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[No Subject]
Posted:
Apr 10, 1998 5:51 PM
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OFFICE MEMO: Dick Pilgrim
Date: Fri, 10 Apr 1998 14:49:40 -0700
To: math-teach@forum.swarthmore.edu
From: rpilgrim@ucsd.edu (Dick Pilgrim)
Subject: Re: Harvard Precalculus
I, like Ron Ferguson, have tried a variety of ways to introduce trig with different groups of students ("gifted" highschoolers, nontraditional CC students, etc.). I now believe that the unit circle
introduction is best left for classes where you know the students have had the prerequisite geometry and introduction to right-triangle trig, although it would be nice if that was put into a function
context.
It is very difficult for many students to move to a nonalgebraic definition for values of a function. The unit-circle approach is a big step for them. Look at the trouble they have with the logarithm
function now matter how you approach it. Sometimes it is even worse with a calculator - they are convinced that the values are based on some mysterious procedure, probably handed down to Charlton
Heston on a very stormy day.
* Date: Thu, 9 Apr 1998 17:44:19 -0400 (EDT)
* From: Michael Paul Goldenberg <mikegold@umich.edu>
* Subject: Re: Harvard Precalculus
*
* I sincerely wonder if this is as much of an either/or situation as Dom
* seems to be portraying it to be. Do post-Sputnik books only present one of
* the two ways of considering trig functions that Dom mentions? Is there a
* "right" order in which to introduce the two ways of conceptualizing basic
* trig functions? If so, why? I'm about to teach a trig course at a
* community college; haven't seen the book or syllabus yet (will next week)
* and I'd be interested in the thinking behind Dom's claims and other folks'
* sense of all this.
-------.
My biggest problem with the precalculus books is the tendency to fill them with every topic that any potential customer might request. I have 10 weeks (30 lectures max) for precalculus - I'm not sure
a $75, 900 page, 5 lb. book is appropriate. Whatever happened to "Lean and Lively?"
* Date: Thu, 9 Apr 98 09:42:02 GMT
* From: "Domenico Rosa" <rosa@teikyopost.edu>
* Subject: Harvard Precalculus
*
* Last weekend I attended a conference at Cape Cod Community College, and I
* had the oppotunity of examining the precalculus book produced by the
* Harvard group.
* Quite frankly, I did not examine this "reform" book very carefully.
* However, I noticed that it maintains the post-Sputnik feature of doing
* review material for the first 100 pages (I forgot to check if it contains
* the axioms of a field).
* One feature that really disturbed me is the fact that this book perpetuates
* the perverse post-Sputnik introduction of the trigonometric functions in
* terms of coordinates on the unit circle.
* sine = y-coordinate
* cosine = x-coordinate
* tangent = y/x
etc
Dick Pilgrim
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