Why did somebody recommend to me a blog called A Portrait of a Math Teacher as an Aging Man? Are they trying to tell me something? I’m not sure that I should be thrilled about that 😀. Nevertheless, the recommended blog turns out to be worth reading. I want to comment on a recent post in it: “Thinking about Trig.”
The author, who styles himself “mrdardy” — which I keep misreading as “Mr. Darcy” — begins this post in a way that might answer the question of why the blog was recommended to me:
In the fall I will be teaching a section of Precalculus Honors at my school. I have not taught that course in about six years so I have not spent a bunch of time thinking about teaching trig functions for awhile. Our Precalc Honors class starts off with a study of Trig and I am thinking about an opening day activity that might plant a number of seeds that we will need to germinate over time.
OK, that rang a bell: I have just finished teaching a section of Honors Precalculus after a gap of three years, and we indeed started off with a lengthy study of trig, and we needed an opening-day activity. Dardy goes on to say “I want to play with some data that is periodic in nature and try to generate some hopefully interesting questions.” I like that idea better than what we did — more on that below — since periodic data form the heart of modern trigonometry at the high-school level. So I did a Google image search for “periodic functions,” and here is the upper-left corner of what I found:
What strikes me right away is that there’s only one graph (the one at the lower left) that’s a straightforward trig function. That suggests a destination, but probably not a beginning. We want to start with data. Dardy offers various traditional ideas, such as number of hours of daylight, temperature, tides, all of which offer opportunities for periodic functions, and all of which are ones that we work with at Weston and at CSA.
Oh — I promised to comment on what we did instead of this. Even though periodic functions are in some sense the heart of the course, we started with an activity that used triangle trig in a challenging way. The advantage, of course, is that it ties in which what the students did as freshmen in geometry. The disadvantage is that it was very different from what they would be doing in the coming months. Personally, I thought the disadvantages outweighed the advantages.