A while ago, I published a newsletter on literacy, with education professor Emily Solari. There were big lessons there, and I’m happy to see (not due to me, obviously) that the importance of phonics has come to the fore in the past couple of years. Many people wrote in to ask whether there were a similar set of lessons for math or, more generally, what we know about math learning.

I’m delighted today to talk about these questions with Shalinee Sharma, co-founder of the nonprofit curriculum development company Zearn. I got to know Shalinee during the pandemic, and I wrote about some of the warning signs on lost learning coming out of the Zearn data as early as spring 2020.

This is one where it may be good in audio, but the transcript is also below if you’re a reader.

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Emily: I am incredibly pleased to be here with Shalinee Sharma, the CEO of Zearn, who is going to talk to us about math. So to get started, can you just introduce yourself a little bit and tell us very briefly about Zearn?

Shalinee: Hi, Emily, thanks for having me. My name is Shalinee Sharma, and I am the CEO and co-founder of Zearn. By way of an intro, I will just say that I took a wandering path to math and I am by no means a math genius. I’m exactly the opposite. And I am proof of the core mission of Zearn, which is: all kids are math kids. And about 10 years ago with a bunch of teacher friends, I founded an education technology nonprofit called Zearn and we built a learning platform where we teach kids math. And we build a technology that complements teaching. We’re used by one in four elementary school kids in the country. And as I mentioned before, the core belief of Zearn is that all kids are math kids. And when you’re on Zearn, making mistakes is how you learn, and we try to make math both fun and make sense.

Emily: Are you used primarily in schools? Primarily by individual parents? Just to give people a sense of, like, where are they seeing Zearn?

Shalinee: Sure. So that was simpler before the pandemic began about two and a half years ago…

Emily: Everything was simpler before the pandemic began.

Shalinee: So most of the time, if you read all the educational studies, and even as we see the math scores come out, you’ll see that math is taught and learned in schools. That’s where we build our math brains. Whereas we’ll see with the test scores that come out soon that reading is something that happens at home and at school. Personally, I would love to see math learning happening in more places, but because math learning is happening in school, that’s where we started and we began.

And so Zearn’s user experience and how it’s built is, really, it’s built by teachers for teaching. So if you’re inside of the Zearn experience, you’ll see it as technology that really complements teaching. And so before the pandemic, as a result, 99% of the use of Zearn was during the school day, during the school weeks, and if it was the weekend or the summer, the app usage was almost gone. Once the pandemic hit, that changed pretty dramatically. And so math moved out of the school day into summer, into after-school hours, into what looks like weekends.

That isn’t just because parents jumped on. So a lot of parents did sign up and create free accounts, as a nonprofit. We want to make great math accessible to all kids. And so you can set up a free account on Zearn.org as a parent, as a teacher, and as a tutor, and support kids learning math. But also we support schools and districts with all sorts of additional supports and services. And for that, there’s a fee, and that allows us to be a sustainable organization.

And so pushing math out of the traditional 8 to 3, Monday to Friday, months of the school year — that is happening, and it’s driven by states creating after-school programs and tutoring programs, or it’s driven by local communities supporting their students. After school, community centers — it’s driven by parents. So what you will see now is the Zearn usage on the app platform data bleeds out of the school day, bleeds into the summer. I think that’s wonderful, because children do need some extended time and support for the time that they missed. And we certainly, as a technology, can fit anytime in the day; you just load a browser. So we’re really excited to support all of those new extended-time areas of math learning that are happening.

Emily: Yeah, and we’re going to come back, I have some questions about pandemic-related things, but I wanted to ask something that has been on my mind because we’ve seen so much of this discussion in reading.

So when we talk about literacy of late, there has been a strong push, movement, in the direction of recognizing that phonics is really important. And that in a lot of places we’ve been effectively teaching reading wrong, with too much focus on balanced literacy and not enough on the basics of phonics. And so if I wanted to summarize that, I would say there are many people who would say we’ve literally been doing this wrong for several decades. Is that true in math? Is there a phonics equivalent in math that we’re missing?

