QUOTE(loops @ Mar 14 2006, 05:51 PM)

A good teacher of anything makes the concepts, their discovery, application, context and motivation for discovery, so interesting and involving that you remember without obvious effort at memorisation. My father taught me science, and more importantly, his endless fascination. I teach problem solving as a detective game... you are given the clues...Also, I teach my students to learn only *how* to remember, by which I mean, the starting point and the process involved. This way they get it right when (and not if) they have a different problem to analyse. And when they solve a new problem on their own, their enjoyment is immense: absolutely nothing replaces that key experience. As much as I want to help them, I have to refrain.
This is very true. So many teachers simply do not have any imagination when it comes to teaching so I agree with your sentiments wholeheartedly and just wish I could have had a slightly better teacher, especially for the second year!
QUOTE(loops @ Mar 14 2006, 05:51 PM)

I have thought quite alot about creativity in maths, where do the new theorems I prove come from, and the answer is, I really don't know. They bubble up seemingly by themselves. I get really interested in a topic, do lots of mathematical experiments, draw pictures and "meditate" ie clear my mind. It's definitely non-verbal. Sometimes the solution of some puzzle I just "know" without being able to articulate it at all, I then have to work quite hard to write it up for someone else to see the solution.
I know what you mean to a limited extent.I used to enjoy looking for patterns in maths to and would often point them out to my teacher to be told (of course) that so-and-so devised that in year x. For instance I remember trying to work out a pattern for squared numbers (eg. 6^2 + 8^2 = 10^2) and trying do devise formulae to fit the patterns. Sadly, as I don't actively do any advanced maths now, that part of my mind is mostly inactive. Had I gone to uni, I would almost certainly have done maths and/or music. The reason I didn't go was out of choice.
QUOTE(loops @ Mar 14 2006, 05:51 PM)

I started to play the piano to balance the maths, as I'm mildly obsessive, and maths for 15 hours a day is exhausting. As far as I can tell, music uses a quite different part of my brain than maths does. I couldn't do painting and drawing (my earlier obsessions) becauses it uses the same part, it just wasn't a relaxation. But learning to play piano is much more than relaxation, it's like suddenly discovering France exists after only knowing Germany (I'm not expressing myself very well, but I hope you get the idea)
You don't need creativity to play the piano, this is true. It can't really be compared to drawing in that sense I suppose as playing is recreating what someone created years ago.