Doing the Math: Beyond Mere Calculations

Doing the Math: Beyond Mere Calculations

All of my friends know I study math, but they don't bring it up very often--except during that moment at the end of a meal. Invariably someone looks at the check and then looks at me, saying, “You’re a Math Person. Why don’t you figure all this out?”

Does my friend think this is what we mathematicians study? Check-Splitting 101? Advanced Tipping? In conversation, the phrase “do the math” often means merely “do the calculations.” This reduction demonstrates a general misconception about mathematics. Success in math requires a lot more than strength in dealing with calculations. Although calculations are important, mathematics also requires abstract thinking, a keen sense of analogies, and disciplined reasoning skills.

One way educators ensure that math students develop strength in aspects beyond calculation is by including assessments that have simple calculations or lack them entirely. National Council for Teachers of Mathematics (NCTM) encourages teachers to ensure students are “adept at visualizing, describing, and analyzing situations in mathematical terms…[and] able to justify and prove mathematically based ideas.” State assessments at the high-school level, such as the New York State Regents Exam for Algebra, use open-ended assessments where students get partial credit for an answer that is correct but has a minor miscalculation. The newly released Common Core Standards claim to “plac[e] a premium on students’ ability to explain math problems, not simply compute them,” according to Education Week. Every list of mathematics standards goes beyond calculation.

The role of calculation in mathematics affects the debate over the effectiveness of calculators in the classroom. Arguments against the daily use of calculators in classrooms seem to conflate calculation and mathematics. Ideally, the use of calculators enables students to explore, conjecture, and verify conclusions more efficiently. Technology can carry the burden of cumbersome calculations, so that students can focus on representation, interpretation, and articulation, all crucial mathematical skills. With incorporation of new technology to assist complex calculations, and assessment to emphasize other aspects of the study of math, maybe fewer people will be turned away by the frustrations of miscalculations.

The aspects of mathematics that most excite me—the specificity of its representations, the elegance of a well-constructed proof, and ideas of infinity—deal less with calculation than with logic, linguistics, and philosophy. I “do the math” when I’m maximizing what I can pack in my carry-on luggage, Tetris-style. I “do the math” when I construct arguments or provide counter-examples. I “do the math” each time I think abstractly. Perhaps if the aspects of mathematics that go beyond calculations are better developed in all levels of study, particularly in elementary and secondary schools, more people will thrive in math classes enough to consider themselves Math People. Until then, hand me that check.