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Episode Summary:

Dr. Jo Boaler is here to discuss her new book “Math-ish,” where she introduces findings that advocate for viewing mathematics through a real-world lens, termed “math-ish.” 

This approach reshapes our perceptions of math, data, and personal capabilities. Recognizing the significance of diversity in individuals and varied learning strategies allows everyone to thrive. 

Whether numbers instill a sense of competence or cause anxiety varies widely among individuals. Dr. Jo Boaler, a Stanford researcher and esteemed professor of mathematics education, contends that embracing these individual differences is crucial for tapping into our fullest potential in mathematics.

Lean into this conversation and you’ll come out the other side with an innovative approach focusing on estimation and deeper conceptual understanding, which has proven more effective and preferred by students over traditional methods. 

You’ll also learn about breaking away from rigid, rule-based learning to allow students to utilize their own problem-solving skills….and much more.

Resources:

Math-ish by Dr. Jo Boaler [Book]

Mathish.org [Website]

Youcubed Facebook Group

Attention District Math Leaders:

How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? 

What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

Book a short conversation with our team now. 

Episode Summary:

Attention (A)

How can we revolutionize math education to make it more engaging and meaningful for students?

Interest (I)

This episode dives into the innovative approaches to math education proposed by Dr. Jo Boaler, offering solutions to the common problem of student disengagement and resistance towards math.

Desire (D)

Listeners will learn about the importance of integrating creativity and flexibility into math teaching, the benefits of promoting critical thinking and problem-solving skills, and strategies to overcome resistance to change in math education.

Action (A)

Tune in now to discover how Dr. Jo Boaler’s new book “Math-Ish” can help you transform your math classroom and inspire a love for learning in your students.

FULL TRANSCRIPT

00:00:00:04 – 00:00:22:17

Jo Boaler

I mean, one of the defining moments for me that I still think back on and have been thinking about in recent years is when I was in elementary school and my it was just arithmetic and I wasn’t interested and didn’t really engage much with it. And then a teacher invited us to design that.

00:00:22:17 – 00:01:00:09

Jon Orr

There is Dr. Jo Bowler and she is here to discuss her new book, Math ish, where she introduces findings that advocate for viewing mathematics through a real world lens termed math ish. This approach reshapes our perceptions of math data and personal capabilities. Recognizing the significance of diversity in individuals and varied learning strategies allows everyone to thrive. Lean in to this conversation and you’ll come out the other side with an innovative approach focusing on estimation and deeper conceptual understanding which has proven more effective and preferred by students over traditional methods.

00:01:00:15 – 00:01:24:07

Jon Orr

You’ll also learn about breaking away from rigid rule based learning to allow students to utilize their own problem solving skills and ish a little bit more.

00:01:24:09 – 00:01:28:14

Kyle Pearce

Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pearce

00:01:28:14 – 00:01:31:14

Jon Orr

And I’m Jon Orr we are from makemathmoments.com.

00:01:31:16 – 00:01:41:06

Kyle Pearce

This is the only podcast that coaches you through a six step plan to grow your mathematics program, whether it’s at the classroom level or at the district.

00:01:41:06 – 00:01:56:19

Jon Orr

Level. And we do that by helping you cultivate in foster your mathematics program like strong, healthy and balanced SRI. So if you master the six parts of an effective mathematics program, the impact that you are going to have on your teachers, your students will grow and reach far and wide.

00:01:56:21 – 00:02:23:15

Kyle Pearce

Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence and get back to enjoying the planning and facilitating of your mathematics program for the students or the educators that you serve. Well. Hey. Hey there, Joe. Welcome back to the Kicking Math Moments That Matter podcast. It has been a while. Like if we I mean, luckily when you were first on it was episode ten.

00:02:23:15 – 00:02:42:11

Kyle Pearce

So it makes the math and the mental math really easy here because I think this is episode 290 that is going to be coming out and I don’t know, I don’t have to do any carrying nothing. I know very quickly that we’re talking about 280 episodes ago of weekly podcasts and you’re back.

00:02:42:13 – 00:02:43:11

Jo Boaler

Amazing.

00:02:43:11 – 00:02:57:00

Kyle Pearce

And you’re still doing amazing things in mathematics and helping people to push their beliefs, their perspectives and their understanding of mathematics forward. So welcome back. How are you doing? Where are you coming to us from? And just fill us in.

00:02:57:02 – 00:03:09:22

Jo Boaler

I am here in California on Stanford campus and yes, I’m going to keep going even with all the people who are hating on me. I’m just the naysayers messages.

00:03:09:24 – 00:03:15:18

Jon Orr

This is the good work you’re doing, you know, because of that, you’re making waves in the right way. Right. And I think I guess.

00:03:15:24 – 00:03:18:09

Jo Boaler

Yeah, that’s when the haters come out.

