Shalinee Sharma: Revolutionizing Math Education for Every Student

Guy Kawasaki:
Hello, my name is Guy Kawasaki. This is the Remarkable People podcast. Thank you for joining us. As you know, we're on a mission to make people remarkable, and today we have another remarkable guest. Her name is Shalinee Sharma and we're going to talk about math. Now, she's the CEO and Co-founder of Zearn, and this is a nonprofit educational organization to help kids learn math and what a wonderful goal and what a wonderful implementation of this lovely strategy of hers.
And she has written a new book that I think you'll find fascinating. It's called Math Mind: The Simple Path to Loving Math. That has a nice cadence to it, Shalinee. I like that cadence. Anyway, so we're going to be talking about math today. So Shalinee, welcome to Remarkable People.
Shalinee Sharma:
Thank you so much, Guy. I am so excited to be here. And I so enjoy your podcast.
Guy Kawasaki:
Oh, you say that to everybody who interviews you, but. I read your book and as I'm reading it I'm thinking, my God, this book is like a combination of Carol Dweck meets Ken Robinson meets Mary Murphy. It's like The Growth Mindset and Educational Mindset and the Unleashing the Power of Youth all combined. So I loved it, as you can tell.
Let me just jump in here. So first, a really basic question, which is tell us why learning math is important at all?
Shalinee Sharma:
Yeah, thank you so much, first of all, for what you shared about the book and for actually asking such an important baseline question, why does math matter? And one could even ask why does math matter now? But let me just start with the basics that we know as facts. Leaving aside the heart, let's just hit the headfirst.
Algebra completion is the most predictive activity that a young person can do kindergarten through twelfth grade to predict that they'll graduate from high school, get admission to college and graduate from college. That one single activity, algebra completion. And on the other side, failing algebra is predictive of dropping out of high school. In career, algebra completion, again, eighth grade or high school algebra completion is predictive of a massive difference in lifetime earnings.
And so what we can see in the actual facts is how important math is in K-Twelve for your whole life. And I think then we can start to explore why, why is that happening? And what I would posit is that math is the place that every child gets to participate in a reasoning course.
And if you think about the core ways we get through any job and lots of interesting problems that we experience as grownups, that they require two core skills, reasoning through the problem and being able to communicate effectively to navigate the problem. And so algebra and math in general is the reasoning course we all get to take.
And what I'd say is that when you and I were in school, the marketplace didn't demand numeracy like it does now. And so when we think about participating in jobs in the marketplace, numeracy is even more important than it used to be. Further, just with the kind of information that we get overloaded with to solve problems in our everyday life, to even participate in our democracy, to understand the news, numeracy is a baseline.
Guy Kawasaki:
Let me ask a really simplistic question. People throw around the phrase math and algebra, but can you precisely define what is algebra? Is algebra, if you buy two oranges and they're fifty cents each, how much did you spend? Is that algebra? Or what exactly is algebra? So we know what is so predictive.
Shalinee Sharma:
I love that question. What is algebra is actually a more than century long debate.
Guy Kawasaki:
We only got an hour.
Shalinee Sharma:
Yeah. And debate ends with two options of what algebra is. So algebra is either solve for X. So it's teaching the schema structures, tools, procedures to allow young people and adults to solve for X. Does that mean that when a first grader is doing a problem where there is an X hidden, there are six pencils all together, one friend grabbed three, how many pencils were left in the container? Is that algebra? It actually is, right? So that's solve for X.
Now the second thing that then makes it the classification of algebra that is typically a later middle school or early high school course is where we introduce moving to almost exclusively notation as opposed to concrete context and objects, that we still can utilize that. And we start to move to multiple variables, we're solving for a system of equations.
Said another way, if I have two equations, X plus Y equals Five, and then I have another equation, two-X plus Y equals seventeen, I can solve both variables. And so these are the arbitrary and real lines. But I think when we think about what's most predictive and what's most important is solving for X, which we do all the time in our lives.
