The Role of Technology in Teaching

I occasionally use my iPhone while tutoring if I want to show someone a particular graphic – a photo of the Bay of Fundy or a map of Alexandria and Syene, for example.

Today I found a new way to use it during a math lesson. I asked my student whether the sine function is even or odd. He didn’t know what that meant, so I told him the algebraic rule (a function $f$ is odd if $f(x) = f(-x)$ for all $x$).

We graphed the sine function on his TI graphing calculator, and I told him, “Okay, now spin the calculator around 180 degrees to hold it upside down.” The graph looks the same. This is true for all odd functions because a 180 degree rotation is the transformation $x \to -x, y \to -y$.

Next we looked a the graph of cosine, but when we rotated that 180 degrees, it didn’t look the same any more. Cosine isn’t odd. Instead, I got out my phone, handed it to him, and told him to use the surface of the phone as a mirror to look at the calculator screen. The reflection of the graph looks the same as the original, as it does for all even functions, since this is the transformation $x \to -x, y \to y$.

I guess it shows that using too much technology is a turn-off. I hope this doesn’t reflect on me poorly.