I have written before about my philosophy of learning math. I tell my students that one needs to do math wrong first, before one can figure out how to do it right. This, after all, is the logic of doing homework. Homework gives students a chance to mull over problems and possibly go down blind alleys, only to eventually learn how to solve a problem in a way that works. I have also seen such a theory applied to many areas in life. It is often the case that we need to make our own mistakes so as to learn how not to make those same mistakes again.
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