## Friday, November 26, 2010

### My Math Alphabet: C is for Calculus

C is for Calculus, Which Gets Me Jobs

Calculus helped me get both of my full-time community college positions, and it was calculus that got me back to teaching in the first place. I love calculus.

The Slope of a Curvy Line
Back in the early nineties I was doing user support for a progressive internet provider, known as PeaceNet, EcoNet, Institute for Global Communications, and a few other xNets. We worked out of a small office in San Francisco, and I did phone support all day, helping people all over the country get online, while also trying to write manuals and learn more in between calls.

In January of 1995 I flew to Seattle to visit some friends, and on the way back home I sat next to a man who was a Native American AIDS activist. We talked about many things, and at one point I explained to him what calculus is:
You know how in algebra, you graph lines, and find the slope? The slope tells the rate of change, which is important in lots of real-life applications, but most of those don't make straight lines. Finding the slope for a curvy line is what calculus does.

If we draw a tangent line to a curve, we can define the slope of the curve to be the same as the slope of that line. The problem is that a tangent line to a curve only touches it in one point, and you need two points to find the slope. So we cheat. We use the point of tangency, and then for a second point we look at secants  (lines that touch the curve in two places) through that point, with the second point sliding closer and closer to that first one, so that the secant line is twisting closer and closer to the tangent line.

I drew lots of diagrams on our napkins, something like this (though of course I couldn't animate mine). And he told me I should be teaching. He suggested I get a job at an Indian college. I missed teaching, so I looked up the Indian colleges, and thought about it.  I was too tired of moving to new places to go for it, but that got me started on looking into community colleges, and that summer I applied at a number of colleges back in Michigan, where my family is.

What's It Good For?
One of my interviews was at Muskegon Community College, only an hour away from my family in Grand Rapids. During my teaching presentation, JB, who was on the committee interviewing me (they were all pretending to be my students) asked, "So what's this good for? Anything?" I asked what he was interested in.

JB: "Rocks." (He's a geology teacher.)

SV: "Hmm, well, would it be possible to know the shape of a layer of rock underground, and want to know its volume?"

JB: "Yeah!"

SV: "And would it be likely for the shape to have a circular shape, so it would be the same in any direction from a central point?"

JB: "Oh yeah, that's common."

SV: "OK. What if it were shaped like this..." And I drew a hypothetical rock layer formed by two parabolas crossing. We imagined it spinning around the y-axis. I then explained how to use something the textbooks call the 'shell method' and I call the 'tin can method', to figure out the volume.They were impressed, and I got the job.

Related Rates
I worked there for six years, and was happy with my work. But I wanted to adopt a child, and it became clear I wasn't going to be able to adopt in Muskegon. (As a single pagan lesbian, I just wasn't the sort of family the social workers were looking for there.) I decided to try to move back to Ann Arbor, or back to the Bay Area. During my interview at Contra Costa College, I had to do an unplanned lesson. I got to choose between linear algebra and calculus, and then they would give me a topic. I considered doing the more advanced linear algebra topic, in order to impress them, but decided it might backfire if I couldn't explain it well enough. I stuck with calculus, and they asked me to explain related rates.

That's one of my favorite topics (I know, lots of pseudo-context in those problems, but I think they're neat!), and I enjoyed getting to play with it. I had thought my planned lesson went well, but later found out they weren't particularly impressed with that, and it was my impromptu talk on related rates that got me the job. They must have seen my eyes light up as I started to explain how one rate of change was related to another, and how we could solve our problem using those relationships.

I adopted my son a year and a half after I moved back out here; I'm now the happy mama of an 8-year-old. I've been at CCC for nine years now, and I love the diversity of my college. Thank you, calculus!