Guy Kawasaki:
You got me with the solving for X is something we do all the time in our lives, but when do you ever solve for X and Y in life? Normal life. Maybe somebody at Google in statistics or something, but when does a "normal" person shopping at Costco ever solve for two variables?
Shalinee Sharma:
Every time they're at Costco. And they may not need to do that in pencil and paper, but having that structure in their brain and that schema will make that Costco treasure hunt way more fun. It will. So let's assume for a minute that your Costco monthly budget is one hundred dollars and you're wandering Costco and there's things you are definitely going to get, for example, almonds or coconut water, those you have to get on your list.
But then you have a little bit of money left for some fun at Costco, which Costco always presents. And the X and the Y is what I have to get, in what quantities and what I might want to get. And I still have to solve inside a hundred dollars.
And so we're actually doing that every day all the time in budgets, when we think about how much can we spend on a trip to the movies or a trip to Disney World versus how much we can spend on the things we have to spend. Those are actually multivariable equations. Now, we may not lay them out that way and there may not be utility in laying them out, but that doesn't mean that that way of thinking isn't in the mind.
Guy Kawasaki:
Now, if I were talking to the Shalinee of physics or statistics or chemistry, wouldn't that Shalinee say, "Physics is everywhere around us. When your car breaks or doesn't break and hits the wall, what makes an orange, physics is everywhere, chemistry is everywhere, reading is everywhere. So pretty soon everything is everywhere." So is math special? Or is it that this is your area of expertise?
Shalinee Sharma:
I think math needs a little bit of a boost. So the idea that reading is everywhere and literacy is non-negotiable is really what I hope we get to with numeracy. And I think physics is one of the most beautiful applications of math that there is. But what I'd say is that the reason for my focus on math or the reason that I wrote the book about math is I really do think in our world today math needs a boost.
The way I would describe it is if you think about a classroom full of kindergartners and you think about all the grownups that love those kindergartners, so those can be their teachers, their families, their caregivers. When those kids are in their kindergarten classroom, there is an expectation that they will learn to read. And then there's a hope that they'll love to read. And we don't approach math that way.
So we don't have an expectation that every single child will be numerate and we don't even dare have a hope that they would all have some part of mathematics they love. I think about when my thirteen-year-old boys became eight years old. When I was eight years old, my favorite book series was the C. S. Lewis Narnia series, and it was really magical for me.
And I tried over and over to get my eight-year-olds to love Narnia too. For the parents out there, you know how that went. It didn't work. But I was filled with this hope and desire that they could love this book the way I did. And I want people to be filled with that hope and desire that their children can love math too.
Guy Kawasaki:
And how did we get to this place where people don't have an expectation about math that they have about reading? What happened? Does math have a marketing problem?
Shalinee Sharma:
I think so. I think math does have a marketing problem. How I'd say how we got to this place is we just haven't gotten to the other side yet. If we could transport ourselves in a time machine 200 years into the past when the majority of humans were not literate and couldn't read, then we might encounter, we'd likely encounter similar beliefs and stereotypes about who could read and who couldn't read and how magical and special reading was.
And maybe even thinking of it as some rare genetic ability, which we know and have proven is all of humanity is nonsense. Today there are more people on earth, the population growth has been explosive and a greater percentage of them are literate. And it's because, amongst other things, it's because we all have a common belief and expectation that every human can read. We don't yet have that in math, though it is emerging.
The second thing I'd say though is that the experience of learning math can feel humiliating and that is shaped by our attitudes in mathematics. One of the things that, to share a Carol Dweck or a Mary Murphy and the mindset, you might see in a math classroom a poster that says, "Making mistakes is how you learn."
But in a lot of classrooms that poster, children don't feel that making mistakes is how they learn. They feel that making mistakes is how they get punished. And so they don't make mistakes, which means they don't learn. And so this is one of the tricky parts we have in math teaching and learning today, which is opening up both the pedagogy, the way we learn, as well as the mindsets, the learner mindsets to really support an openness to learning in math classrooms for all kids.
