Jo Boaler: Empowering Students Through Innovative Math Education

Guy Kawasaki:
I'm Guy Kawasaki and this is Remarkable People. We're on a mission to make you remarkable. Helping me in today's episode is Jo Boaler. 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, Boaler 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. Prior to her role at Stanford, Boaler served as the Marie Curie Professor of Mathematics Education in England. She co-founded youcubed, an organization dedicated to providing resources and ideas to inspire and excite students about mathematics.
Boaler has received several honors, including the National Science Foundation Early Career Award, the NCSM Kay Gilliland Equity Award in 2014, and the CMC Walter Denham Mathematics Leadership Award in 2015. She has authored nineteen books and numerous research articles. Her latest book is called Math-ish: 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. All 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 Jo Boaler was attacked by Tucker Carlson and Elon Musk. That should tell you something.
I'm Guy Kawasaki, this is Remarkable People, and now here's the remarkable Jo Boaler. I 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 sixty-four." So that kind of stopped my preparation because I was saying, "How can there not be sixty-four squares?"
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 sixty-four, so why is the answer not sixty-four?
Jo Boaler:
Well, you're exactly right, that if we look at an eight by eight chessboard there are the sixty-four 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.
Guy Kawasaki:
So I passed the test?
Jo Boaler:
Yes, you did.
Guy Kawasaki:
We can end this recording right now.
Jo Boaler:
Yes.
Guy Kawasaki:
Can we go someplace? Just a temporary diversion here. You can tell me no, you don't want to do this, but I got to ask you about this whole Tucker Carlson thing. What the hell happened there?
Jo Boaler:
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 twenty 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. I was sitting, just having a usual Friday night at home when I started to see all this hate mail filling up my email, and I said, "What has happened? I don't understand this." 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. That started a pretty tumultuous time.
Guy Kawasaki:
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.
Jo Boaler:
Exactly.
Guy Kawasaki:
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?
Jo Boaler:
One of the things why they're against this is kind of a deep question. I 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.
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, and 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. So as soon as we entered into that realm of, "Let's not have students who were of a young age in tracks," that alerted a set of people that things were going to change.
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.
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 was a really odd situation that all of the news about it was negative, yet all of the educators in the state supported it.
Guy Kawasaki:
When you say the very successful people, are you talking about people successful in the math profession or successful as titans of Silicon Valley? Who are these people who are trying to perpetuate the old way?
Jo Boaler:
Both, some particularly powerful people in Silicon Valley are 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, all of the leaders, the CEOs I spoke to said they're not going to come because you are coming."
So they really did a good job of making me the enemy of kids advancing in math, so that is how they think of me. It's really distressing actually.
Guy Kawasaki:
Jo, 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?
Jo Boaler:
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. What I don't support is writing off students from a young age, but yeah, that's basically where we are.
Guy Kawasaki:
I have to say I'm just scratching my head. 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. 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, it's really venture capital disease, and now you should tell teachers how to teach and all that. I just want to throw up. I just want to throw up, I tell you.
Jo Boaler:
Yeah, you're definitely naming something there. That was part of the distressing thing about the pushback of the framework. There'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."
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 believed that, "A maths professor says it's wrong," they shared it with everybody. Nobody stopped to think, "Does a maths professor understand the K-12 education system?" That didn't come up for anybody. It's been quite a few years working on this.
Guy Kawasaki:
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? Are there threats on your life? What happens?
Jo Boaler:
Yes, I did get threats on my life, and my children's, which is particularly scary. 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.
It's 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. I don't know what to say about that really, but it does seem to be the way we're going, and 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 teaches love, and are accessed by millions of teachers, and 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, 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 similar kind of attack, but people are surprised that it's a person in maths education, that surprises them.
Guy Kawasaki:
No 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?
Jo Boaler:
What makes maths narrow? It's really come from our textbook companies in the US, somebody set out all the standards that are important in mathematics. 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." What the textbooks have done is take all these short statements about maths and turn them into narrow questions for students.
