Teaching Statement

I like to teach a wide variety of courses, not just in my specialty of discrete mathematics. Liking a variety is part of why I am at Swarthmore. I particularly enjoy teaching introductory courses where I can help students understand some fundamental grand ideas. I have very much enjoyed teaching calculus, linear algebra, discrete mathematics, and statistics (before Swarthmore had 2 statisticians.)

At the more advanced level I have particularly enjoyed teaching introductory analysis, as well as courses in my specialty. In particular, I am the person here who knows the most about linear programming, mathematical game theory, and mathematical biology.

Teaching Style

The first thing students notice about my courses is email. I use it all the time -- for assignments, for follow-up commentary to lectures, for ancillary handouts, for answering questions. I was one of the first on campus to start using it (15 years ago!) and today I am still one of the heaviest users for course purposes. I'm logged all the time while in my office, frequently when home. Questions and comments sent to me by email usually get answered in an hour or two if I am in my office, within 12 hours if I am at home. Now, with the introduction of a Course Management System (the Web based "Blackboard"), I may do more of my electronic interaction with students through that than through straight email, but the effect will be similar.

According to course questionnaires, most students really like the online contact. It works especially well for students who are shy about coming to my office, or for whom getting to my office is inconvenient. On the other hand, I am delighted to interact with you however you like -- in person, by phone, in class, email, etc. There are lots of learning styles, and I try to provide information in many different ways in hopes that at least some of it comes in a form most congenial for you.

Another thing students notice are my inventions -- problems I make up in addition to problems from the text. Problems -- both solving them and posing them -- is perhaps the thing that first got me interested in mathematics as a kid, and I think I am now a pretty good problem poser. I used to specialize in hard problems, but now my goal is to make up problems that clearly get at some point. Many of these problems are still to be done with paper and pencil, but I also make up various computer problems and labs. Most mathematicians, including me, feel that

the best way to learn math is
through solving many problems of just the right challenge level.

I probably spend at least half my course time preparing problems and solutions, and you should spend at least half you time on the problems too.

I like to teach both classes and seminars. I like giving lectures. I think I have a knack for getting to the point and being clear, while showing my enthusiasm for the subject -- at least this is what students tell me in evaluations. I seem to be good at knowing what is hard for people. I also enjoy making up examples that get at key points; this is closely related to problem writing.

Interestingly, I do better lecturing to large classes (30 or 40) than to small classes (10-20). Somehow I draw more energy from, and thus deliver more energy back to, a larger group -- maybe because I get more questions and comments (natural if there is a fairly constant comment rate per Swattie).

However, there is a lot of evidence now that lectures just don't work for most students (perhaps even Swarthmore students) no matter how clear and engaging the professor is. A great explanation isn't enough; you've got to try it yourselves. Therefore, even in lecture classes I try to do less lecturing these days and spend some time having you work at your seats, or in groups at the board, or have you write little summaries of what class was about, etc.

In seminars the satisfaction has always been seeing what you do, since I am more a coach, getting you to present things, even if your work is incomplete or you are not sure you are right, and getting you to cooperate with each other.

I both classes and seminars, I like the Socratic method -- asking a lot of questions and making you develop your understanding through answering. The Socratic method used to be a norm -- students used to understand that it was meant for their benefit. Or at least I thought they understood it, for they didn't complain about it. But now we get feedback indicating that many students feel questions are meant to intimidate them. So I try very hard these days not to be intimidating -- I ask more gently, wait longer for answers, applaud partial answers, show my delight when someone's false start eventually led the class to reach a good conclusion, and in general, explain why I am asking questions. But this does take a lot more time. I wonder: has an old understanding (about the purpose of questioning) broken down, or were we teachers wrong to think there ever was an understanding?

I am also very eager for you to ask your own questions. I think I am good at understanding what you are trying to ask (because I seem to have a good sense of what students misunderstand). However, if I am not sure I understand your question, I will ask you to try again until I do understand it. Try me and see. Don't be afraid to ask.

Writing

Writing is an essential form of communication, especially for subtle material like mathematics. Some people think writing and mathematics are disjoint activities, but far from it. In mathematics you use all the tools of ordinary language plus the additional conventions of mathematical symbolism -- solutions consist of both words and symbols. So writing plays an important role in my courses. I have liked giving PDCs, and will probably give whatever replaces them. We cannot expect that you will just pick up the special conventions of writing in mathematics by osmosis; we have to teach them.

Tests

Since I like making up problems, I like making up tests. I think I write good ones. But this claim depends on the meaning of "good" for tests. There seems to be a lot of misunderstanding these days by students about what tests are for. The purpose is not to humiliate you, or to give you some sort of trauma hardening. The primary purpose is to induce you to do a thorough review of the material. Determining a major component of your course grade is secondary. The purpose of a thorough review is to consolidate your learning. Learning concepts and material is the purpose of taking courses.

A secondary purpose of tests is to make you see the material is a new way. In addition to standard problems, I like to write some questions which provide a slightly different context than you have seen; will you see the connection and solve the problem?

This part of this essay used to be titled "Teachng Style". However, these days there is considerable opinion that disussing teaching style is barking up the wrong tree; we should be discussing your Learning Style. In this regard, consult my complementary statement How I learn. How do You?. My teaching style is based on my learning style; I'll change it if your learning styles are quite different.

Modern Teaching Dogmas

There has been a lot of ferment nationwide about math education in the last 20 years, and as a result, the received wisdom in many quarters includes With regard to these views I am somewhat conservative. I think they are overblown and certainly false as absolutes. For instance, yes, you have to grasp (construct) some things on your own (and will have more fun that way) but you will move along much faster if a good book and a good teacher save you from having to construct most things. As for research, mathematical research is fairly far removed from the sort of problem solving most people, even most mathematically trained people, do in their professional lives. In many cases it is much more important to learn key concepts and approaches which will make general problem solving much easier. Certainly the primary purpose (at least when I teach most undergraduate courses) is to learn beautiful and powerful concepts and methods.

Invitation

If any of what I say about teaching appeals to you, I look forward to having you in my courses.

Steve Maurer


Last updated: 8/17/01
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