My first year teaching (which seems like a much longer time ago than it was), the administration asked us to observe at Providence High School. Providence is by all measures a “good” school, and I did get at least one thing out of the visit. It was just hard for me to see a connection between Providence, a predominantly white, middle-class school in a nice neighborhood, and my school, a majority-minority, high-poverty school.
Providence, a large, polished public school, bears no resemblance to HGS either. But the one thing I did get out of the visit was a project that one of the classes was doing, a project that I’ve had a lot of success doing here. Some things do transcend – creating sine curves out of colorful straws is apparently one of them.
The unit circle is an important but initially mystifying document, whereas trigonometry is strictly visual. We started with just setting up trig ratios with right triangles they could see. No problems there. Then I introduced them to the unit circle, posing the question: where can you see right triangles?
This was more of a challenge, but an interesting one. Once they were curious, it became a lot easier to explain the connection from trig to the circle.
The project works like this: first, they wrap a string around the circumference of the circle, marking where each of the angles hits. Then that string becomes the template for their x-axis. They use straws to measure the sine, the distance from the x-axis to the angle, or the “opposite” side.
Creating these graphs in such a physical, hands-on way helps them to grasp onto some of the more abstract stuff to come… and it does get pretty abstract.