As long as being good at math means doing well on multiple choice tests and in contests, we will continue to fail to identify and nurture some of the best mathematical minds.
Example: I have a colleague who has a deep understanding of math and how it works. On every test she took in high school, she got every item that she completed correct because she worked not only to plug in formulas but to understand why she was using a particular formula and what one could do with that formula in other contexts. But she never finished a test, so received only average grades. She hates tests and contests---and the hours of memorization they entail. There is no place in the math world for her kind of learning and thinking.
I meet many students, who, like my colleague, were not interested in math for math's sake, but wanted to understand it and see what it could do. These students end up abandoning math because it's usually taught like a meaningless game, disconnected from anything most students value.
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