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For high school math teachers, I'm a second year geometry teacher in a parochial school. I'm taking alternate route classes in education theory for certification, but I'm anxious about teaching math in public schools. My teaching method is "classical", in other words, I teach more or less the book material and let the class practice together or on their own. I assign a lot of homework every night. I don't have a "lesson plan" that appeals to higher thinking for every topic. I will answer questions about applications if students ask, but I tend to stray from the idea of introducing integral calculus, for example, in a geometry class. I find the students either don't understand it or don't appreciate its power and therefore calculus is trivialized. I have heard a lot about the "discovery learning" geometry method, and I have ordered the book. I'm trying to be open-minded about education theory and different approaches to math, but what I don't understand is how Asian students can master classically taught mathematics at quite an early age, but American students cannot. This is really frustrating to me, and by "changing" (notice I didn't say dumbing down) mathematics education in America, are we teachers really saying "No, American kids can't do classical math anymore"? I'd love to hear some responses from high school math teachers...
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