Shalinee Sharma is the CEO and co-founder of Zearn, a nonprofit dedicated to transforming K-8 math education. Zearn’s online math platform is used by one in four elementary and one million middle-school students nationwide. In addition to her role at Zearn, she serves on the Braven board of directors, is a Pahara-Aspen Fellow, and is co- chair of the Brown University Advisory Council for the College. As a child of refugees, she is passionate about universal access to an excellent education.
Below, Shalinee shares five key insights from her new book, Math Mind: The Simple Path to Loving Math. Listen to the audio version—read by Shalinee herself—in the Next Big Idea App.
1. All kids are math kids.
I am not a math prodigy, but in sixth grade, I transferred schools and was unexpectedly placed in honors math. After our first test, Mr. Snyder said, “You did well. If you try your very best, you could be just as good as the boys.” It was a terrible thing to say by today’s standards, but it rocked my middle school world. I knew I was behind where I needed to be, but I heard Mr. Snyder’s inspiring message: If I worked hard, I could not only catch up, but I could compete with the best.
It changed my self-expectations. I had already unconsciously decided that I was just lucky to be in the room and that I would spend the year hanging on for dear life. Mr. Snyder told me that I belonged in that room and that if I made the effort, I could thrive.
With that emboldening knowledge, I worked hard. In that hard work, I found the beauty and pleasure of math itself—not the relief of doing well on a test, not the reward of pleasing others, but the plain sensation of enjoyment when solving a puzzle or finding a path that leads to everything making sense. I was pleased as ratios fell into place on a ratio table, and I felt the intense “Aha!” moment of understanding that y does in fact equal mx + b when I plotted points on the coordinate plane.
I became one of the math kids. I wasn’t born one, but I discovered that I could transform into one. That discovery has made all the difference in my life, and it can make all the difference in yours, too.
2. Myths prevent us from building a math mind.
Many people say that they hate math, but what they really mean is they hated the things they did in math class. They hated the experience of nonstop time pressure, memorizing meaningless formulas, and being forced to solve problems the exact way the teacher instructed. They were miserable because their learning was built on myths.
To renounce the myths, you need to state the opposite realities, as follows:
- Speed isn’t everything. Automaticity—the ability to call upon key facts and skills quickly and reflexively—is vital in math. When we have automaticity or fluency of math facts and procedures, we free up working memory to apply to the hard math problem in front of us. Timed activities help build up this capability.
But speed kills fun and creativity. If you know an engineer, programmer, or scientist, ask them how long it took them to figure out a recent work problem. I guarantee they’ll tell you that they spent days, weeks, months, or even years working out solutions. Speed is only one essential tool in learning math. Overemphasizing it leads to neglecting others—reducing rigor and increasing math anxiety.
- Tricks are not the answer. Math is a set of axioms or rules of the universe that you can trust completely. But we often teach it as a set of arbitrary-seeming, unconnected tricks.
Algorithms are not tricks. The standard addition algorithm always works whether you are adding two-digit numbers or ten-digit numbers, whereas the “bow tie method” for adding fractions will let you down once you move beyond two addends. Algorithms always work.
- There is no single way. You’ve been conditioned to believe that there is one correct or proper way to solve a problem. Reject this conditioning. Be open-minded and exploratory rather than single-minded and reactive when faced with a math problem. Consider the difference between answer-getting and problem-solving. Answer-getting is when math is taught as a rigid set of steps to follow.
Problem-solving is a creative cognitive process in which you strive to deepen your understanding. There are many ways to solve a problem, and they usually require visualizing it. In real-world STEM contexts, people discuss many ways of attacking a problem before they even begin their work. Their goal may be to find a more elegant, cheaper, or faster approach. The myth that there’s a single way to solve a math problem keeps people from ever experiencing this process.
3. We must teach math with pictures and objects.
From birth, we are programmed to do math with pictures and objects. This is supported by the way math is taught in the highest-performing countries, and it’s a core insight from Zearn’s learning dataset of billions of math problems created by millions of children. Recognizing this reality guides the way to a superior alternative to the math most of us were taught.
