On Purpose


Corey Andreasen teaches math at Sheboygan North High School in Wisconsin. He was a 2015 recipient of the Presidential Teaching Award for Excellence in Mathematics and Science Teaching.

Dear Corey:

I was so happy to read in July that you’d won the Presidential Award for Excellence in Mathematics and Science Teaching. That’s an incredible accomplishment, and I know I was but one of many friends who were proud for you, proud of you, and proud to know you.

I was a bit surprised, then, to receive your email four months later saying that you were thinking about leaving the classroom. “20 years,” you wrote. “I’m tired. I’ve done a pretty good job of it for a long time, but I feel like I need a change.”

A bit surprised…but not entirely. At its best, inspiring students to become better, more complete versions of themselves can be a most uplifting experience: the sharing of ideas, the shaping of minds. At its best, there is perhaps nothing more fun — certainly nothing more important — than teaching. Yet as you know, it is very rarely at its best. As a community, we have somehow managed to turn this most human pursuit into what is too often and for too many a soul-crushing exercise in standardized testing, intellectual disengagement, and the spiritual anesthesia of low expectations. Twenty years? That’s an impressive run, and I can understand your fatigue.

To be honest, I’m in a similar place myself. Ignoring grad school and long-term sub jobs, I’ve been in education for around ten years, and for the past six have worked almost non-stop on Mathalicious. In September we finally reached a years-long content goal, and shortly after I left for sabbatical. Before leaving, I cleaned out my desk and said to Ginny, “I don’t know if I’ll be back.” 47-percent-life-crisis. Inflection point. Whatever we call it, I needed to step back and evaluate what I’d contributed, whether I had anything left to offer, and — most importantly — what purpose I wanted to serve.

What’s Real?

In 2009, when Congress was debating the Affordable Care Act (aka Obamacare), I attended a town hall meeting in Reston, Virginia, a relatively well-educated part of the country. I expected the discussion to be a productive one, but before it started people were already screaming and referring to one another as tyrants and idiots, fascists and frauds. While I understood how important the issue was, I didn’t understand why it had to be so divisive. Insurance is pretty straightforward: How much insurance is worth is simply a function of how likely someone is to get sick and how much it’ll cost to fix them.

After the meeting, I went home and began working on the first version of the Mathalicious lesson, Licensed to Ill, in which students use the concept of expected value to explore health insurance from the perspectives of both consumers and providers. “Adults might not be able to discuss the issue constructively,” I figured, “but sixth graders can.” Since then, I’ve come to view math class as a place where students can discuss, wrestle with, and maybe even help resolve some of the most important issues facing society.

I was therefore interested when, during his standing-room-only presentation at CMC-South a few years ago, Dan Meyer suggested that the real-world is “overrated” when it comes to math class, and that a topic is only real to someone if it’s relevant. “Is health insurance real to students,” he mused, implying that if not, perhaps we shouldn’t teach it.

It’s an interesting question and one I’ve been thinking about ever since: What is the purpose of math education, and what does it mean for the experience to be complete?

Looking At: Math As Object of Inquiry

If you ask teachers to define the purpose of math class, I suspect many would say something along the lines of, “To help students become better problem solvers.” As a community, we seem to equate learning math with solving problems, where the goal is to illustrate some underlying mathematical concept: proportionality, linearity, etc. Unfortunately, the tasks we’ve traditionally relied on for this are often so forced as to be caricatures of themselves.


Confronted with problems like these, students frequently ask of math, “When will I ever use this?” Yet as many educators have pointed out, this may not be their real question. Instead, “When will I use this?” may be code for, “I don’t get this and I feel dumb.” Traditional tasks often reveal so much information on the front-end that students interpret their responsibility as to calculate an answer rather than to engage in a problem-solving process.

A number of people I admire in the math education community are taking a straightforward approach to improving these suffocating tasks: tear them down, clean them up, and reconstruct them in a way that better sparks curiosity. Where the goal is to help students puzzle over mathematical concepts like volume, their premise is that we don’t necessarily have to create new, more “relevant” problems. We can just approach the old problems differently, the way task developers are doing with Makeover Monday.

