Invisible sage

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.

About Joanne


  1. Wow

    What sane person would expect a bunch of 8th graders (even those with math aptitude) to FIGURE OUT A THEOREM?

    Most mathematical theorems, even the simple ones, took adults years to figure out. Some still haven’t been solved – and some even get Nobel Prizes for solving theorems.

    Perhaps the teacher can ask the 8th grade students and assign them to design an earthquake proof school; if you give them enough time they might figure out by themselves how to do it.

  2. Mike, a diag in Texas says:

    Remember that old chestnut about a 1000 monkeys tapping on typewriters would eventually produce works by Shakespeare?

    Sounded like the above comment to me. LOL.

  3. Do education students/teachers who believe in constructivism believe that Driver’s Ed should be done in a constructivist manner? If you had a simulator so that the danger to others was removed, would they think that was the best way to teach driving? what about flying a plane? (have any of them ever successfully landed a plane in Microsoft’s Flight Simulator ?)

    This is not tongue-in-cheek. Is it really that since language acquisition just *happens* for humans, that they believe all of these other skills can be, too? What do they believe shouldn’t be taught this way?

  4. Walter E. Wallis says:

    Perhaps let them develop their own number system?

  5. Perhaps let them develop their own number system?

    Well, with guidance, of course. Nothing wrong with guided discovery is there?