Shalinee Sharma: Revolutionizing Math Education for Every Student

28:46A simple example could be people are very tall. And if you're six foot seven, you have a different chance at being able to play professional basketball than if you are five foot seven. And so of course there's talent and passion, and those are different by person. And of course they fall in a bell curve, but that is unrelated to what I'm talking about. So of course there are a subset of children who will grow up to be professional NBA players, but that doesn't mean every single child can't play sports and can't participate on a team sport and get all the value of it. And no one ever opposes those two things, right?

29:25I would just say another example I'd say is of course there are going to be people who write Pulitzer prize winning novels, but that doesn't mean that you spending time in creative writing isn't extremely valuable for you and for others who get to read it and enjoy it. What if somebody says, I can go to Siri or I can go to Alexa and say, I have$100 to spend at Costco. I got to buy$50 worth of broccoli and meat. How much do I have left over? And Siri and Alexa and chat, GBT, anything will answer you. Why do I have to learn math? What do you say to that person? The same question could be asked, which is I can have Siri read any book aloud to me or Alexa, for example.

30:07I have asked other teachers that question. Yes. Yeah. And during the pandemic, when my sons were in third and fourth grade and I was working, a lot of times we would just have, you know, Alexa read books aloud to our kids as something that was a reasonable activity. So I think these tools are amazing and they increase engagement. They increase accessibility. Sometimes a child might be a later reader and this still lets them participate. So we can use a lot of these tools to support accessibility, to support on ramps for kids. But what we also know is the other side of a world with these kinds of tools is one with a lot more information, is one with a baseline of numeracy expected to be a lot higher as well as literacy.

30:52It's this funny kind of double edged sword, which is we can use these tools and we should. They are phenomenal on-ramps. We use them all through Zern. And so we should use these tools as on-ramps for students, but also know that this world, this digital and AI driven world now sets higher expectations of what humans can do. And so that's what's actually happening right now. Let's say that your kids or one of your sons has dyslexia. So reading is extremely hard for him, right? And before you would say, wow, if you cannot read, how are you going to get information about how to do things and how to learn how to, anything that's written in text.

31:35But now, you could, son, you can just go to YouTube and ask the question, how do I add an HP printer to a wireless network? You don't need to read that. There's a YouTube, there's probably 500 YouTube videos that explain that. So don't worry about your dyslexia, son. You don't need to be able to read. You can do everything is online. Can't you say the same thing about math? Yeah, I think for children who have learning differences, I don't think that parents of children who have dyslexia would want, I have a very good friend whose son is diagnosed as dyslexic. She doesn't want her son to not be able to read, but she wants a little more space and time to help her son read successfully, but then still be able to participate in everything with rigor.

32:21Actually, her son is very good at mathematics and loves it and feels really smart in math class. But if he has to read the problem, the word problem, then he doesn't feel that way. And so a read aloud support, like Zern has read aloud supports everywhere in YouTube, there would be accessible read aloud supports. That lets him still participate. And so maybe another child will be proficiently reading by second grade and this child might need till fifth or sixth. But in that time, what we want to be able to do is still let that child participate. For example, this child has an amazing ability to draw, an amazing ability to participate in math, just a phenomenal athlete, a great thinker, such a funny person.

33:02These are all the other attributes of the child. And if being unsuccessful in reading holds him back from participate in everything, you can imagine his confidence, his personality, all of that getting crushed. And so instead, what we want to do with when children do have learning differences, we don't want to lower our expectations and goals for those children. There are no parents out there who want that, but they just want different timelines and different supports so that kids can still access it. And so I would say the same in math. If digital tools are supporting your participation in mathematics, that's wonderful.

33:36And we should use all those tools. But that doesn't mean that we have a lower expectation. We still want that child to participate. When it comes to math, I'm constantly on this question about why math is so different. When it comes to math, I swear there are people who say of their kids, Johnny or Jane just isn't good in math. He's an athlete or she's creative. She can write, but she just cannot do math. They're saying, well, you cannot do math, but you can do other stuff. So don't worry about math. But aren't you kind of saying that everybody should have a basic level of mathematical facility?