So their experience of learning math is often just going through lots and lots of short questions that are not meaningful to them, and really just targeted at teaching it a sort of narrow method.
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, where they see that it's helping them in the world, and we don't have that in classrooms.
A lot of people have had the narrow maths experience, and left maths as early as they can, or worse, they've really come to believe that they can't do it. Many times people feel that if they can't do it, they're not a full person, that there's something wrong with them. Maths 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.
The book, my new book, Math-ish, is really about making maths a much more interesting subject for students. One 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.
Guy Kawasaki:
What I don't understand is for many people, 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, 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 the equivalent of the Navy SEALs' Hell Week where the purpose is to get people to drop out, right?
Jo Boaler:
Right.
Guy Kawasaki:
How did we get to this place?
Jo Boaler:
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.
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.
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. What we need is to teach them to make sense of problems, and be able to interpret results so that they can make important contributions.
Guy Kawasaki:
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. What's a problem people will face where they're using math, they need math? They may not even realize that this is the kind of math we need, not the ability to solve a quadratic equation on a SAT.
Jo Boaler:
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 II, which is that course where you're doing lots and lots of algebraic equations.
Now there's pushback, and people are 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 II 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.
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.
The students in data science did significantly better than the students in Algebra II, even though it was a test of algebra, because the kids in Algebra II 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.
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. One place that this would've 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. 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.
In a 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. 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." There's a 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?"
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 method to do by hand, that in the modern world are always done by computers, and instead ask students to program those into a computer and analyze the results. 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.
Guy Kawasaki:
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 a 100,000 people who didn't get a vaccination died. Should you get a vaccination or not?" Do you think a lot of people would say, "No, vaccination is too dangerous," are you talking about that basic a level?
Jo Boaler:
I do. 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 the 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.
Guy Kawasaki:
Madisun and I are surfers, we love to surf, and 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." 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 than you're going to get eaten by a shark, but they still say, "No, I'm afraid of sharks." How do you even deal with it?
Jo Boaler:
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. I am 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?" So there's a strong need to help our students with this kind of data literacy.
Guy Kawasaki:
So if I was plopped into a data science course as opposed to an Algebra II course, what would I immediately notice as the difference between data science and algebra?
Jo Boaler:
One of the big differences is, 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. In an Algebra II 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." 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."
Guy Kawasaki:
Wait, 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?
Jo Boaler:
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 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, "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 and more calculus?"
If I am a college, and many students take data science in year three, and then statistics in year four, a piece of that 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 and lots and lots of algebra?
That would be more sensible than saying, "Let's ban data science for everybody." 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.
Guy Kawasaki:
You could make the case that data science is more important to the survival of society than advanced math.
Jo Boaler:
Absolutely. Absolutely, and of course if you take a data science course, you are more likely to develop perhaps a critical perspective on things that are sent to you in the world. So there is some line of thinking that people don't want our whole population to have that data awareness.
Guy Kawasaki:
Yeah. God forbid people could think like that. 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 the research refutes that.
Jo Boaler:
It does refute that.
Guy Kawasaki:
Kids need math because it's going to help them develop their brains.
Jo Boaler:
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. 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. We 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 are building mental models of ideas, that's how we exist in the world.
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.
So 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.
Guy Kawasaki:
Could you make the argument that an abacus or a slide rule is a good thing? That's more visual, it's more tactile.
Jo Boaler:
Yeah, 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 maths. 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. It's really no wonder finger, any sort of finger work leads to really greater maths achievement. But what was your question?
Guy Kawasaki:
No, I was thinking when you're talking about tactile and visual, and not just solving equations, that an abacus is tactile.
Jo Boaler:
Oh, yeah. So an abacus is great, it's tactile, it gets finger used, that's what made me think about the fingers, yes. 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.
Guy Kawasaki:
I was coming, that was my next question. So tell me what the ish in math is.
