Universities and/or Education

The other paradigm is that of teaching as a "helping" profession. In this model, the student comes to a teacher because he has a desire to learn something, and the works cooperatively with the student to help him achieve his goal.

I think that both these paradigms are always at work to some extent, but in my experience, the capitalist paradigm is always by far the domininant one in our system of formal education, whereas the cooperative model is much stronger in the many classes I have experienced outside the academic system.

I am convinced, in fact, that the main reason many employers look for employees with college degrees is not because of their knowledge and skills, but because the university is a fairly good simulation of the corporate world, and it is fairly reasonable to hope that someone who has functioned reasonably well in meeting the requirements in school will also function satisfactorily in meeting the requirements at work. the corporate world. Students are given assignments, they work on projects, they meet deadlines. They learn skills such as listening for extended periods of time to people talking about things which are not very interesting and remembering a large part of what was said.

Going to school is the first real job that an individual in our society has. Employers have long since given up the hope that a high school diploma is evidence that a student has learned anything worthwhile. However the diploma is evidence that the person has been successful in the job of going to high school, and thus is more likely to be successful in fulfilling the requirements of some other job.

More and more, I think that the undergraduate college degree is looked at in somewhat the same light. It seems reasonable that students who have been successful in the university environment will mostly likely be the kinds of workers who will be capable of learning, will complete assignments conscientiously and on time, and will be capable of doing adequate preparation for presentations or other types of performance.

In fact, I find that although certainly some students are simply incapable of learning mathematics on a given level, for the most part -- especially in the courses beyond calculus -- the difference between a B student and a D student is the willingness to do assignments thoroughly and on time, and the willingness and ability to be prepared for tests, as well as good testmanship skills.

An employer may not care that much whether an employee can do integrals using partial fractions or prove that there's only one simple group of order 60, but at least there's some chance that someone who has been a mathematics or physics or chemistry major will be able to use manuals and not be completely intimidated by technical books and in general will be capable of learning technical material to some extent.

In non-technical fields, there are still important academic skills that students learn, such as the ability to express ideas in writing, to defend one's ideas in a rational fashion, to use a library resourcefully, and to locate information in books. When I was a student, attaining mastery of basic academic skills was something I placed a lot of value on. Traditionally, I think that a mastery of such academic skills was considered just as important as the possession of specific knowledge in characterizing someone as an ``educated person.'' And certainly becoming an educated person was at least as important to me as a student as getting a degree or qualifying myself for future employment.

But most students today, at least here at the University of Hawaii, don't seem to find any value at all in that kind of mastery. I am shocked that students routinely find ways of getting by without doing the required reading in a course, or making an effort to do a good job on the written work. Of course partly this is undoubted due to the nature of UH as a commuter school in a small agricultural state, where most of the students have jobs, and going to college is something they do in their spare time. However, I think that to some extent it is a reflection of a nationwide trend.

I have to acknowledge, though, that the academic skills we teach, with the strong emphasis on ideas and information expressed in written form, do not always serve students well. In the world today, visual presentation of ideas and information is very important. And yet most students will go through four years of college without ever learning anything about graphics, film, or video.

One wonders whether students can be entirely blamed for seeing university courses as concerned with things which are esoteric and obsolete, when so much emphasis is placed on fiction but almost none on cinema, which is certainly the dominant narrative form in our culture. Likewise, there are a large number of courses on poetry, in many different languages, but almost none on song, which has a much more powerful impact on contemporary society.

Especially in upper level courses, we try and teach students how to be professors. After all, being professors is the only thing we faculty really know how to do, so what else are we qualified to teach?

One sees this very much in the selection of courses offered at major universities. In the Mathematics Department, for instance, there are a small selection of ``service courses,'' offered because students in engineering or computer science or whatever need them, and which are offered rather grudgingly. Then there are the serious mathematics courses --- i.e. the ones which will help prepare students for graduate school.

Courses in subjects like Projective Geometry --- an inherently fascinating subject, and easily understandable by undergraduate students --- have long since gone by the wayside, since they are no longer pose interesting research questions. (Sometimes, as here, a little projective geometry is included in the geometry course taken by prospective high school teachers.) On the other hand, courses like Modern Algebra and Real Analysis where the subject matter is inherently much less interesting are part of every mathematics curriculum, because in these areas there is a wealth of current research.

I don't think that we can force students to learn to think but making them do assignments. I think that the thing that creative writing teachers so often say about writing also applies here: Thinking is something that can't be taught, but it can be learned.

Giving students an overall view of mathematics is always an important secondary consideration in my teaching, because I know that it's hard for students to get any sense of what mathematics is really like. Unlike in many other disciplines, there is no Mathematics 101 course to give a survey of the whole discipline. And the course descriptions in the college catalog are useless to a student because one has to take the course in order to learn how to understand the description.

Some students don't care about learning about mathematics as a whole, though. When they're taking a calculus course, they just want to learn calculus. These students are not very happy with me, because, they say, ``He spends a lot of time going off on tangents. He wasted a lot of time in class talking about stuff that wasn't even on the exam.''

But looking back on it, it doesn't seem that anything I ever learned in order to pass a test had much ultimate value to me. What was worthwhile were the courses that showed me that a particular subject was really interesting, and gave me the general shape of the landscape in that area, so that I knew what kinds of books to look for.

I sometimes hear students say about one of their mathematics teachers, ``I always thought math was a boring subject, until I had Professor Soandso's course. That was when I started realizing that it could be really interesting/exciting/beautiful, and I started wanting to learn more of it.'' That's the sort of thing I would like to be able to give my own students, although I think that I'm rarely successful at it.

As a student, I never tried to take easy courses. And looking back on it now, I'm certainly glad that I didn't.

Most students in mathematics courses, especially lower level courses, are definitely not looking for a challenge. They don't necessarily object to a course being hard, but they also want it to be routine, in the sense that basically there are a set of instructions laid out for them to follow. Favorable course evaluations from mathematics students will consist of statements such as, ``He makes it really easy,'' or ``He makes it really clear.''

I, on the other hand, consider it a good idea for lectures to be occasionally just slightly over the head of most students. (I find that I often manage to accomplish this without even trying!) If students can follow everything in class easily, then they may learn a lot of subject matter fairly well, but, in my opinion, they're not accomplishing much as far as learning how to learn.

I found as a student that the times I really learned things in my classes were not when the teacher gave a really clear lecture that carefully laid out all the little pieces and showed how they fit together. On the contrary, I found that I learned the most from the things that didn't quite make sense to me in class or in a book, so that I had to later sit down with a paper and pencil and start scribbling down equations until I figured out the point that was bothering me.

This clash of objectives between me and my students --- my desire to have them figure things out for themselves --- is one of the main things that often makes me think that my teaching is not worthwhile and that I'm wasting my life doing it. I will assign problems designed to make students think, and many students will immediately come to my office and say, ``I don't understand how to do this problem. There doesn't seem to be anyplace in the books or my notes from class that shows how to do a problem like this.''

My reaction in these cases will depend on my assessment of the student, and also on whether I like him/her or not. If I think that the student is incapable of thinking for himself, or has not interest in learning to do so, or if the student is such a pain in the ass that I want to get rid of him as soon as possible, I'll simply show him the answer to the problem so that he'll go away. In this respect, I think I'm not a very good teacher.

But if a student seems intelligent and seems really interested in learning mathematics, then I'll give him/her some questions to think about that will help put him/her on the right track. (The interesting thing is that this is often interpreted as favoritism toward the first type of student, whereas I see it as exactly the opposite.)