AI transcript
0:00:12 I’m Guy Kawasaki and this is Remarkable People.
0:00:15 We’re on a mission to make you remarkable.
0:00:18 Helping me in today’s episode is Joel Bowler.
0:00:22 She is a professor of education at Stanford University.
0:00:28 She joins a handful of people who have been on Remarkable People more than once.
0:00:34 She began her career as a secondary mathematics teacher in urban London schools including
0:00:37 Haverstock School in Camden.
0:00:42 After teaching, Bowler received a master’s degree in mathematics education from King’s
0:00:43 College London.
0:00:49 She then completed her PhD in mathematics education at the same university and won the
0:00:57 award for best PhD in education from the British Educational Research Association in 1997.
0:01:03 Prior to her role at Stanford, Bowler served as the Marie Curry Professor of Mathematics
0:01:05 Education in England.
0:01:12 She co-founded U-Cubed, an organization dedicated to providing resources and ideas to inspire
0:01:15 and excite students about mathematics.
0:01:20 Bowler has received several honors including the National Science Foundation Early Career
0:01:30 Award, the NCSM K. Gilliland Equity Award in 2014, and the CMC Walter Denham Mathematics
0:01:33 Leadership Award in 2015.
0:01:37 She has authored 19 books and numerous research articles.
0:01:44 Her latest book is called Mathish, Finding Creativity, Diversity and Meaning in Mathematics.
0:01:50 In this book, she shares research on embracing a diverse approach to learning math and providing
0:01:55 seven principles to reframe our relationship with the subject.
0:01:59 All of what you just heard is a typical, remarkable people introduction.
0:02:05 It’s a long story and it would take a lot to explain what happened and it would also
0:02:09 take a lot of research to get both sides of the story.
0:02:15 But suffice it to say that Joe Bowler was attacked by Tucker Carlson and Elon Musk.
0:02:18 That should tell you something.
0:02:19 I’m Guy Kawasaki.
0:02:31 This is Remarkable People and now here is the remarkable Joe Bowler.
0:02:37 I was prepping for this interview and I was reading your book and I came to this sample
0:02:43 question where you said, “How many squares are in this 8-byte?”
0:02:47 And you said the answer is not 64.
0:02:53 So that kind of stopped my preparation because I was saying, “How can there not be 64 squares?”
0:02:58 And then I thought maybe she says, “If you look at it, you could have 2-byte 2-squares,
0:03:03 3-byte 3-squares, 4-byte 4-squares that could be in different parts of the 8-byte 8″.
0:03:05 So what is the answer to that?
0:03:12 In fact, I even went to LLM and I asked, “How many squares are in an 8-byte 8 chessboard?”
0:03:17 And it said 64, so why is the answer not 64?
0:03:23 Well, you’re exactly right that if we look at an 8-byte 8 chessboard, there are the 64
0:03:28 1-byte 1-squares, but then there are the 2-byte 2-squares and the 3-byte 3-squares and the
0:03:29 4-byte 4-squares.
0:03:34 It’s actually a great activity that we give to students and ask them because they can
0:03:35 look for patterns.
0:03:41 It’s a nice example of a mathematical investigation where it would help you to start with a smaller
0:03:47 board and that’s one of the things we hope kids learn from it, that taking a smaller
0:03:52 case is really valuable when you’re working on a difficult problem.
0:03:56 So if you start with a 2-byte 2-board, it’s easier to see the number of squares inside
0:04:01 it and then a 3-byte 3-square and you start to see the pattern, which is what it’s all
0:04:03 about for us.
0:04:05 So I passed a test.
0:04:08 Yes, you did.
0:04:10 We can end this recording right now.
0:04:11 Yes.
0:04:19 Can we go someplace, just a temporary diversion here that you can tell me, no, you don’t want
0:04:25 to do this, but I got to ask you about this whole Tucker Carlson thing.
0:04:28 What the hell happened there?
0:04:31 What happened and it’s still happening, unfortunately.
0:04:37 What that was, was I was asked by the state of California to be one of the writers of
0:04:40 a new mathematics framework.
0:04:44 There were five writers, but the ideas of the framework came from an elected committee
0:04:53 of 20 leaders and focus groups met across the state, the committee met, the writers wrote
0:05:01 up their ideas and people decided they wanted to stop the ideas of the framework and they
0:05:06 decided to try and do that by basically targeting me, I don’t know any other way to describe
0:05:07 it.
0:05:14 And yeah, I was sitting just having an usual Friday night at home when I started to see
0:05:21 all this hate mail filling up my email and what has happened, I don’t understand this.
0:05:28 And then somebody showed me that Tucker Carlson had put my image on his show and said that
0:05:33 I was trying to promote social justice and mathematics through the framework.
0:05:34 And that was it.
0:05:38 Yeah, that started a pretty tumultuous time.
0:05:45 In a sense, you are promoting social diversification and justice through the framework, right?
0:05:50 You’re trying to make math more accessible to more students.
0:05:51 Exactly.
0:05:55 So in a sense, what they said you’re trying to do is correct.
0:05:58 But why is it such a big controversy?
0:06:00 Why are they against this?
0:06:05 One of the things why they’re against this is a kind of a deep question.
0:06:12 I would say my own take on it is there are people who’ve been very successful in mathematics
0:06:14 in their lives and they are the people who are against it.
0:06:18 If you look at the people who are pushing back on the framework, it is all those who’ve
0:06:23 been extremely successful and they like the system as it is.
0:06:28 They know how to get their own children to excel in the system, proposing changes that
0:06:34 would broaden the access to mathematics to many more children is not something that those
0:06:38 who are in that position particularly want.
0:06:42 So for some people, their motives were not very egalitarian.
0:06:45 They really wanted to keep the system as it was.
0:06:50 And some of those people then spread lies about the framework.
0:06:57 So one that was spread around a lot was that we were stopping children being able to accelerate
0:07:00 and stopping them being able to take algebra in eighth grade.
0:07:03 This was the big lie that was sent around.
0:07:10 In fact, what the framework does is recommend that people not put young children in elementary
0:07:16 school into different tracks that then cement their pathways from that point onwards.
0:07:22 So as soon as we entered into that realm of let’s not have students who were of a young
0:07:34 age in tracks that alerted a set of people that things were going to change and unfortunately
0:07:37 they spread these ideas widely.
0:07:45 It turns out that very successful people are able to influence the media considerably.
0:07:51 So if you saw any news about the framework, then it’s likely to be negative.
0:07:58 The reporting of the framework was almost entirely based on sharing the STEM professors
0:08:00 who didn’t want it.
0:08:03 Nobody shared all the educators who did want it.
0:08:07 And then when it went to the state board for approval, it was unanimously approved and
0:08:12 backed by the California Teachers Association and educators across the state, all the equity
0:08:14 groups across the state.
0:08:21 So it’s a really odd situation that all of the news about it was negative, yet all of
0:08:25 the educators in the state supported it.
0:08:30 When you say the very successful people, are you talking about people successful in the
0:08:35 math perfection or successful as titans of Silicon Valley?
0:08:39 Who are these people who are trying to perpetuate the old way?
0:08:44 Both, particularly some particularly powerful people in Silicon Valley amongst the people
0:08:46 who don’t want math changes.
0:08:53 I was actually at a really nice garden party sort of lunch that was arranged for people
0:08:58 who are working to help students in different countries.
0:09:05 And the organizer said to me, “Oh, all of the leaders, the CEOs I spoke to said they’re
0:09:08 not going to come because you’re coming.”
0:09:17 So they really did a good job of making me the enemy of kids advancing in math.
0:09:18 That is how they think of me.
0:09:22 Joe, I am having an unabody experience here.
0:09:30 You’re telling me that the CEOs of tech companies are on this warpath with you because you’re
0:09:34 trying to make math more accessible to more kids.
0:09:35 Did I repeat that right?
0:09:36 Yes.
0:09:38 Yes, that’s definitely true.
0:09:43 And I think many of them have believed things that have been shared about the framework
0:09:46 and about me that aren’t true.
0:09:51 I absolutely support kids going forward and accelerating if they’re ready to do that.
0:09:58 What I don’t support is writing off students from a young age, but yeah, that’s basically
0:09:59 where we are.
0:10:06 I have to say, I’m just scratching my head and I know a lot of VCs and there’s a transition
0:10:12 when you cross over into extreme wealth where all of a sudden you think that your wealth
0:10:16 makes you smarter and an expert in everything.
0:10:22 So now you run a private equity fund or a hedge fund and all of a sudden now you’re an
0:10:29 expert in plagiarism and academic circles and it’s venture capital disease and now
0:10:33 you should tell teachers how to teach and all that.
0:10:38 I just want to throw up, I just want to throw up.
0:10:40 Yeah, you’re definitely naming something there.
0:10:44 That was part of the distressing thing about the pushback of the framework.
0:10:50 There’s a maths professor at Stanford who was one of the leading people against it who
0:10:54 shared websites saying all the research inside it is wrong.
0:10:56 This is where I’m going to show it’s wrong.
0:11:02 And if you look at what he’s written, it just shows that he doesn’t understand educational
0:11:08 research and is actually using something they use in maths that you don’t use in educational
0:11:12 research to say all of these studies should be discredited.
0:11:18 A lot of people believe that a maths professor says it’s wrong, they shared it with everybody.
0:11:25 Nobody stopped to think, does a maths professor understand the K-12 education system?
0:11:26 That didn’t come up for anybody.
0:11:31 It’s been quite a few years working on this.
0:11:33 Okay, one last question about this.
0:11:39 So now you’re this target of Tucker Carlson who’s, by the way, going to go to Russia to
0:11:43 interview Putin to help us explain Russia while he’s at it.
0:11:47 Now that he’s conquered maths, he’s going to take on world peace.
0:11:50 What happens when your inbox explodes?
0:11:52 Is it just inbox and you can just ignore stuff?
0:11:55 Is it social media or are there threats on your life?
0:11:57 What happens?
0:12:04 I def, I did get threats on my life and my children’s, which is particularly scary.
0:12:11 Stanford at one point decided to add my house to their nightly patrols to check on me.
0:12:16 It’s more than just getting nasty emails, it is threatening.
0:12:21 So it’s a really odd, this seems to be the world we live in now that somebody hears some
0:12:26 words from Tucker Carlson and then immediately sends a death threat based on it.
0:12:31 And I don’t know what to say about that really, but it does seem to be the way we’re going.
0:12:33 And I got through it.
0:12:34 The framework was passed.
0:12:37 My life started to go back to normal.
0:12:42 I have a website at Stanford where we share free resources for teachers that teachers
0:12:48 love and are accessed by millions of teachers and everything seemed to, you know, I could
0:12:51 go back to that important work.
0:12:58 So then yesterday it all kicked off again and somebody shared the group that’s against
0:13:03 me shared that they were going to tell Stanford to fire me.
0:13:08 And so I’m back now, I’m back trying to deal with this.
0:13:11 It’s also a new theme in academia.
0:13:18 Climate scientists are under similar kind of attack, but people are surprised that it’s
0:13:22 a person in math education that surprises them.
0:13:23 No kidding.
0:13:25 Like I said, my head is exploding.
0:13:27 I just don’t get this.
0:13:33 Of all the things in the world, you have to pick a fight on why this anyway, let’s get
0:13:35 off this cesspool here.
0:13:42 I first, I want you to explain the concept of narrow maths.
0:13:45 What makes maths narrow?
0:13:47 What makes math narrow?
0:13:53 And to really come from our textbook companies in the US, somebody set out all the standards
0:13:55 that are important in mathematics.
0:14:00 And I learned through my framework work that nobody actually meant that as a guide to teaching.
0:14:03 It was more of a, this is all the detail of everything.
0:14:08 And what the textbooks have done is take all these short statements about maths and turn
0:14:11 them into narrow questions for students.
0:14:16 So their experience of learning maths is often just going through lots and lots of short
0:14:20 questions that are not meaningful to them.
0:14:28 And really just a targeted, a sort of narrow method where we have a lot of research that
0:14:35 shows that we want to engage students in bigger, more complex problems where they get to think
0:14:42 and reason and talk to each other and solve mathematical issues in the world and really
0:14:47 make maths something that’s meaningful to them, but they see that it’s helping them
0:14:49 in the world.
0:14:52 And we don’t have that in classrooms.
0:14:57 And a lot of people have had the narrow maths experience and left maths as early as they
0:15:04 can or worse, they’ve really come to believe that they can’t do it.
0:15:12 And many times people feel that if they can’t do it, they’re not a full person, that there’s
0:15:14 something wrong with them.
0:15:20 Math has given a lot of status in our society, so it’s important to students to feel they
0:15:22 can be successful.
0:15:27 So yeah, we have this experience of narrow maths and it’s been spectacularly successful
0:15:32 at helping only a narrow group of students go forward.
0:15:39 Only some students are inspired by that experience of working through short questions.
0:15:44 And the book, my new book, Math-ish, is really about making maths a much more interesting
0:15:46 subject for students.
0:15:52 One of the initiatives of the framework was to take all of those isolated tiny standards
0:15:58 and to make them into bigger ideas that teachers could organize their teaching around and bring
0:16:01 in rich tasks.