Guy Kawasaki:
But why, Shalinee? Why? Why are we in this place? What happened?
Shalinee Sharma:
I think one way to ask the question is why are we behind other countries who are ahead of us? So for example, there's a test that's taken across all the countries and it's called the PISA test. And it's a high school test of proficiency in mathematics and the United States scores very low compared to other wealthy nations. And for example, one nation that scores very high on that test is Taiwan.
And in that test, at the end they ask that sample of students who take the test, that's a randomly sampled test, they ask them different interesting questions like, if I work harder in math, will I get better at math? And in Taiwan, the students uniformly say yes. And in the United States, the students say no.
And so I think what we have that's quite important to realize is that we have built up a large system that costs a lot of money, that educates fifty-five million students, that is oriented more towards sorting children in mathematics than teaching them all.
The deepest reason of why we have a fixed mindset towards mathematics versus other countries, I don't know that I have the expertise to answer all of that, but I think the evidence that we do have that system that we put a lot of money and time into is one definitely worth reflecting on. And we built our system, which therefore means we could build a different one.
Guy Kawasaki:
For a long time prior to the pandemic, lots of people were obsessed with the math SAT score and then the SAT score became optional. So do you think that is going to make the situation better or worse? The case for making it worse is that without SATs necessary, people aren't going to be forced to learn math.
The opposite argument could also work, that now people explore math with less risk because they don't have to worry about this SAT thing hanging over them. What do you think of standardized testing of math now that you just discussed how low we score in math?
Shalinee Sharma:
Yeah, I'm not an expert on standardized testing, but I can still share some thoughts. What I would say about the SATs, and this is from reading newspapers as opposed to having personal deep expertise on the SATs, is that many universities that took away the SATs are now bringing them back.
And they find that they can actually get to a more diverse and qualified candidate pool for their universities by bringing the SATs back. I think both Brown University and Dartmouth University published both research on that and then altered their orientation to admission. So the question mark of whether the SATs are better or worse is still out for public debate.
With regard to standardized tests then, if they put too much pressure on the learning system, because I think your question is perhaps these standardized tests put too much pressure onto the learning system, which doesn't allow us to explore. In Taiwan, there's more pressure with regard to standardized tests. Same in Japan, which is another very high-performing country in terms of mathematics.
In Japan, there are more children who are proficient in calculus than we have students proficient in algebra. Singapore is also a very high-performing country in terms of mathematics. So is Estonia. And all of them have higher pressure exam structures than we do. So I don't think the broad data set would then say that when we take out the exam and the pressure of the exam, we could therefore get to something better as a default.
But I think there is no question that math can be taught where the orientation is just to get to an answer. Here's a simple story or a metaphor that I love to share, which is, so Guy, imagine if you have a reading test tomorrow and the reading test tests you on, let's say fifty words, but you actually don't know how to read. So we can pretend this reading test is in Hindi or a foreign language that you don't happen to know.
I'm just making a guess that you don't know that language. And you aren't taught the letters and the sounds and how to sound them out and put them together. But the way you choose to do it is you memorize the picture. So you see a picture and you say, "That means house." And then you see another picture and you say, "That means book, and this is how you learn it." And because you're Guy, let's say tomorrow you get an A on that test, you nail it.
Guy Kawasaki:
Let's say.
Shalinee Sharma:
Let's say, let's try it. But because you're just a normal human being, actually you're a remarkable human being. But what will happen next week, because you have a brain that's a human brain, is you'll start to forget because that learning wasn't presented to you in a durable fashion where you developed understanding of ideas or deeper schema or structures. You used a different form of learning, which is just a more disposable form of learning of just fast memorization.
And also that memorization didn't have any connections. And so that's the kind of stuff just falls right out of our heads. And so what would happen is while you got an A on that test next week or two weeks later, you actually would not be able to read. You would only be able to read for the test and then two weeks later you'd forget how to read. And this is an approach to math called answer getting.
