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This sounds extremely similar to the way I was personally taught trigonometry, calculus, linear algebra, and tensor calculus. First you are asked to work out some monstrous 4 page problem by hand. Then you have a lecture on the specific tricks in each of those courses (SOC-CAH-TOA, differentiation by dropping the power, linear algebra by matrices, tensor calculus by superscript-subscript interaction). Then you are asked to do the same problem again in 3 lines... Perhaps it's not outright failure, but you are forced to "discover" an advanced concept for yourself before being given the proper tool. I feel perhaps the author is too bold with:
"Singapore, the land of many math geniuses, may have discovered the secret to learning mathematics (pdf). It employs a teaching method called productive failure (pdf), pioneered by Manu Kapur, head of the Learning Sciences Lab at the National Institute of Education of Singapore." I feel a bit more research will show that this is an extremely well established teaching methodology. I mean, who _wasn't_ taught integration in this manner? ["Given the curve f(x), find the area under the curve from x=0 to x=10" so you pick a bunch of random points, find the value of f(x) at those points, multiply by however far you chose to put the points apart, go in with the wrong-but-kind-of-close answer "Oh, by the way, there's this thing called integrating, sit down for a sec kids"] |