Limitless Learning - A Conversation with Professor Jo Boaler

Welcome to the Future Learning Design Podcast.

I absolutely reject that dichotomy because the pathway to equity is also the pathway to excellence. We see that when teachers teach in those ways, the inequities disappear. Students still reach the highest levels, but we can't predict which students are going to reach those levels by their racial group or their gender.

Hello and welcome to another episode of the Future Learning Design Podcast.

My name's Tim Logan and the podcast is brought to you in partnership with Notosh. This week's episode is a fabulous conversation I had with the amazing Dr. Jo Bowler, who is the Nomellini and Olivier Professor of Education at Stanford University. Her former roles have included the Mary Curie Professor of Mathematics Education in England and a maths teacher in London comprehensive schools. Her PhD won the National Award for Educational Research in the UK, and she is an elected Fellow of of the Royal Society of the Arts in Great Britain and a former president of the International Organization for Women in Mathematics Education. Jo founded YouCubed.org to give teachers, parents, and students the resources and ideas they need to inspire and excite students about mathematics. And she is a White House presenter on women and girls. Jo is currently co-leading a K-12 data science initiative and was named one of the 8 educators changing the face of education by the BBC. Her work has been published in the New York Times, Time magazine, The Telegraph, The Atlantic, The Wall Street Journal, and many others. She's the author of 18 books and numerous research articles. Her latest book is Limitless Mind: Learn, Lead, and Live Without Barriers, and she is currently working on a new book about diversity in mathematics.

Hi Jo.

Hello.

Good morning. How are you?

Ah, very nice.

Brilliant. Thank you so much. Well, yeah, no, it's really wonderful to be able to talk to you. I've had the privilege of talking to some educational heroes, let's say, on the podcast, Dylan William and John Hattie and different people, and you are very high up my list. So I'm slightly nervous, but very excited.

That's really nice of you, Tim. Thank you. And I'm looking forward to the conversation.

It's great. So, I mean, the first thing So there's a huge amount in your work, obviously around maths and in your more recent work, which is more expansive and really interesting. I'd love to talk to you about, if we start with the maths slide, obviously you've been following the California Math Framework story very closely and there's all sorts of really interesting things which I'd love to talk to you about around that as well. But one of the, just to kind of start in on it, one of the things that particularly fascinates me about having been a teacher and then worked with schools in different roles is the debate between, you know, what you could broadly call the trads and the progs, you know, the slightly false dichotomy around pedagogy and curriculum. But maths is often the kind of paradigm case that, you know, comes up in a lot of these discussions. And rigor, rigor particularly is one of these really super interesting concepts. Right. I enjoyed Trina Wilkerson's piece about The 3 Rs of mathematics being rigor, relevance, and responsiveness. And, and I think just so if we could start maybe with that idea of rigor. Yeah. Why don't we start with that? Why is that such a contested term? Yes.

So I am one of the 5 authors who were tasked with writing up the ideas of a committee of 20 elected educators who met for a year and formed the ideas of the framework. You wouldn't know that reading the press response. They write as though I just sat down and wrote it one day.

Yeah.

But yeah, so in the framework, one of the things I particularly appreciate about it, one of the mathematicians on the committee actually was the one heading this, was a sort of redefinition of what rigor means. What we see in a lot of debates about mathematics education is people who push for content saying it's rigorous when what they really mean is it's very inaccessible to students and therefore it weeds out. Plenty of students and they're happy about that. And I know that that's what's called rigor is inaccessible often because we don't teach it well. So one of the things that is written in the framework is a redefinition of rigor, which is really about can students use and apply this concept in different situations? Rigor is not, can I repeat a procedure over and over again? It's how am I using this in different ways and in applied contexts and situations. And so I like that definition of rigor. It is what we should be aiming for with students.

Yeah. No, and it's interesting. I was also reading there's different conceptions of the idea of rigor, but just that it was just lots of advanced content, almost equating it to essentially Algebra 2, you know, just about the the advancement of the content as one definition, but then I also really liked what you put in the framework about that it's not about abstraction.

Yeah.

Because I think, I think that's really interesting that often rigor is seen as how quickly can you get as abstract as possible.

Right. Yes. One of the things I've been working on in my recent career is really trying to change the conversation about abstraction.

Yeah.

People think that for a long time there's been a belief that there's kind of a hierarchy that you start with visuals and physical physical objects in order to get to this higher level, which is abstract. But if you look at the work that's going on in Silicon Valley, for example, where I live, all of these engineers that are producing amazing new products, working with very high-level mathematics, it's all visual.