And so a lot of what you might be learning in math is just to memorize, but you don't know why anything is happening. And when we teach math that way, which is not how math is taught in those top performing countries, it's a very pressure-filled, very anxiety-filled experience, especially when you take tests because to study for those tests, you memorize your way to the answers. You don't understand.
I'll give you a simple example which is I didn't learn until I was in my forties why anything times zero is zero. N times zero is zero is a proof. And on Zearn we teach that to third-graders. And what that means is when you hit in algebra two or in calculus, when you hit a quantity times zero, what I used to do on the test is freeze for a second, get really anxious for a second and say, "What's the rule about times zero? What's the rule? Is everything zero? Is everything one?"
And then also three raised to the power of zero is one and just all these different things to memorize. But when you actually teach why things are happening, you teach the axioms, you can release that pressure and just understand.
So just think about how if you grabbed any book off a shelf, even if it was difficult, you could feel calm and confident because you would be able to read it. So a reading test wouldn't be this pressure-filled experience. You'd be like, "I can read." What if a math test felt like that because you understood?
Guy Kawasaki:
I think the reading test versus the math test is because the precision of grading of a math test, you either got the right answer or you didn't, right? Whereas reading tests, I would say more vague or more subtle than that.
But wait, did I hear you right? Did I hear you say that in these countries that lead in math, it's very high pressure and memorization-based? But I thought you're trying to make the case that high pressure memorization is not good. But then you're saying that the countries that lead use those not good methods. So did I hear this wrong or is there an explanation there?
Shalinee Sharma:
Yeah, no, I appreciate that question. So what we see in those top-performing countries and what we see in the bright spots of top-performing schools in this country is what we call integrative complexity. Two things can be true, right? It's not black or white, it's gray. And what does that mean? The distinction I was trying to make is that in those high-performing countries, they have higher pressure tests than the SATs, way higher.
For example, those tests determine which high school you go to. Those tests, you can or can't stay with your friends. You can imagine the pressure around that. What else is interesting in those countries though, when they present mathematics, they don't present math as memorization alone and they don't present math as big ideas, problem solving and that complexity alone, they present both.
So how does that play out? I've spent time I visiting math classrooms in Singapore and Japan. And so from a firsthand experience is I was in this amazing third grade classroom in Japan where children were proving that the area of a triangle was one half base height.
They had construction paper, scissors, they were cutting up rectangles and they were proving that if you cut a rectangle in half, that's half, and then you multiply the base times the height, that will be the area inside. And they were having lots of fun doing it. And that's a deep proof and a deep amount of understanding. But what preceded that portion of the math lesson was maybe five or seven minutes of a fun game where kids were memorizing their multiplication tables, but in a fun, gamified way.
Because the problem is if you have one without the other, you either have a memorized wrote version of math, like the reading test, or you have a lot of concepts, but you can't do the math because your working memory gets overloaded when you're trying to do algebra because adding thirteen plus eighteen overwhelms your brain. And so that's what we can learn from the other countries, which is this notion of both, concepts and procedures, or integrative complexity.
Guy Kawasaki:
Now, just to be a devil's advocate, what if I said to you, "Yeah, okay, so Japan, Singapore, Estonia score very high on math, but I don't exactly see a lot of creativity coming out of those countries. I don't see Facebook, I don't see Google, I don't see Apple, I don't see any of these tech successes. Yeah, maybe they're great mathematicians and accountants, but they're not creative." Not that I necessarily believe what I just said, but somebody could say something like that, to which you would counter what?
Shalinee Sharma:
Yeah, so I think we also need to understand that there are wonderful parts of our education system and not throw it all away. There are parts of our education system that do help produce some of the most valuable and interesting companies like the ones you named. So I don't think that we can look at these countries and say, "Let's, lock stock, take every dimension of their education system." Here we're talking about one thing, which is math proficiency.
One thing you can see, for example, in the latest CHIPS bipartisan legislation, which was an overwhelmingly set of bipartisan legislation to support the increase of microchip manufacturing in the United States was the worry across fifty governors that we don't have enough tertiary candidates in STEM in this country.