Jo Boaler:
Yeah. You made me think about that when you talked about slide rules, and I'll tell you why it connects to that. So I make an argument that in maths classrooms maths is very precise, it's always precise, but in the real world, almost always when we use numbers, they are ish numbers, and those are good enough.
Some different examples are like how much of the moon can I see? Or how much rain fell last night? Or how old are you? Or how long will this drive take to the airport? Or how much paint do I need to paint the wall? All of these are actually not very precise numbers, they're ish numbers. That's a disconnect for kids. Precise is important, but we need those to be more in balance.
But I also know that when kids are ishing numbers, I can give you an example, if I asked you to work out or asked anybody to work out, let's say 287 divided by nine, most people could give an ish answer to that. They couldn't do the precise calculation in their head; they could give an ish answer.
But being able to ish an answer means you have numbers set, and when you ish you're staying at that conceptual level of the what do these numbers mean. When we go into the precise mode, what happens is a lot of kids get lost in that precision.
I hear from teachers, "My students don't have number sense. They do these calculations and they give wild answers. They don't think about what the numbers are." My recommendation in the book is before anybody does a calculation, any student in any classroom, you should ask them to ish the number first because then they're staying at that conceptual level.
Anyway, I put that recommendation in the book, I've been talking about it, and I get this email from a teacher saying, "This was amazing. I went to my classroom, I asked the kids to ish numbers, and we looked at the precise number and they talked about the difference, and they started asking each other, what's your ish number?"
She said something amazing happened, that all these students who don't normally engage in maths are suddenly jumping in and sharing their ish numbers. We went down and we videoed the class, we're putting the video on our website, and all these kids are engaged. The principal came into the lesson with us, and she was beaming from ear to ear.
She said, "These students who are sharing ish numbers are the ones who are normally outside the office because they are so badly behaved in the class." These students, when we talk to them were saying, "This is the world, ish numbers are our world. They're what we use when we talk about time, when we pour things out and measure liquids."
Now, maths is meaningful to them, and it's also keeping them at this really important conceptual level. Anyway, I've just become very excited about ish. When I was sharing Math-ish to an audience, one of the audience members said, "Oh, my father was a rocket scientist, and he talked about how they used to measure with slide rules, and really had to have an ish idea of what their measurement was.
But now they just do it all with technology, and so they make mistakes because they're not ishing the number, they're just taking this number from the technology and using it, and mistakes are happening much more often." So that was what made me think about your slide rule thing.
One last thing. If people say to me, "Isn't ishing the same as estimating?" My answer to that is it is the same thing, but when we ask students to estimate a number, they often think, "Oh, this is another mathematical method," and they calculate it precisely and round it off to make it look like an estimate.
But when we ask them to ish numbers, something amazing happens and they become more free, and they're more willing to share their ish numbers. I'm pretty excited about it as a concept, and teachers are very excited about it so that makes me excited.
Guy Kawasaki:
I have to say I love the concept, and I have a suggested alternate title, although the book's laid in granite, it's ready to come out or it's out already, but I'm going to give you all the caveats why this is a lousy title.
Jo Boaler:
Okay.
Guy Kawasaki:
You also have to be old to understand this, but a title for your book could have been Thirty Something, because when you say what's 275 divided by nine, you say, "Thirty something," right?
Jo Boaler:
Right. Right.
Guy Kawasaki:
But that was a great TV show.
Jo Boaler:
Oh, it was? Yeah. Now we have other TV shows with ish in the title, but yes, I think that could have been that.
Guy Kawasaki:
So you make a passionate appeal why, maybe because you're British, but it should be maths plural, not math, right? So why didn't you name your book Maths-ish?
Jo Boaler:
There were two reasons I didn't call it Maths-ish. I do say maths, and I do prefer maths because it's short for mathematics, all the ways of being mathematical, and I found math, the word math, very narrow-sounding. In England, we do call it maths, but I didn't call it Maths-ish for two reasons.
