The Thinking Classroom

When I plan out a lecture, I always remind myself that learning requires thinking. By thinking, I don't mean a student racing to copy down my words into a notebook, as I spew out a hundred facts a minute. Thinking likewise doesn't mean reading powerpoint slides, or becoming hypnotized by the glare of the projector. Lastly, thinking does not mean watching me think. By thinking, I mean forming one's own thoughts and making one's own logical inferences.

To create a "thinking classroom" it seems clear that I shouldn't be lecturing at all. Rather, I want to ask a series of bite-sized questions, each of which immediately triggers the next question in the student's mind. The point is to force the student to come up with both the answers and the questions. Why is it so important that the student generates the questions? The answer is simple. In my experience, the only points you recollect when reviewing for an exam are your own thoughts and confusions from class, the questions of your friends, the questions of the cute guy or girl in the next row, and not much else.

This may sound easy enough except for the fact that after so many years of not thinking during class, I find that students are terrified to actually think during class. They're convinced that they'll miss the powerpoint flying by, or will forget to copy down some important definition. The only way I know to alleviate this fear is to promise students a complete handout after class consisting of every word covered during class. Knowing that the handout will be coming, students are able to relax enough during class to think through the material.

Creating a thinking classroom requires planning. Understanding the material myself does not suffice. I strive to anticipate the deductions and inferences that the students will be making, and at the same time be ready in case they take a different path. I wish to create a comfortable environment for thinking -- a note-free, slide-free environment, where the only thing to look at is a single uncluttered board. People often ask me whether the preparation required to create this environment is really worth my time. My answer is that for every hour I spend preparing, I am saving one hour for each of 100 students. That always sounds worth it to me.

I have learned a great deal from the students I have taught. They have shown me how people think: what is logical and what isn't. This has helped me profoundly in writing up my own research. I have also benefitted greatly from two renowned teachers: I am a follower of Dick Karp's motto "prepare, prepare, prepare" and Manuel Blum's motto "respect your students".