0:16:08 What I don’t understand is for many people, okay, obviously there is a small segment that
0:16:12 they love it because it’s going to help their SAT score.
0:16:17 They figured it out, blah, blah, blah, and get into Ivy League schools and all that.
0:16:24 But how did we get to this place where I think much of the student population and parent
0:16:27 population, they just dread math.
0:16:33 They see math as like the equivalent of the Navy Seals Hell Week, where the purpose is
0:16:35 to get people to drop out.
0:16:39 Right, look, how did we get to this place?
0:16:40 How did we?
0:16:41 That’s a good question.
0:16:45 Many years ago, when mathematics was put into the curriculum in schools, it was really
0:16:48 there to help people work in shops.
0:16:53 So they needed to be good at calculating with numbers.
0:17:00 And curriculum was set out in the 1800s that went from all of that calculating with numbers
0:17:02 into algebra and geometry.
0:17:07 And we have continued to teach those exact ideas hundreds of years later, even though
0:17:10 the mathematics of the world has changed a lot.
0:17:16 And we don’t need to teach kids to be little calculators because we actually have tools
0:17:20 in our modern society that does that work better than they do.
0:17:26 What we need is to teach them to make sense of problems and be able to interpret results
0:17:37 so that they can make important contributions.
0:17:46 So give me an illustration of an example where the ability to solve narrow math is not nearly
0:17:52 as relevant in modern society as this more generalized creative approach.
0:17:57 So what’s the problem people will face where they’re using math, they need math, they may
0:18:04 not even realize that this is the kind of math we need, not the ability to solve a quadratic
0:18:06 equation on an SAT test?
0:18:13 I’ll tell you a story and this is also a controversy that’s happening now in California.
0:18:17 We have developed a data science course in our center at Stanford.
0:18:19 It’s a one year high school course.
0:18:24 And there has been the moves in California and across the country to have that be a
0:18:30 high school course for students that is an alternative to say algebra two, which is that
0:18:33 course where you’re doing lots and lots of algebraic equations.
0:18:37 Now there’s pushback and people saying it shouldn’t be, but we developed this course
0:18:43 and we studied it and inside our study, we gave students who are in algebra two classes
0:18:48 and students in the data science class the same test question.
0:18:53 And it actually asked them to look at some data and develop a function to make sense
0:18:54 of it.
0:19:02 So we gave them some data about health and poverty in different countries and what people’s,
0:19:07 how many calories people took in and how that related to their lifespan and asked them to
0:19:09 make sense of that table of data.
0:19:14 So the students in data science did significantly better than the students in algebra two, even
0:19:21 though it was a test of algebra, because the kids in algebra two just learn all these formulas.
0:19:25 And when they come to seeing a table of real data from the world, they don’t know how to
0:19:29 apply those formulas to the table.
0:19:33 It’s a really basic kind of algebra concept that you can look at numbers and plot them
0:19:36 and see the relationship.
0:19:37 And they just didn’t know how to do it.
0:19:39 They had all these formulas.
0:19:46 And what we teach the kids in data science is to make sense of a situation and to analyze
0:19:50 patterns and to see what’s happening.
0:19:56 One place that this would have really helped in recent years is understanding COVID data.
0:20:02 When the pandemic was happening, our screens were filled with linear relationships shown
0:20:09 on graphs, the relationship between vaccines and mortality, all sorts of different things.
0:20:17 And if students haven’t learned to look at a situation like that and make sense of it,
0:20:21 they were not in a good position to be helped during the pandemic.
0:20:27 Yeah, in the modern world, what we need students to be able to do, I think Conrad Wolfram puts
0:20:29 it well.
0:20:34 People probably have heard of Conrad Wolfram, he created Wolfram Alpha with his brother
0:20:40 and Mathematica and their technology powers, both Alexa and Siri.
0:20:43 And he says, this is what we do mathematically in our jobs and in our world.
0:20:46 We form a question.
0:20:50 We work out how to make that into a computable answer.
0:20:54 We do the computation and then we analyze the results.
0:21:00 But there’s four part process, but in school, it’s all about just doing the computation.
0:21:06 So students aren’t given situations where they ask their own question and then they
0:21:11 think, how can I make this into something I can calculate to find something important?
0:21:17 And one of the things he’s done is he’s made an entire high school curriculum taken out
0:21:23 all the parts where students are learning methods to do by hand that in the modern world
0:21:30 are always done by computers. And instead, our students to program those into a computer
0:21:32 and analyze the results.
0:21:37 And it’s taken, it’s freed up a lot of time so students can now work on these really
0:21:42 cool projects like designing drones and analyzing music.
0:21:45 So that is the idea.
0:21:50 We can do a lot better in our maths teaching if we really think about what the students
0:21:51 really need.
0:21:57 We need them to reason and problem solve and solve complex problems.
0:22:02 We don’t need them rehearsing methods that don’t mean anything to them.
0:22:08 This is somewhat of a facetious hypothetical question, but do you think if you asked your
0:22:15 random American sample, let’s say you told them one out of five million people who got
0:22:24 a COVID vaccination died, but one out of 100,000 people who didn’t get a vaccination died?
0:22:26 Should you get a vaccination or not?
0:22:30 Do you think a lot of people would say, no, vaccination is too dangerous?
0:22:34 Are you talking about that basic level?
0:22:39 And what we’ve done in maths education is make people afraid of maths and afraid of
0:22:44 numbers. So they probably wouldn’t even engage in their thinking.
0:22:50 Many people will look at numbers and move away from them and not look at a graph, not
0:22:54 look at a set of numbers, it just provokes fear and anxiety.
0:22:57 Yeah, I do think that.
0:22:59 Madison and I are surfers.
0:23:02 We love to surf.
0:23:08 And we always, I always encounter people when I say you ought to try surfing.
0:23:13 And they say that, no, because I could get eaten by a shark.
0:23:17 And then I point out, there have been like, I don’t know, three shark attacks, fatal shark
0:23:20 attacks in the world this year.
0:23:26 The most dangerous part of surfing is driving over the hill from Menlo Park to Santa Cruz
0:23:32 on Highway 17, much higher probability you’re going to die because a truck runs you over
0:23:35 then you’re going to get eaten by a shark.
0:23:38 But they still say, no, I’m afraid of sharks.
0:23:40 Like, how do you even deal with it?
0:23:46 I would say you deal with that by giving people a good mathematics education where they’re
0:23:50 able to make sense of probabilities.
0:23:56 Probability is an area that people are totally terrified by and won’t engage with.
0:24:01 Yeah, I’m a strong believer that giving people a high quality education is going to protect
0:24:05 them in many ways in the world.
0:24:07 Understanding probabilities is one.
0:24:12 Also in the modern world, we know that young people are going to be sent a lot of data
0:24:18 and data visuals that are incorrect, that are intended to mislead them.
0:24:24 And we need to protect them by being used to looking at data and data visuals and thinking.
0:24:25 Who sent this?
0:24:27 Why did they send it?
0:24:28 What does it mean?
0:24:32 Is it all the data or is it manipulated in some way?
0:24:38 And so there’s a strong need to help our students with this kind of data literacy.
0:24:47 So if I was plopped into a data science course as opposed to an Algebra II course, what would
0:24:52 I immediately notice as the difference between data science and Algebra?
0:24:59 One of the big differences is students start with a data set and they are encouraged to
0:25:01 ask questions of that data.
0:25:04 What can we learn about the world through asking a question?
0:25:06 It’s their own question.
0:25:10 And then they use methods to interrogate it.
0:25:12 They’re going to learn some technology in data science.
0:25:21 We’re going to learn a little bit of coding and use data platforms that are really helpful.
0:25:25 And they’re going to come up with a result and they’re going to interpret that result
0:25:27 and communicate it.
0:25:33 In an Algebra II course, they’re probably going to be moving symbols around a page.
0:25:37 And we are coming up with the different symbols.
0:25:41 The students who take the data science courses are very clear about this.
0:25:43 This is meaningful mathematics.
0:25:45 It means something to me.
0:25:46 I understand it.
0:25:49 This isn’t just pushing symbols around a page.
0:25:52 It’s something that’s powerful for the world.
0:25:58 So, it’s amazing that we now have people pushing back on students learning data science saying
0:26:02 they should not have a data science course in high school.
0:26:06 And the particular pushback we’re getting now is people saying we shouldn’t have a data
0:26:11 science course in high school because it’s not got enough Algebra in it.
0:26:20 Wait, it hasn’t enough Algebra in it in order to prepare you for the SAT in order for you
0:26:21 to go to the Ivy League?
0:26:24 Is that kind of a thing?
0:26:30 Yeah, some people are genuinely worried that if you want to be in a STEM major in college,
0:26:33 then you need a lot of Algebra.
0:26:37 But instead of saying, well, let’s, because one of the things we know about data science
0:26:41 is a lot of kids go into it feeling like math, they hate math.
0:26:44 They never want to do another math course.
0:26:49 And then they realize that math can actually be interesting and they become excited about
0:26:50 it.
0:26:52 They want to go further in STEM.
0:26:57 So a better move from these people who are concerned about maybe they need to go, they’re
0:26:58 going into STEM.
0:27:03 They need a lot of Algebra is to think about what could we offer them after data science
0:27:07 that could bridge into more Algebra, more Calculates.
0:27:12 If I am a college and I have students coming who’ve taken many students take data science
0:27:17 in year three and then statistics in year four, APC that stats maybe.
0:27:22 If I have a student coming through that statistics pathway, is there a bridging course I can
0:27:27 offer at the college so that they can get more onto that Calculus track of lots and
0:27:29 lots of Algebra?
0:27:34 That would be more sensible than saying let’s ban data science for everybody and in their
0:27:38 banning of data science for everybody, they’re doing that for kids who are never going to
0:27:44 go into STEM and for whom that data science course is actually really important.
0:27:49 You could make the case that data science is more important to the survival of society
0:27:52 than advanced math.
0:27:53 Absolutely.
0:27:54 Absolutely.
0:27:59 And of course, if you take a data science course, you’re more likely to develop perhaps
0:28:04 a critical perspective on things that are sent to you in the world.
0:28:10 And so there is some line of thinking that people don’t want our whole population to
0:28:13 have that data awareness.
0:28:14 Yeah.
0:28:16 God forbid people could think like that.
0:28:17 Yeah.
0:28:23 So what about the pushback that people say we have to teach math this way because it helps
0:28:29 the human brain develop problem-solving techniques, which seems to me you just said refutes.
0:28:32 The research refutes that.
0:28:33 It does.
0:28:38 Kids need math because it’s going to help them develop their brains.
0:28:43 It does develop their brains, but the math that really develops their brains is one that’s
0:28:45 what I call multi-dimensional.
0:28:50 One of the things we know about our brains is we have five different pathways that can
0:28:52 process mathematical ideas.
0:28:56 Two of them are visual pathways at the back of the head.
0:29:01 And so we also know that mathematicians, when they’ve looked at their brains as they’re
0:29:08 working on math, what’s different from other academics is they’re using those visual pathways.
0:29:13 So on our website, U-Cubed, we make a lot of the mathematics visual.
0:29:18 We know that students are really helped by a visual or a physical model of mathematical
0:29:19 ideas.
0:29:25 I really like some of the recent neuroscience that’s showing that as we go around the world,
0:29:31 all of us, we’re building mental models of ideas.
0:29:33 That’s how we exist in the world.
0:29:39 So this scientist, Jeff Hawkins, gives an example of knowing a stapler.
0:29:46 If I was to ask you what you know about a stapler, you would probably say, I know what
0:29:47 it looks like.
0:29:48 I know what it feels like.
0:29:49 I know what it sounds like.
0:29:51 I know what happens when I use it.
0:29:55 You have built all of these ideas about a stapler.
0:29:59 And in maths, we need to build those mental models for kids.
0:30:04 So when they’re just going through number calculations, they are developing one area
0:30:05 of their brain.
0:30:12 But if they’re building, and if they’re drawing, and they’re seeing maths conceptually, and
0:30:17 then their brain is getting a full workout, they’re getting these different pathways involved.
0:30:24 I think the brain argument that narrow maths is building your brain doesn’t work for me
0:30:28 because narrow maths might strengthen one area of the brain, but it’s leaving completely
0:30:34 neglected the other areas that we really need to exercise.
0:30:41 Could you make the argument that an abacus or a slide rule is a good thing?
0:30:42 That’s more visual.
0:30:43 It’s more tactile.
0:30:44 Yeah.
0:30:49 And recently, I think an abacus is a great tool for students’ learning.
0:30:53 One of the things we’ve learned from neuroscience in recent years is how important our fingers
0:31:00 are, and that students who develop greater knowledge of their fingers do better in maths.
0:31:04 Fingers are like a number line that we carry around with us, and they directly map into
0:31:07 a part of the brain that’s using that.
0:31:14 So it’s really no wonder any sort of finger work leads to really greater maths achievement.
0:31:17 But what was your question?
0:31:23 No, just I was thinking when you’re talking about tactile and visual and not just solving
0:31:27 equations that an abacus is tactile.
0:31:28 Oh, yeah.
0:31:30 So an abacus is great.
