This is a great saga of the exploits that great teachers do little "teaching". My guess is that poor Mr. Hoffman probably asked a lot of questions, questions that stimulated students to ask similar questions of themselves in anticipating his questions, which made them into scholars.
One should be fortunate enough to have a teacher who is this incompetent as often as possible.
I was fortunate to have studied with Hubert Butts, who not only never answered a question, but rarely, if ever, completed a sentence. His 17 Ph.D.'s will also confirm that every really good problem that came along his way for research purposes was given to a student. His attitude seemed to be that if a student solved the problem then there were two recipients of the rewards.
Michael Keyton St. Mark's School of Texas Dallas
On 7 Nov 1995, Tom Davis wrote:
> In article <firstname.lastname@example.org>, email@example.com (Problem of the Week) writes: > |> I have found it to be the case that the best way to test my understanding > |> of something is to discuss it, or even better try teaching it to somebody > |> else. It is this _discussion_ of mathematics that makes me want to be a > |> teacher as opposed to a mathematician who only gets to "do" math. What > |> are other ways in which we can test whether or not a student has learned > |> something? > > I think teaching is by far the best way to learn something. In high > school in my Advanced-placement math class, our teacher, Mr. Hoffman, > never understood anything, and he was so pathetic that we students took > turns teaching him and the rest of the class calculus. At the end of > the year, the 14 kids in the class got 11 scores of "5", one of "4", and > two of "2" on the advanced-placement exam -- fabulous results. > > When I came back to visit my high school the next year, I talked to a > student in Mr. Hoffman's calculus class, and was horrified to find that > Mr. Hoffman hadn't learned anything from our class, and that years' > class was also having to teach him every detail about calculus. > > Mr. Hoffman also coached the tennis team, and years later, I met someone > who had played on his team. It turns out poor Mr. Hoffman didn't know > anything about tennis, either, and the stronger players had had to teach > him about the sport from scratch. The amazing thing is that nearly > every year, my high school won the state tennis championship! > > Mr. Hoffman was clearly the best teacher I ever had in my life, but the > sad thing is that even knowing exactly how he did it, I can't imagine > myself emulating him. He was so good at feigning ignorance and getting > pity that none of us figured him out until years later. > > When I taught math in college, I always volunteered to teach classes > that I didn't know much about. I probably did twice as much "homework" > as the students, terrified because every day I imagine so many questions > they could ask that I couldn't answer, and I studied like crazy so I'd > know the answers. Looking back on it, those were the classes where my > students learned the most, too -- having just thought very hard about > the subject, it was very clear to me what parts were difficult and > needed lots of explanation, and what parts were "obvious". >