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Posted:
Apr 10, 1998 5:51 PM


OFFICE MEMO: Dick Pilgrim Date: Fri, 10 Apr 1998 14:49:40 0700 To: mathteach@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 righttriangle 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 unitcircle 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 postSputnik 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 postSputnik 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 postSputnik introduction of the trigonometric functions in * terms of coordinates on the unit circle. * sine = ycoordinate * cosine = xcoordinate * tangent = y/x etc
Dick Pilgrim



