Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea, *then* give them some technique. But not too much.

From Lockhardt’s lament (pdf); via Scott at Shtetl-Optimized.

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June 20, 2009 at 6:04 pm |

It is not clear to me what works. I was not particularly interested in mathematics or any thing. I joined math, honours course in Loyola College, Madras since I was not old enough to go to an Engineering College. We normally believed what teachers said without really understanding any thing and got through the examinations. We had an one hour week class by one Krishnamurthy which was a kind ; filling up gaps’ discussion kind of course; I do not think that there was even an examination. He just explained concepts like functions, graphs and then started on a discussion of numbers, explained a bit of sets, rational numbers, real numbers etc and Cantor’s proof that real numbers are not countable. Suddenly mathematics did not seem to be just recipes and calculations but one of concepts and careful reasoning. I was hooked. In my case, it was not problems but a careful though cursory explanation of some of the things that one was using (real numbers) which got me started. Once I got interested, I found most other classes boring and cut classes, went on to study mostly by myself.

For some others it may be problems or something else. There are probably several studies. I would guess that things may vary from region to region, even caste to caste, and of course from individual to individual. Possibly, one can try to find out a few threads which will help a large number of students but I feel that there may not be one sure method. Sometimes even examinations helped. After being exposed to different, some boring topics in a course, suddenly seeing all of it one intense study at the end, if there is some coherence to the course, is also helpful in my case.

June 20, 2009 at 9:19 pm |

Dear Swarup,

At least three points on which I agree:

[1] It takes just one good teacher to get you hooked;

[2] Almost everything you really learn are through self-study; and,

[3] No single methodology of teaching works for everybody.