Much of what we teach kids during their first decade of math education relies on students’ blind compliance and memorization of rules and facts. We reward correct answers, but we do not not encourage students to think independently about what these rules and facts might mean in the bigger mathematical picture.Yes, but I could depend on any course evaluation comments I ever received to include gripes about questions being excessively "open-ended", whatever that meant.
Tracy Zager, a math-education specialist and the author of the forthcoming book “Becoming the Math Teacher You Wish You’d Had,” explained in an email why this kind of math education fails students: “It was never a sensible idea to try to have students memorize first and understand later; this approach to mathematics instruction is structurally flawed. I really feel for these parents and this kid, but the frustration they face is inevitable. If we teach kids math without understanding, we build on a house of cards.”Particularly if the students go much beyond ordinary arithmetic. Thus does calculus become a stumbling-block.
That house of cards will be fragile, and liable to collapse, when students move from elementary mathematics to complex problem-solving, said Steven Strogatz, an author and a professor of applied mathematics at Cornell University.I had some success, if students had either sports experience or military experience, in treating intellectual practice as akin to basic training or to conditioning drills. The couch-potatoes posed a different set of challenges.
“If you follow the rules, you can do pretty much everything that’s expected of you without ever having to think imaginatively,” Mr. Strogatz said in an email. “This is not the way math should be taught, even at an elementary level. There really ought to be problem solving and imaginative thinking all the way through while kids master the basics. If you’ve never been asked to struggle with open-ended, non-cookbook problems, your command of math will always be shaky and shallow.”
Mr. Strogatz suggested, however, that this math teacher isn’t wholly to blame for her students’ frustration. “This teacher may have been brought up in a culture in which skill at problem solving is seen as a matter of talent; either you have it or you don’t,” he said. “Everyone can be taught techniques and strategies for better problem solving, and can be taught to feel pleasure in the struggles that make us smarter. With practice, all of us can get much better at it.”