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[No Subject]
Posted:
Apr 13, 1998 12:55 PM
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OFFICE MEMO: Dick Pilgrim
Date: Mon, 13 Apr 1998 09:54:20 -0700
To: Gerald Von Korff <vonkoent@cloudnet.com>, math-teach@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 post-Sputnik 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 pre-summary,
* before they learn any particular approach.
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