Shalinee: I love that question. I love so many of your questions, Emily. And so I love this question too, and I’m so happy to share and also sad to share that the answer is, yes, we are doing it wrong and there is something that is missing.

When you see students succeed in math or you see entire countries succeed in mathematics, in a way that our country isn’t, there are a few commonalities that we see. The first one, I think, should be a relief to all of us, because it’s actually how our brains work, which is that x’s and ys and symbols and all that gobbledygook — it’s hard to understand. And so, even if you’re a world-leading economist, you are going to try to understand what you’re working on with pictures, with metaphors, and with really concrete and simple representations in your mind. I was listening to a podcast recently, and there was the creation of a periodic table of elements, which [was by] a scientist named Mendeleev, and he just kept thinking about elements and then he just dreamed a table and he was like, okay, if I just put it in a table, it will all make sense. And so this idea that even people at the very top of their games as scientists or mathematicians, they still need pictures — they still need full representations.

And that is the equivalent of the focus on phonics. We need to make it concrete. The human brain, the majority of our experience on earth, is in the concrete world. We understand concrete. And all of mathematics can be represented concretely.

So I’ll just give you the simplest example, which is, unfortunately, a tricky question for a lot of people, but what number is bigger: one-half or one-third, which one is a bigger number? Okay. So if I asked you that question, you might have to think for a minute, because one-half is a bigger number than one-third, but two is a smaller number than three. And so that’s confusing. And so then you might memorize some rule, which is when you’re looking at fractions, you flip it and the bigger numbers are smaller. Okay. Gosh, good luck remembering that. Instead, imagine a cake. Do you want half of it? Or do you want a third of it? Okay, I still don’t get it. Do you want a cake? Do you want to split it with two people or do you want to split it with three people? No, I’ll just split it with two people. I want to have that cake.

Well, the more we can help children and adults bring all of these symbols into what they really mean using stories, concrete objects, pictures — the more math makes sense, the more children understand math. And this is what you see uniformly in all the top OECD countries, that is the core structure of their mathematics. So that’s what I would say if I had to pick only one thing. There’s a couple more, but I would leave it with concrete pictures and objects.

Emily: I find that interesting, because it is reflective of the differences I see in the way I learned math and the way my kids are learning math. And I will say I’m very pleased with the way my kids’ school does math, although occasionally I am wondering why it’s not the way that I did it. Like a concrete example for me is in how we approach multiplication. So when I was in school, we really more or less just started with: there are a set of facts called multiplication tables, and you memorize them and that’s the beginning of multiplication. They explain: there’s a symbol, it’s called “x,” it’s multiplication. Maybe we spent seven minutes on what it meant and then we just went to memorization. And when my kids started multiplication, there was so much emphasis on the idea of arrays, years of discussion of arrays, and we’re putting the cans in a row and we’re trying to understand what that means.

And only once we got really far down that road did we get into, okay, actually it’s helpful if you’ve memorized these facts, but that was so, so secondary to the way that I learned it. And I think for many parents, it feels a little bit weird, right? And it relates to some of these new math ideas that the way that our kids are learning, this is not the way we learned it.

And it makes us feel, in some ways, a bit afraid and also unable to engage with it. So, you know, my daughter will come home with these… she’s got some thing in fractions where there’s a big one and she seems to find it very helpful, but I can’t figure out what it’s about. And I think a lot of parents have that sort of, there’s a discomfort, which maybe we already had with math and is even worse when our kids are coming home doing math in ways we don’t expect.

Shalinee: Yeah, I mean, I think you’ve hit three topics. And at some point, I’ll let you guide us to delve into all of them. For a lot of folks, success in math or lack of success in math made them question themselves as learners. Like, am I a good learner? And your success in math when you were 7 or 8 was defining that. Well, I’m a good learner only at some things, or I’m a great learner, or, when it gets hard, that’s a sign I should stop. Or when it gets hard, that actually is learning. That’s what that feeling is.

And so, so much of the definition in our framing of learning and what is learning, unfortunately, it was framed in often humiliating and high-stakes ways in math, and it didn’t have to be like that. So I think that’s one thing that’s coming up for all of us. And the second thing is this question of concepts versus procedures. And there’s a great Economist piece, where in the Economist voice they’re critiquing America as if we’re like their dumb little brother, which is their voice, which I love.

