I first encountered Shalinee Sharma back in the early summer of 2020. Shalinee runs an online math platform called Zearn, which serves many schools in the U.S. and many more individual children. In the midst of the COVID pandemic, Zearn was teaching my kids math *and* providing some of the most compelling early evidence on the impacts of remote learning on math scores (conclusion: bad).

Since that time, Shalinee has continued to be one of my favorite people to talk with about math and math education. I would say, in the nicest possible way, that she is a math zealot — a person who really, truly believes that all kids can not only succeed in math but love it.

Her new book, *Math Mind*, puts that belief onto the page. It’s a guide to how we can make all kids “math kids.” The book is great for many reasons — it’s something you’ll want to give as a gift to both your child’s best math teacher and their worst one — and today we talk about why she wrote it, what she hopes people will get from it, and how schools can do math better.

Here are three highlights from the conversation:

## Do kids learn math through memorization?

It’s a metaphor, but it’s very intentionally provided, which is because in math we prize memorization over understanding, and we should just do both. If you get into these silly math wars, people are like, “Well, should you memorize or should you understand?” And it’s like, well, how about both?

Let’s take that with multiplication. This is one of my favorite problems. Tell me the proof to why n times zero equals zero. When I ask most folks the answer to that question, they don’t know the answer.

**Why are my kids being taught math differently than I was?**

The way my kids seem to have learned this, they eventually did get to some kind of stacking and carrying, but the first thing and the way that they default to, is this “we’re breaking it up into the pieces and we’re adding the…” I’m not even sure I could really replicate it, but it definitely involves breaking things down and combining them. Can you explain to me why that’s a good idea instead of the stacking?

If we’re going to add, let’s say, 37 and 13, the answer can only be 50. That’s it. There’s no other option. Emily, you’re welcome to stack in your head, but I’m going to say 30 plus 10 plus 7 plus 3. That’s just how I want to do it. And I know a 7 and 3 are automatically a 10, so I’m really just going to add 30 plus 10 plus 10. And so what that tells me is, I get to do it my way and you can do it your way. And what it allows for is creativity and problem-solving.

And then the meta learning, why that really matters in real life — particularly if you think about your work and how creative your work has been — is that we need STEM workers, and we need workers in general to think about problems creatively and think about many ways to solve them. And so when we teach mathematics in a way where children have many ways at the problem, their many ways are accepted, though the answer is still 50. There’s no other option, but there are many ways at it.

Now, I’m not saying that new math is always presented with that big-picture lesson — that it’s about creativity, trying a different way, feeling empowered in mathematics — but it absolutely needs to be. And if you think about the children who feel most successful in mathematics and then are in a position to go on to do a STEM degree, they have that lesson in their own head.

**What do we need to change about our math education system? **

In contrast, the idea that kids could go to kindergarten through eighth grade and come out with the vast majority of them failing any math test you give them, including the NAEP or these well-regarded math tests, so thus they’re innumerate, is completely acceptable. And instead of blaming the adults where we say, “Let’s not be mean to the kids, because they’re not math kids. It’s okay, they love ballet and soccer.” You’re like, what? How is that related to what we’re talking about? And so I think the first is just belief, and we just don’t have it collectively. Parents don’t believe yet enough in their kids. Teachers don’t yet believe enough in their students. Governors don’t believe enough in this. We just don’t have enough belief. The first is just, let’s believe.

If you give me a second one, I would say that it’s what I talked about earlier, which is we have to pair understanding with memorizing. And the best way to understand really anything, but especially math, is simple pictures, concrete context — just make it feel real, not abstract and theoretical. What’s a negative number? Well, think about sea level is zero, and then you dive into the ocean — that’s a negative number. And then you climb a mountain, well, that’s a positive number. Okay, I’m not talking about things that are extremely elaborate, but bringing pictures, real context.

We just need pictures to be a part of mathematics. And right now what happens is we have abstract symbols that are shorthand for pictures, and that shorthand for pictures, we need. You can’t draw a picture at the SAT, right? So if you’re taking the SAT, you need to be doing more abstract mathematics. So I’m not against, in high-stakes contexts, abstract mathematics, but you have to pair that with understanding, and the simplest path to understanding are pictures.

## Full transcript

*This transcript was automatically generated and may contain small errors.*

When I got to high school, I still thought of myself as a math kid, but by the end of high school I didn’t. There came a point at which I decided I wasn’t that good at math. I hit something that I found really hard and I didn’t have the mentorship, the advice, the stick-to-itiveness to push through that. And now if you asked me, “Are you good at math?” I would say “Not really”. And I realize how that sounds. I have a PhD in economics, I do data for a living. But I don’t think of myself as someone who’s very good at math. And I think that is a position widely shared by almost everyone, whether it was the end of high school, sometime in college, sometime in elementary school, I think most of us at some point decided, well, I’m not really a math kid.

