When my son asks me how something works, I often don’t have a satisfactory answer. After all, I can’t rip open my digital device and show him the parts in action. In sharp contrast, we can see exactly how a bicycle works—we have an open window to its technical soul.
The problem is that fewer and fewer of our everyday tools have these open windows, and this really can’t be good for any of us. So when it comes to teaching, I prefer examples that come with an open window. I think this is a big part of what students want when they ask, “What is this good for?” After all, students master video games, without any direct application in mind; but they can see the entire picture.
I remember one day way back in the 1980’s walking through a field that probably no longer exists. I realized that I could calculate the height of the tree that was 30 feet from me, without climbing it. I did the calculation, even though no one asked me to do so. My enthusiasm was a result of understanding the whole point—I could gain information about a large triangle just by knowing things about right triangles with a hypotenuse of unit length. To me, this is trigonometry.
In this 3 minute video, I attempt to capture the excitement I had walking through the field. In the video, there is no field, but there is a clear story. For teachers, there will be a lot more to discuss after your students are done watching it. I hope you enjoy it!