0:31:31 It’s tactile.
0:31:33 It gets finger used.
0:31:35 That’s what made me think about the fingers.
0:31:43 And yes, one of the ideas in my book that I share, maybe I could share this now, is the
0:31:47 idea of approaching maths with an ish lens.
0:31:48 I was coming.
0:31:50 That was my next question.
0:31:54 So tell me what the ish in math is.
0:31:55 Yeah.
0:31:58 You made me think about that when you talked about slide rules, and I’ll tell you why it
0:31:59 connects to that.
0:32:00 But yeah.
0:32:03 So I make an argument that in maths classrooms, maths is very precise.
0:32:06 It’s always precise.
0:32:13 And in the, but in the real world, almost always when we use numbers, they are ish numbers.
0:32:19 And those are good enough and some different examples are like, how much of the moon can
0:32:24 I see or how much rain fell last night or how old are you or how long will this drive
0:32:28 take to the airport or how much paint do I need to paint the wall.
0:32:31 All of these are actually not very precise numbers.
0:32:32 They’re ish numbers.
0:32:38 That’s a disconnect for kids and precise is important, but we need those to be more
0:32:44 in balance. But I also know that when kids are ishing numbers, I can give you an example.
0:32:53 If I asked you to work out or asked anybody to work out, let’s say 287 divided by nine,
0:32:58 the most people could give an ish answer to that they couldn’t do the precise calculation
0:32:59 in their head.
0:33:01 They could give an ish answer.
0:33:04 But being able to ish an answer means you have numbers sent.
0:33:11 And when you ish, you’re staying at that conceptual level of the, what do these numbers mean?
0:33:15 And when we go into the precise mode, what happens is a lot of kids get lost in that
0:33:16 precision.
0:33:21 So I’m recommending to teachers, I hear from teachers, my students don’t have number sense.
0:33:24 They do these calculations and they give wild answers.
0:33:27 They don’t think about what the numbers are.
0:33:33 And my recommendation in the book is before anybody does a calculation, any student in
0:33:37 any classroom, you should ask them to ish the number first.
0:33:40 Because then they’re staying at that conceptual level.
0:33:41 Yeah.
0:33:45 So anyway, I put that recommendation in the book, I’ve been talking about it.
0:33:49 And I get this email from a teacher saying, this was amazing.
0:33:53 I went to my classroom, I asked the kids to ish numbers.
0:33:55 And we looked at the precise number.
0:33:58 And they talked about the difference.
0:34:01 And they started asking each other, what’s your ish number?
0:34:05 And she said something amazing happened that all these students who don’t normally engage
0:34:10 in maths are suddenly jumping in and sharing their ish numbers.
0:34:12 We went down and we videoed the class.
0:34:17 We’re putting the video on our website and all these kids are engaged.
0:34:21 The principal came into the lesson with us and she was beaming from ear to ear.
0:34:25 She said, these students who are sharing ish numbers are the ones who are normally outside
0:34:30 the office because they are so badly behaved in the class.
0:34:36 And these students, when we talk to them, we’re saying, well, this is the world ish
0:34:42 numbers are our world, they’re what we use when we talk about time, when we pour things
0:34:49 out and measure liquids and now maths is meaningful to them.
0:34:52 And it’s also keeping them at this really important conceptual level.
0:34:55 So anyway, I’ve just become very excited about ish.
0:35:01 When I was sharing maths ish to an audience, one of the audience members said, oh, my father
0:35:05 was a rocket scientist.
0:35:12 And he talked about how they used to measure with slide rules and really had to have an
0:35:15 ish idea of what their measurement was.
0:35:18 But now they just do it all with technology.
0:35:23 And so they make mistakes because they’re not ish-ing the number, they’re just taking
0:35:27 this number from the technology and using it.
0:35:29 And mistakes are happening much more often.
0:35:34 So that was what made me think about your slide rule thing.
0:35:40 And one last thing, if people say to me, well, isn’t ish-ing the same as estimating?
0:35:43 And my answer to that is it is the same thing.
0:35:49 But when we ask students to estimate a number, they often think, oh, this is another mathematical
0:35:55 method, and they calculate it precisely and round it off to make it look like an estimate.
0:36:03 But when we ask them to ish numbers, something amazing happens, and they become more free,
0:36:09 and they’re more willing to share their ish numbers, I’m pretty excited about it as a
0:36:12 concept and teachers are very excited about it.
0:36:14 So that makes me excited.
0:36:21 I have to say I love the concept and I have a suggested alternate title, although books
0:36:25 laid in granite and it’s ready to come out or it’s out already.
0:36:30 But yeah, I’m going to give you all the caveats why this is a lousy title.
0:36:38 But I will say you also have to be old to understand this, but a title for your book
0:36:47 could have been 30-something because when you say what’s 275 divided by 9, you say 30-something,
0:36:48 right?
0:36:49 Yeah.
0:36:50 But that was a great TV show.
0:36:51 Oh, it was?
0:36:52 Yeah.
0:37:01 Now we have other TV shows with ish in the title, but yes, I think that could have been
0:37:02 that.
0:37:10 You make a passion appeal why maybe because you’re British, but it should be maths, plural,
0:37:13 not math, right?
0:37:18 So why didn’t you name your book maths-ish?
0:37:22 There were two reasons I didn’t call it maths-ish.
0:37:27 I do say maths and I do prefer maths because it’s short for mathematics.
0:37:35 All the ways of being mathematical and if I math, math, the word math, very narrow sounding
0:37:40 and in England we do call it maths, but I didn’t call it maths-ish for two reasons.
0:37:44 One, the publishers always make me write math because it’s going to an American audience
0:37:48 and the book is full of the word math anyway.
0:37:57 But also maths-ish is a bit of a tongue twister and it’s hard to say and so I don’t worry
0:38:00 so much about it sounding narrow when it’s math-ish.
0:38:02 It’s not a narrow word like math.
0:38:03 Okay.
0:38:13 Now, so in this perfect world or this fantasy world, maybe someday there’s a SAT-ish, right?
0:38:14 Oh yeah, right?
0:38:20 Or you could have approximate answers just to measure your reality and your reasoning,
0:38:22 not your precision.
0:38:26 That would be a great idea actually.
0:38:31 It would measure kids’ number sense, which is what they really need in the world.
0:38:34 Actually you reminded me that there was ish-ing.
0:38:38 One of my arguments I give in the book is that ish-ing is really helpful with standardized
0:38:39 tests.
0:38:40 Wow.
0:38:46 A lot of time they give standardized test questions and ask you which of these is correct, which
0:38:50 of these answers is correct and of course you can ish your way to the correct answer
0:38:53 a lot better than you can calculate it.
0:38:58 Along with the standardized test questions given out to students across the country and
0:39:07 NAIT question, they were asked 7/8 plus 12/13 and then they were given four choices.
0:39:14 Is that closest to 1, 2, 19 or 21?
0:39:21 You can probably think 7/8 is nearly 1, 12/13 is nearly 1, so there’s a chance it would
0:39:22 be 2.
0:39:30 The most common answer given by 17-year-olds was 19 and the second most common, the second
0:39:32 most common answer was 21.
0:39:33 How can that be?
0:39:38 So that happens because these kids dive into calculating.
0:39:45 They have never ish-ed questions in their lives, so they look at that 7/8 plus 12/13
0:39:53 and they think I have to do a calculation and so they get lost in the calculation.
0:40:01 Obviously the 19 is the 7 plus 12 and the 21 is the 8 plus 13, but it’s tragic and
0:40:07 could be avoided if we got these kids getting used to ish-ing numbers and this is why I’m
0:40:12 finding that teachers immediately know how powerful this idea is because they know that’s
0:40:18 what students need, but they haven’t had a way of getting them to do that and feel comfortable
0:40:19 about it.
0:40:24 If you were to apply narrow math to that problem, step one is to what?
0:40:28 Find the common denominator so you can get it exactly right.
0:40:37 Step one would be, yes, to add 8/13, you’d have to find a number that 8/13 goes into and
0:40:41 convert them into common denominators and add the numerators.
0:40:45 It’s a whole method that they tried to do.
0:40:48 Seriously, this could be a matter of life or death.
0:40:52 If you have to make a calculation like that and you come up with 19 when it’s closer to
0:40:57 2, that’s you literally could endanger yourself, right?
0:40:58 I agree.
0:41:04 Yeah, and if you’re using maths in the workplace and you’re making those kind of errors, one
0:41:09 thing teachers always say is we want students and employers say we want people to know when
0:41:13 an answer is reasonable and that’s what ish-ing is so helpful with.
0:41:17 It’s giving kids that idea of what’s reasonable.
0:41:21 One of the students we interviewed when we went to the school that day said, “Oh, I get
0:41:26 so annoyed in maths that we do a calculation and then we have to do the whole thing again
0:41:28 to check it’s right.”
0:41:32 But now I don’t need to do that because I ish the answer first and then I can see from
0:41:35 my calculation whether it’s right.
0:41:40 And yeah, I just think there’s many uses of ish-ing.
0:41:41 I love the concept.
0:41:46 Joe, I think life is one big ish, if you ask me.
0:41:47 I agree.
0:41:48 Right?
0:41:49 Life is an ish.
0:41:52 You can ish your way through your life and do a little bit of it.
0:41:53 It’s like surfing.
0:42:01 The waves are one to two ish or they’re right, they’re four, they’re dead ish.
0:42:05 You don’t need to know it’s 4.65 feet.
0:42:06 You don’t need to know that.
0:42:08 That’s another really good example.
0:42:11 I should add surfing to my list of examples.
0:42:18 And if people took more of an ish approach to then things in their life, not just numbers,
0:42:19 it would help them.
0:42:23 You know, it’s not about these binary right and wrong.
0:42:28 I know that a lot of kids fear maths, a lot of kids and a lot of adults.
0:42:34 And actually what they fear is that precision that it’s right or wrong and often they’re
0:42:37 wrong and that is what they fear about it.
0:42:43 And when we take an ish approach to numbers, it really stoppens the edges of maths for
0:42:47 kids as well as giving them access to that conceptual thinking.
0:42:52 So I should say what I’m not saying because I get misquoted in the media all the time
0:42:58 now and I’m not saying that precision is not important, but I am saying we should be more
0:42:59 balanced.
0:43:06 And when kids are both ishing and being precise, it gives them a much more powerful experience.
0:43:09 Up next on Remarkable People.
0:43:12 Sometimes high achieving students are very narrow in their thinking.
0:43:16 They’ve been successful, but there’s only one way they can think about it.
0:43:22 And they sit in a group with a different kind of student who sees something visually and
0:43:27 it’s surprising to these other students and they learn a different way of approaching things.
0:43:37 So I do think diversity in all sorts of forms of diversity enriches students experiences
0:43:39 and schools.
0:43:43 Become a little more remarkable with each episode of Remarkable People.
0:43:49 It’s found on Apple Podcast or wherever you listen to your favorite shows.
0:43:54 Welcome back to Remarkable People with Guy Kawasaki.
0:43:59 I think much of your book is discussing about how because of the teaching techniques or
0:44:06 because of the expectations of society that there’s much, I don’t know, negativity and
0:44:12 stuff surrounding math and there’s like people who believe that you either have a math brain
0:44:17 or you’re not, which is completely contrary to Carol Dweck’s thinking.
0:44:22 And so apply the growth mindset to math.
0:44:28 It is what I love to do and I’ve been inspired by Carol Dweck’s work and really decided
0:44:34 about 10 years ago to try and get it into math education more because we have a population
0:44:41 about over 90% of parents in a survey said that their children either had a math brain
0:44:43 or they don’t or they didn’t.
0:44:48 That myth of the math brain is still very widespread.
0:44:54 And so yeah, Carol Dweck has shown and neuroscientists have shown that our brains are constantly changing
0:44:58 and developing and growing and connecting.
0:45:06 One of the pushback to the framework was the anti-mindset people who said that mindset
0:45:10 is wrong and it shouldn’t be in the framework.
0:45:12 There’s a whole group of people who are against mindset.
0:45:16 It turns out I really think that any good idea in the world these days, there will be
0:45:23 people against it somewhere, but it’s very important to math that teachers know that
0:45:26 students can learn what they’re teaching.
0:45:31 Many teachers still think their role is to figure out who’s the math person and who’s
0:45:32 not.
0:45:35 And so it’s been important to change that.
0:45:43 And do math teachers come to this kind of conclusion because they’re basically expected
0:45:50 and they’re reviewed on their capacity for their students to get high standardized test
0:45:51 scores.
0:45:53 Is that the root of the problem?
0:45:55 Standardized test scores are a part of the problem.
0:46:02 The massive amount of standards in the curriculum is part of the problem.
0:46:03 Teachers don’t go into depth on anything.
0:46:07 They have to skim through lots and lots of methods.
0:46:11 There’s a few parts to the problem in education.
0:46:14 But standardized testing is one of them.
0:46:18 And if you teach narrow maths, if that’s what you think maths is, and that is what most
0:46:26 people think maths is, this narrow subject of calculations and methods, if you teach
0:46:29 narrow maths, then only some students will be successful.
