# 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:

- They can choose a one-time payment of $1 million.
- 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 2^{29}, 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:

- Procedural fluency
- Conceptual understanding
- 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?

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Thank you for the ideas. I have been reading about the importance of the relevance of math in the classroom and how relating real world problems to the kids may improve their self-esteem in math and how they look at it. This was a great place to get started.

Hi Karim Thanks for the article. I like to use directly related questions to get kids interested. If a students play sports, I ask a question regarding their stats or time. For a computer game player, I ask about the bullet drop from a snipers gun shooting from 500 yds out. Yes someone had to calculate that. For business minded students, I ask a how much would you pay your employee for overtime if... and so on. The correct answer isnt important. It is the fact that regardless of what you do in life, be it retail, playing sports, or business, math is involved. Thanks for posting.

edited to correct typos

Hello. I need to voice a disagreement here. As the article began, it said students are frustrated when just given formulas. and I agree with that. However, look at the second bullet from the 3 bullets on common core, it's conceptual understanding. If you want to engage girls in math, focus on conceptual understanding, not applications. I would not have pursued math for the applications, that's almost a post-script for me. I have taught for years, and coached math, and inspire girls that continually pursue math and computer science degrees, because they love the theoretical inquiry. I realize there's a spectrum of interest, but a focus on applications is like ignoring girls. If you want girls to be interested, focus on deep conceptual understanding. They get it. Math is not science, please don't treat it like science. Science will teach applications. Or teach applications as a post-script after conceptual. In fact, I teach concept first, then algorithm, then application. OK, I could go on about this, I'll get off my soapbox now. I know this won't be popular, but it's true.

This is exactly the type of dialogue we are looking to have this Tuesday and every week on our Google+Hangouts On Air show "Teacher Talk Live" Check it out!

https://plus.google.com/events/ceunuvte6hvmuns4onpq1vq2u14

One of my favorite subject is Math. During the time of this subject, I stand out the most in class. Then I also notice that some of my classmates didn't seem interested in learning this subject. Some of them said that they don't give an importance of it because if we reach the college they wouldn't teach it anymore. But if you come to think of it, there are many application in real-life that contain relevancy to Math that others don't give any importance on it. There is a saying that if you want to posses that skill you must know a way to learn it.

I always like to relate Math to Brain Teasers, Puzzles, even some logic type games. One example I have used in my classroom, is the game, Rush Hour. For those of you not familiar, it involves a small red taxi that needs to exit a blocked parking garage of other cars and trucks. Players start off from an easy mode to those more complex. Once a student works it out, I will mention "how did they figure it out?" or if they are starting a new level, I will get them to look at the problem backwards. Car A has to move, then Car B, etc. I explain that this is sometimes what we have to do in life and use math. I also have a shelf of brain teaser puzzles, logic games, etc. that I will have students used if they are finished with the daily assignments or if they came to class early. When I do work out math problems or present new topics, I will go back to these puzzles or mention that at first they thought they were hard, but they worked them out. They had to follow a process. They had to use logic. We do the same thing in math. I also like to show several different ways to work out a math problem. I tell the students, pick a method you would like to use.

Why Math" is sometimes evidence of a student just venting frustration as they wrestle with a difficult concept or procedure, which is fine. At those times I might tell the story of how I saved summer camp by using trigonometry. True story. But as the author points out, "Why Math" is a great question. As teachers we aspire to pre-empt the question by making the lesson overwhelmingly interesting and meaningful, but as Laura alluded, at the high school level it can be hard to contextualize everything in the real-world. I've tried my best with the materials I've authored and used over the past 15 years. Quadratic functions can be explored through accelerating race cars, Usain Bolt and dropping rocks on the moon. Square root functions are a little tougher, but sailboat length and corresponding boat speed suffice. Statistics is a softball: count the green m and m's, collect heights and heart rates and so on. And all these models can be further developed on the way to Calculus. I think the hardest thing about high school is time and testing, which can make it difficult to give students the freedom to experiment and discuss. Nevertheless, given the space to do so, students will begin to see themselves as mathematicians, and math as a verb which leads to a deeper understanding of how the world is put together. Thanks for the post! www.couragetocore.com

I agree that these are great ideas but the best reason is because it is fun/enjoyable. I teach Maths because I like numbers and the way they function. I enjoy using my accumulated knowledge and skills to resolve unknowns and to make sense of the world. I always make this my first response and I will use the types of suggestions you have made to back up what I say. It is very important that we work in the affective domain as well as the cognitive domain to inspire and instruct in Maths. If we don't move them emotionally, we won't budge them cognitively. I need to share this part of me with my students if I am to be effective. My English teacher friends/colleagues teach English because they love words; they enjoy reading and take endless pleasure in the way language can be expressed verbally, textually and visually. That's what makes them good teachers. That's what makes us effective. It is important to engage the heart, because then you can engage the mind.

You are so right, john_jmadden! Those teachers who love their subject matter and can impart that passion to their students will have a great impact on their students' appreciation of the subject. Helping students see your fascination with numbers will no doubt help them to appreciate and enjoy your class.

One way to answer this question is to look to those strange folk that have devoted their lives in pursuit of mathematics. A common pattern amongst celebrated mathematicians of past and present is the intrinsic beauty and wonder they find in the subject. Their emotions are relatable to anyone that has derived pleasure from solving a jigsaw or any other puzzle. Much like love, it is a feeling that transcends strict definition.

Math needs no why.

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