Yeah.

And physical. It's not abstract. And yes, there's abstract mathematics in there, but it's really not a hierarchy where the top is abstract One of the mathematicians I love to share, Maryam Mirzakhani, was the first woman in the world to win the Fields Medal. And she was very sadly taken from us at a young age, but her work was entirely visual.

Yeah.

And she asked me if I would be the chair of a PhD defense of one of her students. And I went to the math department that day and I sat in this PhD defense and watched this young woman share all of her PhD work. And again, it was all visual. She didn't have any numbers in the whole conversation. And I remember sitting there that day and thinking students would be so surprised about this.

Yeah.

That this is what high-level mathematics is. So yeah, I think you're right to raise that question of abstraction. You know, abstract maths is great, but we need just as important is that visual and physical mathematics.

Yeah, absolutely. I think that's almost It's a broader conversation around that kind of rush to abstraction as well. Even culturally, just the way we value vocational education versus academic education, it's almost— there's a similar kind of thing going on there, it seems to me. We value that abstract knowledge somehow, just decontextualized and abstract knowledge somehow we value that more.

Right. I have a friend actually who had a lot of special needs in school, did not, was not regarded very highly by teachers, was fantastic with his thinking and his hands and can see things and do things with physical objects that are just remarkable. And he ended up working his way up through the ranks of engineering companies. He is so sought after. He's working for Tesla at the moment. So sought after by these top engineers. They have the students who've gone through engineering degrees and have all the abstract knowledge, but it's him they want.

Interesting.

And I mean, that just, I think, really underscores the point you're making. We haven't valued students doing that kind of vocational work and it's just as important.

Yeah. There was another take on rigor, which I also wanted to get your perspective on with, I think it was referenced in the, in the math framework, but the Dana Center 2019 report and they almost framed rigor as the use of a, of maths as a language. And I've, I've always thought that was quite an interesting idea that thinking about, so what do they say? Rigor in mathematics is a set of skills that centers on the communication and use of mathematical language. Ability to integrate, because you also, I mean, you talk about integrating conceptual understanding, strategies for problem solving, and then applications are learned. So there is, there's something about that kind of integration piece and being able to fluently speak a language, which involves integration. I don't know. There's something interesting there.

I mean, I definitely see mathematics as a language that you can lay upon the world to make sense of the world. And once you have that language and you're thinking of mathematics as a a language that helps you in the world, you start to see things differently in the world. You start to get greater insights about things that are happening in the world. So I definitely like that thinking about maths as a language.

Yeah. And I suppose then if we go back to the kind of way that maths is often taught, and then Trina's other two Rs, the relevant and responsive. Yeah, I've heard you talk about the other maths because there's, you know, there's, I mean, again, not wanting to position of some kind of false dichotomy between one or the other, but you know, there's many different shades of maths, right? But there is a kind of a traditional sense of maths being taught very didactically and through lots of drill and, you know, lots of repetition, modeling, et cetera. I mean, what is it that you then are articulating? I mean, obviously, you know, many people will know your work very deeply for YouCubed and all of the amazing work you do to kind of show this other maths, but how would you describe that?

Yeah, I will describe it by saying I teach undergrads at Stanford and I teach them a course called How to Learn Maths. And they come into the course with very high-level maths achievement. And they're kind of split. Some of the students love maths and they want to take my course just to get another mathematical opportunity. And the other half hate it and are quite traumatized by the subject, even though they've got to Stanford. So they're done pretty well, but I introduced them to the neuroscience of our brain. We talk about how we really want to be making connections in our brain when we learn maths. That means seeing it visually, interacting with it physically, with words, with patterns, just many ways of seeing maths. And we do a lot of work where they get to see and understand concepts that previously they had memorized in class.

Yeah.

And they are so moved by this experience. Every year I get this group of undergrads and every year they say, I don't want to go back to that version of maths that I experienced where I was just given rules to learn and methods to memorize. I just don't want to go back. I want to keep this, the experience of maths that's more multidimensional and it's about deep understanding. So, yeah, I definitely think we can give people a totally different experience of maths.

Yeah, interesting. And it also strikes me there's a kind of a parallel somewhere with the kind of algorithmic thinking that seems to be dominating a lot of the way that, you know, things, tech, etc., is developing that hasn't necessarily always got us into the best, you know, given our previous off-recording conversation about climate change.

Exactly. We definitely have to have people who have more understanding than that and putting people in charge of the world who have good tech skills and have got great achievement through their tech work. And now suddenly they're making decisions on major social media platforms and is really not, it's pretty irresponsible and we should really be thinking about that, I think.

