Why Math?

Dear Math-Teacher-To-Be:

According to a recent Raytheon survey, 44 percent of middle school students would rather take out the garbage than do their math homework. On the 2012 Programme for International Student Assessment, American high school students placed 27th among their OECD colleagues, demonstrating a troubling lack of problem-solving and critical-thinking skills. Only 11.6 percent of high school graduates express an interest in pursuing STEM in college. Of these, just over half meet the ACT college readiness benchmark in math.

To many students, math is a bunch of random skills to memorize and regurgitate, a series of steps with no meaning or relevance to their lives. For generations, an emphasis on rote instruction -- do this, then do that -- has left students wondering, "What does this mean?" and "When will I ever use it?"

What students are really asking, of course, is, "Why math?" It's a good question. You're about to enter the classroom. Before you do, ask yourself: Why do you want students to learn math? Why do you want to teach it?

A 2012 MetLife survey found that teacher job satisfaction is at its lowest in over 20 years. I imagine this is particularly true for math teachers who, along with their ELA counterparts, operate beneath the specter of annual high-stakes testing. In this environment, a meta-reflection like "why?" may seem unaffordably luxurious, like contemplating the nature of happiness in a hurricane.

But let's give ourselves permission to silence for a moment the cacophony that we've constructed around education, and to consider: Why math?

Why Math? The Typical Answers

The obvious answer is, "Because students will need it one day." That’s true. Many students will also need bifocals one day, but that's probably not enough to convince a 12-year-old to start saving her allowance. "One day" is pretty abstract and honestly a bit of a punt when used to justify, "Do page 17, 1-73, odd."

Another answer: "Because math helps students solve problems." That's also true. There's a classic task in which students are presented with two scenarios:

1. They can choose a one-time payment of $1 million.
2. They can receive a penny on the first day, two pennies on the second day, four pennies on the third, and so on, for a month.

Students work in groups to determine which option is better. Some draw pictures. Others create tables. Over the course of the task, students discover that on the tenth day, the penny option would only yield 512 pennies. But by the thirtieth day, it would yield 2²⁹, or roughly 1 billion pennies: more than $11 million.

While this is a surprising answer, the goal of the task is less the solution and more the act of figuring out. Students get an opportunity to become more flexible in their thinking, and also to reveal some underlying mathematical structure (in this case, exponential growth). This is important. Indeed, it's crucial.

But it's not enough. For some student will inevitably ask, "But nobody offered me $1 million. This is stupid. Why should I care?" And when he does, how should we respond?

Why Math? A Possible Answer

Why math? Why exponential growth?

Because exponential growth allows us to determine how fast the human population is growing and to discuss its implications for global food production and clean energy. Exponential growth allows us to explore how video game consoles have changed and to predict whether we're building the Matrix.

In sixth grade, students learn how to convert from fractions to percentages. Why percentages? Because they allow us to determine whether Wheel of Fortune is rigged and debate the fairest way to tip at a restaurant. Students learn the difference between median and mean, and how to draw a box plot. And these tools allow us to analyze how wealth is distributed in the U.S. and consider what it means to live in a fair society.

• Unit rates? How long does it take to burn off a Big Mac, and should McDonald’s rewrite its menu in terms of exercise?
• Ratios? How does the media we consume affect our happiness?
• Permutations? How many shoes can you design on NIKEiD, and at what point does this cause paralysis-by-analysis?
• Linear functions? Is college worth the cost?

Why math? Because math helps us to be healthier. It challenges us to be kinder. It motivates us to be more curious.

In 2009, we as a country tore ourselves apart in our debate over healthcare reform. We screamed at one another at town hall meetings and called those who disagreed with us traitorous and un-American. And yet there's nothing inherently divisive about health insurance. It's just expected value: the probability of your getting sick multiplied by the cost to treat you.

Mathematics allows us to discuss important issues in a meaningful, constructive way. Why math? Because it allows us to be better citizens.

Math: A Lens Onto the World

The Common Core State Standards define "rigor" as an equal emphasis on three areas:

1. Procedural fluency
2. Conceptual understanding
3. Application

Students need to develop basic skills; they must be able to solve a proportion. Students must also develop an understanding of concepts; they must understand what proportionality means.

And yet while math is an object of inquiry, it’s also an object for inquiry. Galileo spent many hours studying and refining his telescopes, yet his primary motivation was not the device itself but what he could do with it: gaze at the cosmos. For generations, we have presented to students a version of mathematics characterized largely by rote procedures and conceptual puzzles. A math class without authentic applications is like an astronomy class where students spend the year calibrating a telescope but never actually look at the stars. Math allows us to better understand the world and to live more meaningfully in it.

• How do temperatures fluctuate over the year, and do you see evidence of long-term climate change? (Trig functions)
• What is the likelihood of finding life on other planets? (Fraction multiplication)
• How does your memory deteriorate over time. . . and how much can you really trust it? (Exponential decay)

Why math? Why math class? Because math class can be the place where students discuss the most important and thought-provoking questions that face us as a species.

Your Legacy as a Teacher

You are about to enter teaching. Sometime this fall, you'll open your classroom door for the first time. That's a huge moment. Congratulations. One day, though, you'll leave teaching and close that door for the last time. In between those moments, what do you want to accomplish? There's an entire structure to help decide that for you: standards and tests, interventions and curricula. Yet even in the most rigid of circumstances, the most important decisions ultimately come down to you.

When you close that door for the last time, what conversations do you want to have had? To all your former students -- thousands of adults now out in the world -- what lessons do you want to have taught? What thoughts do you want to have inspired? And how do you want their lives to be better for their time in your classroom?

Or to put it another way: Why math?