QUOTE(Boo Radley @ Mar 14 2006, 04:45 PM)

Whenever you write an essay, write a piece of music, paint a picture or choreograph a dance, you are breaking new ground, so to speak. What you have done has never been done before as you have done it, there is no 'truth' about what it should or shouldn't be. I class this as non-linear
At the top level, yes, but 100,000 exam A-level exam essays on e.g. Shakespeare's King Lear will be as similar as 100,000 A-level Biology exam essays on the Human Genome..... My point was that badly taught school science should not be confused with the real thing. It's obvious that badly taught school music is not the real thing, but the same doesn't seem to be allowed for maths and science.
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To pass my biology A-level, I found I had to memorise, memorise, memorise! After the concepts had been understood, the job was to remember Rhizobium, Human Chorionic Gonadotrophin, etc.
I would be interested to know which aspects of science you were referring to and what sort of maths you teach.
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. I teach maths at university to PhD level, and do research myself.
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 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)
Cheers