Yeah.

Yeah. And I think what you say there about the kind of trauma that some people bring from that experience of, I mean, obviously, you know, we see people, some people thrive in what you might call the traditional math class, right? The kind of abstractness and the Very few people, but yes, a few. Yeah, no, absolutely. But you know, you do see it happening. And I mean, that's right. There's a kind of structure and there's a clarity and there's a— they suited to the abstractness, let's say. Yeah, partly.

Well, all the people who like certainty, they like to learn rules. They don't like any areas of uncertainty or that traditional math suits them in that way.

Yeah, but I think some of the debate around, and that seems to have been happening around the California Math Framework and that idea about that there's some kind of trade-off relationship between making maths more inclusive and then ultimately equitable, as we'll get onto later, but the trade-off relationship between that and the rigor piece. And it just seems like that's a really dangerous thing to those two things to position against each other.

Yeah, I think that they are very clever talking points that have been put out by the people who don't want change. The way I think about mathematics in the system in the US, although this is true in many countries, but in the US in particular, we have a system where very, very few students get to the highest levels. Calculus, for example, which a lot of the arguments are about, 16% of students in the US take calculus in school.. And most of the students are pushed out of that pathway at an early age. Yeah. So we have put forward recommendations that allow more students to go forward and allow more students to be successful. Those who were the ones who were in that 16% don't necessarily want more students to get to higher levels. They're pretty happy with the system they have. And so they have put out this idea that, oh, you are going to do that by making maths easier. Which is not true. We will do that by making systems available to students so they can get to higher levels. One of the most clear, most reliable research facts that is out there is that students cannot learn unless they're given the opportunity to learn. And most students in the US don't get to higher levels in maths because they are not given the opportunity to do that.

Yeah.

So, yeah, it's very sad that it's come down to this big argument. And, you know, the argument is in against the ideas in the framework is entirely coming from people who have been very successful in mathematics.

Yeah.

But it also, my observation was that they're also justifying the kind of tracking that you're, the framework is pushing back against with the argument that higher education institutions are requiring calculus and therefore that's what justifies that we have to maintain the status quo.

Yeah, which is, you know, wrong in a couple of ways. One way it's wrong is even if higher education institutions did require calculus, we're not enabling many students to get there. So clearly we need to change that. But it's also the case that there's big change happening at the K-12 sector. If you read the admission statement that Harvard has on their website, they very clearly state calculus is not a requirement for coming to Harvard. Many courses don't require it. And even if you are in courses that require it, you can take it when you come to the university.

Right.

Yeah.

So that's true of most universities. In fact, the mathematical associations, the national math associations, say very clearly they would prefer it if students took calculus in college. So this rush to calculus is also not very productive. Two-thirds of kids who take calculus in school either retake it in college or take a lower-level course. So it's not working. It may be working for a small handful of kids, but as a broader system, we know it's, it's not working well.

Yeah. And the other, the other part to that is that there are other directions that seem to be emerging within mathematics that maybe are more interesting, responsive to, you know, young people's lived reality and technology, i.e., the data science thing that you've been working on with Steve Levitt. And I'd love to ask you about that because I think, you know, the be-all and end-all of calculus, right? But actually there's this whole other area of understanding the world and sense-making through maths that maybe is actually just more important and relevant.

Yeah, I agree with you. I mean, maths is a very broad field and why have we only valued Calculus for the highest achievers and said that is the route to go to. Calculus is important. I mean, I'm, I'm a big fan of Steve Strogatz. He has a beautiful book called Infinite Powers about all the ways calculus is used in the world, but it's not the only important mathematics. And there's a pathway that can start with a course in data science and maybe lead to a higher course in statistics that is absolutely critical. And in fact, these new courses in data science, we have one on our own YouCubed website, and there are a couple of others as well. What we're finding is students are completely engaged. They see the relevance of the work they're doing. They're exploring datasets and asking questions of the world. It's— and they're amazed that this is a really engaging maths class. Of course, they're learning a lot of high-level mathematical ideas and techniques, but they're applying it to real data. And yes, it's entirely valuable and a great pathway for kids, but that one is also being attacked by people who don't want that change.

Oh, really? Interesting. In what way?

People are saying don't offer data science in schools because we want students to take calculus. So in California, for example, the, the colleges communicated that students can now take data science instead of Algebra 2.

Right.

And go on this data science stats pathway. And thousands of students are doing that now.. But the critics say we want everybody doing Algebra 2. That is the course that everybody should do. Then that sets them up for calculus.

