Joe Niederberger posted Jun 20, 2013 8:48 PM (http://mathforum.org/kb/message.jspa?messageID=9141378): > GS Chandy says: > >A couple of years later, we had a math teacher who > did not insist on mindless, 'by-rote' mugging, who > tried to demonstrate that math could be very <snip> > > That's interesting. You've had an experience like > many have had, where some particular teacher out of > the multitude strikes a resonant chord. > > Can you say give a detail or two about a moment when > you first started to feel this intellectual > about-face? > <snip> > It was very long ago, and I don't know if my memory is perfectly accurate about how it happened.
It was a longish process (as I recall), but I think it was mostly:
b) the sense I got from him that he really himself found math to be truly fascinating and that math was not really all that loathsome 'by-hearting' that (some; not all) previous teachers had tried to make me do.
However I do recall one specific piece of 'math via non-math' that he showed us. It was an explanation of the Mobius strip, including:
i) the demonstration that it had only 1 side (as contrasted with the two sides of the strip of paper it was constructed from; the two or more sides of practically everything around us);
ii) the quite astonishing phenomenon of two interlinked Mobius strips being formed if one cut along the original Mobius strip. I recall we were all quite stunned when he first demonstrated this to us. Then he convinced us that this was based on real math, which we would be able to reach if we would learn what we believed was 'boring stuff'. I also recall that he did not 'turn on' ALL his students - but he certainly turned me on and a fair number of others.
I also recall that he NEVER did try to force us to 'by-rote mug up' anything at all: he preferred to show us 'interesting stuff' like the Mobius, etc - he also discussed 'relativity', 'space-time', time-dilatation, and so on and so forth (all of which, he said, could become accessible to us if we would learn how to do the 'hard stuff' and solve plenty of problems in that hard stuff.
Those of us that he did manage to reach soon decided (more or less on our own) that we should do the 'hard stuff' of math by doing plenty of problems, etc, etc. And then we also discovered (to some extent on our own) plenty of interesting and useful tricks about how to do stuff with numbers that had earlier been boring but which now suddenly had become quite interesting.
(In the book about OPMS that I'm planning, I shall probably carry this instance as an 'example' of 'structuring' without doing 'formal structuring'. 'Structuring' is something that we all do all our lives, right from childhood, probably from infancy.
(Specifically in this case, I am talking of the following process: "To become interested in 'A' COULD STRONGLY CONTRIBUTE TO become interested in 'B',...., ...., which in turn COULD STRONGLY CONTRIBUTE TO become interested in 'X'. 'X' of course being the process of "convincing myself that it is worth my while to do the hard work of learning my 'times-tables' and stuff like that").
*Added later: Needless to say, I myself at that time knew nothing about the 'chain of CONTRIBUTIONS' that I noted above. Neither, I think, did my teacher, a Mr Maiden. But he actually did it in practice, and thereby helped a good number of us overcome our earlier fear and loathing of math.
I trust the above is useful and at least partly responds to your request for information.