More on Constructivism (John Dewey)
Apparently my last missive ruffled some feathers, which I knew would happen sooner or later. It is one thing to express self-righteous indignation about ed school, but when it crosses the line into criticism of constructivist or “discovery learning”, then it’s like a Congressman talking about revamping Social Security.
The terms “constructivist” and “discovery learning” mean different things to different people. To the ed school gurus as well as book publisher/snake oil salesmen peddling their wares to school boards who eat this stuff up (and make the final decisions on what textbooks to adopt) it means students construct their own knowledge out of whole cloth. To the more traditional-minded, it means the connection that students make between information given to them directly and applied in new situations, or which lead to new insights.
Students may remember having made a connection all on their own, but may not remember the guidance and information that a teacher or book imparted that got them there. There may be an “illusion” of pure discovery at work here: people see what they want to see. One interesting case in point is the TIMSS Videotape classroom study of math and science classes in other countries. When the video was released, constructivists said “See? See? Japanese students work in groups, are given challenging problems without instruction on how to solve them, and the student has to invent his or her own solutions.”
But an interesting paper by Alan Siegel of NYU in fact shows just the opposite. (You can find his paper here, but best to right click and then download rather than try to view online; it takes forever that way which may result in adding to an already foul mood for some of you after reading what I have to say in this letter.) Siegel describes the presentation of a geometry problem in a Japanese classroom and notes that the teacher provides a key theorem to students prior to presenting them with a problem to solve using that theorem.
The problem was quite good and since all of us in Mr. NCTM’s class each have to present a problem to the class during the semester, I chose that one. I thought it would be interesting to see just how easy or hard it would be for the students in class to solve the problem given the theorem prior to the problem, just like in the Japanese classroom. In the video, the eighth graders were not able to solve it, even with that knowledge; they eventually got it through expert coaching from the teacher. Many constructivists do not seem to remember the teacher providing the theorem beforehand, nor that the teacher was a “sage on the stage” disguised as a “guide on the side”.
So I presented the problem to the class, saying I would like their feedback on whether such problem is appropriate for eighth graders. After my initial presentation of the problem I told them I would give them three minutes to work on it, but not to feel they had to solve it—I just wanted to reconvene at that time and then discuss it as a class. (This is in fact what they did in the Japanese classroom). All fell silent and worked at their desks. (Note to adherents of people-working-in-small-groups: In our class, when we are given a problem to solve, most of us like to solve it in isolation. When instructed to work in groups, one person in the group generally dominates. My mind becomes paralyzed and I crave being left to my own devices.)
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.
Now, I fully expected that no one would solve the problem in the three minutes and I would have to be “guide on the side” and coach them to see how to apply the theorem, thus proving to all who believe in constructivism that students can still “discover” when given information directly. I forgot that my classmates all have a math or science background and are not eighth graders. Three of my classmates solved it within a minute and others were on their way. Nevertheless, my oversight in not presenting the theorem did reveal something important: As smart and experienced as my classmates are, no one was having any great insights into a solution until I 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. Just like people who in their memory believe they discovered all that was important in math. In short, anyone who was a constructivist at the beginning of the evening, was still a constructivist at the end of it.
Before I leave, I must correct a statement I made in response to one of my commenters to my last letter. With respect to constructivism I had said, “I agree some of it is good. I also believe some of it is wretched.” The word “some” in the second sentence should have been “most”. My apologies.
With full disclosure and open heart, I remain