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I agree that the path to insight goes through a lot of work, including memorization and repetition, but I know people who have taken that path and ended up with little to no insight. For example, my sister had "no head for math" but got As in high school calculus through sheer hard work and repetition. She worked and reworked homework problems so much that she could solve almost any test problem by remembering the homework problem most similar to it and using the homework solution to guide her. To this day she insists that she never understood the first thing about it even though she was one of the better students in an honors calculus class. She went on to do the same thing in college calculus (and got As once again) but she felt lost the whole time and said that if any test she took had come back marked "F" instead of "A," she would not have been surprised in the least.

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