Anne Marie Crinnion
Just Excuse Her Already
Orderly progression of logic defines the subject whose predictability I relish. Math is full of rules: geometry theorems few ever really learn, addition facts people use their physical digits to solve, and trigonometric relationships with mnemonics that many find harder to remember than their actual content. Yet one elementary rule tends to stick with people long past their high school calculus class. Maybe it’s a punch at Nike’s “no excuses” slogan. Whatever the reason, the American math student has always felt the need to excuse that oh so dear Aunt Sally. It’s a catchy way to recall the order of operations: PEMDAS. Please Excuse My Dear Aunt Sally. More than just through mantras, however, math is remembered through optimism, through the hope of receiving more. For in excusing my dear Aunt Sally, there seems to be a hierarchical order for the entirety of the operations. The realization that multiplication and division are treated equally and performed simply in the order that they appear in the problem often shocks students. It’s natural to want to multiply first; our culture emphasizes that more is better. The same is true for addition and subtraction; the natural instinct is to add before subtracting, for increases are associated with happiness. The beauty of math is that it’s emotionally neutral. Adding and subtracting occur on the same operational level, yet math is oriented and taught towards the positive. That’s why trigonometry frustrates so many students: the unit circle on which all radian operations and subsequent trigonometric functions are based is oriented counterclockwise. It’s a progression that initially seems backwards. With the idea of time as a constantly increasing phenomenon calibrated to the movement of clocks, clockwise is thought of as the positive, increasing direction. Thus, orientating towards the reverse in trig is something I often help my students with. Among the younger students I tutor, I have yet to come across someone who tells me that division is easier than multiplication. Perhaps if division and subtraction were emphasized in elementary school over their counterparts, subtle changes would arise in our culture. Would the overall mindset change towards a more egalitarian society? The emphasis on division could result in increased charity; the general view may shift towards a thought that dividing one’s acquisitions is more important than multiplying one’s wealth.
It’s possible we need to start to think that People Everywhere Direct Message Sir Arthur: PEDMSA. Rather than confusing students with my own idea of social change, however, I revert back to the trusted PEMDAS. Every time I tutor, I feel so grateful that figuring out the order of mathematical operations is facilitated by the imperfection of my aunt. Sally is proof that there is room for pardon in the world; imperfections can lead to irrefutable lessons. If a student commits the grave error of doing multiplication before exponentiation, my excusatory mantra saves the day, or at least, the problem. My dear aunt becomes an acronym; reduced, like one should do with all fractions, but never irrelevant. Aunt Sally truly gives order to the operations, yet she will always be remembered as arithmetic’s quintessential scapegoat.
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