Quotations XIII: Mathematics Education Is Much More Complicated than You Expected

Registrations have been rolling in for our homeschool co-op, and the most popular classes are full already. Math doesn’t seem to be a “most popular” class. I can’t imagine why! Still, many of my students from last year are coming back for another go, and I am getting spill-over from the science class waiting list.

Anyway, I have started planning in earnest for our fall session. As usual, I look to those wiser than myself for inspiration…

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

— Paul Halmos

On a more serious note:

It seems quite unrealistic to judge a curriculum by its general outline, or to judge a course by its syllabus. We can “cover” very impressive material, if we are willing to turn the student into a spectator. But if you cast the student in a passive role, then saying that he has “studied” your course may mean no more than saying of a cat that he has looked at a king. Mathematics is something that one does.

— Edwin E. Moise

This one came to mind as I started reading our elementary math club book for this fall, Creative Problem Solving in School Mathematics.

Polya has become the Marx and Lenin of mathematical problem solving; a few words of obeisance need to be offered in his name before an author can get down to the topic at hand.

— Jeremy Kilpatrick [pdf 97KB]

All of the above were quoted by Rosemary Schmalz in Out of the Mouths of Mathematicians: A Quotation Book for Philomaths.

Finally, when I downloaded the Jeremy Kilpatrick article, I found this gem:

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

— E. G. Begle