A student I tutor, who is very bright but not really motivated in math, is taking "precalculus". Last year, he took a kind of intermediate algebra type course in which the homework vastly overdrilled him on trig functions. This year they are going over substantially the same stuff and overdrilling him again. He now knows the stuff cold, and finishing his homework is just a meaningless time-waster for him. If he had any chance of becoming interested in the math, this overdrilling is or rather has killed it. (Though when I posed the triangle puzzle to him that I posted to math-fun earlier today, he instantly guessed the correct answer, modulo a set of measure 0.) --Dan Henry wrote: << . . . But who on Earth actually uses [mixed fractions, etc.] & why do we torture kids this way? No wonder people hate math. . . .

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"Things are seldom what they seem." --W.S. Gilbert