Out of the Labyrinth: Setting Mathematics Free

QUOTES:

"Now math serves that purposed in many schools: your task is to try to follow rules that makes sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride."

"To teach it now as if it were A Rule, or (even more intimidating), The Law, is to pretend that what took years of experiment and ingenuity is as obvious as your nose. And then, because you never really had a chance to understand what was going on ("A negative times a negative is a positive, because that's the way it is!"), whenever you need this rule again it will come as just that - an arbitrary fiat, enforced by Them...The only reasonable conclusion for a struggling student to draw from such pretense is that he is irremediably stupid, of that Mathematics works in mysterious ways, its wonders to perform." (p. 9)

"...and so a teacher, who is supposed to develop our powers of inquiry, becomes instead a messenger of Received Truth." (p. 9)

"Even when designing less extreme teacher-proof curricula, an inevitable consequence is that the texts become learner-proof too; the problem-writers so want to guarantee that their unseen students will succeed, that they can't leave them to figure out relations for themselves, but merely check them. Problems intended to foster discovery are given in such small spoonfuls that you needn't see the idea behind them at all (or even realize there was an idea) in order to answer each question in the sequence." (p. 136)

"So teaching is not about 'lowering' the level of the material to meet the kids, but rather about looking at it from the same angle they are." (p. 232)

Kaplan, R., & Kaplan, E. (2007). Out of the labyrinth: Setting mathematics free. New York, NY: Oxford University Press.