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I agree entirely with this article. From my own experience, I did a lot of abstract maths in undergrad and really hated it because I couldn't figure out what all these Groups, Topologies, Normed Vector Spaces, etc were all about. What was the use of learning all these things without some practical application? It was only later on when I started to learn more about the people behind these theories, and the challenges that motivated them, that it became more interesting. The founders of all this knowledge were trying to get one thing or the other done, and this is what motivated them to construct these mind bending abstractions.

I think it is a lot more effective to give students challenges rather than knowledge. When they get stuck (and they will get stuck eventually), then give them the knowledge they need to overcome their obstacles. Of course, you never know, without having some pre-determined way of solving something, the students might end up discovering a smarter ways of solving the same problems!




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