DanMeatballs1 DanMeatballs3 DanMeatballs4
Meatballs, Dan Meyer

By inviting students to make predictions, solicit information, and approach solutions in their own ways, activities like the revised version of the meatballs task do a better job of engaging students in meaningful problem-solving than do their textbook equivalents. Not only that, but their thoughtful structuring helps students understand concepts and generalize them to other contexts: from meatballs in a pot of sauce to ice cubes in a glass of water to pennies in a wishing well. If I were still in the classroom, I would incorporate activities like Dan Meyer’s Three Acts:

These are nice contexts for illustrating proportions, sine functions, and areas, and are accessible to all students. I admire the work that Dan and others are doing to facilitate problem solving, and I think this work is needed.

However, if our goal as educators is to provide students with a complete math experience, I don’t think simply making over the existing experience is enough. Tasks like Three Acts provide useful contexts for looking at mathematical concepts — meatballs as a way of looking at volume; pennies as a way of looking at area — but they don’t address why these concepts are worth learning in the first place. Educators who believe that such tasks are sufficient effectively present mathematics as one giant puzzle: an endless string of Sudokus. Of course, math is much more than that. If students are reasoning today about how long it takes to pop bubble wrap just so they can reason tomorrow about how long it takes to fill up a sink, don’t you hope they’ll eventually raise their hands again and ask, “No, seriously: When will we ever use math?”

Looking With: Math As Object for Inquiry

While math is beautiful to look at, it also exists to look with. The way I see it, mathematics is like a telescope: a powerful tool that humans have developed and refined over time to better understand the world. While it’s important to study concepts like reflectivity and aberration, the reason astronomers care about them is not because they want to look at telescopes but because they want to look through telescopes at something else. Math allows us to explore the something else. For instance…

In size-7, a pair of Nike Free Run sneakers weighs 14.6 ounces. In size-13, a pair weighs 20.6 ounces. EIther way, the shoes cost $100. This means that while people with larger feet are paying $4.85/ounce, people with smaller feet are paying $6.85/ounce, or almost 50% more. In sixth grade, students learn how to calculate unit rates. Should people with small feet pay less for shoes, and should Nike charge by weight?

Olympic sprinter Usain Bolt is the world’s fastest man. He’s also one of the tallest. Standing more than 6 feet 5 inches, Bolt towers over his competition. In seventh grade, students learn how to solve proportions. Do taller sprinters have an unfair height advantage, and should sprinters run distances based on their heights?

The probability of picking a winning Powerball ticket is low…very low. However, there’s a point at which the jackpot is so big that the expected value of a ticket is greater than its cost. In high school statistics, students learn how to calculate combinations and permutations. When it is worth buying a Powerball ticket?

Unit rates. Proportions. Combinations. These are beautiful concepts by themselves. I find these concepts powerful, though, when we apply them to better understand how the world works…and to discuss how we think it should.

That said, while I think it’s great that students discuss alternatives to one-price-fits-all and understand the mathematics of lotteries, I’ll be honest: These aren’t topics that inspire me on a deep level. I think the lessons are interesting and are worth teaching; indeed, I think a student’s math experience is only complete if it consistently involves authentic applications like these. I’m just saying that when I finally decide to leave education and look back on my career, if people are still spending money on lottery tickets and if tall sprinters are still winning gold medals, I won’t lose any sleep over it.

Looking With: Math As Object for Citizenship

However, there are certain topics that I do lose sleep over. When I ponder the ultimate purpose of math education, there are certain conversations that I find myself caring about a lot.

When the housing market collapsed, the decline in property taxes left municipalities around the country scrambling to meet their budgets. Cities like Ferguson, Missouri increasingly turned to speeding tickets and other fines, even adding monthly fees when people couldn’t pay them on time. This had a terrible effect on low-income residents, some of whom lost their cars, lost their jobs, and even went to jail. In eighth grade, students learn how to solve systems of linear equations. How long will it take someone on minimum wage to pay off a ticket?

