Shalinee Sharma spoke with Emily Freitag about the task of supporting the math learning needs of students that have had interrupted schooling. 

Shalinee Sharma is the Co-founder and CEO of Zearn, a nonprofit curriculum publisher and software developer and creator of Zearn Math, a K-5 math curriculum and professional development platform that supports daily differentiation and engagement in mathematics teaching and learning.

Watch the full conversation or read the abridged Q&A below.

EF: Please tell us about your journey as a learner and what that teaches you about learning.

SS: In thinking about my own journey as a learner, I struggle to find just one story that represents my experiences. Instead, several memories come to mind—kind of like a movie—of different times when I felt really proud of myself as a learner, or embarrassed, or mad. It’s always these intense emotions. One salient thing that sticks with me as I think through these emotions is that as a child, I thought that getting something right was magical, as opposed to something that I had control over. As a young learner, I was definitely a people-pleaser. I just wanted my teachers to like me and to be a good girl. I would get a good grade or a smiley face on my paper, and I often didn’t know the inputs I had to put in to get that output. I just thought of it as magic. As a result, I would be superstitious and try to do whatever I could, such as wear specific clothes. However, I got really lucky over my learning journey because a few teachers took the time to disabuse me of those notions and teach me how to learn.

One example is the idea of simple learning practice, being able to repeat back what I’d just learned. I would close the chapter I finished reading in a science or social studies text and say back what I think happened in that reading. Let’s say someone is teaching me a math concept. Can I now change up the numbers and do it again? Those sorts of prompts and tips got me through my learning journey. At some point—and for me, that point was college—I finally understood that learning was less about luck and more about whether I could master a topic by reaching a deep understanding, ensuring I understood the topic by repeating back what I’d learned and moving forward from there.

EF: I appreciate hearing that story. So tell us from your experience at Zearn. From the data you all look at, and from your experience across education, what do you feel that we can really anchor to as we prepare to support the learning needs of students that have had interrupted schooling?

SS: The most difficult year of American education will be next year, not this year. And this year was already very challenging. We actually learned many of the answers to supporting the learning needs of our students a long time ago, and they’re sitting deep in the research base. I’ll just give you a couple examples—though there’s certainly more than two. We’ll stick with math because that’s an area in which I have deeper knowledge.

We know that kids are more successful in learning, enjoying, and retaining content over long periods of time when they experience concepts in new contexts. Mathematics, which is conceptual, makes more sense when presented as an idea versus a series of procedures or a trick. How I remember math as a child, and how math is often taught, is that you flip the page to the next chapter and see a brand new thing that you are going to learn. By contrast, when math is presented as a slow progression of a few big ideas, we see that children learn it better and enjoy it more. They are also able to then show that understanding in new contexts and over a longer period of time.

As we think about how we approach math at any time—and certainly within the constraints of the coming year—there’s no room for math by card tricks. We really have to teach the few deep ideas of math. This is the type of takeaway we learned and articulated in the 1990s when America did really poorly on the TIMSS exam relative to other countries. Those studies were conducted by famous researchers like Jim Stigler, and then synthesized by Tom Loveless at Brookings, and their findings are just as important next year as they’ve been over the last 20 or 30 years. 

As we think about how we approach math at any time—and certainly within the constraints of the coming year—there’s no room for math by card tricks. We really have to teach the few deep ideas of math.

The second example I’ll share is that when teachers build the pedagogical content knowledge of the exact thing they’re going to teach—not the standards or abstract concepts, but the exact unit and lessons—they are much less likely to skip children over the hard work in a grade. We see this in jaw-dropping ways in our data. Teachers are basically half as likely to skip kids over the most important work within a grade. I’ll give you a specific example. In second grade, one of the culminating difficult concepts in math is multi-digit addition and subtraction with regrouping. We see that when teachers build pedagogical content knowledge of this topic, they’re much less likely to skip kids over that content. That content was historically sitting in third grade in many states, and so teachers who taught for a long time are thinking, “This is third grade. I don’t need to do this.” But when we take the time to build that pedagogical content knowledge, kids get better exposure.

