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Posted:
Apr 13, 1998 12:55 PM


OFFICE MEMO: Dick Pilgrim Date: Mon, 13 Apr 1998 09:54:20 0700 To: Gerald Von Korff <vonkoent@cloudnet.com>, mathteach@forum.swarthmore.edu From: rpilgrim@ucsd.edu (Dick Pilgrim) Subject: Re: Harvard Precalculus
In general I agree with the idea of letting students know that there are many ways of looking at a "thing." However, in the case of the trig functions I see the circular functions as a generalization of right triangle trig. The latter began as numerical applications as a direct result of similar triangles whereas the circular functions are a modern construct to produce periodic functions of the reals. Back in Dom's bad old days of postSputnik the isometry of the two was an interesting topic for the "honors" senior math class. Now they all do calculus.
Dick Pilgrim
* Date: Fri, 10 Apr 1998 14:11:59 0500 * From: Gerald Von Korff <vonkoent@cloudnet.com> * Subject: Re: Harvard Precalculus * * The more ways that you look at something, the more you understand it. When you * see that two ways of looking at something are actually two views of the very same * thing, you empower your understanding of both. Moreover, since some students * resonate with one particular way of looking at something, and others with some * different way, don't you reach more students by presenting both ways? And isn't * it sort of deceptive to conceal the second way of looking at something when you * know it is out there. * * Why can't you introduce the trig functions by telling the kids right up front * that there are many ways of looking at these functions; that you will introduce * each of these ways; that you will introduce each of these ways over a period of * time. Why can't you give them a peek at each of these ways, a presummary, * before they learn any particular approach.