Emily: I love that part of The Economist. If you listen to it in audio and they read it in the British accent, that’s the win.

Shalinee: Perfect. And the piece concludes with something like — I’m not going to get it, as you know, exactly right — but something like, as usual, America is swaying from one end to the other end of the pendulum and just can’t get it right.

And so that’s what’s going on with learning concepts like arrays, which are concepts that the most advanced STEM workers are applying to their work. And so it’s an idea you better understand if you want a STEM career, and it’s also an idea that makes multiplication easier and simpler to understand. But you can spend so much time in arrays that actually you don’t know what three times three is. And then, on the other hand, there’s how I learned multiplication, which is just straight memorization. And then, you know, you sprinkle on top of that my parents from India who were like, well, why don’t you just memorize your 15-times tables too.

Emily: That’ll be more efficient, just go all the way.

Shalinee: And it’s not on the test! And so, this kind of rote memorization. And it is the case that if you look at the last, probably 70 years of America, at least since the 1950s, you see American education swinging from one pendulum to the other. And what you see consistently [in] countries that are outperforming the United States is they do both. So they are able to present concepts so children understand multiplication. And they’re able to get automaticity with key facts so that children’s working memory is cleared and they can do other things and they’re not sitting and putting cans out to figure out what nine by nine is. Cause you can’t bring thousands of cans to the SAT. So you gotta at some point know this stuff.

But the last thing I would just want to say is that I could not explain why three times zero is zero in college. Like, I couldn’t explain that. And you know, that’s startling to me that I can’t explain that. My children can.

Emily: What is the explanation, just for those of us who are now struggling with this?

Shalinee: So let’s say, we always say that when we’re multiplying, we’re talking about plates of cookies. Obviously, I’m talking about cakes and cookies, so you can see where my mind is this morning. So three plates with zero cookies on them. That’s what three times zero means. So you have three plates in front of you and they all have zero cookies on them. So how many cookies are on all the plates? “Mama, that’s a dumb question. Zero. There are no cookies on any plates.” So much clarity, right? And so, okay, got it. So then what’s three times one? Well, there are three plates and each has one cookie on it. Obviously, there are three cookies.

And that is proof-level thinking, right? That’s all the way to getting to a proof, to a fundamental axiomatic understanding of mathematics. Think about that. So that’s one of the cool things, is when we do present concepts to children, they can understand math at the axiomatic level.

Emily: I think that’s great. I mean, the other thing that has happened in this more recent period that I find very interesting is the earlier move to representational mathematics — to the idea of things that look kind of like algebra showing up for even my first grader, where it’s three plus fill-in-the-blank is five. What is the blank? And recognizing that that is effectively algebra, but it’s not presented in this scary way where it’s an x, but then later when you get to the x, it’s like, I saw this before so it’s not so terrifying.

Shalinee: We’re starting to hit some of the other things that are back to, like, the science of reading. So the first one I said was pictures and objects. And the second one we just talked about, that other countries are doing, is they’re balancing concepts and procedures, concepts and memorization. They’re balancing that — we tend to swing. And this is the last one you just hit, which is building mathematical understanding so it’s flexible, and that flexibility you name is algebra, which could be a great name for it. But that flexibility gives you the trust in math. So if I added these numbers, how do I know that I’m right? Well, I can subtract them. I’m totally in control of this. Using a technical term, this is autodidactic. I check myself and I can learn myself if I’m right or wrong. And so that’s what we teach when we teach three plus blank is five. We teach that it can go in both directions and that it must go in both directions. And so you have a way to always check.

Emily: Yeah, which of course reinforces more than just having memorized the three plus two is five, which is a fact devoid of the broader context. This is not what we’re going to talk about today, but one of the things that always comes up for me here is the realization that as we make some progress on doing this in the elementary school math, I would really like us to make more progress on data parallel to this. So, you know, my kids, I think, learn this kind of math really well. The truth is when we get to data, they think that data is just asking your friends how many pets they have and putting it in a chart. And that to me is not all of the things that you can do with evidence. Maybe someday we can develop some more tools for having people understand correlation and causality in the first grade, but we’ll do that offline.