So those are PhD candidates in STEM fields like for example, electrical engineering or other vital fields to actually build all those chip manufacturing facilities. So a lot of the companies you just named rely on the education systems of other countries to train people to that level of mathematics to come and work here, which is also a great part of our country and a great part of our country's innovation, but we can also help our own students be that successful as well.
So what I would say is we're not looking totally at every part of these education systems and saying, "Let's transplant them." But we're looking really specifically at specific parts of the education systems, like the percentage of children who know algebra and thinking about what are some of the great things we can bring over into our education system.
Guy Kawasaki:
I've read your book about the horror stories of people making these decisions where there's eighteen chairs and there's twenty students and the teacher says, "Look to your right, look to your left. One of you is going to be gone." That kind of thing. Why? I don't understand this. You would not say that in an English class or a Spanish class or anything. Why is math so linked with anxiety?
Shalinee Sharma:
And humiliation too. I think there are so many myths around math that start quite young, and they might be in the movies, or they might be in popular culture, but they're also in math class every day.
So for example, my ninth grade classroom, which you might be referencing, actually amazing math teacher, I learned so much mathematics, but he really thought it was important to let us all know that he would be failing a portion of us out of the ninth grade honors math class because we wouldn't all make it to calculus.
Crazy. That was a group of kids who had selected themselves into honors math, had all the motivation in the world, might've needed some additional supports to get to calculus, there might've been some kids who needed some additional supports, but that was the mindset.
I can't fully get myself back into the nineties mindset of why one might have thought that way, but I'd say today with digital tools and with AI tools, any child in that ninth grade math class who is struggling with, I don't know, inverse functions or whatever chapter we were on, can Google their way to a great YouTube video, can get unbelievable amounts of supports.
Google Gemini, they can take a picture of their math problem and see it laid out step by step. Tools like Zearn. There is not a scarcity of supports. And maybe in my teacher's mind in ninth grade, maybe he did see this as a very scarce amount of learning input that could be provided and he had to ration that across eighteen students instead of twenty, which today is truly silly and nonsense.
Guy Kawasaki:
But couldn't you make the case that if you went out for the football team, the football coach would say, "There's sixty people here, fifty are going to make the team. So one out five of you is not." I hope I did the math right just now, but one out of five of you is not going to be on this team,” and that's basketball, that's football, that's the debate club. Life is not necessarily a no-cut sport." What's the problem if you math teacher said that?
Shalinee Sharma:
Yeah, I think that is okay for advanced mathematics or for things that people are choosing. So if I cut you from reading because in second grade you weren't showing the kind of progress I needed you to show, and so I was like, "Forget it, you will finish elementary school but you will not be able to read."
Guy Kawasaki:
That sucks.
Shalinee Sharma:
It's criminal and certainly sucks. Now, if for example, we cut you because there's only a certain number of children in a senior elective on Shakespeare and only eight students can join and everyone had to write an essay to talk about how they wanted to join and your essay didn't make it, you're the ninth student, you are going to be fine. That's fine. I didn't take away anything essential from you. I didn't take away your ability to read.
And maybe you'll take a different elective about, I don't know, dystopian novels. You will be fine. And it's completely fine if, at upper mathematics, one child is pursuing physics and another is pursuing statistics or they're choosing not to pursue upper math whatsoever and they have found another passion like history or science, it's all fine. But to take away what I would say is basic numeracy is not fine.
Now, people can do it in different speeds. I am a believer in the fact that there is a bell curve of talent. A simple example could be people are very tall and if you're six foot seven inches you have a different chance at being able to play professional basketball than if you are five foot seven. 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 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.
I 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.
Guy Kawasaki:
What if somebody says, "I can go to Siri or I can go to Alexa and say, 'I have a hundred dollars to spend at Costco. I got to buy fifty dollars’ worth of broccoli and meat. How much do I have left over?' And Siri and Alexa and ChatGPT, anything will answer you. Why do I have to learn math?" What do you say to that person?
