Anyone who knows me personally knows that I'm not very good at math. Oh, I can do basic math. Algebra. I loved Geometry. But anything above that level, and I'm done, just flat out unable to do it.
I've always felt a little stupid because of that. Some folks are able to whiz through math like it's nothing, making what is a prolonged torture for me look like a third grade reading book. The more I learn about how US Education is failing our young students, the more I'm wondering if perhaps the problem was not my ability to learn, but the teaching of the subject?
I looked through his textbook, one of whose authors was a recent president of NCTM, and I was surprised to find very few proofs of anything. More troubling, most theorems in the book were stated as postulates—that is, propositions stated without proof—and students were told to memorize them. The problems at the end of the chapter required students to do only a few simple proofs.
Proofs in geometry class have been a mainstay of mathematics. In fact, proofs were always considered an essential part of high school geometry, not only because of their importance in higher math, but because learning the rules of logical argument and reasoning has applications in science, law, political science, and writing. To see proofs being shortchanged in a geometry textbook was shocking.
Algebra texts were in no better condition, in terms of presentation and content—or, rather, their lack of content. Even if you accept the argument that geometry in general, and proofs in particular, are unnecessary for students to learn, at least algebra should be taught properly, since algebra is the common language of, and gateway to, all of higher math. The absence of clear explanation and logical development left students I later tutored in algebra as lost as my geometry student. Their textbooks (and, probably, their teachers too) encouraged them to use a graphing calculator. Operations with algebraic fractions, like a¼b + c¼d, were given little attention, to say nothing of quadratic equations, once the pinnacle of any first-year algebra course. Instead, the quadratic formula is presented for the students to memorize and apply—if it is even mentioned at all.
I remember being taught like that. "Mr. Teacher, what is this for?"
"Just memorize it".
"What would I use it for?"
"Just memorize it, Dave"
"But WHY does it work like this?"
"Darn it Dave, just memorize it!"
And now I'm not very good at math.