So I wanted to step back to the pandemic at least briefly to talk about recovery. So one of the things that I’d been studying over the last couple of years, and I know we’ve talked about, is the fact that there have been tremendous learning losses broadly more in places that were more remote, but in general this has not been a period of tremendous learning for kids. And it means that a lot of kids are coming into this school year, but also came into the last school year, very far behind. And there are a couple of different ways one could approach someone who is coming into the fifth grade effectively not having done fourth-grade math. One way that we can approach that is to redo fourth-grade math in the fifth grade and then somehow try to do it more. Another way we can do it is start with the fifth-grade math and try to backfill. Do you want to tell me what you guys have learned about the right way to do that?

Shalinee: Yeah. So, we have millions of kids doing billions of problems on our web application. And so with that, there’s so much data, and I too have a love of data analytics, as you do, Emily, though I rely on these wonderful data scientists in the Zearn team. But we’re always combing and looking and asking our data questions. And so one of the questions we asked last school year, as teachers are going back into the classrooms and schools getting started, was what exactly should kids do who had missed… Let’s take the example, I’m a mom, I have fifth-grade twin boys. Fourth grade was heavily disrupted for my children and they were starting fifth grade. And so the question is very real for me and hits home, which is what should fifth-grade teachers be doing?

As luck would have it, because there’s so much activity on the app, there’s a natural experiment that one of your fellow data science advocates for the first grade, Steve Levitt, we were chatting with him and he sort of discovered that as we were talking things through and how behavior on the application was working, he’s like, I think there might be a natural experiment inside the app that happened then. He’s like, so you’re telling me that some teachers went back and retaught a lot of fourth grade and they made that instructional decision using your software, this technology that complements teaching, that’s what they chose to do? And some teachers began with fifth grade and either the software itself supported students with the bits of fourth and third they needed exactly when they needed it, and occasionally supported with a little bit more fourth, but primarily took kids through fifth grade. And I said, yeah, that did happen. He’s like, great, let’s look at it. What happened?

And I’m not exaggerating when I say that, when I saw the analysis, I fell out of my chair. I could not believe it. I made everyone do it again. So both sets of children had fourth grade disrupted. One group went back and did many, many lessons, weeks of fourth grade before they moved to fifth grade. And one group of children started with fifth grade and only had snippets, surgical slices of fourth grade put in as they were moving through fifth grade.

So obviously the group of students that did mostly fifth grade got more fifth-grade math learned. But what was shocking is the fifth-grade students, the students who did mostly fifth-grade content, they struggled less. So they threw up fewer struggle alerts on our platform. When a student is struggling, an alert hits the teacher, and those students threw up fewer alerts. So somehow doing the fifth-grade content and only getting presented with help when they didn’t understand it was easier for the children to work through than redoing swaths of fourth grade that they had experienced the year before, but it didn’t make sense then, doesn’t make sense now.

I can’t exactly explain either the brain science of that or the psychology of that; it’s astounding. And more to come in the next month or two — we’ll come back and share it with you, but we’re doing that analysis again at a deeper level to see what it continues to show.

Emily: That’s incredible and in some ways surprising, but I think also extremely valuable, not just for pandemic recovery, but in general, for thinking about how we help kids move forward and how we address inequities and all of the other questions that have been exacerbated, but they’re not new to this period.

Okay. So I am going to end there because I feel like you and I, as usual, could talk for like three hours. But we’ll save it; we’ll have you back. Thank you for doing this, and I really appreciate it. And I will say just for people who are listening that my kids really love Zearn. It generates a lot of interesting data and also is quite fun. They have particular teachers that they like the best.

Shalinee: Who do they like the best?

Emily: Mrs. Johnson. She’s popular.

Shalinee: For a long time my kids’ favorite teacher was Mr. Sawicki, who they thought was Mr. Zucchini.

Emily: We like Mr. Sawicki, he’s good. All right, thank you so much.