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Math: How We Teach It V.S. How We Do It
I came to teaching in an unusual route: I got my Ph.D. in Space Physics before becoming a teacher of remedial math for the army. This means I had several decades of using high-level math before trying to teach low-level math. When I started teaching, I realized that I didn’t remember how I was taught, and so decided to just teach it the way I did it. This was mind-blowing to other teachers. My students would ask me why they were taught to do everything the hard way, and I couldn’t answer them.
After much thought, I realized a couple of things:
- low-level math focuses on teaching methods rather than ideas. The teacher understands the ideas and has trouble explaining them because they are so basic, so they show the method instead. This trains the student to trust the method, but not understand why the steps are done. The reason people have trouble in calculus is that there IS NO specific method and you have to understand what you’re doing and determine the steps from what you want to do.
I explain the difference to my students like this: Say I needed you to exit the room. I could tell you to stand up, turn 90 degrees to your right, take 2 steps forward, turn another 90 degrees to your right, take 12 steps forward, turn 90 degrees to your left, and take 9 steps forward. Or I could say “Please leave the room” and you’ll look to…