So the gateway drug to calculus. Yes.

It's really unfortunate because data science is important. It's really engaging kids and many students. I mean, in, in our own studies of our course being taught in schools, about 60% of the kids taking data science are also taking Algebra 2. It's really not a one or the other argument anyway.

Yeah. And maybe could you give a little bit of background to Steve Levitt if people don't know? Because as I understood it from Freakonomics and he approached you, right, to kind of have this kind of conversation.

Yeah. Steve Levitt, a famous economist at the University of Chicago. And I think many people know his Freakonomics book. He called me kind of out of the blue, not one of my usual kind of calls, not in maths, not in education, but he called me and said, would you 'Help me try and change high school maths and have data science be an option for kids.' And I said, you know, 'Yes, definitely sign me up.' And we've been working since then to try and open high school mathematics so there are more choices for students and students can choose a data science pathway. Not just that, we're also trying to bring data science or data literacy, at least, into all levels of maths from kindergarten up. Kids can be collecting data and looking at data. And developing that really important understanding.

Yeah. Yeah. That's interesting. Can I ask you briefly about the younger years? Because I mean, often the conversation gets, it's about high school maths, but I think that's really interesting you brought that in because one of the, the ideas in the, in the math framework, the big ideas language, I thought was interesting. And I wanted to ask you about as well. And maybe that relates to some of the kind of number sense or that, you know, the ways that the younger learners are picking up maths, especially with data science early. But yeah, what, why did you pick up that idea of big ideas for the math framework? And, and how does that work?

It was while I was working on the California Math Framework. So I was already pretty busy with my Stanford job also, but the state asked us to help teachers during the pandemic. This was a pandemic initiative. And they said, you know, clearly it's really hard to teach everything, which I very strongly believe teachers have too much to teach every year. And can we highlight for them the more important content?

So.

I thought that was a really valuable role. And instead of doing what people have done in the past, which is to say, well, this content is more important and this is not so important, we reorganized all the content in the standards into what we called big ideas. And we recommended to teachers, focus in on these through rich, deep activities. So we set that out. It's on the State Department website. It was unanimously passed through the State Board last year.. And we hope it will guide people and guide publishers as they think about what to aim for. One of the problems we've had in mathematics education is for many students, it's just this long list of methods, disconnected methods they have to remember. Whereas if we can organize into big ideas, it's much more meaningful. It allows teachers to have more time to not be spending time focusing on these small methods. So data is a big idea and it's a big idea at every grade level. And that was one of the things we were able to do in this reorganization of content is really sort of highlight those data connections.

Yeah, no, that's interesting and strikes— I mean, quite a bit of my work is with the IB and with IB curriculum. And obviously that, you know, there is a big focus on concept-based curriculum and there's obviously not quite the same language and not quite the same conceptualization necessarily, but there's definitely correlation there between between those ideas of clustering important ideas together so that you can, you know, almost visualizing them like the schema in your brain, you know, as you learn.

Yeah, absolutely. And this really aligns. I'm working on a new book at the moment and I'm putting into this book a model of teaching that draws greatly from the psychologists who look at expertise. They really study how experts hold knowledge as well as educators and neuroscientists. I'm pulling them all together to make this teaching model. But one of the key things that's communicated is experts hold knowledge in what they call conceptual chunks, which you could also think of as big ideas. They're not isolated pieces of information. They are connected, bigger concepts.

Yeah.

So getting that bigger connected concepts to kids is really what we were hoping to do in that reorganization of content.

That's brilliant. And there's something really, I find really interesting in that because often the expertise research is the thing that gets reached for in support of a much more didactic, knowledge-rich curriculum, right?

Yeah. And I know why traditional math teachers say, oh, we, you know, this expertise research is what we do, because one of the things that they focus on is practice. Anders Ericsson was a really great researcher on this, but what he defines and others define as deliberate practice is nothing like the practice in traditional math classrooms. And he says very clearly that if you're engaging in deliberate practice, you're developing these mental representations of big ideas. So kids are, you know, really going deeply into ideas and seeing them visually or maybe physically and developing these really strong mental representations. That doesn't happen in a traditional math class. That's The kind of practice that they say is being held up by these expertise researchers is very different from the meaningless practice that kids are doing in classrooms.

That is interesting because it's the argument often is that the novice learner learns just, just learns differently to the expert learner. And therefore, if we, if we model everything on the way that an expert learns, you know, it's not actually going to support the novice learner who just does not, doesn't have those developed schema. Already. But I think that's, it always feels like a bit of a false dichotomy because there's always, I mean, I've had similar conversations around concept-based learning. It's like, surely there is a way to more efficiently present and provide different learning experiences that enable that conceptual connection to develop more quickly, right? Surely.

Yeah. And help those novices get on a pathway towards expertise.

Yeah.

To say that these people just are thinking differently is a very deficit way of thinking about people because anybody can develop that expertise if they're taught in the right ways.

Yeah, that also then comes back to this whole equity conversation as well, right? Because I think from some of the debates around the California Math Framework that I've listened to, it's— there is again this kind of trade-off relationship between the kind of equity point, and therefore if you're, if you're creating more equity, you must be reducing the level of rigor.

That's right.

Right, going back to where we started.

Yeah, and I absolutely reject that dichotomy because the pathway to equity is also the pathway to excellence. I mean, we, those two things of excellence and equity are not in conflict at all. And we see that in many, many studies. We see that when teachers teach in those ways, the inequities disappear. Students still reach the highest levels, but we can't predict which students are going to reach those levels by their racial group or their gender.

Yeah. Which the very fact that you can, I mean, just tells you something deeply, deeply problematic about the whole picture, right?

It does. Yeah.

Yeah.

Maybe then if we could switch slightly to, obviously you, you are deeply steeped in the whole maths world and maths education and still, but you then also moved slightly beyond that to expand your horizons into a broader book called Limitless Mind: Learn, Lead, and Live Without Barriers. And I just would love to ask you about that briefly. I mean, what was it that you felt— yeah, what was the kind of impetus to move beyond the maths domain and into something broader?

Yes, there was a very clear impetus for me, which was I wrote a book a few years ago called Mathematical Mindsets, and it got all these ideas out to maths educators that, you know, rejecting the ideas that some students can't learn and sharing the amazing research on making mistakes is really important. Struggle's really important.

Yeah.

Seeing it visually is really important. But the big feedback I got from readers of that book was, you have to get this out to more people. You have to get this out to our administrators need to read this and parents need to read this. And they said to me, but don't put math in the title because then they won't read it. True. So that was really the impetus. I thought they're right. Other people do need this. It's not just about maths. And that's something I hear often when I give presentations, that people will come up to me and say, oh, I can use this in my history teaching, and this is— I use this in my science teaching. It's really not just about maths.

Yeah. And in the book, you lay out 6 keys of learning. And I'm just curious, which are the ones that you particularly kind of keep coming back and back to? Like, which ones still do you just use all the time?

I think one that I'm really uplighting in my current new— in the new book I'm working on just keeps coming back. Is so important is the value of having students engage in struggle and feel good about struggle. We know that's the best time for our brains. We know that's when our brains are on fire with growth and connectivity. We know that the highest achieving people in the world are those who persist through times of struggle, who feel comfortable, maybe even feel good about that time of struggle. And they are the ones who have made it and have gone forward. I mentioned Steve Strogatz earlier. We have a video on our website where he talks about doing a really hard maths problem in a room full of mathematicians and how he was stuck and he couldn't do it. And he shared that with this group of mathematicians and said, you know, I'm stuck, can't do it. And he said it was embarrassing. They were sitting next to these mathematical people. And then other people in the room started saying they were also stuck and they also couldn't do it. And They had this great conversation, but I have this video in one of my online courses and the overwhelming response to this video is teachers saying they are completely shocked that a high-level mathematician struggled.

Yeah.

And this is the problem we have about this idea of struggle. People think it's bad. People think that high-level people don't struggle and it's become this something we avoid when it's really the most important part of learning and I find that when I teach students, which we regularly teach middle school students and high school students in summer camps, and we share with them, we want you to struggle. We're giving you difficult work because we want you to struggle.

Yeah.

And that's our goal. And it shifts them in their thinking about it. They're more willing to persist and keep going because they know it's what a good time— we show them how good struggle is for their brains. I think that's an important piece.

Definitely. Fascinating. And for me, there's a kind of a humanity and a humility to that as well. I mean, just that idea that watching somebody you admire who, and you admire them intellectually and in all sorts of ways, but watching them admit that they are struggling, there's something really connecting and important about that, I think.

I think it's really powerful. And Steve, I'm talking a lot about Steve now, but he was in a podcast recently with Steve Levitt, who we just talked about.

Economist.

So great conversation the two of them are having in which Steve Strogatz, the mathematician, says he bungled his way through his math degree in college, getting the lowest grades in his math courses of any courses he took. And I just love hearing top mathematicians talk about this because it's not what people think.

It's true.

And it really helps.