One, the publishers always make me write math because it's going to an American audience, so the book is full of the word math anyway, but also Maths-ish is a bit of a tongue twister and it's hard to say. So I don't worry so much about it sounding narrow when it's Math-ish, it's not a narrow word like math.
Guy Kawasaki:
Okay. Now, so in this perfect world or this fantasy world, maybe someday there's a SAT-ish, right?
Jo Boaler:
Oh, yeah, right.
Guy Kawasaki:
Where you could have approximate answers just to measure your reality and your reasoning, not your precision.
Jo Boaler:
That would be a great idea actually. It would measure kids' number sense, which is what they really need in the world. Actually, you reminded me that there was ishing. One of my arguments I give in the book is that ishing is really helpful with standardized tests.
Guy Kawasaki:
Why?
Jo Boaler:
Lots of time they give standardized test questions and ask you, "Which of these is correct? Which of these answers is correct?" Of course you can ish your way to the correct answer a lot better than you can calculate it. One of the standardized test questions given out to students across the country, a NAEP question, they were asked seven-eighths plus twelve-thirteenths, and then they were given four choices.
Is that closest to one, two, nineteen or twenty-one? You can probably think seven-eighths is nearly one, and twelve-thirteenths is nearly one, so chance that it would be two. The most common answer given by seventeen-year olds was nineteen. The second most common answer was twenty-one.
Guy Kawasaki:
How can that be?
Jo Boaler:
So that happens because these kids dive into calculating, they have never ish questions in their lives. So they look at that seven-eighths plus twelve-thirteenths, and they think, "I have to do a calculation," and so they get lost in the calculation.
Obviously, the nineteen is the seven plus twelve, and the twenty-one is the eight plus thirteen, but it's tragic, and could be avoided if we got these kids getting used to ishing numbers. This is why I'm finding that teachers immediately know how powerful this idea is because they know that's what students need, but they haven't had a way of getting them to do that, and feel comfortable about it.
Guy Kawasaki:
So if you were to apply narrow math to that problem, step one is to what? Find the common denominator so you can get it exactly right?
Jo Boaler:
Step one would be, yes, to add eight and thirteen. You'd have to find a number that eight and thirteen goes into, and convert them into common denominators, and add the numerators. It's a whole method.
Guy Kawasaki:
Seriously, this could be a matter of life or death. If you have to make a calculation like that and you come up with nineteen when it's closer to two, you literally could endanger yourself.
Jo Boaler:
I agree. Yeah. If you are using maths in the workplace, then you're making those kind of errors. One thing teachers always says, "We want students," and employers say, "We want people to know when an answer is reasonable," and that's what ishing is so helpful with, it's giving kids that idea of what's reasonable.
One of the students we interviewed when we went to the school that day said, "Oh, I get so annoyed in maths that we do a calculation, and then we have to do the whole thing again to check it's right. But now I don't need to do that because I ish the answer first, and then I can see from my calculation whether it's right." I just think there's many uses of ishing.
Guy Kawasaki:
I love the concept. Jo, I think life is one big ish if you ask me.
Jo Boaler:
I agree.
Guy Kawasaki:
Right? Life is an ish.
Jo Boaler:
You can ish your way through life and do a lot better.
Guy Kawasaki:
It's like surfing, the waves are one to two ish.
Jo Boaler:
Right?
Guy Kawasaki:
Right. There are four ish. You don't need to know it's four point sixty-five feet.
Jo Boaler:
You don't need to know that. That's another really good example. I should add surfing to my list of examples. If people took more of an ish approach to then things in their life, not just numbers, it would help them. It's not about these binary right and wrong. I know that a lot of kids fear maths, a lot of kids and a lot of adults, and actually what they fear is that precision that it's right or wrong, and often they're wrong, and that is what they fear about it.
When we take an ish approach to numbers, it really softens the edges of maths for kids, as well as giving them access to that conceptual thinking. I should say what I'm not saying because I get misquoted in the media all the time now, and I'm not saying that precision is not important, but I am saying we should be more balanced. When kids are both ishing and being precise, it gives them a much more powerful experience.
