OFFICE MEMO: Dick Pilgrim Date: Mon, 13 Apr 1998 09:54:20 -0700 To: Gerald Von Korff <email@example.com>, firstname.lastname@example.org From: email@example.com (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 post-Sputnik the isometry of the two was an interesting topic for the "honors" senior math class. Now they all do calculus.
* Date: Fri, 10 Apr 1998 14:11:59 -0500 * From: Gerald Von Korff <firstname.lastname@example.org> * 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 pre-summary, * before they learn any particular approach.