11:32 AM
I've been thinking about yesterday's discussion with @Jenny and about what advice to give. I looked in to the coursera offerings and found some that seem to be very relevant. You could just take such a course (or three) to get some background. However...
I'm left with the dilemma about whether that would actually work or not. Some people, often those who have had poor teachers, think that they just don't "get" math and have little insight. For such people an online course seems, to me, to be not very useful because...
Students in such courses are given a lot of material and many examples to work out, but little contact with an actual person who is wise in the ways of math (or cs or ...). I think it is possible to gain insight into a subject in a number of ways, but working with a professional seems to me to be the best. It is a forest v trees issue. The courses focus on detail, the student may not ever get the big picture.
So, I'm left with the question: Is it possible to teach insight in a subject rather than just the details. In my own experience, I had deep insight into some areas of math and almost none in others. But I had better teachers in the former than the latter.
I could grok analysis fine, but advanced algebra, while I could do it ok left me without inspiration or insight. Similarly I was something of a star in point-set topology but a loser in algebraic topology.
I think that in many ways insight is the most important thing. How can we teach it? Can it even be done online?