Shalinee Sharma:
The same question could be asked, which is I can have Siri read any book aloud to me, or Alexa, for example.
Guy Kawasaki:
I have asked other teachers that question, yes.
Shalinee Sharma:
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 Alexa read books allowed 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. It's this funny double-edged sword, which is we can use these tools, and we should, they're phenomenal on ramps.
We use them all through Zearn. And so we should use these tools as on ramps for students, but also know that this digital and AI driven world now sets higher expectations of what humans can do. And so that's actually happening right now.
Guy Kawasaki:
Now let's say that your kids or one of your sons has dyslexia, so reading is extremely hard for him. 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 anything that's written in text.
But now, 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. Do everything is online." Can't you say the same thing about math?
Shalinee Sharma:
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.
Actually, 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 Zearn 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 efficiently 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, has an amazing ability to draw, an amazing ability to participate in math, just a phenomenal athlete, a great thinker, such a funny person. These 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 and we should use all those tools. But that doesn't mean that we have a lower expectation. We still want that child to participate.
Guy Kawasaki:
But 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." And they're saying, "You cannot do math, but you can do other stuff. So don't worry about math." But aren't you saying that everybody should have a basic level of mathematical facility?
Shalinee Sharma:
Yeah, 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. I had a twin who was reading pretty successfully in kindergarten, which makes him an early reader. It was odd how fast he learned how to read. And then the other twin wasn't really a fully successful reader until 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?
Guy Kawasaki:
This is a great story, but I believe in fact that is happening with math.
Shalinee Sharma:
I assure you it's happening. That is your belief and I'm here to bring you data. It is happening. But Zearn, we prove every day that the primary way to learn math is to do math. And that when kids do math, they learn math. 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.
Guy Kawasaki:
So then let's just numerate for us the basic myths of math so that people know when they're basically saying something wrong or copying the wrong attitude, what are the myths that we should avoid?
Shalinee Sharma:
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 the math is just about speed. So let's say you have minute math, so there's a problem and you have sixty 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 sixty seconds, so I'm dumb, but there's somebody else who can do this problem in sixty seconds, so 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 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, thirteen plus eighteen takes all our computing power.
What ends up happening is we can't do that advanced mathematics, and so we do need automaticity, but math is not a running race with only one person winning that is not math. But Zearn, 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 Beilock, 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. So 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, 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, and they were in fact slower.
So the graduate 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 undergrad 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.
The 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 forty-five 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. So 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. So 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, 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 enormous and unappetizing and too much sugar, so 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.
Guy Kawasaki:
Wow. 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. That 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 Wolfram level Mathematica here. Where did we go wrong to be in a place like that?
Shalinee Sharma:
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. So 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'd say there are four, you'd think I was nuts.
But 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 or 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-old’s and you can show them a quarter of a cake or a third a piece of cake and ask them which one they want and they'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, that's because they get to continue their intuition in mathematics.
Guy Kawasaki:
Since you brought up the subject of intuition, now let's make a transition to what are the best practices of teaching math?
Shalinee Sharma:
Yeah, 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 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.
Now those pictures are graphs, and they're often line charts or functions, and that's how they're describing a lot of what they're doing. But you can think of Watson and Crick, we're able to understand the double helix when they could see it, when they could imagine a picture. And so 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, the fractions classroom, it is all symbolic notation. Now, 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-ten 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? It means you can reduce it and get to what? No, what does it mean?
And so what does eight fourths mean? In Zearn 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 then 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, when 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 eight 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.
Guy Kawasaki:
Well, 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.
Shalinee Sharma:
One half.
Guy Kawasaki:
And Americans answered two over two, which is one, but 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.
Shalinee Sharma:
And for the folks who love math, or when parents identify one kid 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 in 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, and then they're in the game 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.
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.
And 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.
Guy Kawasaki:
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. Just focus on your writing or your art.' And now I'm hearing this and now 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. What do I do?"