34:17Yeah, what I'm saying is math is taught. Of course, there are a small set of people who have genetic gifts, and they can learn to read much faster, or they can play music much more quickly, or they can break a four minute mile and others can't. So of course, that is true and that will always be true. But what I'm saying is that norm where parents themselves will say, oh, this kid's just not a math kid, where we describe it as a rare genetic ability is wrong and has no science behind it and that math can be taught. And it is totally okay if it comes slower to others and faster to others. Let me give you an example with my own twins.

35:01I had a twin who was reading pretty successfully in kindergarten, which makes him an early reader. It was sort of odd how fast he learned how to read. And then the other twin wasn't really a fully successful reader till the back half of second grade, which makes him a late reader against these kind of norms. Can you imagine if in our household, we said or one of those children were to think that only one was supposed to read?

35:32That's a great story, but I believe, in fact, that is happening with math. I assure you it's happening. That is your belief, and I'm here to bring you data. It is happening. And at Zern, we prove every day that the primary way to learn math is to do math, and that when kids do math, they learn math. And so it isn't the case that now kids can develop at different paces. That's normal. But it isn't the case that we need to sort for those who have the rare genetic gift. We can teach all kids math. So then let's just numerate for us the basic myths of math so that people know when they're like basically saying something wrong or copying the wrong attitude.

36:20What are the myths that we should avoid? Yeah. So three myths, I think, And there could be more, but I'll share three. First, let me start with the top line, that there's a math kid. That's the top line myth. But let me share three in detail. One is that math is just about speed. So let's say you have minute math. So there's a problem and you have 60 seconds to do it. You can imagine that children will look at a problem and say, and we have research that proves this, that children will say, I can't do this problem in 60 seconds, so I'm dumb. but there's somebody else who can do this problem in 60 seconds.

36:56So this problem is for them. As opposed to, I can learn how to do this problem. I can get started in this problem. I can share how I'm approaching solving this problem. Now, as I said earlier, there is an integrative complexity here. Without automaticity or fluency of your math facts, math becomes too hard. It's just like how your computer, if you have too many simultaneous programs running and your computer just turns off, crashes, that metaphor is really apt. That's what happens to our brains. So if we're doing advanced mathematics and adding, as I shared earlier, an example, 13 plus 18 takes all our computing power.

37:36What ends up happening is we can't do that advanced mathematics. So we do need automaticity, but math is not a running race with only one person winning. That is not math. But Zern, we have a team of engineers, when they're solving interesting, hard computer science problems that are math, they're not shouting out answers as fast as they can. And they're not racing each other. They're calmly solving problems. There's a professor who's now the president of Dartmouth University, Sian Bylock. And she wrote this great book called choke. And what she did was she was testing speed and whether or not experts go faster and testing these hypotheses.

38:20So she structured this great experiment where she had physics undergraduates who had completed one course in physics compete against physics graduate students and professors of physics. And she gave both groups an accessible, it was a difficult problem, but accessible to the physics undergraduates who had done one course. And she was measuring and she timed them and she was measuring the speed at which they'd finished the problem plus the accuracy. And one prediction was that the undergraduates would be less accurate. And that prediction turned out to be correct. But the second prediction she had was that the graduate students and the professors, the experts, would be faster.

38:59And they were in fact slower. So the graduate student and physics students took much longer to set up the problem. But when it came to calculating, they actually flew through that. They were able to calculate correctly and quickly, but they took a lot of time to pause and set up the problem. The undergrads sped through setting up the problem and sped through the calculations. And often they set up the wrong problem. So even if they calculated correctly, they got the answer incorrect. And so this is something to understand, which is that it is about fast and slow. But a lot of times we position math as it's about fast.