Guy Kawasaki:
Great. I love this concept. I think much of your book is discussing about how because of the teaching techniques, or because of the expectations of society that there's much, I don't know, negativity and stuff surrounding math. There's people who believe that you either have a math brain or you're not, which is completely contrary to Carol Dweck's thinking, and apply the growth mindset to math.
Jo Boaler:
Which is what I love to do. I've been inspired by Carol Dweck's work, and really decided, about ten years ago, to try and get it into maths education more, because we have a population, about over 90 percent of parents in a survey said that their children either had a maths brain or they don't, or they didn't. That myth of the maths brain is still very widespread.
So Carol Dweck has shown, and neuroscientists have shown, that our brains are constantly changing, and developing, and growing, and connecting. One of the pushback to the framework was the anti-mindset people, who said that mindset is wrong and it shouldn't be in the framework. There's a whole group of people who are against mindset it turns out.
I really think that any good idea in the world these days, there will be people against it somewhere, but it's very important to math that teachers know that students can learn what they're teaching. Many teachers still think their role is to figure out who is the maths person and who's not, and so it's been important to change that.
Guy Kawasaki:
Do math teachers come to this kind of conclusion because they're basically expected, and they're reviewed on their capacity for their students to get high standardized test scores? Is that the root of the problem?
Jo Boaler:
Yeah, I think standardized test scores are a part of the problem. The massive amount of standards in the curriculum is part of the problem. Teachers don't go into depth on anything, they have to skim through lots and lots of methods. There's a few parts to the problem in education, but standardized testing is one of them.
If you teach narrow maths, if that's what you think maths is, and that is what most people think maths is, it's narrow subject of calculations and methods, if you teach narrow maths, then only some students will be successful.
So it perpetuates this myth that teachers have, that only some students can be successful. It's not about the way they're teaching, it's just the way of the world. It just reinforces their idea that to be good at maths, you're just a special kind of person, and only a few people can be that kind of person.
Guy Kawasaki:
But at extremes, surely, there must be some people who are just gifted in math or gifted in physics. You can't say that Stephen Wolfram is a random person.
Jo Boaler:
Some people have developed incredible brains, this is not an argument that people are the same. The question is though, how did he develop that brain? My problem with the idea of a gift is it's very fixed, like you have it or you don't, whereas we know that everybody's on a growth journey. You can't make a cutoff point and say, "You have a gift. You don't have a gift."
Everybody's on a growth journey and can develop and grow their brains. One of the people I like to share is somebody called Nicholas Letchford, who when he was growing up, his parents were told he was learning disabled, he had a very low IQ. Do you believe in IQ? He graduated from Oxford with a doctoral degree in applied mathematics after huge problems as a younger child learning anything.
We know, we have millions of examples, or we have lots of examples of people who had really strong difficulties and went on to achieve amazing things. It's not that some people are born with something, they end up with something, for sure. There are people whose brains are incredibly powerful, but where does that come from?
Everybody's born with a different brain. Nobody is born with the same brain. Everybody's is different. But the millions of opportunities you have to change your brain as you go through life, even as a baby and in the early years, those opportunities make more difference than differences that we are born with.
Guy Kawasaki:
What if I were, like pushback on you and say, "Okay, so you just cited me one example of someone who had all these learning challenges and was cast into a particular bracket of not being able to do math and overcame that, got a PhD at Oxford, so yeah, you picked one example, but then someone on the opposite side could say, I know this person and he got vaccinated and he died, so that proves vaccination is bad."
One data point either way. How are people supposed to figure out that citing one vaccination death is misleading? What you just did could be just as misleading, no?
