Calculus is like jury duty. Everyone agrees that it’s essential, and any sensible human being will try to get out of it if they can. But panicked right-wingers are currently cluttering the internet with claims that a change in high school calculus teaching is the latest threat to Western Civilization.
I write from experience. I’ve been called for jury duty twice and taken three calculus courses, plus numerical analysis and differential equation classes with a calculus prerequisite. I don’t remember a lot of the calculus and I was rejected both times for jury duty. Maybe because I would have been sending reporters to cover whatever trial I was chosen for. Regardless, they paid me $40.25 both times: $40 for a 20-minute “day” of jury duty, and two bits for a mile or less of travel expenses, another way of saying I walked to the courthouse.
Calculus may make less sense than that, particularly for those who don’t necessarily care whether the derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Of course it is.
But calculus is about measuring change and rates of change. Consider, for instance, the first 14 years after the web browser was introduced in 1993. The internet was changing things, Amazon was growing bigger, and some people still browsed through a dial-up connection while staring at a monitor the size of two microwaves and a flower pot. At the end of the 14 years since then, people are sharing social media memes on hand-held smart phones and tablets. Calculus can help the sociologist understand the social change involved and may let the electronics vendor guess how many tablets to order. The rest of us just need to know whether to swipe left or right.
Or consider the funnel. Cooks, chemists, and lab workers know that the level of liquid in a funnel drops more quickly when the funnel is almost empty, even though the water continues to flow at a more or less steady rate. Why that happens has to do with the volume of a cone, which as we all know is the integral of an infinite number of infinitesimally thin circular disks of thickness dx. That’s valuable knowledge for a chemical company engineer designing a centrifuge that won’t blow up and take half of Hopewell with it, but the cook just needs to stick the pointy end in the top of the jar.
Calculus is for those who want to understand rates of change or need to calculate them. So why take calculus? Because it broadens the mind and helps you understand at least the basics of chaos and motion better, or because you’ll need to engineer something that must work in a changing environment. Why require calculus? Beats the shit out of me.
The Virginia Mathematics Pathways Initiative would try to teach mathematics that students will need in their career and life pursuits. Fox news says the initiative would eliminate calculus. The state superintendent explicitly states that the “traditional high school pathway culminating in the study of Calculus or other advanced courses is not being eliminated. Additional course pathways will include engaging semester courses in statistics, data science, modeling, design, and logic, among others.”
On the other hand, the initiative mentions equity, which has Fox News and its Amen Corner on blogs and social media soiling their ideological diapers. To those people, equity when they say it means how much you can get if you sell your house, and when we say it means socialism, presumably with a side order of gun control. (The documentation also mentions making students “life ready,” but this is about math, not educational jargon. Still, lets call the VMPI the Math Path, because we can.)
In other words, Virginia is making another attempt to improve the way people learn what is for many the most difficult subject area. And conservatives are screeching about something being taken away from them, because equity is mentioned. For those who aren’t selling a house or making stuff up on Fox News, equity means fairness. Can’t have that, can we?
The connections made by the Amen Corner are tenuous. They point not to the state’s standards so much as to a document not mentioned in the standards but alluded to on social media by a proponent of the Math Path. The document alluded to mentions race. Can’t have that either. Racial and ethnic equity in education might mean that students raised in poverty or working class conditions or for whom English is not a first language might have the same chances as white middle class students. Then where would we be?
Or equity might mean teaching students the math skills they might need and use instead of the complex theory behind those skills. A student who’s going to go to community college for an auto mechanics certificate needs to understand how to get the right fuel-air mixture. They don’t need to know that gasoline typically consists of a homogeneous mixture of small, relatively lightweight hydrocarbons with between 4 and 12 carbon atoms per molecule, or that it’s a mixture of paraffins, olefins, and cycloalkanes, which some of you may think of as naphthenes.
From Dr. P.N. Raychoudhury’s Advanced Calculus II class at VCU, I remember an ad in a computer magazine showing a complex integral that left the class groaning. It was long enough ago that I was thinking in Pascal when I considered the integration by parts necessary to solve it. The program advertised could solve it for thousands of dollars, or you could wait forty years and solve it using Dawson's Integral Calculator, free for the iphone. Calculus as app.
From Dr. Walter Elias’s Advanced Calculus I at VSU, I learned of the Behold Method of Mathematical Proof. You write the thing you want to prove on the board, then stand back and say, “Behold!” Your wisdom obviates the need for deductive steps or explanation. Tucker Carlson uses this method in political analysis, although I doubt he learned it in calculus.
From Dr. Sleepy Williams at W&L, I remember that he earned his nickname when he had us writing on the board. I also remember that in September he hand-picked 10 freshmen to take his advanced course on elementary calculus. Soon after mid-terms he announced, “They suckered you in when they told you you was brilliant.” Nobody had the nerve to say he was the one who told us.
A similar thing happened when Fox News recruited faux-brilliant commentators to talk about math education, and they managed to sucker in their viewers and a host of bloggers as well. I’d hate to have people with their critical thinking approach on a jury, especially if I were the defendant. But they’re probably smart enough to get out of jury duty.