is a good way to make this happen,
and I plan to use such content as another way to make my teaching more accessible.
I choose homework and examples to cover in that point the students toward the the-
ory, and then follow up with questions checking their understanding of the theory.
In the spirit that learning is accomplished not just by doing, but by communicating,
I strongly encourage students to work together on homework assignments. More of-
ten than assigning difficult questions, I will give problems that foster communication
skills. This usually takes the form of word problems where the core of the question is
being able to identify the mathematical content and relate it to what is being said. In
my non-mathematical teaching, I have had success with splitting students into groups
to create a short writeup or presentation on some simple concept, and I plan to do
this in my mathematics courses.

I teach with a strong focus on the individual. By guiding students through mathe-
matics, I seek to develop not only their proficiency with a particular subject, but also
more broadly applicable skills, like the careful reasoning and communication skills
that go along with it. I feel that this style of teaching lets my students learn as much
as they can from me, but also lets me learn as much as I can from them.


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