0:46:35 So it perpetuates this myth that teachers have that only some students can be successful.
0:46:38 It’s not about the way they’re teaching.
0:46:40 It’s just the way of the world.
0:46:46 And it just reinforces their idea that to be good at maths, you’re just a special kind
0:46:51 of person and only a few people can be that kind of person.
0:46:59 But at extremes, surely there must be some people who are just gifted in math, right,
0:47:01 or gifted in physics.
0:47:06 You can’t say that Stephen Wolfram is a random person.
0:47:09 Some people have developed incredible brains.
0:47:12 This is not an argument that people are the same.
0:47:16 The question is, though, how did he develop that brain?
0:47:24 And my problem with the idea of a gift is it’s very fixed, like you have it or you don’t.
0:47:26 Whereas we know that everybody’s on a growth journey.
0:47:32 You can’t cut off, make a cut off point and say, you have a gift, you don’t have a gift.
0:47:37 It is on a growth journey and can develop and grow their brains.
0:47:41 One of the people I like to share is somebody called Nicholas Lechford, who when he was
0:47:45 growing up, his parents were told he was learning disabled.
0:47:49 He had a very low IQ, you believe in IQ.
0:47:57 And he graduated from Oxford with a doctoral degree in applied mathematics after huge problems
0:48:00 as a younger child learning anything.
0:48:06 We know, we have millions of examples or we have lots of examples of people who had really
0:48:10 strong difficulties and went on to achieve amazing things.
0:48:13 It’s not that some people are born with something.
0:48:15 They end up with something for sure.
0:48:19 There are people whose brains are incredibly powerful.
0:48:21 But where does that come from?
0:48:22 Everybody’s born with a different brain.
0:48:25 Nobody is born with the same brain.
0:48:26 Everybody’s is different.
0:48:32 But the millions of opportunities you have to change your brain as you go through life
0:48:40 even as a baby and in the early years, those opportunities make more difference than differences
0:48:42 that we’re born with.
0:48:47 What if I were like push back on you and say, okay, so you just cited me one example of
0:48:55 someone who had all these learning challenges and was cast into a particular bracket of
0:49:01 not being able to do math and overcame that, got a PhD at Oxford.
0:49:07 So yeah, you picked one example, but then someone on the opposite side could say, I
0:49:12 know this person and he got vaccinated and he died.
0:49:14 So that proves vaccination is bad.
0:49:21 So one data point either way, how are people supposed to figure out that citing one vaccination
0:49:23 death is misleading?
0:49:26 What you just did could be just as misleading.
0:49:27 No.
0:49:33 Well, no, but I would say that somebody who takes a vaccine has a vaccination and die.
0:49:35 You don’t know why they’ve died.
0:49:39 You can’t say that vaccination caused him to die.
0:49:44 But when you look at people who overcome significant difficulties and go on to learn incredible
0:49:51 things, even one person shows you that can happen, that the way we approach learning
0:49:58 and life can change what happens for you even when you start off in a hard place.
0:50:00 And we have not just one example.
0:50:04 We have many, many examples that show that.
0:50:08 There was a school situation I remember in England that’s really interesting that in
0:50:13 England you take an exam at 16 and they’re in three different levels.
0:50:15 The lowest one, the middle one, the higher one.
0:50:21 And if you get put into the lowest exam, the highest grade you can get is a D. So it matters
0:50:23 which exam you’ll put in for.
0:50:27 And one school I worked with years ago just said, you know what, I’m going to put all
0:50:30 the kids into the highest paper.
0:50:33 And we’re going to prepare them all for the highest paper.
0:50:39 And those kids all got the grades on the highest paper.
0:50:40 She didn’t change her teachers.
0:50:42 She didn’t.
0:50:44 She just said they’re all going to do that work.
0:50:47 And they all got one of those highest grades.
0:50:52 We know that fixing people and deciding people have issues and they can’t learn.
0:50:55 It’s just not the right approach in education.
0:50:58 This is somewhat of a related story.
0:51:07 So I have been able to moderate several panels with chancellors of large universities.
0:51:13 I often ask them about admission policies, about relying on standardized tests and essays
0:51:15 and all that.
0:51:19 And I pose to several of them, like, why don’t we try an experiment?
0:51:26 Why don’t you just say, everybody apply and we are just going to randomly select people
0:51:27 to admit.
0:51:30 And let’s just see what happens.
0:51:38 Does that produce a more successful student body than our laser focus on SAT and college
0:51:41 essay and recommendations?
0:51:45 And I did not get a lot of support for that.
0:51:48 I bet you didn’t.
0:51:50 It’s what the UCs did, actually.
0:51:56 They’ve always used SATs as the filter and measure of whether kids can be successful
0:51:57 in the UCs.
0:51:59 And then they dismantled that.
0:52:03 They got rid of SATs that it’s no longer used.
0:52:06 And what they found was their students are just as successful.
0:52:10 They’re bringing in a more diverse group of students.
0:52:13 They’re more racially diverse.
0:52:16 And they’re doing just as well as when they had the SAT as a filter.
0:52:21 So that kind of is your experiment a little bit.
0:52:27 I think you make a point in your book that by bringing in a diversity of students, some
0:52:34 of whom are not as successful at that point as others, that everybody benefits because
0:52:41 even the ones who are doing better learn from watching how the ones who are not doing better
0:52:43 are learning.
0:52:48 So watching people struggle can help you learn how to be a better student.
0:52:53 And also we know that helping others learn helps yourself.
0:52:59 So we see this when students are in more diverse groups in terms of their prior achievement.
0:53:04 What we find is the ones who are most helped by that are the highest achieving students.
0:53:08 And the reason is they’re spending time helping other students.
0:53:12 And of course, anyone who’s taught knows that the best way to learn something deeply is to
0:53:14 teach it.
0:53:18 And it also means kids think differently.
0:53:21 Sometimes high achieving students are very narrow in their thinking.
0:53:25 They’ve been successful, but there’s only one way they can think about it.
0:53:31 And they sit in a group with a different kind of student who sees something visually and
0:53:33 it’s surprising to these other students.
0:53:36 And they learn a different way of approaching things.
0:53:43 So I do think diversity in all sorts of forms of diversity enriches students’ experiences
0:53:46 in schools and their learning.
0:53:51 And that would take us right back to our friend Tucker Carlson, which is if he understood
0:53:58 this, he would insist on diversification because it would make everybody better, including
0:54:03 a white kid destined for Ivy Legs, right?
0:54:05 It would make everybody better.
0:54:09 And that’s something that people don’t get.
0:54:15 Some of the people who push back on any sort of anti-tracking messages say, “I don’t want
0:54:18 my kids in classes with those kids.”
0:54:24 That’s the insidious underpinning of the pushback on tracking.
0:54:28 People want to keep their kids separate from other kids.
0:54:33 But they don’t know that when we have these environments where students are together and
0:54:37 they’re more diverse in all different ways, it benefits everybody.
0:54:40 That’s definitely what the research shows.
0:54:48 So now my brain is multi-processing and I’m thinking, so if I started surfing with surfers
0:54:53 who are not as good as me, would that make me a better surfer?
0:54:59 If you were teaching them, then probably it would, because the teaching would make you
0:55:00 better surfers.
0:55:04 So I’m going to start telling Madison to teach me how to surf because she would then
0:55:09 be teaching someone not as good as her and it would help her improve too.
0:55:10 That’s right.
0:55:16 My last topic, the topic that I love and I want to understand more is the concept of
0:55:24 metacognition and for those of you listening, that has nothing to do with the intelligence
0:55:26 of Mark Zuckerberg and Facebook.
0:55:28 So what is metacognition?
0:55:32 I never thought of that, Link.
0:55:33 Metacognition.
0:55:38 A lot of people think metacognition is thinking about your own thinking and there is a piece
0:55:45 of that, but metacognition and people with metacognitive ideas, it’s more than that.
0:55:48 It starts with self-belief.
0:55:49 It has growth mindset in it.
0:55:54 You believe that you can do something, but then somebody who’s metacognitive has different
0:55:57 ways to approach a problem.
0:55:59 Maybe they have a range of strategies they’ve learned.
0:56:04 We talked about one at the beginning, trying a smaller case, they have a range of strategies
0:56:09 and they’re willing to try these different strategies out.
0:56:15 They see metacognition in the part of the brain and it’s pretty powerful.
0:56:21 One of the things I do in the book is urge people to teach students how to learn.
0:56:27 I think as maths teachers, we often think I’m there to teach maths, but actually many
0:56:34 kids haven’t learned how to approach maths well and they may have learned counterproductive
0:56:35 ideas.
0:56:41 Teaching kids how to learn, teaching them how to be metacognitive is really important.
0:56:48 Let’s say I’m a parent and I’ve listened to this whole podcast and my kid is 17, 18,
0:56:51 19 years old.
0:56:57 He or she is the product of a school system that was geared towards standardized tests
0:57:04 and Algebra 1, Algebra 2, Algebra 3, so you can get into pre-calculus so that you can
0:57:09 get into calculus so you can get into the Ivy League so that you can have a STEM career
0:57:15 and he hates maths, she hates maths, we got him tutors, we did everything we could, we
0:57:22 dread maths, which what do you do if you’re midstream and you’re stuck in this position
0:57:27 and now you listen to this podcast, you read your book and you’re saying the whole system
0:57:31 is screwed up, what do I do for my kid?
0:57:35 I think what’s really important for all of us is that we develop a playful relationship
0:57:36 with maths.
0:57:42 I see maths as just a playground of ideas that we can try out and investigate things
0:57:48 and so I deal with those people all the time because I’m always running workshops for teachers
0:57:51 and many teachers are in that position.
0:57:57 They hated maths and they saw it as a list of methods to memorize and we introduce them
0:58:03 to playful maths, we give them activities where they’re making connections and seeing
0:58:10 things differently and at many, many times teachers have cried or become very emotional
0:58:16 and said oh my gosh, I just didn’t know maths could be like this and I didn’t know I could
0:58:22 do this and so I think shifting people from that narrow, getting them out of that narrow
0:58:27 maths experience is almost like a therapy people need into seeing maths differently is
0:58:32 really important and some adults go through that transition from reading books, maybe
0:58:38 they read math-ish and that takes them on that path and then they start to engage with maths
0:58:43 differently and some people need more than that, like they need to go to a workshop or
0:58:52 something where they’re able to experience maths differently and that will get them shifting.
0:58:57 Many, many people make that shift and they’re always happy when they make the shift but
0:59:04 we have to encourage more people to make that shift, to see maths differently not as this
0:59:08 rigid set of numbers but as this ish playground.
0:59:11 Okay, but I want you to get really tactical.
0:59:15 I’m listening to this podcast, I’m a real believer, my kid hates math, I’m afraid of
0:59:17 math for his or her future.
0:59:18 What do I do?
0:59:20 What do I do?
0:59:23 Not conceptually, what do I do?
0:59:28 We have a number of resources on our website to help people, one of them is an online class,
0:59:35 it’s completely free, six 50-minute sessions that people can take, it changes their mindset,
0:59:37 it changes their approach to maths.
0:59:42 We have a lot of evidence of that, we’ve studied it with randomized controlled trials,
0:59:46 students who take it, engage differently in maths class afterwards, they score at high
0:59:53 levels on tests afterwards, come to U-Cubed and look at the online class, it’s really
0:59:58 for adults or children and look at the other resources that we share.
1:00:04 I’m really passionate about changing people’s relationships with maths and we have U-Cubed,
1:00:10 we have a new maths app now called Struggly, we have books, many different resources aimed
1:00:16 at really giving people that different maths experience.
1:00:22 I have to admit I love the ish concept, I’m going to become an ish evangelist, you know
1:00:29 where you live your life, approximately, logically, realistically, roughly right.
1:00:36 I love that concept, life is too short to be too precise, so thank you Joe Bowler for
1:00:42 introducing me to this concept, now I’d like to thank the Remarkable People team, that
1:00:50 would be precisely Matt as a Nismar producer and co-author of Think Remarkable, you must
1:00:58 read this book, maybe we’ll rename it Think Remarkable Ish, and then there’s Tessa Nismar,
1:01:04 Tessa prepares me with all the background research and perfects our transcripts.
1:01:10 And speaking of perfection, there is Jeff C. and Shannon Hernandez, sound design engineers
1:01:19 extraordinaire, and finally Luis Magana, Alexis Nishimura, and Fallon Yates, we are the Remarkable
1:01:35 People team, we’re on a mission to make you Remarkable, until next time, Mahalo and Aloha.
0:00:15 We’re on a mission to make you remarkable.
0:00:18 Helping me in today’s episode is Joel Bowler.
0:00:22 She is a professor of education at Stanford University.
0:00:28 She joins a handful of people who have been on Remarkable People more than once.
0:00:34 She began her career as a secondary mathematics teacher in urban London schools including
0:00:37 Haverstock School in Camden.
0:00:42 After teaching, Bowler received a master’s degree in mathematics education from King’s
0:00:43 College London.
0:00:49 She then completed her PhD in mathematics education at the same university and won the
0:00:57 award for best PhD in education from the British Educational Research Association in 1997.