Wherever you live, the temperature will vary over the course of the year. In 2013, for instance, the average monthly temperature in Washington, DC ranged from 19.3° (January) to 66.7° (July). This rise and fall can be modeled mathematically, and temperatures have been fairly consistent over time; DC was only 2° warmer than its long-term average. Yet while humans might not notice such a small change, the earth does. If temperatures continue to go up, storms will intensify, glaciers will melt, and oceans will rise. In trigonometry, students learn how to graph sine functions. How have temperatures changed around the world, and what are the consequences?

I was pretty insecure when I was in high school; I wondered what my friends thought of me, whether my teachers thought I was smart, whether girls found me attractive. Being a teenager has always been hard, but I can’t imagine how much harder it must be today. I read an article in Business Insider not too long ago describing how teens are “spending thousands of dollars on prom outfits so they can look cool on Instagram.” Some are even buying likes. That’s crazy. It’s heartbreaking.

It’s also futile. According to the data analytics company Union Metrics, the average Instagram post gets 80% of its likes and comments within the first eight hours. Having to redefine yourself three times a day just to stay relevant? Convincing yourself that if nobody likes your photo, then you must not be likable? What a terrible thing to feel. Fortunately, in high school statistics, students learn how to create regression curves through scatter plots. How can you become more popular on Instagram…and what are some consequences of constantly having to maintain your personal brand?

Activities like Three Acts are good at helping students develop problem-solving strategies that they’ll need later in life. In addition to reasoning about things like meatballs, though, shouldn’t students also have opportunities to discuss real-world issues that matter?

Big Picture

Of course, learning how to love yourself is not a topic that fits neatly into our traditional conception of math-as-puzzle-solving-class. Social justice is not a Common Core Standard. However, I don’t view this as an argument for why we as math educators shouldn’t include them as goals. Instead, I simply think it’s an indication of how small our imagination has been and an invitation to expand it.

Because isn’t that what public education ultimately exists for: expanding what we think about and broadening what we care about?

As math educators, we need to create better opportunities for students to reason mathematically, solve mathematical problems, and understand mathematical concepts. So let’s do that. But let’s also take the next step and provide students with opportunities to apply those concepts, to use the math they’re learning to answer interesting and socially impactful questions. Only when they do that can they see the bigger picture, namely: the bigger picture.

We live in a world of big pictures. We live in a world of sports and commerce, a world of design and photography. We live in a world where people go to movies, where people go to casinos, where people go on diets, where people go crazy wondering what other people think about them.

We also live in a world where people die because they don’t have health insurance…which brings me back to the question that Dan posed years ago and which I’ve been thinking about ever since: Is health insurance real to students and is it a topic worth teaching?

Medical expenses are the leading cause of bankruptcy in the United States. Even if some students don’t think the issue is relevant to them, they may have classmates who lost their homes or whose parents died because they couldn’t afford their meds. Seven years after the town hall meetings, we as a democracy still have a hard time talking about this in a constructive way. Is health insurance real to students? Health insurance is real, period. I think it’s a lesson worth teaching. I think it’s a conversation worth having. And I think math class is the perfect place to do it.

Next Steps?

Should you stay or should you go? That’s the question, right? You’ve been teaching for a long time, Corey. I don’t know how you define the ultimate purpose of math education or whether you still see a role for yourself in it. What I do know is that after two decades you’ve earned a rest, and I won’t begrudge you if you decide to close out the year, close the classroom door, and start a new chapter.

As for me, I define the purpose of math education as to help students understand the world and live more meaningfully in it: more healthily, more curiously, more kindly. Six years after starting Mathalicious and six months after leaving for sabbatical, I continuing to hear the refrain in my head: Math class as a place for conversations that matter. That’s the world I want to live in. And that’s the experience I’d like to help create.

Whatever you end up deciding, congratulations on everything you’ve accomplished. Whatever path you take, I’ll be cheering for you, and will look forward to seeing you around the bend.

March 10, 2016