Hollywood movies have taught us some very important lessons about teenagers. That any sadness can be solved with a Coldplay montage and ice cream, that we have a very strange obsession with vampires and werewolves, and that our great nemesis is calculus. For example, in Mean Girls, the great obstacle that Lindsay Lohan must overcome is a limit, but since my introduction to calc, I have always wondered why it gets such a bad rap in modern media. So today, let’s look at calculus comparatively with the other high school math and courses.
There are generally four math courses taken by students in high school. Geometry, Algebra 2, pre-calculus or math analysis, and some form of Calculus.
Starting from geometry, there are a few basic principles that we are taught and persist throughout virtually all of mathematics. If I have two points on a graph, connecting them creates a line. If I were to measure how high and how far that line goes I get the slope of that line. And if I plugged those numbers into an equation, I end up with something that looks like y = mx + b. This simple equation is something that high school students will use in geometry, algebra 2, pre-calc, and finally calculus.
Algebra two will teach you how to use this equation and turn it into point slope form and pre-calculus will teach you how to calculate tangent lines and to build piece wise functions using a series of these equations. Out of the 322 pre calculus that Kahn academy defines that pre-calc teaches, 56% of these all use this exact same equation y =mx + b.
Well, it seems that we have found the enemy. If this equation is what is causing high schoolers so much trouble in intermediate maths, it must be even worse in calculus. However, that is exactly what makes calculus so beautiful. The first chapter of any calculus textbook teaches the student about the derivative, a seemingly abstract, but in actuality quite simple, trick to immediately find the slope of any equation. Despite its terrible PR, Calculus ought to be the hero, not the villain of high school math. Using Calculus, the horrors of point slope form and of horizontal and vertical asymptotes disappear. So the next time you hear that incoming junior or senior fretting over his or her first calculus class or do something as blasphemous as taking statistics instead, it is important to remind them that besides from seeming as public enemy number 1, Calculus is never as bad as it seems. And if Lindsay Lohan can do it, i’m sure they can too.