Ideas / Motivation
I don't want to have to be 'motivated' (v. tr.)
I suppose the idea being that the steps of the proof are, in and of themselves, pretty obscure (as Andrew Wiles has said: like 'stumbling around in the dark' http://www.simonsingh.net/doc_titbits.html), so in order to motivate these non-obvious steps, there needs to be some inspiration.
I think this leads to one of my problems with maths. I like to see to build everything up from first principles (a bootstrap process, for the computing folks), but the teaching of maths is in no way a boot process: it's more a direct (but very lossy) transfer of the fete accomplis that is maths according to the educational establishment.
When do you need 'motivation'? When you're trying to get someone to understand why they're doing something that they wouldn't have otherwise thought of for themselves.
I can see that this is a useful tool, but not one to rely on too much. I think the need for motivation implies that a) the student is trying to move too fast, or b) that there is insufficient teaching time, or c) that the study structure is too rigid.
a) If I don't have time to think of it for myself, then I guess we're scraping the limits of what I can take in. I'm certainly not understanding it as deeply as I might like to. Sooner or later it's possible we're going to surpass my limits of understanding completely. I think I like to operate with a greater 'buffer of understanding capacity'.
b) If there is insufficient teaching time (but sufficient study time) then the teacher may have to sketch out a skeleton for individual study well ahead of the student being able to understand the purpose of the later parts of the skeleton. Therefore, in order to transmit the skeleton, a scaffolding of motivation may have to be communicated in order for the student to go away and be able to study to the desired learning objectives.
c) Motivation may also be required if there are lots of possible interesting avenues of exploration. Motivation is then a way of blinkering the student so that they don't get distracted.
All these things make motivation look reasonably bad. It seems to constrain action, reduce autonomy and generally straitjacket the student.
But nevertheless, where there is a clear reason to narrowly focus on a clearly defined learning objective, I think this concept of motivation could be very useful.
But I would suggest that education should not be about clearly defined learning objectives. That sounds like training to me. Education should be about taking off those blinkers and wandering off in all directions. As Kubrick said, 'Interest can produce learning on a scale compared to fear as a nuclear explosion to a firecracker.'
My feeling is that motivation is interest by proxy. You have to really love your teacher if their interest is automatically your interest. In an ideal world this would be the case I suppose. But I guess we have to accept that up to a certain age, the majority of our teachers aren't chosen by us, and we're unlikely to love them as much as would be necessary for interest by proxy to be equivalent to true interest. (Regardless of the fact that 'motivations' are very often textbook ideas, so it's likely the interest is proxied by several levels!)