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 <firstname.lastname@example.org> * 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" <email@example.com> * 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