Three Times Seven

Bob Blitzer wasn’t just a great math teacher; he was a good man: my first openly gay professor–and this was the early 70s–he was a force of nature in the classroom. He drew an inverted parabola on the board. “‘Y equals negative X squared’ looks like a missile,” he began. “No, it doesn’t. ‘Y equals negative X squared’ looks like a breast.”

Can YOU think of a better way to engage adolescents in the subtleties of curve sketching?

Bob was a tireless advocate for struggling students. His office hours weren’t Monday, Wednesday, Friday from 10:00 to 11:00 am. His office hours were any time he was awake. He taught like a mad dog. As long as you were willing to learn, he was willing to teach. No problem was too simple. From what I could tell, no problem was too complex either.

Most importantly, he could tell if you “got it” or not. If you got it, Bob would take you to the next concept in sequence. If not, he would teach you the old concept in a new way. Until you did get it. If he ever got frustrated, I never picked up on it.

I may have forgotten some of the curriculum from that second semester calculus course 40 years ago. (OK, let’s face it: I may have forgotten ALL of the material from that second semester calculus course.) But I remember one pedagogical technique clearly. Bob and I were deep in some problem–finding the volume of a three-dimensional object, say–when we came across some simple arithmetic. Bob paused in his explanation. “So, let’s see, three times seven would be…”

His voice trailed off. I had been piping up, answering questions right along as Bob carried me through the intricate steps of the page long problem. But this time I stopped. “You know what three times seven is as well as I do,” I said respectfully.

What Bob said next has stayed with me for four decades and through the thousands of students to whom I have taught math. “Yes. I just want to make sure you are comfortable as well.”

“Comfortable!” In a math class. What a concept! Comfortable in an advanced math class no less, one with high expectations. (Bob’s tests were brutal–no quarter asked or given. But if you had done every problem in the book three or four times and had studied until you starved to death, you could perform pretty well.)

Bob went on. “If you answer after I pause, then I know you’ve got it. You feel good and we go on to the next step. But if you don’t speak up, you don’t feel threatened.” He paused as if deep in thought. “Math can be intimidating.”

Imagine! Math as comfortable and non-threatening. In high school, my teachers had used their knowledge as a bludgeon. “I know this and you don’t” had been their agenda. “And the reason that you don’t know this is because you are fundamentally flawed.” The antithesis of this attitude, the fact that Bob and I were on the same team, that we both wanted the same thing, was empowering.

That’s a great way to teach,” I said.

Always modest about his ability, Bob replied, “Yeah, well, thanks. But I didn’t think of it myself. I got it from this guy named Socrates.”

***

How many of your children’s teachers are communicating, “We’re all in this together”? How often do your children come home saying, “We’re learning this cool stuff; my teacher is really into it”?

On the other hand, how often do your children come home with worksheets assigned by teachers who are only concerned with quantifying that Tommy got 75% correct?

I’m not suggesting that as parents we must find the Bob Blitzers of the world. They are a rare and possibly vanishing breed in an educational culture that values constant testing over shared engagement. I am hoping that you can allow your homes to be places where learning for its own sake has a place, where learning can be a hoot, where “Y equals negative X squared” can be a breast.