Some thoughts on teaching mathematics.

    I will refrain, with great effort, from expressing my ideas on the abomination called "Math ed". The main reason for this restrain is that this site is likely to be visited by a mixed audience. I have, however, stumbled on some writings by Prof. Underwood Dudley, who expressed my feelings in a way that is much more eloquent than I could have possibly done, and he did it without any deleted expletives. His comments are in a book review written for Math Horizons, vol. 9, April 2002, page 11. The book under review was the world's first mathematics textbook - The Rhind Papyrus. Here is what Mr. Dudley has to say:

    "There are several lessons to be learned from the Rhind papyrus. The most obvious is that instruction in mathematics has changed hardly at all since the subject was discovered. Teachers have been passing mathematics on to the next generation in much the same way over the centuries: problem, solution, practice. As all the teachers of mathematics know, the method does not always work, but if there is a better way, no one has found it in four thousand years of looking.
    Another constant is the emphasis on process and answer. In every age, instructors of mathematics have pointed back to their predecessors with scorn, saying that they taught mathematics by rote, drilling their students to perform mechanically, without understanding. In this age, instructors in every age say, it will be different, we will have our students understand. Every age fails. Many students in every age would just as soon not understand. It would be fine with them to learn the process and let it go at that. Many students have minds that have not developed to the point that they are capable of understanding. It is not their fault anymore that it is the fault of third-graders that they cannot understand Shakespeare. Faced with resistance and incapacity, if instructors (in any age) are to accomplish anything they must concentrate on rules, formulas, and algorithms. Understanding is always to be striven for, but not always to be had. Some students can solve word problems and some cannot, even given the best of intentions by both instructors and students."

If there ever is a Nobel prize or a Field's medal in "Math ed", Dr. Dudley should for sure be the first recipient.