Yeah, absolutely. I, I think there's also a really interesting connection as well with the beat, let's say broadly, the other side of the argument about, you know, more traditional didactic pedagogies because there's, you know, Robert Bjork's idea about desirable difficulties.

Yeah.

And I think there's also something really connecting and interesting there that there's a mutual recognition that productive struggle is important, but maybe some of the divergence is what kind of struggle because obviously you've got all the cognitive load theory argument that, you know, you, right, young people can't solve real life problems because there's too much cognitive of kind of noise going on and they can't get to the heart of what's actually the focus of what they should be learning. But there's a general agreement that productive struggle, desirable difficulty, that's, that's a good thing to get young people to be doing. Yeah.

And where I think again, the sort of traditional pedagogy falls short is if you read Björk and other of these cognitive psychologists, they will talk about Testing is good. You want to keep being tested on what you know so you can make mistakes. And, but what the very best form of testing is self-testing.

Yeah.

And the critical part of students learning from that is a feedback loop where they're getting information on their, what they're doing right and wrong.

Yeah.

So most traditional tests and the grading that happens in classrooms give kids no information.. They get back a test score, they get back a grade. So that feedback loop is missing. So again, that's where people say, oh, this is what we're doing. We're testing students, we're giving them lots of practice, but the practice is not meaningful practice and the testing does not give students any information on ways to improve.

Yeah, absolutely. I mean, it has to be low stakes or no stakes testing, right? I mean, otherwise it just ruins the impact.

Or not even testing at all, you know, or self-testing, as you said, I mean, a lot of students prepare for exams and tests by reading through the notes they have. And the effective way to prepare for an exam or test is to keep giving yourself questions to try.

Yeah.

That does not have to be in a test, not at all.

That sounds like you're advocating for retrieval practice, which would be a, you know, a core tool of the traditional No didactic pedagogue, right? Oh my goodness. There is, I mean—

I have never said, nor do I believe that kids don't need to practice, but it has to be meaningful. So one of the schools that I studied that did this so well was they gave kids opportunities to practice, but all of their practice was done through applying, through applications. So they would learn something and then they would need to apply it in different situations. So if you think about that practice, it's much more demanding than just repeating the same thing in the same kind of situation.

Yeah, absolutely.

It's really about the type of practice, not whether we do it or not.

No, exactly. Obviously I'm being facetious just to illustrate how misrepresented you often are in the media, right?

I am totally misrepresented in the media. So anything we can do to help with that.

Exactly.

Yeah, exactly. So I mean, talking of which, what are your kind of current reflections on where the California debate is, because it's really interesting, even just trying to research it. It's very difficult to find the documentation. Um, that's all been pulled off the website. The only way I could find it was through the Internet Archives, you know, the previous versions of the internet where you can find old documents. It's very interesting how deeply divisive it's been. And I wondered what your reflections are there. Like, is there a connection to the just kind of deeply polarized political conversation in the US or? Why has that stalled so, or seemingly stalled?

I mean, it has been dragged into political discussions, unfortunately, we, because we don't want education to go down that road, that divisive road, as you said.

Yeah.

And I really think the media has been very damaging in all of the coverage of the framework because every time I read a story about the framework, what they want to highlight is conflict. And they share, you know, that there's a group of STEM professors who are against it and here's a link to their petition.

Yeah.

So they're all about making this a conflict. What they don't share is that there's also a petition that many more people have signed, educators, STEM professors, twice as many people in support of the framework. That never makes it into any article because it's not contentious enough.

Of course.

So the framework's done a lot of damage and it was a New York Times article that compared the framework to what was happening in Florida. That made that political connection that we hadn't previously had. And that is unfortunate. It's trying to, you know, pull it into the political framework. So yeah, I think what is the future of the framework? It's supposed to be going to the State Board later this year. And what will go to the State Board? How closely will it match the framework that was made by the committee and the writers? We don't know. And one of the things that I'm most sad about is it is very hard to read what's actually in it. We need a clear summary of what's in it and we need a clear write-up of the process so people aren't left reading really biased news articles about it.

Exactly.

No, absolutely. I mean, the nuance just isn't— there is none, right? You just, you can't get anywhere near any of the nuance. And I watched a discussion and one of your colleagues, Brian Conrad, was in the discussion and he seemed to be one of the people who was, you know, critical of different aspects of the framework. But actually, but actually a lot of what was being said, he seemed to be in quite broad agreement with.

That's right. And this is what makes me so sad. None of the people who are critical of the framework have ever reached out and said, can we sit and talk about it? Can we have a conversation and come to agreements? Because I'm sure agreements could have been made. And when people do sit down and talk, there isn't that much disagreement.