In sixth grade, my wonderful math teacher, Mr. Snyder, was frustrated with our class because we were obsessed with getting the right answers at the expense of deep understanding. He told us a story that illustrated the perils of learning math without understanding it: the tale of A&W’s Third Pounder. In the early 1980s, A&W launched a hamburger that tasted better, according to blind taste tests, and offered more meat than the McDonald’s Quarter Pounder. Their advertising copy read, “A&W has bigger, better third-pound burgers.” The slogan to promote the burger highlighted the quantity: “Third is the word.”
“When the A&Ws team investigated the failure, they discovered that most people believed the Third Pounder contained less meat than the Quarter Pounder.”
The McDonald’s Quarter Pounder offers one-quarter of a pound (or four ounces) of meat. A&W’s better-tasting and bigger burger, with 5.3 ounces of meat, was offered for the same price as a McDonald’s burger. Nevertheless, the product launch failed.
When the A&Ws team investigated the failure, they discovered that most people believed the Third Pounder contained less meat than the Quarter Pounder because the number three is smaller than the number four. Instead of seeing the better deal, they perceived they were being ripped off. To quote education journalist Elizabeth Green, “The Third Pounder presented the American public with a test in fractions. And we failed.” The story of Americans failing at fractions is a story of lost intuition.
4. With the right support, all kids can catch up in math when they fall behind.
In the early years of building Zearn, we conducted a rudimentary analysis of our digital learning approach. The key question we wanted to answer was: What helped students get a question right when they had gotten a similar question wrong initially? We found that when students who had gotten something wrong were then shown another way of solving the problem, they were more likely to get a similar problem correct the next time they encountered it.
A few years ago, with more than fourteen billion completed problems in our dataset, we returned to this line of inquiry. During the depths of the pandemic, I was talking to Steve Levitt, of Freakonomics fame. He asked what we send students back to work on when they struggle. I explained that there is often nowhere to go back to in math.
I told him that the dominant schema is often a waste of kids’ time. Sometimes, students do need to go back and review earlier material, but the reflex to send them back immediately, no matter what is misguided.
Levitt challenged my team: If what we were saying was true, we should prove it. He assured us that our dataset was sufficiently robust and offered creative ideas on how to find a natural experiment in our dataset.
Our researchers got to work utilizing cutting-edge data science methods. First, they built a fixed effect model. This is a model where rather than comparing one cohort of students to another cohort of students, our researchers compared students against themselves. We looked at the Zearn app and saw what happened to the exact same kids when they were able to stay on grade level and shown a different way, compared to when they were taken off grade level and remediated in the traditional way.
“Just a nudge toward an alternative attempt can allow kids to leapfrog forward.”
Even though we were responding to Levitt’s challenge and trying to prove what we already believed was happening, we were still shocked by the strength of the findings. When the same student was shown a different way, she struggled less than when she was taken back and remediated with previous grade-level content. And, of course, because these students stayed on grade level, they completed more grade-level content.
Imagine a seventh-grade student is learning negative numbers and she encounters decimal operations. In the context of an engaging lesson to make sense of negative numbers where we are descending a mountain (positive numbers), passing sea level (0), and then diving into the ocean (negative numbers), she sees a problem—1.4 ÷ 2—and gets stuck. She doesn’t know what to do. A remediation approach would take her back to weeks of fourth- and fifth-grade work to build up her knowledge of decimals.
Now, let’s consider a different way. When she struggled with 1.4 ÷ 2, we could show her this problem next: What is 14 ÷ 2? 7. Right. Easy. Then we would say, decimal operations are exactly like whole number operations, so you are very close to understanding this question. The alternative doesn’t have to be anything complex—just a nudge toward an alternative attempt can allow kids to leapfrog forward.
5. From sorting to teaching.
Math matters for everyone, but we act as if it matters only for a select few. Our education system is built around both overt and quiet classifying of students—what I refer to as sorting.
Ultimately, children don’t have to be told they’re bad at math; they tell themselves. They sort themselves out based on the accumulation of negative messages they’ve received. Further, the sorting system is so crushing (even for those who get sorted into the math pile) that we extinguish their curiosity for math altogether.
That’s the bad news. The good news is that we can all be math people if we change the goal of instruction from sorting to teaching. We came up with this system; we can design a better one.
To listen to the audio version read by author Shalinee Sharma, download the Next Big Idea App today:
