Jo Boaler: Empowering Students Through Innovative Math Education

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0:48I'm Guy Kawasaki and this is Remarkable People. We're on a mission to make you remarkable. Helping me in today's episode is Joel Bowler. She is a professor of education at Stanford University. She joins a handful of people who have been on Remarkable People more than once. She began her career as a secondary mathematics teacher in urban London schools, including Haverstock School in Camden. After teaching, Bowler received a master's degree in mathematics education from King's College London. She then completed her PhD in mathematics education at the same university. and won the award for Best PhD in Education from the British Educational Research Association in 1997.

1:38Prior to her role at Stanford, Bowler served as the Marie Curie Professor of Mathematics Education in England. She co-founded U-Cubed, an organization dedicated to providing resources and ideas to inspire and excite students about mathematics. Bowler has received several honors, including the National Science Foundation Early Career Award, the NCSMK Gilliland Equity Award in 2014, and the CMC Walter Denham Mathematics Leadership Award in 2015. She has authored 19 books and numerous research articles. Her latest book is called Mathish, Finding Creativity, Diversity, and Meaning in Mathematics. In this book, she shares research on embracing a diverse approach to learning math and provides seven principles to reframe our relationship with the subject.

2:36All of what you just heard is a typical Remarkable People introduction. It's a long story, and it would take a lot to explain what happened. And it would also take a lot of research to get both sides of the story. But suffice it to say that Joe Bowler was attacked by Tucker Carlson and Elon Musk. That should tell you something. I'm Guy Kawasaki. This is Remarkable People. And now, here is the remarkable Joe Bowler.

3:11I was prepping for this interview and I was reading your book. and I came to this sample question where you said, how many squares are in this eight by, and you said the answer is not 64. So that kind of stopped my preparation because I was saying, how can there not be 64 squares? And then I thought, maybe she says, if you look at it, you could have two by two squares, three by three squares, four by four squares that could be in different parts of the eight by eight. So what is the answer to that? In fact, I even went to LLM and I asked how many squares are in an eight by eight chessboard and it said 64.

3:54So why is the answer not 64? Well, you're exactly right. If we look at an eight by eight chessboard, there are the 64 one by one squares, but then there are the two by two squares and the three by three squares and the four by four. It's actually a great activity that we give to students and ask them because they can look for patterns. It's a nice example of a mathematical investigation where it would help you to start with a smaller board. And that's one of the things we hope kids learn from it, that taking a smaller case is really valuable when you're working on a difficult problem. So if you start with a two by two board, it's easier to see the number of squares inside it and then a three by three and you start to see the pattern which is what it's all about for us so i passed the test yes you did we can end this recording right now yes can we go someplace just a temporary diversion here that you can tell me no you don't want to do this, but I got to ask you about this whole Tucker Carlson thing.

5:06What the hell happened there? What happened? And it's still happening. Unfortunately, what that was, was I was asked by the state of California to be one of the writers of a new mathematics framework. There were five writers, but the ideas of the framework came from an elected committee of 20 leaders and focus groups met across the state, the committee met, the writers wrote up their ideas. And people decided they wanted to stop the ideas of the framework. And they decided to try and do that by basically targeting me. I don't know any other way to describe it. And yeah, I was sitting just having a usual Friday night at home when I started to see all this hate mail filling up my email.

5:58And I thought, what has happened? I don't understand this. And then somebody showed me that Tucker Carlson had put my image on his show and said that I was trying to promote social justice and mathematics through the framework. And that was it. Yeah, that started a pretty tumultuous time. In a sense, you are promoting social diversification and justice through the framework, right? You're trying to make math more accessible to more students. Exactly. So in a sense, what they said you're trying to do is correct. But why is it such a big controversy? Why are they against this? One of the things, why are they against this is a kind of a deep question.

6:45I would say my own take on it is there are people who've been very successful in mathematics in their lives, and they are the people who are against it. If you look at the people who are pushing back on the framework, it is all those who've been extremely successful. And they like the system as it is. They know how to get their own children to excel in the system. And proposing changes that would broaden the access to mathematics to many more children is not something that those who are in that position particularly want. So for some people, their motives were not very egalitarian. They really wanted to keep the system as it was.

7:26And some of those people then spread lies about the framework. so one that was spread around a lot was that we were stopping children being able to accelerate and stopping them being able to take algebra in eighth grade this was the big lie that was sent around in fact what the framework does is recommend that people not put young children in elementary school into different tracks that then cement their pathways from that point onwards And so as soon as we entered into that realm of let's not have students who are of a young age in tracks, that alerted a set of people that things were going to change.

8:11And unfortunately, they spread these ideas widely. It turns out that very successful people are able to influence the media considerably. So if you saw any news about the framework, then it's likely to be negative. The reporting of the framework was almost entirely based on sharing the STEM professors who didn't want it. Nobody shared all the educators who did want it. And then when it went to the state board for approval, it was unanimously approved and backed by the California Teachers Association and educators across the state, all the equity groups across the state. So it's a really odd situation that all of the news about it was negative, yet all of the educators in the state supported it.

9:05When you say the very successful people, are you talking about people successful in the math perfection or successful as titans of Silicon Valley? Who are these people who are trying to perpetuate the old way? both particularly some particularly powerful people in silicon valley amongst the people who don't want maths changes i was actually at a really nice garden party sort of lunch that was arranged for people who are working to help students in different countries and the organizer said to me oh i want all of the leaders the ceos i spoke to said they're not going to come because you're coming.

9:48So they really did a good job of making me like the enemy of kids advancing in math. So that is how they think of me. Joe, I am having an out-of-body experience here. You're telling me that the CEOs of tech companies are on this warpath with you because you're trying to make math more accessible to more kids. Did I repeat that right? Yes, that's definitely true. And I think many of them have believed things that have been shared about the framework and about me that aren't true. I absolutely support kids going forward and accelerating if they're ready to do that. And what I don't support is writing off students from a young age.

10:37But yeah, that's basically where we are. I have to say, I'm just scratching my head. And I know a lot of VCs and there's a transition when you cross over into extreme wealth where all of a sudden you think that your wealth makes you smarter and an expert in everything. right so now you run a private equity fund or a hedge fund and all of a sudden now you're an expert in plagiarism and academic circles and it's really it's venture capital disease and now you should tell teachers how to teach and all that is i just want to throw up i just want to throw up yeah you're definitely naming something there that was part of the distressing thing about the pushback of the framework.

11:25There's a maths professor at Stanford who was one of the leading people against it, who shared websites saying all the research inside it is wrong. This is where I'm going to show it's wrong. And if you look at what he's written, it just shows that he doesn't understand educational research and is actually using something they use in maths that you don't use in educational research to say all of these studies should be discredited. A lot of people People believed that. A math professor says it's wrong. They shared it with everybody. Nobody stopped to think, does a math professor understand the K-12 education system?

12:05That didn't come up for anybody. Yeah, it's been quite a few years working on this. Okay, one last question about this. So now you're this target of Tucker Carlson, who's, by the way, going to go to Russia to interview Putin to help us explain Russia while he's at it. Now that he's conquered math, he's going to take on world peace. What happens when your inbox explodes? Is it just inbox and you can just ignore stuff? Is it social media or are there threats on your life? What happens? I guess I did get threats on my life and my children's, which is particularly scary. and Stanford at one point decided to add my house to their nightly patrols to check on me it's more than just getting nasty emails it is threatening so it's a really odd this seems to be the world we live in now that somebody hears some words from Tucker Carlson and immediately sends a death threat based on it and I don't know what to say about that really but it does seem to be the way we're going.