Jo Boaler:
Yeah. No, but I would say that somebody who has a vaccination and died, you don't know why they've died, you can't say that vaccination caused them to die. But when you look at people who overcome significant difficulties, and go on to learn incredible things, even one person shows you that can happen, that the way we approach learning in life can change what happens for you even when you start off in a hard place, and we have not just one example, we have many examples that show that.
There was a school situation, I remember, in England that's really interesting. In England you take an exam at sixteen, and they're in three different levels, the lowest one, the middle one, the higher one, and if you get put into the lowest exam, the highest grade you can get is a D, so it matters which exam you're put in for.
One school I worked with years ago just said, "You know what? I'm going to put all the kids into the highest paper, and we're going to prepare them all for the highest paper." Those kids all got the grades on the highest paper. She didn't change her teachers, she didn't, she just said they're all going to do that work, and they all got one of those highest grades. We know that fixing people, and deciding people have issues, and they can't learn is just not the right approach in education.
Guy Kawasaki:
This is somewhat of a related story. I have been able to moderate several panels with chancellors of large universities.
I often ask them about admission policies, about relying on standardized tests, and essays, and all that, and I posed to several of them like, "Why don't we try an experiment? Why don't you just say everybody apply and we are just going to randomly select people to admit, and let's just see what happens. Does that produce a more successful student body than our laser focus on SAT and college essay, and recommendations?"
Jo Boaler:
That's interesting.
Guy Kawasaki:
I did not get a lot of support for that idea.
Jo Boaler:
I bet you didn't. It's what the UCs did actually, they've always used SATs as the filter and measure of whether kids can be successful in the UCs. Then they dismantled that, they got rid of SATs, it's no longer used, and what they found was their students are just as successful. They're bringing in a more diverse group of students, they're more racially diverse, and they're doing just as well as when they had the SAT as a filter. So that kind of is your experiment a little bit.
Guy Kawasaki:
I think you make a point in your book that by bringing in a diversity of students, some of whom are not as successful at that point as others, that everybody benefits, because even the ones who are doing better learn from watching how the ones who are not doing better are learning. So watching people struggle can help you learn how to be a better student.
Jo Boaler:
Also, we know that helping others learn helps yourself. We see this when students are in more diverse groups in terms of their prior achievement. What we've found is the ones who are most helped by that are the highest achieving students, and the reason is they're spending time helping other students, and of course, anyone who's taught knows that the best way to learn something deeply is to teach it. It also means kids think differently.
Sometimes high-achieving students are very narrow in their thinking, they've been successful, but there's only one way they can think about it, and they sit in a group for the different kind of student who sees something visually, and it's surprising to these other students, and they learn a different way of approaching things. So I do think diversity, in all sorts of forms of diversity enriches students' experiences in schools and in their learning.
Guy Kawasaki:
That would take us right back to our friend Tucker Carlson, which is if he understood this, he would insist on diversification because it would make everybody better, including a white kid destined for Ivy Leagues, right?
Jo Boaler:
It would make everybody better, and that's something that people don't get. Some of the people who push back on any sort of anti-tracking messages say, "I don't want my kids in classes with those kids."
That's the insidious underpinning of the pushback on tracking, people want to keep their kids separate from other kids, but they don't know that when we have these environments where students are together, and they're more diverse in all different ways, it benefits everybody. That's definitely what the research shows.
Guy Kawasaki:
Now my brain is multiprocessing and I'm thinking, so if I started surfing with surfers who are not as good as me, would that make me a better surfer?
Jo Boaler:
If you were teaching them, then probably it would, because the teaching would make you a better surfer.
Guy Kawasaki:
I'm going to start telling Madisun to teach me how to surf, because she would then be teaching someone not as good as her, and it would help her improve too.
Jo Boaler:
That's right.
Guy Kawasaki:
My last topic, the topic that I love and I want to understand more, is the concept of metacognition. For those of you listening, that has nothing to do with the intelligence of Mark Zuckerberg and Facebook. So what is metacognition?