We got to a point where mastery was hard, where the thing we were doing was so difficult that we kind of stopped. And we don’t really do that in English. You learn to read and you never decide well, I’m not a reading kid. I’m not good at reading. We all read. But we do often decide we’re not a math kid. And my guest today would like to push back on that. Shalinee Sharma is the founder of Zearn, an online math platform. She has a new book out called Math Mind, The Simple Path to Loving Math. And her core claim in this book is that every kid is a math kid, and that in order to do math education better, in order to serve our kids better, we need to have that core belief about our kids and probably also about ourselves. Every kid is a math kid.

In this conversation, we get into a little more detail about math learning. We talk about the question of memorization versus deeper learning. We talk about creativity and problem solving. We get into the question of why our kids are doing something called the new math and why it terrifies us and looks ridiculous, and nevertheless, still might be a good idea. And we talk about how to get kids excited about the tools of math and how they can unlock the secrets of the universe and be really, really fun.

After the break, Shalinee Sharma.

And when the idea of Zearn came about, which was their idea, the idea that they brought forward is, what if we put the best math teaching and learning up online for free for everyone, could we change the world? And my background, I had worked at Bain & Company, and had done a lot of tech and digital transformation, and I thought, I could be useful to you. That’s a great idea. I could help with that. And it’s actually in working with them that I’ve fallen in love with teaching and teaching and learning, but my main contribution is still actually the arms and legs of the digital transformation of Zearn.

And so Zearn provides that complement, that support to teachers and to families, of that 10 to 20 minutes every day, where it’s practice, but it’s also learning and understanding. One of the issues with just going about doing mathematics and practicing, is if you don’t understand anything, what would be the point of practicing? You need to understand and practice, and that’s really important, and what we offer in Zearn.

It’s a metaphor, but it’s very intentionally provided, which is in math we prize memorization over understanding, and we should just do both. If you get into these silly math wars, people are like, “Well, should you memorize or should you understand?” And it’s like, well just how about both? How about just both? Let’s take that with multiplication. This is one of my favorite problems. Tell me the proof to why N times zero equals zero. When I ask most folks the answer to that question, they don’t know the answer.

If you take that forward and you say well we have three plates and each plate has zero cookies, well if you imagine that in your mind three times zero is zero, now if you have eight plates and they have zero cookies, now if you have a hundred plates and they have zero cookies, well then N times zero is always zero. And an eight-year-old can grasp this and enjoys grasping this.

And again, I’m not saying that we shouldn’t memorize, but if math is viewed by children and by adults as memorizing facts, first of all, that’s the empty calories of learning. But second of all, there is no way to build on that. There’s no way to build understanding. And really the parallel is memorize 400 words, memorize 100 more, and at the end you will be illiterate.

One of the things I… For a lot of parents, I think what is daunting about this, is this idea of the new math. Give you an example where I myself have struggled with what is this? Which is when you’re adding together three digit numbers, two, three digit numbers. And when I was in school, we pretty quickly got to the stacking mechanism, the stacking and carrying. I’m an excellent stacking and carrying, so good that I stack and carry in my head. If you told me add these three digit numbers together, I would imagine them in my head stacked, and I would do the stacking, and the carrying, and then I would give you the number.

The way my kids seem to have learned this, they eventually did get to some kind of stacking and carrying, but the first thing and the way that they default to, is this we’re breaking it up into the pieces and we’re adding the… I’m not even sure I could really replicate it, but it definitely involves breaking things down and combining them. Can you explain to me why that’s a good idea instead of the stacking?

If we’re going to add, let’s say 37 and 13, the answer can only be 50. That’s it. There’s no other option. But Emily, you’re welcome to stack in your head, but I’m going to say 30, plus 10, plus seven, plus three. That’s just how I want to do it. And I know a seven and three are automatically a 10, so I’m really just going to add 30, plus 10, plus 10. And so what that tells me, is I get to do it my way, and you can do it your way. And what it allows for, is creativity and problem solving.

And then the meta learning, why that really matters in real life, particularly if you think about your work and how creative your work has been, we need STEM workers and we need workers in general to think about problems creatively and think about many ways to solve them. And so when we teach mathematics in a way where children have many ways at the problem, their many ways are accepted, the answer is still 50. There’s no other option, but there’s many ways at it.

