At the end of the 50 minute period, we had this. I have a class of 15 Precalculus students, mostly juniors, and I sat in the back of the classroom calling them up more or less randomly to do a particular task on the board. Well, fast-forward to, well, yesterday, and I decided to try this out because I was feeling a bit under the weather and was too weak to move much. At the time I had just come out of Education Grad School and was thinking to myself “yeah, okay, whatever.” Apparently it was one of these stories where the administration always gave him the students who failed the other math teachers’ classes because he could teach the students, despite the fact that this back-of-the-room teaching style was all he did. He would have the students go to the board and do all the problems, especially the weakest students. When I started teaching, someone told me about “the best math teacher they had ever seen.” He was a crusty old guy who sat in the back of the classroom in a leather armchair and eat fish-chips, or something like that. I didn’t realize that you don’t actually have to memorize the Unit Circle: you can figure out the standard points on the unit circle pretty quickly just using those two special right triangles! Until recently, I also thought that the point of studying “Special Right Triangles” was to be able to find sides out quickly in special cases. The way I see it, the only reason to memorize the unit circle might be its use in a small part of Calculus the following year, at which point all the students will have forgotten their precious memorized circle because of summer break and the hose that is Calculus at the start of the year. When I went though, we had to memorize the unit circle.
Maybe I didn’t pay enough attention as a Precalculus Student 13 years ago, but I never saw or knew about the connection between the so-called “Special Right Triangles” (45-45-90 and 30-60-90 triangles).
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