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Sideways comments on Dissenting Views - Less Wrong
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I think this phenomenon illustrates a very widespread misunderstanding of what math is and how ones becomes good at it. Consider the following two anecdotes:
1) Sammy walks into advanced Greek class on the first day of school, eager and ready to learn. He is crushed when, about 15 minutes after the class begins, he realizes he has no idea what the teacher is talking about. Despairing, he concludes that he is "terrible at Greek" and "just dumb".
2) Sammy walks into advanced algebra on the first day of school, eager and ready to learn. He is crushed when, about 15 minutes after the class begins, he realizes that he has no idea what the teacher is talking about. Despairing, he concludes that he is "terrible at math" and "just dumb".
Anecdote 1) just seems ridiculous. Of course if you walk into a language class that's out of your depth, you're going to be lost, everyone knows that. Every normal person can learn every natural language; there's no such thing as someone who's intrinsically "terrible at Greek". The solution is just to swallow your pride and go back to an earlier class. But it seems like anecdote 2) is not only plausible but probably happens rather often. There is some irrational belief that skill at mathematics is some kind of unrefinable Gift: some people can do it and others just can't. This idea seems absurd to me: there is no "math gene"; there are no other examples of skills that some people can get and others not.
Unlike most other subjects, math is cumulative: students are taught one technique, they practice it for a while, and then they're taught a second technique that builds on the previous. So there are two skills required:
*The discipline to study and practice a technique until you understand it and can apply it easily. *The ability to close the inferential gap between one technique and the next.
The second is the source of trouble. I can (and have) sat in on a single day's instruction of a language class and learned something about that language. But if a student misses just one jump in math class, the rest of the year will be incomprehensible. No wonder people become convinced they're "terrible at math" after an experience like that!