39:38The last story I'll tell you which I love. A famous UCLA professor studied American first graders versus Japanese first graders. And he gave both groups of students a problem that was impossible to complete. And the American students sat for less than one minute and then handed the problem back to the teachers. And the Japanese students sat for 45 minutes trying to solve the problem. So just an example of that speed myth. I'll share a couple others more quickly though. So two others are that there's only one way to do a math problem, that the teacher up there showed me the way and I have to copy that way.

40:18So math is actually not creative. Math is about memorizing one way. Actually, that's not what math is at all. Now, there is one right answer, and that's actually beautiful. That makes math empowering and autodidactic. You can teach it to yourself because you can check to see if you got the answer. But there are hundreds of ways to solve a problem. And that invites you into engaging and exciting problem solving. And so that's another really important myth that we see in this country that children come to believe, but we don't see in top performing countries. And then the last myth is one where math is a series of tricks.

40:59So how do I solve this problem? I memorize this trick to do this problem. What is two divided by one half? Whenever I divide by a fraction, I change the division sign to a time sign and I flip the numbers. It's four. Okay. Well, what is two divided by one half? Why would I divide anything by a fraction? Can you give me a real world life example? What is two divided by one half? I don't know. I don't care. I just flip and multiply. That's not a way to learn and love math. And so I'll give you a concrete example of that could be I have two giant cookies and they're too big to give to someone to eat because they're just, they're enormous and unappetizing and too much sugar.

41:44So I'm going to break them each in half. And so now I have four pieces. And so that's a real world example where the math has meaning. So those are myths. Up next on Remarkable People. And so the most interesting question that we have in mathematics that pertains to kids who, let's say you want to help your child in ninth grade really turn it around in math, is how do you catch up and move forward?

42:18Thank you to all our regular podcast listeners. It's our pleasure and honor to make the show for you. If you find our show valuable, please do us a favor and subscribe, rate, and review it. Even better, forward it to a friend. A big mahalo to you for doing this. Welcome back to Remarkable People with Guy Kawasaki. I have to say that one of my favorite stories in your book was about the Burger King promotion where they said that our burger is a third of a pound and McDonald's is selling a burger that is a quarter pound. And people thought that a quarter pounder weighs more than a third pounder.

43:01That was a great story. And why are we at that point that it is something like that, which that's pretty basic. We're not talking about Steve Wolf from level Mathematica here. Where did we go wrong to be in a place like that? Yeah. So that's such a great story. The A &W third pounder versus quarter pounder, the test infractions that America failed. That to me is the exact myth of memorizing math. If I teach you, we're all really lucky that we didn't memorize what four is. We know what four is. So you see four, you can count four. If I ask you, prove to me this is four, you would hold four items and you would say there are four, you know, you wouldn't even, you'd think I was nuts.

43:50But when I say one fourth, what image comes into your mind? What concrete context do you think of? You might, because I just said that, might think of a quarter of a piece of cake or a quarter of a full cake or a quarter of a pizza. You might think of something concrete, but a lot of times the way you would think of it is numerator, denominator, one fourth. Now I need to reduce to the common denominator. You just go right into this disembodied stuff you had to memorize. But you can take two four-year-olds and you can show them a quarter of a cake or a third of a piece of cake and ask them which one they want.

44:30They're all intuitively going to know which one they want. And so a lot of times by the time we teach fractions, we stop teaching the intuition in the mathematics. In whole numbers, every child gets to experience the intuition, right? Five crackers. They're just shouting at you when they're three years old for the quantity they want. And that's really great because they get that intuition. In other countries, the intuition continues. So what I told you about Singapore, the third grade classroom where they were cutting with construction paper to prove one half equals base height by cutting rectangles.