Now, I’m not saying that new math is always presented with that big picture lesson, that it’s about creativity, trying a different way, feeling empowered in mathematics, but it absolutely needs to be. And if you think about the children who feel most successful in mathematics and then are in a position to go on to do a STEM degree, they have that lesson in their own head.

And easier, I say in the book, easier is in the eye of the beholder. And when children are taught that, that part explicitly, so they’re not taught to sort of pare it back some new algorithm or some different way, but when they’re taught explicitly easier is in the eye of the beholder, there’s lots of cool ways we can solve this problem, that’s the big picture lesson that allows for both success and enjoyment in mathematics.

If math is that I kind of have no clue what’s going on, but I’m exactly imitating what the teacher did on the board, that’s not a class where your curiosity is burning and being stoked. But instead if we present it as, look, there’s a bunch of ways to solve this problem, what do you find interesting? Which way do you like to do it? And also the chance to share that with your peers, that’s also very empowering. And so I agree with you that we don’t always present it that way in math teaching and learning today.

In contrast, the idea that kids could go to kindergarten through eighth grade and come out, the vast majority of them failing any math test you give them, including the NAEP or these well-regarded math tests, so thus they’re enumerate, is completely acceptable. And instead of blaming the adults where we say, “Let’s not be mean to the kids because they’re not math kids. It’s okay, they love ballet and soccer.” You’re like, what? How is that related to what we’re talking about? And so I think the first is just belief and we just don’t have it collectively. Parents don’t believe yet enough in their kids. Teachers don’t yet believe enough in their students. Governors don’t believe enough in this. We just don’t have enough belief. The first is just let’s believe.

If you give me a second one, I would say that it’s what I talked about earlier, which is we have to pair understanding with memorizing. And the best way to understand really anything but especially math, is simple pictures, concrete context, just make it feel real, not abstract and theoretical. What’s a negative number? Well, think about sea level is zero and then you dive into the ocean, that’s a negative number. And then you climb a mountain, well that’s a positive number. Okay, I’m not talking about things that are extremely elaborate, but bringing pictures, real context. As you get to your level of mathematics, Emily, you would start using graphs a lot to explain.

I remember we’d go to the farmer’s market, I’d give them each $10 bucks and I’d say, “Go buy some fruits and vegetables. But by the way, you’re a little kid and people think you can’t calculate the change, so calculate the change before you hand over the money to make sure you get the right amount of money back.” The version of that that goes through the entirety of life of at the minimum numeracy is how you navigate the world around you, and those who are numerate are going to take advantage of you. That’s one of the benefits that I definitely bring home, which is don’t be the fool.

I think the other benefits that are in the realm of fun, sit often in the space of science. If you think of also economics, just all these fabulous applications of mathematics that are so interesting to the world around you and I think that with reading, we think the Twilight series is reading, but if reading is learning phonics, learning what words mean, being able to read with fluency, and then you get to read science fiction, to me, I think that the parallel would be you can actually understand an economics podcast and have a lot of fun reading it. You can actually read the New York Times coverage on inflation and actually understand it. It’s basically the access point to understand the world around you.

I think the second thing is just don’t panic math is all around you. And the simplest thing I would say is play board games or card games. There is not a board game or a card game out there that doesn’t have a dimension of mathematics, and there’re very fun, and they’re already sitting there. You know the public health messaging of read to your kid for 20 minutes a night something they love? Have board game night, play board games and card games with your family all the time.

And then the last thing I’d say is that utilize resources when your kid falls behind. The biggest difference between kids who feel… So I don’t know, Emily, if you’ve had this experience. I did. Through the course of high school and college, I felt successful in mathematics, but in middle school I fell really far behind and I just got super lucky. My teacher tried to help me and my dad jumped in as my tutor and I caught up. And one of the things we see in the Zearn data is that kids can catch up when they’re behind. But I think one of the structures in our society is that we believe that when kids fall behind, they’re revealing their math ability so there’s no point in catching them up.

Well, that is absurd and nonsense. We know kids can catch up. We have a really cool fixed effect model analysis of 600,000 students, that show that kids can catch up. I’m telling you at a population level, kids can catch up. And the difference between the kids who catch up and the kids who don’t, is an adult intervenes and gives them the resources and support. And so as a parent, intervene and help your kid access those resources and support. And if you don’t have them, ask your teacher for help. You’re welcome to go to Zearn.org. It’s free. There are other wonderful free resources online, but don’t give up, ask for help.