13:12And I got through it. The framework was passed. My life started to go back to normal. I have a website at Stanford where we share free resources for teachers that teachers love and are accessed by millions of teachers. And everything seemed to, you know, I could go back to that important work. But then yesterday, it all kicked off again. And somebody shared the group that's against me shared that they were going to tell Stanford to fire me. And so I'm back now. I'm back trying to deal with this. It's also a new theme in academia. Climate scientists are under a similar kind of attack, but people are surprised that it's a person in maths education that surprises them.

14:02No kidding. Like I said, my head is exploding. I just don't get this. Of all the things in the world, you have to pick a fight on. Why this? Anyway, let's get off this cesspool here. First, I want you to explain the concept of narrow maths. What makes maths narrow? What makes math narrow? It's really come from our textbook companies in the US. Somebody set out all the standards that are important in mathematics. And I learned through my framework work that nobody actually meant that as a guide to teaching. It was more of a, this is all the detail of everything. And what the textbooks have done is take all these short statements about maths and turn them into narrow questions for students.

14:51So their experience of learning maths is often just going through lots and lots of short questions that are not meaningful to them and really just are targeted at teaching a sort of narrow method where we have a lot of research that shows that we want to engage students in bigger more complex problems where they get to think and reason and talk to each other and solve mathematical issues in the world and really make maths something that's meaningful to them, but they see that it's helping them in the world. And we don't have that in classrooms. And a lot of people have had the narrow maths experience and left maths as early as they can.

15:40Or worse, they've really come to believe that they can't do it. And many times people feel that if they can't do it, they're not a full person, that there's something wrong with them. Math has given a lot of status in our society. So it's important to students to feel they can be successful. So yeah, we have this experience of narrow maths, and it's been spectacularly successful at helping only a narrow group of students go forward. Only some students are inspired by that experience of working through short questions. And the book, my new book, Mathish, is really about making maths a much more interesting subject for students.

16:27One of the initiatives of the framework was to take all of those isolated tiny standards and to make them into bigger ideas that teachers could organize their teaching around and bring in rich tasks. What I don't understand is for many people, Okay, obviously there is a small segment that they love it because it's going to help their SAT score. They figured it out, blah, blah, blah. Yeah. And get into Ivy League schools and all that. But how did we get to this place where I think much of the student population and parent population, they just dread math. They see math as like the equivalent of the Navy SEALs Hell Week, where the purpose is to get people to drop out.

17:16Right. Look, how did we get to this place? How did we? That's a good question. Many years ago, when mathematics was put into the curriculum in schools, it was really there to help people work in shops. So they needed to be good at calculating with numbers. and curriculum was set out in the 1800s that went from all of that calculating with numbers into algebra and geometry. And we have continued to teach those exact ideas hundreds of years later, even though the mathematics of the world has changed a lot. And we don't need to teach kids to be little calculators because we actually have tools in our modern society that does that work better than they do.

18:01What we need is to teach them to make sense of problems and be able to interpret results so that they can make important contributions.

18:17so give me an illustration of an example where the ability to solve narrow maths is not nearly as relevant in modern society as this more generalized creative approach so what's the problem people will face whether they're using math they need math they may not even realize it, that this is the kind of math we need, not the ability to solve a quadratic equation on a SAT test. I'll tell you a story, and this is also a controversy that's happening now in California. We have developed a data science course in our center at Stanford. It's a one-year high school course. And there has been the moves in California and across the country to have that be a high school course for students that is an alternative to say algebra two, which is that course where you're doing lots and lots of algebraic equations.

19:14Now there's pushback and people saying it shouldn't be, but we developed this course and we studied it. And inside our study, we gave students who were in algebra two classes and students in the data science class, the same test question. And it actually asked them to look at some data and develop a function to make sense of it. So we gave them some data about health and poverty in different countries and how many calories people took in and how that related to their lifespan and asked them to make sense of that table of data. So the students in data science did significantly better than the students in Algebra 2, even though it was a test of algebra, because the kids in Algebra 2 just learn all these formulas and when they come to seeing a table of real data from the world they don't know how to apply those formulas to the table it's a really basic kind of algebra concept that you can look at numbers and plot them and see the relationship and they just didn't know how to do it they had all these formulas and what we teach the kids in data science is to make sense of a situation and to analyze patterns and to see what's happening.