0:01:03 Prior to her role at Stanford, Bowler served as the Marie Curry Professor of Mathematics
0:01:05 Education in England.
0:01:12 She co-founded U-Cubed, an organization dedicated to providing resources and ideas to inspire
0:01:15 and excite students about mathematics.
0:01:20 Bowler has received several honors including the National Science Foundation Early Career
0:01:30 Award, the NCSM K. Gilliland Equity Award in 2014, and the CMC Walter Denham Mathematics
0:01:33 Leadership Award in 2015.
0:01:37 She has authored 19 books and numerous research articles.
0:01:44 Her latest book is called Mathish, Finding Creativity, Diversity and Meaning in Mathematics.
0:01:50 In this book, she shares research on embracing a diverse approach to learning math and providing
0:01:55 seven principles to reframe our relationship with the subject.
0:01:59 All of what you just heard is a typical, remarkable people introduction.
0:02:05 It’s a long story and it would take a lot to explain what happened and it would also
0:02:09 take a lot of research to get both sides of the story.
0:02:15 But suffice it to say that Joe Bowler was attacked by Tucker Carlson and Elon Musk.
0:02:18 That should tell you something.
0:02:19 I’m Guy Kawasaki.
0:02:31 This is Remarkable People and now here is the remarkable Joe Bowler.
0:02:37 I was prepping for this interview and I was reading your book and I came to this sample
0:02:43 question where you said, “How many squares are in this 8-byte?”
0:02:47 And you said the answer is not 64.
0:02:53 So that kind of stopped my preparation because I was saying, “How can there not be 64 squares?”
0:02:58 And then I thought maybe she says, “If you look at it, you could have 2-byte 2-squares,
0:03:03 3-byte 3-squares, 4-byte 4-squares that could be in different parts of the 8-byte 8″.
0:03:05 So what is the answer to that?
0:03:12 In fact, I even went to LLM and I asked, “How many squares are in an 8-byte 8 chessboard?”
0:03:17 And it said 64, so why is the answer not 64?
0:03:23 Well, you’re exactly right that if we look at an 8-byte 8 chessboard, there are the 64
0:03:28 1-byte 1-squares, but then there are the 2-byte 2-squares and the 3-byte 3-squares and the
0:03:29 4-byte 4-squares.
0:03:34 It’s actually a great activity that we give to students and ask them because they can
0:03:35 look for patterns.
0:03:41 It’s a nice example of a mathematical investigation where it would help you to start with a smaller
0:03:47 board and that’s one of the things we hope kids learn from it, that taking a smaller
0:03:52 case is really valuable when you’re working on a difficult problem.
0:03:56 So if you start with a 2-byte 2-board, it’s easier to see the number of squares inside
0:04:01 it and then a 3-byte 3-square and you start to see the pattern, which is what it’s all
0:04:03 about for us.
0:04:05 So I passed a test.
0:04:08 Yes, you did.
0:04:10 We can end this recording right now.
0:04:11 Yes.
0:04:19 Can we go someplace, just a temporary diversion here that you can tell me, no, you don’t want
0:04:25 to do this, but I got to ask you about this whole Tucker Carlson thing.
0:04:28 What the hell happened there?
0:04:31 What happened and it’s still happening, unfortunately.
0:04:37 What that was, was I was asked by the state of California to be one of the writers of
0:04:40 a new mathematics framework.
0:04:44 There were five writers, but the ideas of the framework came from an elected committee
0:04:53 of 20 leaders and focus groups met across the state, the committee met, the writers wrote
0:05:01 up their ideas and people decided they wanted to stop the ideas of the framework and they
0:05:06 decided to try and do that by basically targeting me, I don’t know any other way to describe
0:05:07 it.
0:05:14 And yeah, I was sitting just having an usual Friday night at home when I started to see
0:05:21 all this hate mail filling up my email and what has happened, I don’t understand this.
0:05:28 And then somebody showed me that Tucker Carlson had put my image on his show and said that
0:05:33 I was trying to promote social justice and mathematics through the framework.
0:05:34 And that was it.
0:05:38 Yeah, that started a pretty tumultuous time.
0:05:45 In a sense, you are promoting social diversification and justice through the framework, right?
0:05:50 You’re trying to make math more accessible to more students.
0:05:51 Exactly.
0:05:55 So in a sense, what they said you’re trying to do is correct.
0:05:58 But why is it such a big controversy?
0:06:00 Why are they against this?
0:06:05 One of the things why they’re against this is a kind of a deep question.
0:06:12 I would say my own take on it is there are people who’ve been very successful in mathematics
0:06:14 in their lives and they are the people who are against it.
0:06:18 If you look at the people who are pushing back on the framework, it is all those who’ve
0:06:23 been extremely successful and they like the system as it is.
0:06:28 They know how to get their own children to excel in the system, proposing changes that
0:06:34 would broaden the access to mathematics to many more children is not something that those
0:06:38 who are in that position particularly want.
0:06:42 So for some people, their motives were not very egalitarian.
0:06:45 They really wanted to keep the system as it was.
0:06:50 And some of those people then spread lies about the framework.
0:06:57 So one that was spread around a lot was that we were stopping children being able to accelerate
0:07:00 and stopping them being able to take algebra in eighth grade.
0:07:03 This was the big lie that was sent around.
0:07:10 In fact, what the framework does is recommend that people not put young children in elementary
0:07:16 school into different tracks that then cement their pathways from that point onwards.
0:07:22 So as soon as we entered into that realm of let’s not have students who were of a young
0:07:34 age in tracks that alerted a set of people that things were going to change and unfortunately
0:07:37 they spread these ideas widely.
0:07:45 It turns out that very successful people are able to influence the media considerably.
0:07:51 So if you saw any news about the framework, then it’s likely to be negative.
0:07:58 The reporting of the framework was almost entirely based on sharing the STEM professors
0:08:00 who didn’t want it.
0:08:03 Nobody shared all the educators who did want it.
0:08:07 And then when it went to the state board for approval, it was unanimously approved and
0:08:12 backed by the California Teachers Association and educators across the state, all the equity
0:08:14 groups across the state.
0:08:21 So it’s a really odd situation that all of the news about it was negative, yet all of
0:08:25 the educators in the state supported it.
0:08:30 When you say the very successful people, are you talking about people successful in the
0:08:35 math perfection or successful as titans of Silicon Valley?
0:08:39 Who are these people who are trying to perpetuate the old way?
0:08:44 Both, particularly some particularly powerful people in Silicon Valley amongst the people
0:08:46 who don’t want math changes.
0:08:53 I was actually at a really nice garden party sort of lunch that was arranged for people
0:08:58 who are working to help students in different countries.
0:09:05 And the organizer said to me, “Oh, all of the leaders, the CEOs I spoke to said they’re
0:09:08 not going to come because you’re coming.”
0:09:17 So they really did a good job of making me the enemy of kids advancing in math.
0:09:18 That is how they think of me.
0:09:22 Joe, I am having an unabody experience here.
0:09:30 You’re telling me that the CEOs of tech companies are on this warpath with you because you’re
0:09:34 trying to make math more accessible to more kids.
0:09:35 Did I repeat that right?
0:09:36 Yes.
0:09:38 Yes, that’s definitely true.
0:09:43 And I think many of them have believed things that have been shared about the framework
0:09:46 and about me that aren’t true.
0:09:51 I absolutely support kids going forward and accelerating if they’re ready to do that.
0:09:58 What I don’t support is writing off students from a young age, but yeah, that’s basically
0:09:59 where we are.
0:10:06 I have to say, I’m just scratching my head and I know a lot of VCs and there’s a transition
0:10:12 when you cross over into extreme wealth where all of a sudden you think that your wealth
0:10:16 makes you smarter and an expert in everything.
0:10:22 So now you run a private equity fund or a hedge fund and all of a sudden now you’re an
0:10:29 expert in plagiarism and academic circles and it’s venture capital disease and now
0:10:33 you should tell teachers how to teach and all that.
0:10:38 I just want to throw up, I just want to throw up.
0:10:40 Yeah, you’re definitely naming something there.
0:10:44 That was part of the distressing thing about the pushback of the framework.
0:10:50 There’s a maths professor at Stanford who was one of the leading people against it who
0:10:54 shared websites saying all the research inside it is wrong.
0:10:56 This is where I’m going to show it’s wrong.
0:11:02 And if you look at what he’s written, it just shows that he doesn’t understand educational
0:11:08 research and is actually using something they use in maths that you don’t use in educational
0:11:12 research to say all of these studies should be discredited.
0:11:18 A lot of people believe that a maths professor says it’s wrong, they shared it with everybody.
0:11:25 Nobody stopped to think, does a maths professor understand the K-12 education system?
0:11:26 That didn’t come up for anybody.
0:11:31 It’s been quite a few years working on this.
0:11:33 Okay, one last question about this.
0:11:39 So now you’re this target of Tucker Carlson who’s, by the way, going to go to Russia to
0:11:43 interview Putin to help us explain Russia while he’s at it.
0:11:47 Now that he’s conquered maths, he’s going to take on world peace.
0:11:50 What happens when your inbox explodes?
0:11:52 Is it just inbox and you can just ignore stuff?
0:11:55 Is it social media or are there threats on your life?
0:11:57 What happens?
0:12:04 I def, I did get threats on my life and my children’s, which is particularly scary.
0:12:11 Stanford at one point decided to add my house to their nightly patrols to check on me.
0:12:16 It’s more than just getting nasty emails, it is threatening.
0:12:21 So it’s a really odd, this seems to be the world we live in now that somebody hears some
0:12:26 words from Tucker Carlson and then immediately sends a death threat based on it.
0:12:31 And I don’t know what to say about that really, but it does seem to be the way we’re going.
0:12:33 And I got through it.
0:12:34 The framework was passed.
0:12:37 My life started to go back to normal.
0:12:42 I have a website at Stanford where we share free resources for teachers that teachers
0:12:48 love and are accessed by millions of teachers and everything seemed to, you know, I could
0:12:51 go back to that important work.
0:12:58 So then yesterday it all kicked off again and somebody shared the group that’s against
0:13:03 me shared that they were going to tell Stanford to fire me.
0:13:08 And so I’m back now, I’m back trying to deal with this.
0:13:11 It’s also a new theme in academia.
0:13:18 Climate scientists are under similar kind of attack, but people are surprised that it’s
0:13:22 a person in math education that surprises them.
0:13:23 No kidding.
0:13:25 Like I said, my head is exploding.
0:13:27 I just don’t get this.
0:13:33 Of all the things in the world, you have to pick a fight on why this anyway, let’s get
0:13:35 off this cesspool here.
0:13:42 I first, I want you to explain the concept of narrow maths.
0:13:45 What makes maths narrow?
0:13:47 What makes math narrow?
0:13:53 And to really come from our textbook companies in the US, somebody set out all the standards
0:13:55 that are important in mathematics.
0:14:00 And I learned through my framework work that nobody actually meant that as a guide to teaching.
0:14:03 It was more of a, this is all the detail of everything.
0:14:08 And what the textbooks have done is take all these short statements about maths and turn
0:14:11 them into narrow questions for students.
0:14:16 So their experience of learning maths is often just going through lots and lots of short
0:14:20 questions that are not meaningful to them.
0:14:28 And really just a targeted, a sort of narrow method where we have a lot of research that
0:14:35 shows that we want to engage students in bigger, more complex problems where they get to think
0:14:42 and reason and talk to each other and solve mathematical issues in the world and really
0:14:47 make maths something that’s meaningful to them, but they see that it’s helping them
0:14:49 in the world.
0:14:52 And we don’t have that in classrooms.
0:14:57 And a lot of people have had the narrow maths experience and left maths as early as they
0:15:04 can or worse, they’ve really come to believe that they can’t do it.
0:15:12 And many times people feel that if they can’t do it, they’re not a full person, that there’s
0:15:14 something wrong with them.
0:15:20 Math has given a lot of status in our society, so it’s important to students to feel they
0:15:22 can be successful.
0:15:27 So yeah, we have this experience of narrow maths and it’s been spectacularly successful
0:15:32 at helping only a narrow group of students go forward.
0:15:39 Only some students are inspired by that experience of working through short questions.
0:15:44 And the book, my new book, Math-ish, is really about making maths a much more interesting
0:15:46 subject for students.
0:15:52 One of the initiatives of the framework was to take all of those isolated tiny standards
0:15:58 and to make them into bigger ideas that teachers could organize their teaching around and bring
0:16:01 in rich tasks.
0:16:08 What I don’t understand is for many people, okay, obviously there is a small segment that
0:16:12 they love it because it’s going to help their SAT score.
0:16:17 They figured it out, blah, blah, blah, and get into Ivy League schools and all that.
0:16:24 But how did we get to this place where I think much of the student population and parent
0:16:27 population, they just dread math.
0:16:33 They see math as like the equivalent of the Navy Seals Hell Week, where the purpose is
0:16:35 to get people to drop out.
0:16:39 Right, look, how did we get to this place?
0:16:40 How did we?
0:16:41 That’s a good question.
0:16:45 Many years ago, when mathematics was put into the curriculum in schools, it was really
0:16:48 there to help people work in shops.
0:16:53 So they needed to be good at calculating with numbers.
