Toom had written: > > Teachers who cannot teach solving problems will have > > to choose between teaching athletics and retirement. > > They will be replaced by immigrants from Russia. > > On Sun, 26 Jan 1997, Tad Watanabe answered: > So, what does a teacher need to know and be able to do to > teach their students so that they can meet these goals?
Tad, you asked some very important questions, but I have a rule: never answer more that one question at once, so I concentrate on the question cited above. Even this question is tremendous: to answer it more or less completely, I would have to write a book about teaching. I have no time for this now. I only want to say that good teaching is a tradition and cannot be achieved by a single teacher. Tradition of good teaching mathematics is conspucious by its absense in USA. To explain this in detail, I would need to comment several videos of math lessons made in several countries. (I tried to describe my manner of teaching word problems in a paper `In defense of word problems' which is available on request.) It is clear to me that the Russian tradition of teaching mathematics is much better than American, but Russia is not an exception. In San Diego I saw a video of a Japanese math lesson and it was pleasant for me to see how similar to Russian lessons it was. Not because Russia influenced Japan or vice versa, but because both are based on the normal relations: students respect the teacher, the teacher cares about best interests of students. Let me mention a small detail which seems not to have been verbalized by the people who made TIMSS: when the class starts, the Japanese students greet the teacher by standing up. Same in Russia. It is important because it reminds the students that starting this moment they have special duties: to give up everything else, to concentrate on the subject matter and to respect the teacher. When I enter the class in my university, students sit in relaxed manner, and my entrance marks nothing for them. I need to take special measures to bring them into a working condition. I can do it because I am an especially competent teacher, but many American teachers cannot, and their students remain disrespectful throughout the class. It is impossible to teach productively students who do not respect you. Or take the typical American awe for the non-intellectualism: a student who does not care about abstractions is a sacred cow for American educators: all the pedagogy, all the syllabuses, all the textbooks are written primarily for that student to the neglect of others.
Andre Toom Department of Mathematics firstname.lastname@example.org University of the Incarnate Word Tel. 210-646-0500 (h) 4301 Broadway 210-829-3170 (o) San Antonio, Texas 78209-6318 Fax 210-829-3153