EF: And can you make that knowledge just a little more tangible for us? What’s the substance of the launch that they need to do before doing that work?

SS: The specific PCK that we believe is most relevant for teachers to support all their students, based on our data, is a knowledge of what comes before and what’s coming next. This has a huge impact on teachers because when you efficiently present to them what this is building on from first grade, and what are the implications of not doing this for third grade learning, 99.9% of teachers say: “I’m on it.” If you explain how everything fits together, in a teacher-friendly way, that creates deep motivation for teachers.

The second example of specific PCK is to explicitly explain, model, and explore together the multiple access points to math concepts. For example, the standard algorithm is just one way to solve. There are actually other algorithms and representations, like using a place value chart and solving concretely. There are multiple access points, and it’s important to take the time to show how all of these access points work and connect to one another. Teachers then walk away feeling that they have a real toolkit to teach this content. They also implicitly have a remediation toolkit as well, because if a student is stuck, they have a new way to describe the problem using different access points.

The classic approach would be, “What’s four plus two?” That question has nothing to do with grade-level concepts being taught to students. To solve this question, we need to unbundle 100. Right? So we are taking it back down to math from the prior year, which is actually its own concept. In second grade, we’re talking about unbundling. In first grade, we’re adding or subtracting single-digit numbers. Those aren’t the same mathematical ideas. We find that giving teachers an easy-to-use, practical toolkit is really impactful.

This is often not how teachers were themselves taught. But teachers, too, can learn these things. We know we’ve reached them when teachers say, “Wow, I wish I had learned math this way… I have to teach kids this way.” Because it is true that we were not taught math in a way that was very helpful.

EF: Bring us into the tension that we see many educators grappling with between, “I have to meet kids where they are and I have to hold the bar high.” From your data and your understanding of mathematics, what should educators keep in mind as they try to think about what the right thing to do is to help advance student learning?

SS: I think the simple way to think about math is that it’s not actually broken horizontally. “First-grade mathematics” is, in fact, arbitrary. That’s why when we change the standards, we move math from grade to grade—those grades themselves are arbitrary. Math is actually a vertical progression. In third grade, we explore fractions. In fourth grade, we explore fractions in decimals. In fifth grade, we operate with fractions and decimals. This is one vertical idea of math that we’ve taken and broken up into different grade levels. One tricky thing with how we discuss and describe math, is that we will categorize a child as being in second-grade math or we will categorize the work as being second-grade math. But really, this could just be an inefficient or incorrect way to look at it.

For example, a child in third grade could be excelling in multiplication and division because their grounding in addition and repeated addition is really strong. And so if the conceptual description of multiplication and division is as an array, they’ve got it. But then they get to fractions, and things aren’t going well. The reason doesn’t lie in second grade; the reason actually still lies in third grade because we really only open fractions up in third grade. So what would it accomplish to send the child back to second grade? It wouldn’t do anything. What we really need to do is meet that child where they are struggling with third-grade fractions. That’s very important in mathematics. We need to present these concepts in a different way.

That’s why I would say that sometimes, there’s a place to go back—and that’s great. We can efficiently go back, revisit a concept, and come back to grade-level math. But many times, there’s nowhere to go back. We’re just soothing ourselves by saying, “Oh, this child is struggling in third grade; let’s put them in second grade.” There’s no help in second grade for that third-grade math. This is all because we use phrases like “second-grade math”, which is itself a fake construct.

EF: Interesting. Are there real constructs? What are the load bearing walls that we do need to go back to?

SS: I think there are load-bearing walls, and they’re pretty nuanced. We built portions of Zearn Math based on this idea. I’ll give you some examples of load-bearing walls that we see.

By the end of kindergarten, a kindergartener should be able to count in any direction starting with any number, ideally within 100 but definitely within 20. If I say to the child “17” and the direction is “count down.” that child would say, “16, 15, 14”, right? Counting, starting with any number in any direction. It sounds unbelievable that this is a load-bearing wall. But quite literally, children can’t subtract in second grade because of that load-bearing wall. The simple reason is that children spend so much time counting forward. As a result, they can add because they use count-on strategies. But they didn’t get enough practice counting backward—and when we subtract, we are initially counting down as a strategy. So that’s a load-bearing wall.