45:07That's because they get to continue their intuition in mathematics. Since you brought up the subject of intuition, now let's make a transition to what are the best practices of teaching math? There's five I outline in my book, and I'd love to hit one deeply because we didn't get to talk about it as much. And then Guy, I'll let you lead me if we want to cover more. The one I'd love to hit most deeply is pictures, using pictures and concrete objects to make math make sense. The kind of hidden secret I will tell you, which I think, Guy, you've experienced in your professional career, is that top of their game, top of their field, mathematicians, economists, they're still using pictures.

45:53Now, those pictures are graphs, and they're often like line charts or functions. And that's how they're describing a lot of what they're doing. You can think of Watson and Crick were able to understand the double helix when they could see it, when they could imagine a picture. Folks at the top of STEM are incredibly concrete or pictorial when they're describing what they're doing. But along the way, as we teach mathematics, we use concrete items in kindergarten or first grade. And then by the time you get into a fourth or fifth grade classroom, like the fractions classroom. It is all symbolic notation.

46:29Now that symbolic notation is actually shorthand to represent a set of pictures. And it's this fabulous shorthand that mathematicians came up with as the base 10 system was designed and this beautiful common language of mathematics. But what's happened is now we only work in the shorthand and teach the shorthand, But the fastest way to teach what the shorthand means is by bringing back pictures. A simple example I'd give is in third grade, we teach fractions. And we also teach a fraction where the numerator, the number on top, is bigger than the number on the bottom, the denominator. What does that mean?

47:12You know, it means, well, you can reduce it and get to what? No, literally, what does it mean? And so what does eight fourths mean? In Zern and in great math classrooms, you'll see a teacher will take, let's say, two objects, two oranges, and cut each one into four pieces. And so what is eight-fourths? Eight-fourths is two because there were two oranges. Eight-fourths is two groups of four-fourths. All of a sudden, you can so deeply understand what eight-fourths is because you're connecting the intuition. Now, that doesn't mean you also shouldn't get to learn this fabulous symbolic notation, which is pretty cool.

47:56When I was in classrooms in Japan, once the math started, I asked the translator to stop talking because I could follow the mathematics. Because we all, as humans, all 8 billion of us have one beautiful common language to describe mathematics. I believe that learning that symbolic notation has tremendous value. It's really important to teach eight-fourths, but not completely disconnected from meaning, with meaning. Since you brought up pictures, I love the part in your book where you said that there was this multiple choice test about what's the closest thing to one half. One half. And Americans answered two over two, which is one.

48:40But they didn't pick five over eight, which is very close to one half. And then you explained that using pictures. And I really said, wow, see why people might say two over two is closer to one over two than five over eight. But I know five over eight is closer. And for the folks who love math or when parents identify one kid is just gets math, what they're actually describing is that child or that adult can picture it. And that's it. Because the acid test of understanding and math is can you picture it? And that's it. And so guess what you can offer the other child who can't picture it? You can offer them a picture.

49:26And then they're in the game too. too, then they get to participate too. And we don't have to hold it against them that they couldn't think of the picture the first time. Because once you give them pictures, then they can think of pictures, right? So, and I'll tell you something so fun, which is, Guy, you could share your pictures of how you think of something, and I could share my pictures, and they'd be different. But your pictures would shape my problem solving, and mine would shape yours. And so we would really get to start talking about the process of problem solving, and then we'd enjoy it and we get better together.

50:00And that's what happens when we start to move past only the symbolic notation to the meaning. And we start to share the meaning is that in the pictures, we can actually have math be very fun and we can increase our problem solving acuity. We can get better at problem solving. now what if i'm a parent and i'm listening to this podcast and i'm saying oh my god i did things all wrong i stand convicted i told my kid that oh it's okay you're not good at math there's focus on your writing or your art and now i'm hearing this and i now like the scales have been removed from my eyes and now i believe that my kid could be good at math and should love math but he or she's already in the ninth grade.