Yeah.

But that wasn't what happened. They just took up a battle stance and said, okay, I'm gonna form a petition to try and pull it all down. Yeah. If only we had gone forward with people having discussions, we'd be in a different place.

Yeah. As you said already, I mean, the, the, the big ideas part of it, that seems to have been passed already anyway. So that's not actually that new or radical. And then it seemed to be the detracking was quite a big and contentious issue. Why do you think that was? I mean, it obviously relates to some of what we were saying about calculus, but.

So we have a system in many districts across the US. So yes, it does all start with calculus. There are more courses in front of calculus that you need to take as a high school student than there are years of high school. So that's a problem right there, and we should change that. And what that's done is it pull— it has pulled high school courses into middle school, and middle school has said, okay, we need two tracks of students, some of which can get to these high-level courses. And they make those decisions at the beginning of middle school, often in 6th grade. Using data because this is the only data they have. It comes from 4th grade when students are in elementary school. So you have these 4th grade students taking a test that they're not even aware of often that determines what course they get in 12th grade and going forward, whether they go to college, what colleges they go to. So even if you believe that we need different tracks and some students go higher and some don't, I don't know anybody who thinks that is a good system.

Yeah.

That we are taking kids' elementary school achievement and deciding what they do for the next 8 years.

Yeah.

And potentially their future prospects in all sorts of other ways, right?

Way beyond.

Exactly. And beyond. So there, it probably won't surprise anybody that the achievement, and if you look at the students taking calculus, it's highly racialized. Which is just not okay. So that's what we were trying to push back on in the framework. And we were saying, you know, we've got to— one option is delay. If you're going to have kids take this course in 8th grade, please make the decision in 8th grade, not in 4th grade. But that's not how it's represented in the news. In the news, it's all about the framework is detracking, end of sentence.

Yeah. Yeah. I mean, I read one quote that was leftists trying to cancel math class.

That's right. Leftists are canceling math.

I know.

That is how it's being portrayed in some places.

Yeah.

Yeah.

Yeah. But, but also, I mean, very seriously, it was very sad to then read about how much personal attack you've had and you've received. I think, I mean, these are important issues. These are our young people and our children and all of that. Of course, they're important and emotive issues, but but as you said, to not be grown up enough to be able to sit down and have a conversation about it and make really deeply offensive personal attacks on you, I just thought was just horrendous.

Yeah, I mean, that's been the saddest and the worst part of it. People who are not even attacking the ideas, they've just turned the attack onto me as a person. And honestly, they're trying to bring me me down. They're trying to end my career.

Yeah.

And some of these people who are doing this are very powerful, high-achieving, wealthy. I have this Silicon Valley inventor who sold his company to Apple for $60 billion writing to journals and telling them to take down my papers.

Wow.

So it's been really awful actually for me.

Yeah. I'm so sorry. Yeah, just horrendous. I mean, I saw a hashtag #ProtectProfBowler, which was, you know, a small kind of initiative pushing back a little bit. But I mean, my goodness, just, just horrendous.

Most people don't know about it, and that's fine. I don't need them needing to know about, you know, all these awful things being written. But yeah, when I speak to educators and I go out, I do a lot of work with educators, most of them don't know about it, and they're totally behind the ideas in the framework. They're just waiting for it to come out. It's like there's a parallel universe going on with all of this arguing and attacks on social media, and then educators and teachers who are doing the work of maths teaching, and they know what's needed, and yeah, they're in full support.

So, and I mean, to be frank, you know, there isn't necessarily a progressive consensus about— within education about the way the pedagogy should move. And, you know, there's lots of different discussions, but at least they could be had in a grown-up way, right?

About—

based on research or, you know, based on just informed perspectives in a, in a mature way, which is—

I mean, what the people who came after me decided to go to all these districts across the US, serve them with public records requests, which puts districts, you know, takes out their valuable time asking for any work they'd done with me. And then incorrectly shared that I was making all this money off districts, put on Twitter my personal emails that included, you know, discussion of my family. And so they have these really underhand ways of trying to bring people down.

Yeah.

And it seems that it's all legal. They can just go after someone like this. And yeah, why can't we just have conversations and meet and talk and move forward? Why can't we keep the debate about the ideas in the framework, not about a person who was employed by the state to help write it.

