Wednesday, April 25, 2007

Memory Tools

Yesterday I had passed out a colored sheet of paper and asked my calculus class what topics they want to review as a class and also any suggestions on how we spend our class review time. They were to list a topic, and if their topic was already listed, they were to put a check mark by it, so I could gauge popularity. One of the topics they stressed was derivatives of trig and inverse trig functions.

Today, I listed the 12 trig and inverse trig functions on the overhead and discussed memory tools I had for the derivatives of the 6 trig functions (all the "c" ones are negative; there's always 2 secants and a tangent; cotangent is like the pesky little brother of tangent and wants to be just like him; cosecant ditto to secant). Then I gave them 3 minutes, and they were to come up with memory tools for the inverse trig functions. I didn't know how it was going to work, but there were several good discussions going.

As we met back as a class, the ideas were slow at first, and then I don't know what happened, but as a class they came up with several good ones to remember the derivatives of the inverse trig functions (sin^(-1), cos^(-1), ...):

* if the name has a "t" in it, then there's a "+" (1+xx) which looks like "t"
* if there's an "s" anywhere in the name of the function, it involves a "s"quare root
* anything starting with a "c" has a negative (think grade c-)
* we learn sine and cosine 1st, so those are "1-xx" (as opposed to "xx-1")

Whew! I think those may even help me remember the inverse trig derivatives :).

1 comment:

1. You gotta love the derivatives for the inverse trig functions. I love the idea of making the class think of memory techniques for these complicated derivatives. While thinking of ways to remember, the students are remembering. When they take the exam, they will remember this day, and all of the time they spent staring at the derivatives will help bring them to paper. The students came up with some really good memory tools that will come in handy for the exam. Its good to see how students think, and this was a great way to look into their minds. Thanks for the memory tools, I’ll be sure to use them with my students.