Philip J. Davis and Reuben Hersh

What are some of the reasons for resistance, resentment, rejection on the part of students?

First of all there is considerable impatience with the material. Surprisingly, this is often noticeable in the better students. But better students tend to demand instant understanding. Mathematics has always been easy for them. Understanding and intuition have come cheaply. Now as they move into the higher reaches of mathematics, the material is getting difficult. They lack experience. They lack strategies. They don't know how to fiddle around. Understanding is accompanied by pains. It makes little impression to say that the material about to be presented is the end result of centuries of thought on the part of tens or hundreds of brilliant people. The desire for immediate comprehension is very strong and may ultimately be debilitating. (If I don't get it right away, then I never will, and I say to hell with it.)

The key idea is often brilliant but difficult. There may be a psychological unwillingness to accept that there is in the world a brilliance and an understanding which may exceed their own. There may be a sudden revelation that some higher mathematics is beyond them completely and this comes as a shock and a blow to the ego. The resistance may intensify and show up as lack of study, lack of interest, and an unwillingness to attempt a discovery process of one's own.

It is commonly thought that there are ``math types'' and ``nonmath types.'' No one knows why some people take to math easily, and others with enormous difficulty. For nonmath types resistance may be the honest reaction to innate limitations. Not everyone becomes a piano player or an ice skater. Why should it be different for mathematics?

__ Philip J. Davis and Reuben Hersh in The Mathematical Experience.