0:17:00 And curriculum was set out in the 1800s that went from all of that calculating with numbers
0:17:02 into algebra and geometry.
0:17:07 And we have continued to teach those exact ideas hundreds of years later, even though
0:17:10 the mathematics of the world has changed a lot.
0:17:16 And we don’t need to teach kids to be little calculators because we actually have tools
0:17:20 in our modern society that does that work better than they do.
0:17:26 What we need is to teach them to make sense of problems and be able to interpret results
0:17:37 so that they can make important contributions.
0:17:46 So give me an illustration of an example where the ability to solve narrow math is not nearly
0:17:52 as relevant in modern society as this more generalized creative approach.
0:17:57 So what’s the problem people will face where they’re using math, they need math, they may
0:18:04 not even realize that this is the kind of math we need, not the ability to solve a quadratic
0:18:06 equation on an SAT test?
0:18:13 I’ll tell you a story and this is also a controversy that’s happening now in California.
0:18:17 We have developed a data science course in our center at Stanford.
0:18:19 It’s a one year high school course.
0:18:24 And there has been the moves in California and across the country to have that be a
0:18:30 high school course for students that is an alternative to say algebra two, which is that
0:18:33 course where you’re doing lots and lots of algebraic equations.
0:18:37 Now there’s pushback and people saying it shouldn’t be, but we developed this course
0:18:43 and we studied it and inside our study, we gave students who are in algebra two classes
0:18:48 and students in the data science class the same test question.
0:18:53 And it actually asked them to look at some data and develop a function to make sense
0:18:54 of it.
0:19:02 So we gave them some data about health and poverty in different countries and what people’s,
0:19:07 how many calories people took in and how that related to their lifespan and asked them to
0:19:09 make sense of that table of data.
0:19:14 So the students in data science did significantly better than the students in algebra two, even
0:19:21 though it was a test of algebra, because the kids in algebra two just learn all these formulas.
0:19:25 And when they come to seeing a table of real data from the world, they don’t know how to
0:19:29 apply those formulas to the table.
0:19:33 It’s a really basic kind of algebra concept that you can look at numbers and plot them
0:19:36 and see the relationship.
0:19:37 And they just didn’t know how to do it.
0:19:39 They had all these formulas.
0:19:46 And what we teach the kids in data science is to make sense of a situation and to analyze
0:19:50 patterns and to see what’s happening.
0:19:56 One place that this would have really helped in recent years is understanding COVID data.
0:20:02 When the pandemic was happening, our screens were filled with linear relationships shown
0:20:09 on graphs, the relationship between vaccines and mortality, all sorts of different things.
0:20:17 And if students haven’t learned to look at a situation like that and make sense of it,
0:20:21 they were not in a good position to be helped during the pandemic.
0:20:27 Yeah, in the modern world, what we need students to be able to do, I think Conrad Wolfram puts
0:20:29 it well.
0:20:34 People probably have heard of Conrad Wolfram, he created Wolfram Alpha with his brother
0:20:40 and Mathematica and their technology powers, both Alexa and Siri.
0:20:43 And he says, this is what we do mathematically in our jobs and in our world.
0:20:46 We form a question.
0:20:50 We work out how to make that into a computable answer.
0:20:54 We do the computation and then we analyze the results.
0:21:00 But there’s four part process, but in school, it’s all about just doing the computation.
0:21:06 So students aren’t given situations where they ask their own question and then they
0:21:11 think, how can I make this into something I can calculate to find something important?
0:21:17 And one of the things he’s done is he’s made an entire high school curriculum taken out
0:21:23 all the parts where students are learning methods to do by hand that in the modern world
0:21:30 are always done by computers. And instead, our students to program those into a computer
0:21:32 and analyze the results.
0:21:37 And it’s taken, it’s freed up a lot of time so students can now work on these really
0:21:42 cool projects like designing drones and analyzing music.
0:21:45 So that is the idea.
0:21:50 We can do a lot better in our maths teaching if we really think about what the students
0:21:51 really need.
0:21:57 We need them to reason and problem solve and solve complex problems.
0:22:02 We don’t need them rehearsing methods that don’t mean anything to them.
0:22:08 This is somewhat of a facetious hypothetical question, but do you think if you asked your
0:22:15 random American sample, let’s say you told them one out of five million people who got
0:22:24 a COVID vaccination died, but one out of 100,000 people who didn’t get a vaccination died?
0:22:26 Should you get a vaccination or not?
0:22:30 Do you think a lot of people would say, no, vaccination is too dangerous?
0:22:34 Are you talking about that basic level?
0:22:39 And what we’ve done in maths education is make people afraid of maths and afraid of
0:22:44 numbers. So they probably wouldn’t even engage in their thinking.
0:22:50 Many people will look at numbers and move away from them and not look at a graph, not
0:22:54 look at a set of numbers, it just provokes fear and anxiety.
0:22:57 Yeah, I do think that.
0:22:59 Madison and I are surfers.
0:23:02 We love to surf.
0:23:08 And we always, I always encounter people when I say you ought to try surfing.
0:23:13 And they say that, no, because I could get eaten by a shark.
0:23:17 And then I point out, there have been like, I don’t know, three shark attacks, fatal shark
0:23:20 attacks in the world this year.
0:23:26 The most dangerous part of surfing is driving over the hill from Menlo Park to Santa Cruz
0:23:32 on Highway 17, much higher probability you’re going to die because a truck runs you over
0:23:35 then you’re going to get eaten by a shark.
0:23:38 But they still say, no, I’m afraid of sharks.
0:23:40 Like, how do you even deal with it?
0:23:46 I would say you deal with that by giving people a good mathematics education where they’re
0:23:50 able to make sense of probabilities.
0:23:56 Probability is an area that people are totally terrified by and won’t engage with.
0:24:01 Yeah, I’m a strong believer that giving people a high quality education is going to protect
0:24:05 them in many ways in the world.
0:24:07 Understanding probabilities is one.
0:24:12 Also in the modern world, we know that young people are going to be sent a lot of data
0:24:18 and data visuals that are incorrect, that are intended to mislead them.
0:24:24 And we need to protect them by being used to looking at data and data visuals and thinking.
0:24:25 Who sent this?
0:24:27 Why did they send it?
0:24:28 What does it mean?
0:24:32 Is it all the data or is it manipulated in some way?
0:24:38 And so there’s a strong need to help our students with this kind of data literacy.
0:24:47 So if I was plopped into a data science course as opposed to an Algebra II course, what would
0:24:52 I immediately notice as the difference between data science and Algebra?
0:24:59 One of the big differences is students start with a data set and they are encouraged to
0:25:01 ask questions of that data.
0:25:04 What can we learn about the world through asking a question?
0:25:06 It’s their own question.
0:25:10 And then they use methods to interrogate it.
0:25:12 They’re going to learn some technology in data science.
0:25:21 We’re going to learn a little bit of coding and use data platforms that are really helpful.
0:25:25 And they’re going to come up with a result and they’re going to interpret that result
0:25:27 and communicate it.
0:25:33 In an Algebra II course, they’re probably going to be moving symbols around a page.
0:25:37 And we are coming up with the different symbols.
0:25:41 The students who take the data science courses are very clear about this.
0:25:43 This is meaningful mathematics.
0:25:45 It means something to me.
0:25:46 I understand it.
0:25:49 This isn’t just pushing symbols around a page.
0:25:52 It’s something that’s powerful for the world.
0:25:58 So, it’s amazing that we now have people pushing back on students learning data science saying
0:26:02 they should not have a data science course in high school.
0:26:06 And the particular pushback we’re getting now is people saying we shouldn’t have a data
0:26:11 science course in high school because it’s not got enough Algebra in it.
0:26:20 Wait, it hasn’t enough Algebra in it in order to prepare you for the SAT in order for you
0:26:21 to go to the Ivy League?
0:26:24 Is that kind of a thing?
0:26:30 Yeah, some people are genuinely worried that if you want to be in a STEM major in college,
0:26:33 then you need a lot of Algebra.
0:26:37 But instead of saying, well, let’s, because one of the things we know about data science
0:26:41 is a lot of kids go into it feeling like math, they hate math.
0:26:44 They never want to do another math course.
0:26:49 And then they realize that math can actually be interesting and they become excited about
0:26:50 it.
0:26:52 They want to go further in STEM.
0:26:57 So a better move from these people who are concerned about maybe they need to go, they’re
0:26:58 going into STEM.
0:27:03 They need a lot of Algebra is to think about what could we offer them after data science
0:27:07 that could bridge into more Algebra, more Calculates.
0:27:12 If I am a college and I have students coming who’ve taken many students take data science
0:27:17 in year three and then statistics in year four, APC that stats maybe.
0:27:22 If I have a student coming through that statistics pathway, is there a bridging course I can
0:27:27 offer at the college so that they can get more onto that Calculus track of lots and
0:27:29 lots of Algebra?
0:27:34 That would be more sensible than saying let’s ban data science for everybody and in their
0:27:38 banning of data science for everybody, they’re doing that for kids who are never going to
0:27:44 go into STEM and for whom that data science course is actually really important.
0:27:49 You could make the case that data science is more important to the survival of society
0:27:52 than advanced math.
0:27:53 Absolutely.
0:27:54 Absolutely.
0:27:59 And of course, if you take a data science course, you’re more likely to develop perhaps
0:28:04 a critical perspective on things that are sent to you in the world.
0:28:10 And so there is some line of thinking that people don’t want our whole population to
0:28:13 have that data awareness.
0:28:14 Yeah.
0:28:16 God forbid people could think like that.
0:28:17 Yeah.
0:28:23 So what about the pushback that people say we have to teach math this way because it helps
0:28:29 the human brain develop problem-solving techniques, which seems to me you just said refutes.
0:28:32 The research refutes that.
0:28:33 It does.
0:28:38 Kids need math because it’s going to help them develop their brains.
0:28:43 It does develop their brains, but the math that really develops their brains is one that’s
0:28:45 what I call multi-dimensional.
0:28:50 One of the things we know about our brains is we have five different pathways that can
0:28:52 process mathematical ideas.
0:28:56 Two of them are visual pathways at the back of the head.
0:29:01 And so we also know that mathematicians, when they’ve looked at their brains as they’re
0:29:08 working on math, what’s different from other academics is they’re using those visual pathways.
0:29:13 So on our website, U-Cubed, we make a lot of the mathematics visual.
0:29:18 We know that students are really helped by a visual or a physical model of mathematical
0:29:19 ideas.
0:29:25 I really like some of the recent neuroscience that’s showing that as we go around the world,
0:29:31 all of us, we’re building mental models of ideas.
0:29:33 That’s how we exist in the world.
0:29:39 So this scientist, Jeff Hawkins, gives an example of knowing a stapler.
0:29:46 If I was to ask you what you know about a stapler, you would probably say, I know what
0:29:47 it looks like.
0:29:48 I know what it feels like.
0:29:49 I know what it sounds like.
0:29:51 I know what happens when I use it.
0:29:55 You have built all of these ideas about a stapler.
0:29:59 And in maths, we need to build those mental models for kids.
0:30:04 So when they’re just going through number calculations, they are developing one area
0:30:05 of their brain.
0:30:12 But if they’re building, and if they’re drawing, and they’re seeing maths conceptually, and
0:30:17 then their brain is getting a full workout, they’re getting these different pathways involved.
0:30:24 I think the brain argument that narrow maths is building your brain doesn’t work for me
0:30:28 because narrow maths might strengthen one area of the brain, but it’s leaving completely
0:30:34 neglected the other areas that we really need to exercise.
0:30:41 Could you make the argument that an abacus or a slide rule is a good thing?
0:30:42 That’s more visual.
0:30:43 It’s more tactile.
0:30:44 Yeah.
0:30:49 And recently, I think an abacus is a great tool for students’ learning.
0:30:53 One of the things we’ve learned from neuroscience in recent years is how important our fingers
0:31:00 are, and that students who develop greater knowledge of their fingers do better in maths.
0:31:04 Fingers are like a number line that we carry around with us, and they directly map into
0:31:07 a part of the brain that’s using that.
0:31:14 So it’s really no wonder any sort of finger work leads to really greater maths achievement.
0:31:17 But what was your question?
0:31:23 No, just I was thinking when you’re talking about tactile and visual and not just solving
0:31:27 equations that an abacus is tactile.
0:31:28 Oh, yeah.
0:31:30 So an abacus is great.
0:31:31 It’s tactile.
0:31:33 It gets finger used.
0:31:35 That’s what made me think about the fingers.
0:31:43 And yes, one of the ideas in my book that I share, maybe I could share this now, is the
0:31:47 idea of approaching maths with an ish lens.
0:31:48 I was coming.
0:31:50 That was my next question.
0:31:54 So tell me what the ish in math is.
0:31:55 Yeah.
0:31:58 You made me think about that when you talked about slide rules, and I’ll tell you why it
0:31:59 connects to that.
0:32:00 But yeah.
0:32:03 So I make an argument that in maths classrooms, maths is very precise.
0:32:06 It’s always precise.
0:32:13 And in the, but in the real world, almost always when we use numbers, they are ish numbers.