No, absolutely. No, and I'm so sorry to hear all that. And it just, it just feels that there, there's something deeply threatening about the whole conversation, which I'm, I'm not quite sure what it is, but it's very fascinating why it should be so kind of almost existentially threatening to people to have these kinds of conversations about, I don't know, is it the purity of maths or is it like, is it a patriarchal kind of nonsense or I don't know, I've no idea what it is, but it just It seems to be so deeply threatening that, that, yeah, it just prevents any kind of reasoned debate.

I think it's deeply threatening to those who've been very successful in maths. It's not deeply threatening to the population at large that we try and improve maths education. And those who've been very successful in maths, you know, often they also know how their children can be very successful in the same system. So it, it has financial implications.

Yeah.

If you're broadening the playing field and letting more students go ahead and you're threatening the privilege of the ones who know how to get ahead, that is what I see going on.

Yeah. And to be honest, there are multiple, it's not just in maths education, you know, there are multiple of those kinds of global conversations going on where people with privilege are hopefully being forced to to consider, you know, me being one of them, I can recognize, but you know, in different ways, you have to, you have to recognize that and have some humility.

And of course, many people of privilege, many high achieving people do get that. And they're totally, they're behind the changes. If you look at the petition that's in favor of the framework, you'll find many STEM professors. I was at a great meeting in January in Boston, which is the mathematics organizations. Come together, professional mathematicians, college professors. And at those meetings, you would have got no sense of this debate. They were talking about how do we make our teaching more inclusive? How do we, you know, make it better?

Yeah.

So I don't even think this is a, you know, people at the top against everybody else. It's actually a very small group of people.

Absolutely. But a very vocal one.

But very vocal.

Yeah. Yeah. But the other thing I think is also, I'm particularly interested in 4E cognitive science and, you know, some of the different work around that. And I think that goes back to what we were saying about the kind of embodied learning and the visual aspect and the, just the multimodal way that we inhabit the world and understand the world. And the science is increasingly, I think, legitimizing that, that is not, you know, this is not some narrow and evidenceless discussion about learning styles, which, you know, is just nonsense. It's, this is genuinely, we are multisensory physical beings inhabiting a space, trying to understand a space, and we have all sorts of different equipment within ourselves to be able to do that. And so I think also the science is catching up in some ways with some of those kinds of more progressive ideas about teaching and learning, which I think is super exciting.

I work with a neuroscientist in the School of Education at Stanford called Bruce McCandless.

Okay.

And he's great neuroscience and studies education and a study they've just come out with, which is kind of mind-blowing. They're proposing a term called groupitizing. So if you have a collection of 10 dots, you're groupitizing if you say, well, I'm gonna, I see that 10 as 4 and 4 and 2.

Right.

So. What this study has shown is that kids' ability to groupetize, to visually group dots and put them into different groups, predicts their maths achievement all the way up to grade 8. It's a huge predictor of their outcomes on state tests.

Wow.

Almost as big a predictor of parental income, which is a very big predictor.

Yeah.

And when kids are learning to groupetize, the impact of parental income drops right down. I mean, it's a huge activity. Wow. But what's amazing to me is what it's showing is that this act, this visual act of being able to sort objects into groups has such a huge impact. Yet in schools, we're focused entirely on numbers and operations. I mean, I think we're really just at the beginning of understanding how important these visual representations are. And as you say, the neuroscience and all the work that's coming out of cognitive psychology, of neuroscience, Science is just backing up that kids need these visual and physical experiences in learning.

Yeah. Oh, that's brilliant. I'll have to, I don't know that. I'll have to look at that. The other person I really like is Mary Helen Immordino-Yang, who's quite close to you at University of Southern California. And she's, I mean, her research is incredible again, in relation to the way that different, you know, different neural networks are involved in, in the learning process and just toggling back and forth between the detail and the big picture and then back and I mean, it's, it's really fascinating because that's then predicting life outcomes later on in a longitudinal study. Very, very interesting stuff. So, wow. Thank you, Jo. This is so interesting. I just want to honor your time, but just briefly, you, you said you're writing a new book. When's that coming out? Can I, you know, advance publicize that?

So I'm writing it now and it's called Mathematical Diversity. It's about honoring the value of diversity, both in students and in environments, but also in the way we look at and think about maths. So those two things really come together, valuing the difference in people and valuing the different ways we can think about and experience maths. So it's been published by HarperCollins and will be out probably in a year or so. But I mean, I'm enjoying working on it.

Well, looking forward to reading it. And yeah, no, I mean, thank you so much for your time. It's such an honor to be able to talk to you.

Yeah, it's been really great to talk with you. Thank you, Tim. Thank you. I really enjoyed it.

Take care. Thanks, Jo.

Cheers. Bye-bye.

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