20:31One place that this would have really helped in recent years is understanding COVID data. When the pandemic was happening, our screens were filled with linear relationships shown on graphs, the relationship between vaccines and mortality, all sorts of different things. And if students haven't learned to look at a situation like that and make sense of it, they were not in a good position to be helped during the pandemic. Yeah, in the modern world, what we need students to be able to do, I think Conrad Wolfram puts it well. People probably have heard of Conrad Wolfram. He created Wolfram Alpha with his brother and Mathematica and their technology powers both Alexa and Siri.

21:20And he says, this is what we do mathematically in our jobs and in our world. We form a question. We work out how to make that into a computable answer. We do the computation and then we analyze the results. But there's four part process. But in school, it's all about just doing the computation. So students aren't given situations where they ask their own question and then they think, how can I make this into something I can calculate to find something important. And one of the things he's done is he's made an entire high school curriculum, taken out all the parts where students are learning methods to do by hand, that in the modern world are always done by computers.

22:07And instead, our students to program those into a computer and analyze the results. And it's taken, and it's freed up a lot of time. So students can now work on these really cool projects like designing drones and analyzing music. So that is the idea. We can do a lot better in our maths teaching if we really think about what the students really need. We need them to reason and problem solve and solve complex problems. We don't need them rehearsing methods that don't mean anything to them. This is somewhat of a facetious hypothetical question, but do you think if you asked your random American sample, let's say you told them one out of five million people who got a COVID vaccination died, but one out of 100 ,000 people who didn't get a vaccination died, should you get a vaccination or not?

23:07Do you think a lot of people would say, no, vaccination is too dangerous? Are you talking about that basic a level? I do. And what we've done in maths education is make people afraid of maths and afraid of numbers. So they probably wouldn't even engage in their thinking. Many people will look at numbers and move away from them and not look at a graph, not look at a set of numbers. It just provokes fear and anxiety. Yeah, I do think that. Madison and I are surfers. We love to surf. And we always, well, I always encounter people when I say you ought to try surfing. And they say that, no, because I could get eaten by a shark.

23:54And then I point out there have been like, I don't know, three shark attacks, fatal shark attacks in the world this year. The most dangerous part of surfing is driving over the hill from Menlo Park to Santa Cruz on Highway 17. Much higher probability you're going to die because a truck runs you over. Then you're going to get eaten by a shark. But they still say, no, I'm afraid of sharks. Like, how do you even deal with it? I would say you deal with that by giving people a good mathematics education where they're able to make sense of probabilities. Probability is an area that people are totally terrified by and won't engage with.

24:37Yeah, I'm a strong believer that giving people a high quality education is going to protect them in many ways in the world. Understanding probabilities is one. Also, in the modern world, we know that young people are going to be sent a lot of data and data visuals that are incorrect, that are intended to mislead them. and we need to protect them by being used to looking at data and data visuals and thinking, who sent this? Why did they send it? What does it mean? Is it all the data or is it manipulated in some way? And so there's a strong need to help our students for this kind of data literacy.

25:18So if I was plopped into a data science course as opposed to an Algebra 2 course, what would I immediately notice as the difference between data science and algebra? One of the big differences is students start with a data set and they are encouraged to ask questions of that data. What can we learn about the world through asking a question? It's their own question. And then they use methods to interrogate it. They're going to learn some technology in data science. You're going to learn a little bit of coding and use data platforms that are really helpful. And they're going to come up with a result and they're going to interpret that result and communicate it.

