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rpmcruz comments on Learning Mathematics in Context - Less Wrong Discussion

5 Post author: Crux 26 January 2016 10:27PM

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Comment author: Viliam 27 January 2016 10:09:08AM 4 points [-]

Most people are bad at understanding. As students they usually prefer to memorize things, because it is a strategy that works best in short term. When they grow up and become teachers, they recite things to students and expect them to memorize it.

In math, in addition to memorizing facts verbally, there is also a lot of procedural knowledge (solving equations). This is probably one of the reasons most people hate math. But even the procedural knowledge can be taught in the memorizing way; only the verbal memory is replaced by the muscle memory.

Understanding is a step yet beyond procedural knowledge. Most people don't get there; even most teachers don't.

And being able to explain stuff to beginners -- that's the ultimate art. It requires not only having a good understanding of the topic, but also being able to untangle it to a linear thread that can be gradually fed to a human and will allow them to build a proper model of the topic. This requires also an understanding of humans, and an understanding of understanding.

So why aren't most math textbooks better? I guess it's either because there are not enough good mathematicians who also happen to be good at explaining to beginners... or maybe the market for textbooks that teach understanding simply is not big enough.

If you want to learn a specific topic, maybe you could ask about it on LW.

Comment author: rpmcruz 29 January 2016 11:28:07AM 0 points [-]

I graduated in applied math. Some people mock with me, but I keep prominently in my bookshelf both The Complete Idiot's Guide to Calculus and Statistics. That Calculus book was the one that made me understand math and made me passionate about it.