50:47What do I do? Yeah, it's not too late. That gives me a window into the second thing that I would love to share. There's another sort of point of view. Do you hear an ambulance or am I imagining that? That's me. I apologize. I'm in New York City. So that's an ambulance going by. I'm sorry. Well, you know, this is real life. All right. Yeah. So for students who are further along in their math career, let's say ninth grade or middle school, and they don't feel like math kids and they're behind. They have certain parts of mathematics that they have missed or are not as strong at. I think that we think it's over.

51:27And there's a lot of problems with that idea. But one is actually just the structure of math. So there's an idea that math is cumulative. It is. There would be no point in me teaching you calculus if you couldn't add. That would be truly nuts. But this idea that math is cumulative is sometimes understood in both an inaccurate and really literal way, that I have to get 100 on each day of math that preceded. So I have to get 100 yesterday to be able to do the math today. And that just isn't true. And I'll give you an example of how math is only a few big ideas. And while cumulative, there are access points along the way.

52:04So this is a real example in the Zern platform. In seventh grade, irrespective of the pandemic, we teach negative numbers. But post-pandemic, what we see is that a lot of children are shaky on decimal division. And so let's say in seventh grade, we present a question, we're working in negative numbers, we're making it really concrete, we're climbing a mountain for positive numbers, we hit sea level for zero, we're down in the ocean for negative numbers. is it's an engaging lesson. It makes sense. Negative numbers are coming to life for this child. And then they hit a problem, negative 1.4 divided by two.

52:41And their decimal division is shaky. Now there's two options at this fork in the road. One option is we stop teaching negative numbers and we spend two or three weeks in decimal division. But then the problem is the child is two to three weeks behind in negative numbers and perpetually behind. And so the most interesting question that we have in mathematics that pertains to kids who, let's say you want to help your child in ninth grade really turn it around in math, is how do you catch up and move forward? And it is such an interesting and difficult question, but let's come back to this problem.

53:17What we find is when we present to children, okay, leave aside the negative number, leave aside the decimal. What is 14 divided by two? And Guy, what is it? Seven, what do you mean? Seven. So every kid says that. And then we say, okay, almost everything you need to know about 1.4 divided by two. So first, before we do instruction on the decimal system, we say, now let's try one more time. What is 1.4 divided by two? The vast majority say 0.7. And then we say, okay, now what is negative 1.4 divided by two? So we just break it down and connect it to the knowledge they already have. And that helps most kids.

53:58Some kids need additional support to understand, okay, how does the decimal point work? How does base 10 work? And we can add that as a short bit of extended instruction and still stay in the negative numbers work. And so that's what I would say for a lot of older children, eighth graders, ninth graders who have these kinds of gaps in their learned mathematics, it doesn't mean that it's catastrophic or that you have to all the way go back to the beginning. It does need some extended time, but it can be targeted and focused and you can still continue with the learning that you're working on. The other story I would say is like, just think of all the stories of late bloomers.

54:37You know, the, for example, the woman who wrote Hunger Games was in her mid forties when she wrote it. That was her first book ever. And so there's this idea that we have to all figure our Oyo Mas first started playing the cello when he was four. That is so wonderful. And he's beautiful cello player. But the world is not only of yo-yo ma's. And so excellence can arrive at all these different points in time. And there's lots of room in life for late blooming. You brought up the story of Julia Child. She was a spook until her 30s and 40s, right? She didn't become the French chef at eight. That's right.

55:15That's right. And congrats to those who do find their passion at eight. But that does not stop any of us from finding passions in our 40s or 50s or whenever. 60s in my case. Yeah, 60s, 80s. Like you can, yeah, that's not how, life doesn't have to work like that. Okay, my last question. And this is something that I noticed that we had another math educator on named Jo Bowler. And she has written a book called Math-ish, I-S-H. And I notice many places in your book, you didn't exactly say it that way, but you talk about intuition, right? That five-eighths is closer to one-half than two over two. That's an ish kind of thing, right?

