When I arrived at Union, Dean Sorum told me two things that I
have returned to regularly ever since. The first was in response to a
question about what the students here are like; she said "They're very
polite." I didn't know how to take this at the time, but have come to
realize that it is absolutely true. Union undergraduates are some of the
sweetest students I have worked with: they will hold the door open for you;
they apologize if they miss class; they don't close up their books until
you have dismissed them, even if you run a little over time; and they will
try to do anything you ask, as long as you are meticulously clear about
what that is. Like many young math students, however, they are not
comfortable developing their own techniques or drawing connections on their
own, and they are not experienced with abstracting the processes we learn.
For example, most Math 13 students would have no trouble with
the problem "Locate the critical points of the function
*f*(*x*) = *x*^{3} - 3*x*^{2} -
9*x* + 5" but few would know how to answer the question "Under
what conditions does *f*(*x*) = *ax*^{3} +
*bx*^{2} + *cx* + *d* have only one critical
point?'' Both problems use the same techniques, but the first follows a
procedure we outlined in class, while the second asks the student to
understand the meaning of the process. The solution to the latter question
is not hard, but it requires a type of thinking that incoming freshmen, in
particular, are not prepared to do.

I was surprised by the level of resistance on the part of the students
to questions like the later one above, and this prompted Dean Sorum's
second comment. This was to remind me that "They're not like you,"
meaning that most will not go on to graduate school, become
mathematicians, and end up teaching. Of course, I understand this,
and I can accept it; but an obstacle to their real education is that
they don't *want* to be like a mathematician. It is
disappointing to any teacher, and ultimately unhelpful to the students
themselves, when they are more concerned with being done with the
material than in understanding it, or when they are uninterested in
knowing why something works the way it does but only want to know how
to get "the answer."