1.3 Getting to Know Your Teaching
Teaching is exciting and rewarding and can also be fun. Interacting with
bright young people is certainly one of the finer things in life. Explaining
important ideas to a receptive audience is fulfilling, and is also important for
bringing a new generation of young adults up to speed in our discipline. You
are fortunate to be part of a vocation that puts you front and center in this
process. Make the most of it.
What does this mean? First of all, you will get a whole lot more out of
your teaching—and everyone else will too—if you are reasonably good at it.
The ability to teach well is not something you are just born with—like the
ability to hear with perfect pitch. It is a cultivated skill, and one that you
should start working on right away—see Section 2.1. Some of the traits of
a good teacher are simply matters of tending to business: You prepare your
lectures carefully, you write a good syllabus, you choose an appropriate and
readable text. Other traits are special and personal and will require hard
You will probably have had some experience as a teaching assistant, or
TA, and that is an activity that resembles teaching. But really teaching—
being in charge of a class, writing the exams, assigning the grades, handling
the problem situations—is a rather more sophisticated activity.
I may humbly suggest that you consult the book [KRA1], which will give
you the full story on almost every aspect of teaching, and more particularly
of teaching mathematics. God is in the details, and you will find that the
enterprise of teaching is certainly a whole that is greater than the sum of its
parts. Preparation is a big part of being an effective teacher. You want to
convey the immediate and powerful impression that you are a professional
who is on top of the material and who knows how to communicate it. Many
of your other shortcomings will be forgiven, or at least overlooked, if it is
clear that you are a pro who is doing his/her best to do a top-notch job.
You want to be courteous, kind, and fair. I have always gotten along well
with my classes and garnered reasonably good teaching evaluations,4 but in
recent years I have done even better than usual because students warm up
to the fact that I am so easygoing. I think this means that when they come
to me with a problem—a forgotten assignment, or an overslept exam, or a
are a few exceptions, such as the teaching evaluation that said that I should
not be allowed to teach any biped in any state west of the Mississippi.
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