About Teaching & Learning

In my most radical moments, I will say

There is no such thing as teaching.

When I'm trying to be more thoughtful, I will add, "There is only learning, and helping others to learn." So it makes sense to talk about learning first.


There are different kinds of learning, but I refer here to the intellectual kind. To learn means to cause your mind to function in a different way: new memories are created and/or new connections are forged. When you want to learn, it is easy. More than easy, it is barely noticed. Do you remember learning to recognize your family (you were a few weeks old at the time)? Did you struggle to learn your first language? I bet you learned to recognize "more" and "less" pretty easily (when comparing your dessert to your brother's, perhaps). More recently, how hard was it to learn the lyrics to your latest favorite song? your way around campus? You and your brain undergo drastic changes in these moments, just as surely as they do when you study calculus, Russian, economics, and literature. My point here is that

Learning is an act of will.

You must want to learn something before you can. Thus, the easiest way to learn something is to become interested in it. If your interest is spontaneous, there's nothing more to do but to get on with it. But if you find yourself trying to learn something you are not naturally interested in, what do you do?

The most important question to ask at this point is, "Why am I learning this?" You must ask it seriously, and you must search out an answer within yourself. Unless you find yourself in the position of literally belonging to someone else (a slave), then that answer does lie with you. If your first reason is that an authority figure (e.g., teacher or parent) told you to learn it, keep asking. Why did that person recommend the class? What is your ultimate objective in following the advice? Is your goal worthwhile? If you stay with your path, maybe you just need to accept that certain steps are necessary.

Drumming up interest is easier than it may seem. Make it social: talk to others who are also learning, or find someone who is interested (your teacher or an enthusiastic classmate, for example). Spend a little extra time on it, instead of a little less. If you read, look for a book. If you surf, search the net. TV? Who knows, there might be a show that mentions your topic. Look carefully for something, just a tiny thing, that relates the subject to your interests.

Are you happy otherwise? No one who is generally unhappy can do a good job of anything. If much of college is getting you down, check out the College Happiness Guide.

Finally, I know it's boring to hear, so I'll say it fast and only once. Many good things have come from doing something you thought you wouldn't like.

Most of us are most familiar with the learning process taking place in a classroom, although much of our learning is done outside of school and less formally. Personally, the activity I enjoy most in life is learning (see my interests and hobbies). Being on the faculty of a university gives me ample opportunity to indulge that activity, but being in school is not at all necessary. Learning happens wherever and whenever a person wants to learn.

A good classroom student

Study tips for university classes are available. They include general tips, how to read mathematics (it's different from other subjects), how to take a math test, and a review of good classroom habits. In addition, see my first day's lecture on Class, College, and Life, and my comments on ethics in math courses, writing a math paper, and giving a math talk.


Teaching is providing someone with the opportunity to learn. This can be done well, and it can be done poorly. It is never done easily. The teachers we see the most of are those who teach in a classroom. One can also teach through books and other media, even across time, long after one dies.

Classroom teachers are the ones in most direct contact with their students and they usually play several roles. During part of the process they are guides helping students to find and organize information. Later they are fans reinforcing successes, and coaches listening to frustration and giving pointers. Finally, the classroom teacher is a judge who compares each student's knowledge and mastery of the subject to the ideal and gives feedback.

Both students and teachers enjoy the fans and the coaches, and both tend to look at the judges with wariness. It is a difficult dance among these roles, but a teacher is all of them in turn, and makes that clear to the students.

A good classroom teacher

This list is complementary with that of a good classroom student (above).

One of the major ideas behind the NSF-sponsored Interactive Math Text Project is that in order to learn well, students must do.

"Talking isn't teaching; listening isn't learning."

Often the best way to teach is to put up some obstacles (by asking good questions) and then get out of the way. This is also the philosophy behind both discovery learning and the Moore Method of teaching mathematics. Students are always clamoring for an answer, but until they have themselves asked and understood the question, the answer means little.

study tips
Class, College, and Life
back to Margie's home page