And I basically, at that point, decided, you know what? Calculus was kind of the end for me. And I never really seriously thought about being good at math again. I took statistics. It worked out fine, but now if you said, “Are you especially good at math?” I would say, “Not particularly.” It’s not exactly that I think it’s David Speyer’s fault, but I do feel at that point there would’ve been some value to somebody being like, “Hey, you actually are quite good at math. Maybe you’re not as good as David Speyer, but you’re really quite good.” Which is just to say that I think this value of realizing that this could happen to your kid at various points and the intervention could matter.

The first step is to really confront all these myths in math learning. Because if you don’t confront the myths, then it’s, yeah, math sucks, it’s really painful. You’re going to freaking do it. That’s the takeaway. And that’s just terrible. That’s not the takeaway. Math is beautiful and fun and full of dopamine hits of problem solving. So the first thing that I want you to do in the first section of the book, is let’s excavate a lot of those math myths and bin them, let’s put those in the trash and I think we can continuously do that.

And the second is the methods that make math fun, and to really explore those methods. And so those are things like making an easier problem, understanding what’s going on, not memorizing. Actually, the enjoyment of mathematics sits in the way in which we understand it. It’s basically a language, and it’s a really fun, and interesting, and universal language.

And then the last section of the book is what you should do, what are you going to do about it? And really here, I’m thinking most about parents and educators, and thinking about what they can do to support kids. And if there’s one action I really want parents, educators, and everyone to really think about is all kids fall behind at some point in math, all of them. The ones who continue in the world of mathematics and enjoy it, got some additional boost, some support. That could have been an emotional support, that could have been someone who just helped them think about what slope really means. Whatever it was, it wasn’t massive, but they got some additional support, they caught up, and then they kept going. And so when kids struggle in math, it doesn’t mean that it’s the moment now we sort them out of the math pipeline, and it doesn’t represent their fundamental ability. It’s just part of learning. In every other discipline of learning, we allow kids to catch up when they fall behind. In this discipline, we don’t.

My concluding chapter is talking about from sorting to teaching. What if we took the billions of dollars and the millions of hours of effort we’re putting behind math teaching and learning, and we didn’t orient it to sorting out the math kids, but we just oriented it to teaching every single kid math? What might happen?

Whereas in math, you’re moving up the ladder, you add, you subtract, you multiply, you divide, you do fractions. So it feels like you have to either keep going or you fall off the ladder. There’s no tree branching. If reading is a tree, where we can all get up to the limbs and then we walk our way out, and maybe some of us are going a bit higher, but we’re all kind of there, math is it’s a ladder, and when you’re done, we just throw you off into the pit of despair.

But here’s what I’d say, which is the idea of math as a lot of discrete skills, is a very dangerous myth, so let me give you an example. In seventh grade, we find, particularly post pandemic, a lot of seventh graders in the app are struggling with decimal division.

I’ll give you a simple problem, that this is actually in the Zearn app, 1.4 divided by two, can present struggle for students. So now what? Do we not present negative numbers? Because you have to learn all of this decimal division. Well, here’s what shocking finding of how fast kids can often catch up. 14 divided by two, what’s the answer to that question?

And that’s just, I think for parents, for teachers, that message is hard because you’re trying to tell someone you believe in them, while also telling them they got to put more in to get there.

It was totally just like, I’m sure that you can achieve that. But it was so different from how I think that would be presented now, and for probably good reason. But this idea of if you put in the time and you work hard, that is a huge part of what you can achieve, in some ways feels like the belief part of this conversation, just stated in a slightly different way. That I believe in you. It’s not that I believe you can do it, just sitting on your butt and never trying, but I believe that you can put in the time and that you can get there.

There are a lot of ways you can help people find out about us. Leave a rating or a review on Apple Podcasts, text your friend about something you learned from this episode, debate your mother-in-law about the merits of something parents do now that is totally different from what she did, post a story to your Instagram debunking a panic headline of your own, just remember to mention the podcast too. Right, Penelope?

Community Guidlines
## Log in

I love math and think I had an absolutely outstanding math education in K-12. So I’m really sad to see math education getting worse across the board in the US, where common core and its derivatives reign supreme and tie teachers’ hands. My 6yo just finished 1st grade, where his math class was either him trying to explain how he knows the answer to 7+2 to kids who can’t do it, or trying to teach himself math on an ipad. It’s the saddest thing ever. I am very against young kids having electronics in school. It’s no substitute for a teacher actually teaching him. But the teacher spends her time putting them in groups and telling them to explain easy problems to each other. All the individuation is on screens, which I think is scandalous. I am actively looking into where to move where we can have a school that teaches kids the way I was taught: minimal screens, maximal human engagement, customized by ability.