56:04So tell me about ish. Do you think that like ish is good enough that you don't need the exact answer as long as we're in the ish zone? I would say it depends. I think the bigger headline around that is that everyone can build a bath mind and doing so requires adaptability. So when you get stuck solving a problem, there are lots of ways you might go about that problem. So one might be coming down an estimation or an intuition pathway, and that may help support your way to solve the problem. Another, you just may know cold. So if I ask you what two plus eight is, you don't need to estimate it. You just say 10.

56:46You don't even know where it came from. The idea that there's estimation as a tool in problem solving is vital. And there's nobody who is going to get to the highest levels of STEM without really strong estimation. It's critical to have very strong estimation. Often when you're doing precision, you need to pause and say, am I headed in the right direction? Let me take a second and estimate and then let me keep going. So what I would say is that's a critical tool in the math mind, in the math toolkit, which is around intuition and estimation. Am I headed the right way? Should this number be negative?

57:22Should this number be bigger than 3 ,000, smaller than 3 ,000? That's keeping the intuition going. It makes math very enjoyable. It keeps your problem solving mind working. And it's also critical when you get stuck. At the same time, precision in mathematics is vital. Without precision, the bridge will fall down. It will. And so I wouldn't present them as either or, but I'd present them as back to that integrative complexity that precision is the only way through is not adaptable problem solving. It's not a reasonable way to approach. As you mentioned, a lot of times in real life, you may not need to use a precision method.

58:06Sometimes going about a precision method is silly because the estimation is close enough. And what that is, is that's where the real problem solving is going on, when you need to be precise and when you can use estimation and intuition. The other thing I'd say about estimation and intuition is you can get better at it. It's not just something you're born with. Same with precision. You can get better at being precise. It's not just something you're born with. I would like you to just give a pitch for, in a sense, we've been pitching your book the whole time. So I think that's done. But pitch Zern.

58:43Pitch your company. What does this company and website do? Zern's an online math program for elementary and middle school students. everyday kids in tens of thousands of classrooms across the country log into Zern to learn and to practice math. And there's three things that you need to know about Zern, how it works, how it's built, and how to get on it. So let me start with the last. As a parent, you can just get on zern.org and make a free account. Same with as a teacher, you can get on zern.org and make a free account. Schools can also purchase Zern accounts that have all these additional services.

59:18In terms of how it works, Zern has several parts. So the first is that when you log in, you get interactive guided lessons and kids start with a small game that builds fluency. If you're in kindergarten, you're counting the objects on a train. If you're in elementary school, you're doing fun games to practice your multiplication tables. You then move into a video, an interactive video that has pause points where a teacher on screen is presenting mathematics using GIFs, pictures, real world objects, cutting oranges, as I mentioned. And then finally, there's an independent practice portion where students go up a tower of power.

59:59And so there's a gamified way to get to a badge at the end of every lesson. It's built on a lot of what we just talked about, but one of the core ways that it's built is really trying to build that concrete to pictorial to abstract understanding. And the last thing I'd say is there's so much content. So there is a fun lesson for every single day of instruction, kindergarten through eighth grade. This year, one in four elementary school students are registered in the country in the United States are registered with an account and more than a million middle school students. One in four students?

1:00:36In elementary school. In elementary school have a Zern account. Yes. And more than a million of our middle school students in the country. Listen, I'm all about Ish. And even a guy who loves Ish understands that is a humongous achievement. Congratulations to you. Wow. Thank you. All righty. We have come to the end of what I want to discuss. Thank you so much. It's been most interesting and most remarkable. And I thank you for being my guest. And I hope everybody listening to this has a new appreciation for math and learning math and loving math, but also maybe more the democratization of math that math is for everybody.

1:01:19So I hope we've accomplished that in this episode. Thank you very much, Shaloni, for being on our show and good luck with your book. Remember, it's Zern, Z-E-A-R-N, and her book's name is Math Mind. And so that's the follow-up for all of you listening. Thank you very much for listening to Remarkable People.

1:01:45This is Remarkable People.