Another example is helping children move out of counting-on in a scaffolded and intentional way. We have fourth-graders who may see two four-digit numbers stacked with an algorithm. If in the ones place you have two and four, their first step is to count “1, 2, 3, 4, 5, 6” straight up with their hands. At this point, there’s a lot more math coming, and we can’t put that much energy in knowing that two plus four is six, right? This really comes in with what you can call “fast facts”, which make solving problems easier. If I asked you to solve 13 plus 18, it’s a lot of work to count up to 18. But maybe instead you say that 13 plus 18 creates two 10s. And then we have three and eight—and I know two and eight are 10. So that’s one more 10, with a one leftover. The answer is 31. That takes much less cognitive load, right? These are alternative strategies of making easier problems. When we get to fourth grade, and we’re putting all the operations together, children’s cognitive load gets overwhelmed. So that’s another load-bearing wall.

EF: What’s something that people might think they need to go back to that actually they don’t?

SS: When we begin third grade, and multiplication or division isn’t going well, you might say, “let’s go back to second grade.” But there is nothing there for you. There are no load-bearing walls before this work—it’s a new concept. Teach it another way, teach it another way, teach it another way. Let’s say fractions is not going well. There’s nothing behind this. Teach it another way, teach it another way. Over the course of K–5, we open up these big concepts. We need to keep teaching them in different ways and not go back, because there’s not much behind them.

Over the course of K–5, we open up these big concepts. We need to keep teaching them in different ways and not go back, because there’s not much behind them.

EF: There’s a lot of push right now that we have to make sure we’re diagnosing kids when they come back so we know what they need to know. Can you tell us what you think wise and unwise uses of assessment might be when we come back?

SS: I would say it’s important to remember that all our children had a really hard spring—this pandemic is harder on children than it is on adults. Children’s lives are fundamentally social; they are always playing with their friends. That’s what they do. That’s how they learn. Now most of them are isolated at home, and it’s very abnormal. God willing, they do go back in the fall. When we think about how we want to support all these children and whether to “diagnose” them, you have to be sure you are able to do something with information from the diagnosis; you would give them something different based on what you learn. If my own child is diagnosed with needing more support, then you better have those supports. I don’t want a diagnosis that says, you have a terminal illness but there’s nothing we can do about it. Right? If there’s a diagnosis that would actually affect the teaching plan and modify the supports we give to children, that’s very interesting. If we’re not doing that, then don’t do the diagnosis.

Then I think we also have to look at the diagnosis. Is a 45-minute diagnosis going to tell you enough? I want to be sure the diagnosis is expansive enough, covering the right information. At Zearn, the first unit of each of our missions is a diagnostic. It’s the whole unit and is a month long, so I feel really comfortable. You get a month of data as a teacher to make appropriate decisions. I’m nervous giving a 45-minute diagnostic to children who haven’t been in school, and then making big decisions for those children based on the results.

EF: The labeling and sorting decisions we’ve explored can have such adverse consequences on identity in lasting lasting ways.

Any final thoughts? If you were talking to a lot of principals, what would you urge leaders to hold on to?

SS: I would say, this year was so difficult. Thank you for your hard work. And next year is going to be a lot harder. We should think about using the summer to support children as best we can. Think about what a child needs in order to feel successful when they come back. What could they do this summer? They don’t have camp, but what could they do over the summer to feel successful in fourth grade? The summer is not over—it’s just the beginning, and we can email or text families to ask, can we do anything to help?

Again, children are fundamentally social, and their social emotional learning has not progressed normally. So before we double-block reading and math, just remember that they are the ones who had a more isolating and more strange experience than we did. We have to ask, how can we support them?

The last thing I would say is that we also need to use next summer. There’s only so much that can happen in a day for teachers and for students. So let’s do our best to use this summer a bit in addition to all of next year, and next summer as well.