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Traditional math education: a professor explains proofs of selected theorems on a blackboard and students are then required to memorize the proofs and reconstru
by dunkelheit 10y ago
Traditional math education: a professor explains proofs of selected theorems on a blackboard and students are then required to memorize the proofs and reconstruct them during the examination. They are also required to solve a lot of problems that involve proving some consequences of the main theorems or doing some rote calculations using nothing but pencil and paper.
The advantage of this approach is that it works. You can acquire solid intuition this way. But it is arduous as hell and also pretty one-sided - problems are limited to what an average undergraduate can do by hand.
Now, when I think about using computers in math education I don't think of some "javascript doodad" with moving sliders. I imagine instead implementing an algorithm or doing a numerical experiment, learning about possible pitfalls in the implementation, running the algorithm on some real data, seeing it fail etc. I think this experience is pretty valuable too and can nicely complement traditional approach.
- davidivadavid 10y agoThat's why that approach has been offered in courses traditionally called "Numerical analysis" that have been available to math students for... how long?
- dunkelheit 10y agoTaking the sarcasm out, your point is that such thing exists. Agreed. But usually it is just a single course, it does not cover everything. And why it is a separate course at all? Why should you study some field with pencil and paper and then (possibly, after a couple of years) study a subset of that field "numerically"? As an example of what I am talking about, the book "Structure and Interpretation of Classical Mechanics" (a cousin to SICP) tries to teach classical mechanics with the help of computer programs. But this approach remains unconventional.
- davidivadavid 10y agoI should probably not have been sarcastic, especially when I agree completely about the importance of looking at math with a more constructive/computational point of view. Now, I'm not a mathematician or a scientist of any kind, merely a dilettante textbook reader, but I'm not sure that approach is sufficient, or even most efficient to teach all subjects. I think it arises naturally when you approach subjects where it's directly relevant: engineering, complexity theory, type theory, etc. and people who will need those insights will get them in due time. But yeah, broadening the audience could help people get a better appreciation of the connections between pure and applied math.