0:32:19 And those are good enough and some different examples are like, how much of the moon can
0:32:24 I see or how much rain fell last night or how old are you or how long will this drive
0:32:28 take to the airport or how much paint do I need to paint the wall.
0:32:31 All of these are actually not very precise numbers.
0:32:32 They’re ish numbers.
0:32:38 That’s a disconnect for kids and precise is important, but we need those to be more
0:32:44 in balance. But I also know that when kids are ishing numbers, I can give you an example.
0:32:53 If I asked you to work out or asked anybody to work out, let’s say 287 divided by nine,
0:32:58 the most people could give an ish answer to that they couldn’t do the precise calculation
0:32:59 in their head.
0:33:01 They could give an ish answer.
0:33:04 But being able to ish an answer means you have numbers sent.
0:33:11 And when you ish, you’re staying at that conceptual level of the, what do these numbers mean?
0:33:15 And when we go into the precise mode, what happens is a lot of kids get lost in that
0:33:16 precision.
0:33:21 So I’m recommending to teachers, I hear from teachers, my students don’t have number sense.
0:33:24 They do these calculations and they give wild answers.
0:33:27 They don’t think about what the numbers are.
0:33:33 And my recommendation in the book is before anybody does a calculation, any student in
0:33:37 any classroom, you should ask them to ish the number first.
0:33:40 Because then they’re staying at that conceptual level.
0:33:41 Yeah.
0:33:45 So anyway, I put that recommendation in the book, I’ve been talking about it.
0:33:49 And I get this email from a teacher saying, this was amazing.
0:33:53 I went to my classroom, I asked the kids to ish numbers.
0:33:55 And we looked at the precise number.
0:33:58 And they talked about the difference.
0:34:01 And they started asking each other, what’s your ish number?
0:34:05 And she said something amazing happened that all these students who don’t normally engage
0:34:10 in maths are suddenly jumping in and sharing their ish numbers.
0:34:12 We went down and we videoed the class.
0:34:17 We’re putting the video on our website and all these kids are engaged.
0:34:21 The principal came into the lesson with us and she was beaming from ear to ear.
0:34:25 She said, these students who are sharing ish numbers are the ones who are normally outside
0:34:30 the office because they are so badly behaved in the class.
0:34:36 And these students, when we talk to them, we’re saying, well, this is the world ish
0:34:42 numbers are our world, they’re what we use when we talk about time, when we pour things
0:34:49 out and measure liquids and now maths is meaningful to them.
0:34:52 And it’s also keeping them at this really important conceptual level.
0:34:55 So anyway, I’ve just become very excited about ish.
0:35:01 When I was sharing maths ish to an audience, one of the audience members said, oh, my father
0:35:05 was a rocket scientist.
0:35:12 And he talked about how they used to measure with slide rules and really had to have an
0:35:15 ish idea of what their measurement was.
0:35:18 But now they just do it all with technology.
0:35:23 And so they make mistakes because they’re not ish-ing the number, they’re just taking
0:35:27 this number from the technology and using it.
0:35:29 And mistakes are happening much more often.
0:35:34 So that was what made me think about your slide rule thing.
0:35:40 And one last thing, if people say to me, well, isn’t ish-ing the same as estimating?
0:35:43 And my answer to that is it is the same thing.
0:35:49 But when we ask students to estimate a number, they often think, oh, this is another mathematical
0:35:55 method, and they calculate it precisely and round it off to make it look like an estimate.
0:36:03 But when we ask them to ish numbers, something amazing happens, and they become more free,
0:36:09 and they’re more willing to share their ish numbers, I’m pretty excited about it as a
0:36:12 concept and teachers are very excited about it.
0:36:14 So that makes me excited.
0:36:21 I have to say I love the concept and I have a suggested alternate title, although books
0:36:25 laid in granite and it’s ready to come out or it’s out already.
0:36:30 But yeah, I’m going to give you all the caveats why this is a lousy title.
0:36:38 But I will say you also have to be old to understand this, but a title for your book
0:36:47 could have been 30-something because when you say what’s 275 divided by 9, you say 30-something,
0:36:48 right?
0:36:49 Yeah.
0:36:50 But that was a great TV show.
0:36:51 Oh, it was?
0:36:52 Yeah.
0:37:01 Now we have other TV shows with ish in the title, but yes, I think that could have been
0:37:02 that.
0:37:10 You make a passion appeal why maybe because you’re British, but it should be maths, plural,
0:37:13 not math, right?
0:37:18 So why didn’t you name your book maths-ish?
0:37:22 There were two reasons I didn’t call it maths-ish.
0:37:27 I do say maths and I do prefer maths because it’s short for mathematics.
0:37:35 All the ways of being mathematical and if I math, math, the word math, very narrow sounding
0:37:40 and in England we do call it maths, but I didn’t call it maths-ish for two reasons.
0:37:44 One, the publishers always make me write math because it’s going to an American audience
0:37:48 and the book is full of the word math anyway.
0:37:57 But also maths-ish is a bit of a tongue twister and it’s hard to say and so I don’t worry
0:38:00 so much about it sounding narrow when it’s math-ish.
0:38:02 It’s not a narrow word like math.
0:38:03 Okay.
0:38:13 Now, so in this perfect world or this fantasy world, maybe someday there’s a SAT-ish, right?
0:38:14 Oh yeah, right?
0:38:20 Or you could have approximate answers just to measure your reality and your reasoning,
0:38:22 not your precision.
0:38:26 That would be a great idea actually.
0:38:31 It would measure kids’ number sense, which is what they really need in the world.
0:38:34 Actually you reminded me that there was ish-ing.
0:38:38 One of my arguments I give in the book is that ish-ing is really helpful with standardized
0:38:39 tests.
0:38:40 Wow.
0:38:46 A lot of time they give standardized test questions and ask you which of these is correct, which
0:38:50 of these answers is correct and of course you can ish your way to the correct answer
0:38:53 a lot better than you can calculate it.
0:38:58 Along with the standardized test questions given out to students across the country and
0:39:07 NAIT question, they were asked 7/8 plus 12/13 and then they were given four choices.
0:39:14 Is that closest to 1, 2, 19 or 21?
0:39:21 You can probably think 7/8 is nearly 1, 12/13 is nearly 1, so there’s a chance it would
0:39:22 be 2.
0:39:30 The most common answer given by 17-year-olds was 19 and the second most common, the second
0:39:32 most common answer was 21.
0:39:33 How can that be?
0:39:38 So that happens because these kids dive into calculating.
0:39:45 They have never ish-ed questions in their lives, so they look at that 7/8 plus 12/13
0:39:53 and they think I have to do a calculation and so they get lost in the calculation.
0:40:01 Obviously the 19 is the 7 plus 12 and the 21 is the 8 plus 13, but it’s tragic and
0:40:07 could be avoided if we got these kids getting used to ish-ing numbers and this is why I’m
0:40:12 finding that teachers immediately know how powerful this idea is because they know that’s
0:40:18 what students need, but they haven’t had a way of getting them to do that and feel comfortable
0:40:19 about it.
0:40:24 If you were to apply narrow math to that problem, step one is to what?
0:40:28 Find the common denominator so you can get it exactly right.
0:40:37 Step one would be, yes, to add 8/13, you’d have to find a number that 8/13 goes into and
0:40:41 convert them into common denominators and add the numerators.
0:40:45 It’s a whole method that they tried to do.
0:40:48 Seriously, this could be a matter of life or death.
0:40:52 If you have to make a calculation like that and you come up with 19 when it’s closer to
0:40:57 2, that’s you literally could endanger yourself, right?
0:40:58 I agree.
0:41:04 Yeah, and if you’re using maths in the workplace and you’re making those kind of errors, one
0:41:09 thing teachers always say is we want students and employers say we want people to know when
0:41:13 an answer is reasonable and that’s what ish-ing is so helpful with.
0:41:17 It’s giving kids that idea of what’s reasonable.
0:41:21 One of the students we interviewed when we went to the school that day said, “Oh, I get
0:41:26 so annoyed in maths that we do a calculation and then we have to do the whole thing again
0:41:28 to check it’s right.”
0:41:32 But now I don’t need to do that because I ish the answer first and then I can see from
0:41:35 my calculation whether it’s right.
0:41:40 And yeah, I just think there’s many uses of ish-ing.
0:41:41 I love the concept.
0:41:46 Joe, I think life is one big ish, if you ask me.
0:41:47 I agree.
0:41:48 Right?
0:41:49 Life is an ish.
0:41:52 You can ish your way through your life and do a little bit of it.
0:41:53 It’s like surfing.
0:42:01 The waves are one to two ish or they’re right, they’re four, they’re dead ish.
0:42:05 You don’t need to know it’s 4.65 feet.
0:42:06 You don’t need to know that.
0:42:08 That’s another really good example.
0:42:11 I should add surfing to my list of examples.
0:42:18 And if people took more of an ish approach to then things in their life, not just numbers,
0:42:19 it would help them.
0:42:23 You know, it’s not about these binary right and wrong.
0:42:28 I know that a lot of kids fear maths, a lot of kids and a lot of adults.
0:42:34 And actually what they fear is that precision that it’s right or wrong and often they’re
0:42:37 wrong and that is what they fear about it.
0:42:43 And when we take an ish approach to numbers, it really stoppens the edges of maths for
0:42:47 kids as well as giving them access to that conceptual thinking.
0:42:52 So I should say what I’m not saying because I get misquoted in the media all the time
0:42:58 now and I’m not saying that precision is not important, but I am saying we should be more
0:42:59 balanced.
0:43:06 And when kids are both ishing and being precise, it gives them a much more powerful experience.
0:43:09 Up next on Remarkable People.
0:43:12 Sometimes high achieving students are very narrow in their thinking.
0:43:16 They’ve been successful, but there’s only one way they can think about it.
0:43:22 And they sit in a group with a different kind of student who sees something visually and
0:43:27 it’s surprising to these other students and they learn a different way of approaching things.
0:43:37 So I do think diversity in all sorts of forms of diversity enriches students experiences
0:43:39 and schools.
0:43:43 Become a little more remarkable with each episode of Remarkable People.
0:43:49 It’s found on Apple Podcast or wherever you listen to your favorite shows.
0:43:54 Welcome back to Remarkable People with Guy Kawasaki.
0:43:59 I think much of your book is discussing about how because of the teaching techniques or
0:44:06 because of the expectations of society that there’s much, I don’t know, negativity and
0:44:12 stuff surrounding math and there’s like people who believe that you either have a math brain
0:44:17 or you’re not, which is completely contrary to Carol Dweck’s thinking.
0:44:22 And so apply the growth mindset to math.
0:44:28 It is what I love to do and I’ve been inspired by Carol Dweck’s work and really decided
0:44:34 about 10 years ago to try and get it into math education more because we have a population
0:44:41 about over 90% of parents in a survey said that their children either had a math brain
0:44:43 or they don’t or they didn’t.
0:44:48 That myth of the math brain is still very widespread.
0:44:54 And so yeah, Carol Dweck has shown and neuroscientists have shown that our brains are constantly changing
0:44:58 and developing and growing and connecting.
0:45:06 One of the pushback to the framework was the anti-mindset people who said that mindset
0:45:10 is wrong and it shouldn’t be in the framework.
0:45:12 There’s a whole group of people who are against mindset.
0:45:16 It turns out I really think that any good idea in the world these days, there will be
0:45:23 people against it somewhere, but it’s very important to math that teachers know that
0:45:26 students can learn what they’re teaching.
0:45:31 Many teachers still think their role is to figure out who’s the math person and who’s
0:45:32 not.
0:45:35 And so it’s been important to change that.
0:45:43 And do math teachers come to this kind of conclusion because they’re basically expected
0:45:50 and they’re reviewed on their capacity for their students to get high standardized test
0:45:51 scores.
0:45:53 Is that the root of the problem?
0:45:55 Standardized test scores are a part of the problem.
0:46:02 The massive amount of standards in the curriculum is part of the problem.
0:46:03 Teachers don’t go into depth on anything.
0:46:07 They have to skim through lots and lots of methods.
0:46:11 There’s a few parts to the problem in education.
0:46:14 But standardized testing is one of them.
0:46:18 And if you teach narrow maths, if that’s what you think maths is, and that is what most
0:46:26 people think maths is, this narrow subject of calculations and methods, if you teach
0:46:29 narrow maths, then only some students will be successful.
0:46:35 So it perpetuates this myth that teachers have that only some students can be successful.
0:46:38 It’s not about the way they’re teaching.
0:46:40 It’s just the way of the world.
0:46:46 And it just reinforces their idea that to be good at maths, you’re just a special kind
0:46:51 of person and only a few people can be that kind of person.
0:46:59 But at extremes, surely there must be some people who are just gifted in math, right,
0:47:01 or gifted in physics.
0:47:06 You can’t say that Stephen Wolfram is a random person.
0:47:09 Some people have developed incredible brains.
0:47:12 This is not an argument that people are the same.
0:47:16 The question is, though, how did he develop that brain?
0:47:24 And my problem with the idea of a gift is it’s very fixed, like you have it or you don’t.
0:47:26 Whereas we know that everybody’s on a growth journey.