26:07In an Algebra 2 course, they're probably going to be moving symbols around a page and coming up with the different symbols. The students who take the data science courses are very clear about this. This is meaningful mathematics. It means something to me. I understand it. This isn't just pushing symbols around a page. It's something that's powerful for the world. So it's amazing that we now have people pushing back on students learning data science, saying they should not have a data science course in high school. And the particular pushback we're getting now is people saying we shouldn't have a data science course in high school because it's not got enough algebra in it.

26:52Wait, it hasn't enough algebra in it in order to prepare you for the SAT, in order for you to go to the Ivy League? Is that kind of the thing? Yeah. Some people are genuinely worried that if you want to be in a STEM major in college, then you need a lot of algebra. But instead of saying, well, let's, because one of the things we know about data science is a lot of kids go into it feeling like math they hate math they never want to do another maths course and then they realize that maths can actually be interesting and they become excited about it they want to go further in stem so a better move from these people who are concerned about maybe they need to go they're going into stem they need a lot of algebra is to think about what could we offer them after data science that could bridge into more algebra, more calculus.

27:48If I am a college and I have students coming who've taken, many students take data science in year three and then statistics in year four, AP stats maybe. If I have a student coming through that statistics pathway, is there a bridging course I can offer at the college so that they can get more onto that calculus track of lots and lots of algebra? that would be more sensible than saying, let's ban data science for everybody. And in their banning of data science for everybody, they're doing that for kids who are never going to go into STEM and for whom that data science course is actually really important.

28:24You could make the case that data science is more important to the survival of society than advanced math. Absolutely. And of course, if you take a data science course, you're more likely to develop perhaps a critical perspective on things that are sent to you in the world. And so there is some line of thinking that people don't want our whole population to have that data awareness. Yeah. God forbid people could think like that. Yeah. So what about the pushback that people say, we have to teach math this way because it helps the human brain develop problem-solving techniques, which seems to me you just said refutes, the research refutes that.

29:13It does. Kids need math because it's going to help them develop their brains. It does develop their brains, but the maths that really develops their brains is one that's what I call multidimensional. One of the things we know about our brains is we have five different pathways that can process mathematical ideas. Two of them are visual pathways. They're at the back of the head. And so we also know that mathematicians, when they've looked at their brains as they're working on maths, what's different from other academics is they're using those visual pathways. So on our website, YouCubed, we make a lot of the mathematics visual.

29:53We know that students are really helped by a visual or a physical model of mathematical ideas. I really like some of the recent neuroscience that's showing that as we go around the world, all of us, we're building mental models of ideas. That's how we exist in the world. So this scientist, Jeff Hawkins, gives us an example of knowing a stapler. If I was to ask you, what do you know about a stapler? You would probably say, I know what it looks like. I know what it feels like. I know what it sounds like. I know what happens when I use it. You have built all of these ideas about a stapler. And in maths, we need to build those mental models for kids.

30:40So when they're just going through number calculations, they are developing one area of their brain. But if they're building and if they're drawing and they're seeing maths conceptually, then their brain is getting a full workout. They're getting these different pathways involved. I think the brain argument that narrow maths is building your brain doesn't work for me because narrow maths might strengthen one area of the brain, but it's leaving completely neglected the other areas that we really need to exercise. Could you make the argument that an abacus or a slide rule is a good thing? That's more visual, it's more tactile.

31:25Yeah, definitely. I think an abacus is a great tool for students learning. One of the things we've learned from neuroscience in recent years is how important our fingers are and that students who develop greater knowledge of their fingers do better in math. fingers are like a number line that we carry around with us and they directly map into a part of the brain that's using that so it it's really no wonder finger any sort of finger work leads to really greater maths achievement but what was your question no just i was thinking when you're talking about tactile and visual and not just solving equations that an abacus is as tactile oh yeah so an abacus is great it's tactile it gets finger use that's what made me think about the fingers and yes in one of the ideas in my book that i share maybe i could share this now is the idea of approaching maths with an ish lens i was coming that was my next question so Tell me what the ish in math is.