After a conversation with a colleague yesterday, I started doing some serious thinking. In the several semesters that I have taught Trigonometry, which I think totals about 5 or 6 times, I have been using our adopted textbook which takes the unit circle approach to introduce students to trigonometric functions. In other words, the functions are defined in terms of the coordinates of points on the outside fo the unit circle where an angle subtends the circle.
Now, I have varied when the right triangle approach is introduced, but it has always been after the unit circle definition. In the current version of the text, it isn’t until the following chapter that the old familiar SOHCAHTOA (sine is opposite over hypotenuse, etc.) is even brought up. Every time I teach Trig., I feel uncomfortable waiting this long, especially since, when I am calculating the value of these functions in my head, I am picturing right triangles. Perhaps it is simply because it is the way I taught, but I have always been better able to make the students grasp how to calculate the trig. functions this way.
Of course, as a mathematician who has used trig functions in all sorts of higher level courses, such as Differential Equations or Analysis, I see the validity in conveying to students the functional nature of the trig functions which is something they see much better through the unit cricle approach. Nevertheless, the students just don’t seem to grasp the functions as well, this way. That has been my experience.
In response, I started doing a little literature searching this morning. It is really the first time I seriously made an effort in looking into research in Mathematics Education. So, if any of you readers out there know of a good place to look or can quickly find any articles on the methodology in teaching trigonemetry, I would appreciate your help. For the rest of you, how were you taught and did you prefer a particular method.