0:47:32 You can’t cut off, make a cut off point and say, you have a gift, you don’t have a gift.
0:47:37 It is on a growth journey and can develop and grow their brains.
0:47:41 One of the people I like to share is somebody called Nicholas Lechford, who when he was
0:47:45 growing up, his parents were told he was learning disabled.
0:47:49 He had a very low IQ, you believe in IQ.
0:47:57 And he graduated from Oxford with a doctoral degree in applied mathematics after huge problems
0:48:00 as a younger child learning anything.
0:48:06 We know, we have millions of examples or we have lots of examples of people who had really
0:48:10 strong difficulties and went on to achieve amazing things.
0:48:13 It’s not that some people are born with something.
0:48:15 They end up with something for sure.
0:48:19 There are people whose brains are incredibly powerful.
0:48:21 But where does that come from?
0:48:22 Everybody’s born with a different brain.
0:48:25 Nobody is born with the same brain.
0:48:26 Everybody’s is different.
0:48:32 But the millions of opportunities you have to change your brain as you go through life
0:48:40 even as a baby and in the early years, those opportunities make more difference than differences
0:48:42 that we’re born with.
0:48:47 What if I were like push back on you and say, okay, so you just cited me one example of
0:48:55 someone who had all these learning challenges and was cast into a particular bracket of
0:49:01 not being able to do math and overcame that, got a PhD at Oxford.
0:49:07 So yeah, you picked one example, but then someone on the opposite side could say, I
0:49:12 know this person and he got vaccinated and he died.
0:49:14 So that proves vaccination is bad.
0:49:21 So one data point either way, how are people supposed to figure out that citing one vaccination
0:49:23 death is misleading?
0:49:26 What you just did could be just as misleading.
0:49:27 No.
0:49:33 Well, no, but I would say that somebody who takes a vaccine has a vaccination and die.
0:49:35 You don’t know why they’ve died.
0:49:39 You can’t say that vaccination caused him to die.
0:49:44 But when you look at people who overcome significant difficulties and go on to learn incredible
0:49:51 things, even one person shows you that can happen, that the way we approach learning
0:49:58 and life can change what happens for you even when you start off in a hard place.
0:50:00 And we have not just one example.
0:50:04 We have many, many examples that show that.
0:50:08 There was a school situation I remember in England that’s really interesting that in
0:50:13 England you take an exam at 16 and they’re in three different levels.
0:50:15 The lowest one, the middle one, the higher one.
0:50:21 And if you get put into the lowest exam, the highest grade you can get is a D. So it matters
0:50:23 which exam you’ll put in for.
0:50:27 And one school I worked with years ago just said, you know what, I’m going to put all
0:50:30 the kids into the highest paper.
0:50:33 And we’re going to prepare them all for the highest paper.
0:50:39 And those kids all got the grades on the highest paper.
0:50:40 She didn’t change her teachers.
0:50:42 She didn’t.
0:50:44 She just said they’re all going to do that work.
0:50:47 And they all got one of those highest grades.
0:50:52 We know that fixing people and deciding people have issues and they can’t learn.
0:50:55 It’s just not the right approach in education.
0:50:58 This is somewhat of a related story.
0:51:07 So I have been able to moderate several panels with chancellors of large universities.
0:51:13 I often ask them about admission policies, about relying on standardized tests and essays
0:51:15 and all that.
0:51:19 And I pose to several of them, like, why don’t we try an experiment?
0:51:26 Why don’t you just say, everybody apply and we are just going to randomly select people
0:51:27 to admit.
0:51:30 And let’s just see what happens.
0:51:38 Does that produce a more successful student body than our laser focus on SAT and college
0:51:41 essay and recommendations?
0:51:45 And I did not get a lot of support for that.
0:51:48 I bet you didn’t.
0:51:50 It’s what the UCs did, actually.
0:51:56 They’ve always used SATs as the filter and measure of whether kids can be successful
0:51:57 in the UCs.
0:51:59 And then they dismantled that.
0:52:03 They got rid of SATs that it’s no longer used.
0:52:06 And what they found was their students are just as successful.
0:52:10 They’re bringing in a more diverse group of students.
0:52:13 They’re more racially diverse.
0:52:16 And they’re doing just as well as when they had the SAT as a filter.
0:52:21 So that kind of is your experiment a little bit.
0:52:27 I think you make a point in your book that by bringing in a diversity of students, some
0:52:34 of whom are not as successful at that point as others, that everybody benefits because
0:52:41 even the ones who are doing better learn from watching how the ones who are not doing better
0:52:43 are learning.
0:52:48 So watching people struggle can help you learn how to be a better student.
0:52:53 And also we know that helping others learn helps yourself.
0:52:59 So we see this when students are in more diverse groups in terms of their prior achievement.
0:53:04 What we find is the ones who are most helped by that are the highest achieving students.
0:53:08 And the reason is they’re spending time helping other students.
0:53:12 And of course, anyone who’s taught knows that the best way to learn something deeply is to
0:53:14 teach it.
0:53:18 And it also means kids think differently.
0:53:21 Sometimes high achieving students are very narrow in their thinking.
0:53:25 They’ve been successful, but there’s only one way they can think about it.
0:53:31 And they sit in a group with a different kind of student who sees something visually and
0:53:33 it’s surprising to these other students.
0:53:36 And they learn a different way of approaching things.
0:53:43 So I do think diversity in all sorts of forms of diversity enriches students’ experiences
0:53:46 in schools and their learning.
0:53:51 And that would take us right back to our friend Tucker Carlson, which is if he understood
0:53:58 this, he would insist on diversification because it would make everybody better, including
0:54:03 a white kid destined for Ivy Legs, right?
0:54:05 It would make everybody better.
0:54:09 And that’s something that people don’t get.
0:54:15 Some of the people who push back on any sort of anti-tracking messages say, “I don’t want
0:54:18 my kids in classes with those kids.”
0:54:24 That’s the insidious underpinning of the pushback on tracking.
0:54:28 People want to keep their kids separate from other kids.
0:54:33 But they don’t know that when we have these environments where students are together and
0:54:37 they’re more diverse in all different ways, it benefits everybody.
0:54:40 That’s definitely what the research shows.
0:54:48 So now my brain is multi-processing and I’m thinking, so if I started surfing with surfers
0:54:53 who are not as good as me, would that make me a better surfer?
0:54:59 If you were teaching them, then probably it would, because the teaching would make you
0:55:00 better surfers.
0:55:04 So I’m going to start telling Madison to teach me how to surf because she would then
0:55:09 be teaching someone not as good as her and it would help her improve too.
0:55:10 That’s right.
0:55:16 My last topic, the topic that I love and I want to understand more is the concept of
0:55:24 metacognition and for those of you listening, that has nothing to do with the intelligence
0:55:26 of Mark Zuckerberg and Facebook.
0:55:28 So what is metacognition?
0:55:32 I never thought of that, Link.
0:55:33 Metacognition.
0:55:38 A lot of people think metacognition is thinking about your own thinking and there is a piece
0:55:45 of that, but metacognition and people with metacognitive ideas, it’s more than that.
0:55:48 It starts with self-belief.
0:55:49 It has growth mindset in it.
0:55:54 You believe that you can do something, but then somebody who’s metacognitive has different
0:55:57 ways to approach a problem.
0:55:59 Maybe they have a range of strategies they’ve learned.
0:56:04 We talked about one at the beginning, trying a smaller case, they have a range of strategies
0:56:09 and they’re willing to try these different strategies out.
0:56:15 They see metacognition in the part of the brain and it’s pretty powerful.
0:56:21 One of the things I do in the book is urge people to teach students how to learn.
0:56:27 I think as maths teachers, we often think I’m there to teach maths, but actually many
0:56:34 kids haven’t learned how to approach maths well and they may have learned counterproductive
0:56:35 ideas.
0:56:41 Teaching kids how to learn, teaching them how to be metacognitive is really important.
0:56:48 Let’s say I’m a parent and I’ve listened to this whole podcast and my kid is 17, 18,
0:56:51 19 years old.
0:56:57 He or she is the product of a school system that was geared towards standardized tests
0:57:04 and Algebra 1, Algebra 2, Algebra 3, so you can get into pre-calculus so that you can
0:57:09 get into calculus so you can get into the Ivy League so that you can have a STEM career
0:57:15 and he hates maths, she hates maths, we got him tutors, we did everything we could, we
0:57:22 dread maths, which what do you do if you’re midstream and you’re stuck in this position
0:57:27 and now you listen to this podcast, you read your book and you’re saying the whole system
0:57:31 is screwed up, what do I do for my kid?
0:57:35 I think what’s really important for all of us is that we develop a playful relationship
0:57:36 with maths.
0:57:42 I see maths as just a playground of ideas that we can try out and investigate things
0:57:48 and so I deal with those people all the time because I’m always running workshops for teachers
0:57:51 and many teachers are in that position.
0:57:57 They hated maths and they saw it as a list of methods to memorize and we introduce them
0:58:03 to playful maths, we give them activities where they’re making connections and seeing
0:58:10 things differently and at many, many times teachers have cried or become very emotional
0:58:16 and said oh my gosh, I just didn’t know maths could be like this and I didn’t know I could
0:58:22 do this and so I think shifting people from that narrow, getting them out of that narrow
0:58:27 maths experience is almost like a therapy people need into seeing maths differently is
0:58:32 really important and some adults go through that transition from reading books, maybe
0:58:38 they read math-ish and that takes them on that path and then they start to engage with maths
0:58:43 differently and some people need more than that, like they need to go to a workshop or
0:58:52 something where they’re able to experience maths differently and that will get them shifting.
0:58:57 Many, many people make that shift and they’re always happy when they make the shift but
0:59:04 we have to encourage more people to make that shift, to see maths differently not as this
0:59:08 rigid set of numbers but as this ish playground.
0:59:11 Okay, but I want you to get really tactical.
0:59:15 I’m listening to this podcast, I’m a real believer, my kid hates math, I’m afraid of
0:59:17 math for his or her future.
0:59:18 What do I do?
0:59:20 What do I do?
0:59:23 Not conceptually, what do I do?
0:59:28 We have a number of resources on our website to help people, one of them is an online class,
0:59:35 it’s completely free, six 50-minute sessions that people can take, it changes their mindset,
0:59:37 it changes their approach to maths.
0:59:42 We have a lot of evidence of that, we’ve studied it with randomized controlled trials,
0:59:46 students who take it, engage differently in maths class afterwards, they score at high
0:59:53 levels on tests afterwards, come to U-Cubed and look at the online class, it’s really
0:59:58 for adults or children and look at the other resources that we share.
1:00:04 I’m really passionate about changing people’s relationships with maths and we have U-Cubed,
1:00:10 we have a new maths app now called Struggly, we have books, many different resources aimed
1:00:16 at really giving people that different maths experience.
1:00:22 I have to admit I love the ish concept, I’m going to become an ish evangelist, you know
1:00:29 where you live your life, approximately, logically, realistically, roughly right.
1:00:36 I love that concept, life is too short to be too precise, so thank you Joe Bowler for
1:00:42 introducing me to this concept, now I’d like to thank the Remarkable People team, that
1:00:50 would be precisely Matt as a Nismar producer and co-author of Think Remarkable, you must
1:00:58 read this book, maybe we’ll rename it Think Remarkable Ish, and then there’s Tessa Nismar,
1:01:04 Tessa prepares me with all the background research and perfects our transcripts.
1:01:10 And speaking of perfection, there is Jeff C. and Shannon Hernandez, sound design engineers
1:01:19 extraordinaire, and finally Luis Magana, Alexis Nishimura, and Fallon Yates, we are the Remarkable
1:01:35 People team, we’re on a mission to make you Remarkable, until next time, Mahalo and Aloha.
In this captivating episode of Remarkable People, Guy Kawasaki sits down with Jo Boaler, a trailblazing professor of education at Stanford University. Together, they dive into the transformative power of embracing a multidimensional approach to mathematics education. Boaler shares her groundbreaking research on reframing our relationship with math, emphasizing the importance of creativity, diversity, and meaning in the subject. Discover the seven principles that can revolutionize the way we learn and teach mathematics, empowering students to develop a deep understanding and appreciation for the subject. Join us as we explore how a shift in mindset and approach can unlock the potential of math education for all.
—
Guy Kawasaki is on a mission to make you remarkable. His Remarkable People podcast features interviews with remarkable people such as Jane Goodall, Marc Benioff, Woz, Kristi Yamaguchi, and Bob Cialdini. Every episode will make you more remarkable.
With his decades of experience in Silicon Valley as a Venture Capitalist and advisor to the top entrepreneurs in the world, Guy’s questions come from a place of curiosity and passion for technology, start-ups, entrepreneurship, and marketing. If you love society and culture, documentaries, and business podcasts, take a second to follow Remarkable People.
Listeners of the Remarkable People podcast will learn from some of the most successful people in the world with practical tips and inspiring stories that will help you be more remarkable.
Episodes of Remarkable People organized by topic: https://bit.ly/rptopology
Listen to Remarkable People here: https://podcasts.apple.com/us/podcast/guy-kawasakis-remarkable-people/id1483081827
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