All sorts of annoying little details have to be immediately recalled in Calculus. There you are trying to find an equation of a tangent line and BAM, not knowing the value of sin(pi) stops you cold. Or you're comparing which differential equation model grows faster and suddenly you have no idea if e^x grows faster than x^2.

Enter an old idea, stolen from any number of teachers in your past and here, explicitly from a workshop I attended a year ago. Every so often I'll package up annoying little information like that into a "test" to start the day. I'll have instructions to number 1-15 or something and I'll ask them a host of trig values, sin(pi), -cos(pi), etc. Or I'll show them some pictures of functions and ask for the associated vocabulary word. Or mix the two. It's no different than spelling tests or multiplication tests, minus the "minute math" panic attack part.

The teacher in question would collect these and grade them. She asks 10 questions, every day, on a variety of old and new things, often repeating questions. Simple little knowledge that needs to be in the front of your brain by May. She wasn't really interested in the grades, just being able to perceive that her students were getting better.

Here's the 40-graph Parent Function set I use:

I have them know sin/cos (and limited tan) values for 0, pi/6, pi/4, pi/3, pi/2, pi, 3pi/2, and 2pi. In the future this exercise will probably include other simple things like fundamental trig derivatives/integrals, and possibly some first and second derivative type stuff.

It's been 4 weeks and a simple thing like this already has me feeling better about our progress.

AuthorJonathan Claydon