In a math education class taught by Mr. NCTM, future teacher “John Dewey” asked classmates to tackle a geometry problem he found on a tape of a Japanese eighth-grade math class.
After about a minute, I saw that people were perplexed, not getting anywhere, and I suddenly realized that in my excitement: I forgot to present the theorem they would need to solve the problem. I apologized and called for their attention and explained the key theorem they would need.
His classmates, all with math and science backgrounds, did well with the problem — but only after he presented the theorem.
I led a discussion about the appropriateness of the problem for eighth graders. The people who solved the problem immediately thought that perhaps I should not give the theorem and let them “discover” it. Others who had a tougher time with the problem said, well, if you did that, maybe you should coach them to come up with the theorem rather than expecting them to do it on their own. Or maybe giving them the theorem wasn’t such a bad thing.
I suspect that the ones who had the easiest time were under the illusion that the theorem was superfluous and easily discovered. They forgot that a few minutes prior they were struggling until I told them what they needed to know.
Those who started as believers in constructivism ended as believers.