Jo Boaler:
I never thought of that link. Metacognition, a lot of people think metacognition is thinking about your own thinking, and there is a piece of that, but metacognition and people with metacognitive ideas, it's more than that. It starts with self-belief, it has growth mindset in it, you believe that you can do something.
But then somebody who's metacognitive has different ways to approach a problem, maybe they have a range of strategies they have learned, we talked about one at the beginning, trying a smaller case. They have a range of strategies, and they're willing to try these different strategies out, and then they see metacognition in a part of the brain, and it's pretty powerful.
One of the things I do in the book is urge people to teach students how to learn. I think as maths teachers, we often think I'm there to teach maths, but actually many kids haven't learned how to approach maths well, and they may have learned counterproductive ideas. Teaching kids how to learn, teaching them how to be metacognitive is really important.
Guy Kawasaki:
Let's say I'm a parent, and I've listened to this whole podcast, and my kid is seventeen, eighteen, nineteen years old, he or she is the product of a school system that was geared towards standardized tests, and Algebra I, Algebra II, Algebra III, so you can get into pre-calculus, so that you can get into calculus, so you can get into the Ivy League, so that you can have a STEM career.
He hates maths. She hates maths. We got him tutors. We did everything we could. We dread math. What do you do if you are midstream and you're stuck in this position? Now, you listen to this podcast, you read your book, and you're saying, "The whole system is screwed up. What do I do for my kid?"
Jo Boaler:
I think what's really important for all of us is that we develop a playful relationship with maths. We see maths as just a playground of ideas that we can try out and investigate things. So I deal with those people all the time because I'm always running workshops for teachers, and many teachers were in that position, they hated maths, and they saw it as a list of methods to memorize, and we introduced them to playful maths.
We give them activities where they're making connections and seeing things differently. Many times teachers have cried or become very emotional, and said, "Oh, my gosh, I just didn't know maths could be like this, and I didn't know I could do this."
So I think shifting people, getting them out of that narrow maths experience, it's almost like a therapy people need, in to seeing maths differently is really important. Some adults go through that transition from reading books, maybe they read Math-ish, and that takes them on that path, and then they start to engage with maths differently.
Some people need more than that, they need to go to a workshop or something where they're able to experience maths differently, and that will get them shifting. Many people make that shift, and they're always happy when they make the shift, but we have to encourage more people to make that shift to see maths differently, not as this rigid set of numbers, but as this ish playground.
Guy Kawasaki:
Okay. I want you to get really tactical. I'm listening to this podcast. I'm a real believer my kid hates math. I'm afraid of math for his or her future. What do I do? What do I do? Not conceptually, what do I do?
Jo Boaler:
We have a number of resources on our website to help people. One of them is an online class, it's completely free, six fifty minute sessions that people can take. It changes their mindset. It changes their approach to maths. We have a lot of evidence of that. We've studied it with randomized controlled trials. Students who take it engage differently in maths class afterwards, they score at high levels on tests afterwards.
Come to youcubed and look at the online class, it's really for adults or children, and look at the other resources that we share. I'm really passionate about changing people's relationships with maths. We have youcubed, we have a new maths app now called Struggly, we have books, many different resources aimed at really giving people that different maths experience.
Guy Kawasaki:
I have to admit, I love the ish concept. I'm going to become an ish evangelist, where you live your life approximately, logically, realistically, roughly right. I love that concept. Life is too short to be too precise. So thank you Jo Boaler for introducing me to this concept.
Now I'd like to thank the Remarkable People team, that would be precisely Madisun Nuismer, producer and co-author of Think Remarkable. You must read this book. Maybe we'll rename it Think Remarkable-ish. Then there's Tessa Nuismer, Tessa prepares me with all the background research, and perfects our transcripts.
Speaking of perfection, there is Jeff Sieh and Shannon Hernandez, sound design engineers extraordinaire. Finally, Luis Magaña, Alexis Nishimura, and Fallon Yates. We are the Remarkable People Team, we're on a mission to make you remarkable. Until next time, mahalo and aloha.