BY GABE MIZRACHI

The power rule: bring the exponent next to the coefficient, multiply them and subtract one from the exponent. The quotient rule: denominator times the derivative of the numerator minus numerator times the derivative of the denominator, all over the denominator squared. Amazing!

These holy calculus rules are two of many formulas we are taught during our time at MHS. They’re written on the board, we copy them down, we use them on worksheets and tests and life goes on. We’re satisfied with a formula as long as it gives us the right answer and a one hundred on our test. But you have to wonder: don’t these rules sound like magic tricks? Well, believe it or not, they aren’t. If you’re looking for the reason why math formulas work, you’re reading the wrong article. This is not an issue of not believing in math, it’s an issue of the way we learn it.

Much of the math we know is memorized, like lines in a play. Everyone can sing the quadratic formula song to the tune of “Pop goes the Weasel,” but that’s simply because it’s catchy. Recently, we were told to memorize the derivatives of trigonometric functions by walking around and reciting them to ourselves mindlessly. This is not learning math, this is mental imprinting. There are comprehensive benefits to understanding why they work – if on a test a student forgets a formula, he or she can figure out what it is by deriving it instead of trying to remember what it looked like on a sheet. It might seem like a waste of time to explore the background of a rule or formula, but it can come in handy when you draw a blank during a test.

An understanding of math is like a house. When you look at the house from the street, you see the pretty roof and painted walls. But they cannot be intact without the foundation, which you do not see. In mathematics, the roof is the miraculous formula. Yes, the derivative of cscx is cscxcotx, but that’s just what you see and use to plug in numbers – there’s more behind it. To fully comprehend a formula, it has to be explained fully, just as a roof and walls need to be built upon a foundation – otherwise, it collapses. So the next time your math teacher throws a bunch of gibberish x’s, a’s and thetas at you, don’t say “Okay,” say “Why?”