Shalinee Sharma:
Yeah, it's not too late. That gives me a window into the second thing that I would love to share. There's another point of view for me.
Guy Kawasaki:
Do you hear an ambulance or am I imagining that?
Shalinee Sharma:
That's me. I apologize, I'm in New York City, so that's an ambulance going by. I'm sorry.
Guy Kawasaki:
Well, this is real life.
Shalinee Sharma:
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. And 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, that 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 a hundred on each day of math that preceded. So I had to get a hundred 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. So this is a real example in the Zearn 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. It's an engaging lesson, it makes sense. Negative numbers are coming to life for this child. And then they hit a problem, negative one and four tenths divided by two, and 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 this is such an interesting and difficult question, but let's come back to this problem. What we find is when we present to children, "Okay, leave aside the negative number. Leave aside the decimal. What is fourteen divided by two?" And Guy, what is it?
Guy Kawasaki:
Seven, what do you mean?
Shalinee Sharma:
Seven. So every kid says that. And then we say, "Okay, almost everything you need to know about one and four tenths divided by two." So first, before we do instruction on the decimal system, we say, "Now let's try one more time. What is one and four tenths divided by two?" The vast majority say seven tenths.
And then we say, "Okay, now what is negative one and four tenths divided by two?" So we just break it down and connect it to the knowledge they already have, and that helps most kids. Some kids need additional support to understand, okay, how does the decimal point work? How does base-ten 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 mean some extended time, but it can be targeted and focused and you can still continue at the learning that you're working on.
The other story I would say is just think of all the stories of late bloomers. For example, the woman who wrote Hunger games was in her mid-forties when she wrote it. That was her first book ever. Domas first started playing the cello when he was four. That is so wonderful and he's a beautiful cello player, but the world is not only of the Domas. So excellence can arrive at all these different points in time, and there's lots of room in life for late blooming.
Guy Kawasaki:
You brought up the story of Julia Child. She was a spook until her thirties and forties. She didn't become the French chef at eight.
Shalinee Sharma:
That'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 forties or fifties or whenever. Eighties.
Guy Kawasaki:
Sixties in my case.
Shalinee Sharma:
Yeah, sixties, eighties. Life doesn't have to work like that.
Guy Kawasaki:
Okay, my last question, and this is something that I noticed that we had another math educator on named Jo Boaler, 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 eights is closer to one half than two over two. That's an ish kind of thing, right? So tell me about ish. Do you think that ish is good enough, that you don't need the exact answer as long as we're in the ish zone?
Shalinee Sharma:
I would say it depends. I think the bigger headline around that is that everyone can build a math 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 ten.
You 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? Should 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 and 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. Sometimes going about a precision method is silly because the estimation is close enough. And what that 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.
Guy Kawasaki:
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 Zearn, pitch your company. What does this company and website do?
Shalinee Sharma:
Yeah. Zearn's an online math program for elementary and middle school students. Everyday kids in tens of thousands of classrooms across the country log into Zearn to learn and to practice math. And there's three things that you need to know about Zearn, 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 Zearn.org and make a free account. Same with as a teacher, you can get on Zearn.org and make a free account. Schools can also purchase Zearn accounts that have all these additional services.
In terms of how it works, Zearn 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 an interactive video that has pause points where a teacher on screen is presenting mathematics using gifts, 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.
And 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 in the United States or registered with an account, and more than a million middle school students.
Guy Kawasaki:
One in four students in elementary school have a Zearn account?
Shalinee Sharma:
Yes. And more than a million of our middle school students in the country.
Guy Kawasaki:
Listen, I'm all about ish and even a guy who loves ish understands that is a humongous achievement. Congratulations to you. Wow.
Shalinee Sharma:
Thank you.
Guy Kawasaki:
Alrighty. 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 the more the democratization of math, that math is for everybody. So I hope we've accomplished that in this episode. Thank you very much, Shalinee, for being on our show.
Shalinee Sharma:
Thank you so much.
Guy Kawasaki:
And good luck with your book. Remember, it's Zearn, 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.