00:03:18:11 – 00:03:41:01

Jon Orr

Right? Right. Either I’m making this up or I’ve heard this somewhere is that if you’re going to do some any sort of impactful work and it’s not necessarily education, but it’s like something that if you if you’re making a dent in making a wave that’s impactful, you don’t make friends along the way and you’ve made lots of friends, but you’ve also got some people coming out of the woodwork to kind of try to support us, push you down back and what.

00:03:41:01 – 00:03:46:01

Kyle Pearce

Are the kids call them? Hashtag haters, I think might be the maybe the expression.

00:03:46:05 – 00:03:50:14

Jo Boaler

Set of haters. Yeah, I come to know them well.

00:03:50:16 – 00:04:18:07

Kyle Pearce

Yeah. As John saying, I really do think as much as that is probably not what you were after when you began this journey. The reality is just to highlight that what John just said, it’s so true that you are having an impact and people are getting attention. And that means the people who are loving your work, implementing your work, understanding the work, it’s reaching them, but it’s also reaching the other groups that have not had the same shifts.

00:04:18:07 – 00:04:46:11

Kyle Pearce

And I’m going to argue that a lot of these individuals that generally are maybe against some of the things we’re trying to do in mathematics education is because they are feeling vulnerable themselves, right? When you don’t have a conceptual understanding of mathematics, if what you’re doing is you’re actually you’re going, well, I mean, I thought I was good at math and you’re telling me that I don’t fully understand all of the mathematics and I don’t like that.

00:04:46:15 – 00:05:12:09

Kyle Pearce

That’s sort of like a translation that I feel a lot of people have. It’s it’s very humbling, you know, And you have to be humble in order to be able to accept that along the way. And I know I struggled with it myself personally. I didn’t go out hating people at the beginning, but at first when I recognized and I think we shared it on some of our earlier episodes, I had a math moment myself where I had a professor in second year university say, You don’t know anything about mathematics.

00:05:12:09 – 00:05:35:13

Kyle Pearce

And for a very long time I did not understand what that meant. Only I was mad, I was very upset. And I don’t think Twitter was around at the time when that happened, but I didn’t go around voicing it openly. But the reality was it took me many years teaching to actually understand what he meant, and he meant that I didn’t have a conceptual understanding of the math.

00:05:35:13 – 00:05:39:13

Kyle Pearce

I was very procedural and I knew procedures and that was it.

00:05:39:13 – 00:05:43:11

Jo Boaler

So probably not the best way to share that with you. But I.

00:05:43:13 – 00:06:06:03

Kyle Pearce

Know exactly. And we we joke about that. I say, you know, I feel like he could have been more helpful in terms of letting me in on the secret there. But I do now recognize at least what it was. So when we were with you last time, this is many years ago, we had asked you about a math moment and now we’re going to maybe change it up a little bit here on episode 290.

00:06:06:03 – 00:06:21:05

Kyle Pearce

We’re going to ask you what’s a math moment that you feel has sort of resonated with you over the last five, maybe ten years since your math mindsets book and since the last time we had spoken here on the podcast.

00:06:21:07 – 00:06:52:24

Jo Boaler

I mean, one of the defining moments for me that I still think back on and have been thinking about in recent years is when I was in elementary school and maths. It was just arithmetic and I wasn’t interested and didn’t really engage much with it. And then our teacher invited us to design something as a project and we had to design something that flew and we had to research it and make it.

00:06:53:01 – 00:07:22:01

Jo Boaler

And I still remember that project to this day. I was probably ten when I worked on it, but it meant something to me. I was engaged with it. I cared about this thing. I was making. There was maths in it. I loved doing that maths, so I’ve often thought about that. Why did I not like maths? And then eventually school and then I remember that amazing moment, a piece of time we worked on that project.

00:07:22:03 – 00:07:42:22

Jon Orr

Yeah. And it’s obviously it’s stuck with you and it’s probably influenced the work that you do now. Like it can’t not probably influence it otherwise. We don’t remember these things like it. Usually these memories influence the thinking. We have the perspectives, we have the beliefs we have. How do you feel like that influenced the educator you’ve become?

00:07:42:24 – 00:08:10:08

Jo Boaler

Well, I certainly experience myself lots of maths classes that were very engaging for me. I could do it. I could answer their short questions and speed through, but it just wasn’t interesting to me. And another really important moment for me was actually when I was older doing A-level maths, which is something we do in England when you’re 17, 18 and the teacher gave was completely different any teacher had ever had before.

00:08:10:10 – 00:08:44:09

Jo Boaler

She would ask us to talk about the questions in groups and that just changed everything for me. Now, this was this subject we had ideas about and we could connect with other people. It wasn’t this solitary just sit and do questions. So all of that experience really changed me and made me who I am. I also remember vividly during my A-level years with a different teacher when the teacher said, This may be what I said ten years ago, I was curious to know, but the teacher said, As anybody goes, any questions?

00:08:44:09 – 00:08:55:00

Jo Boaler

And I said, Yes, I have a question. And he said, Oh, you have a question about that. And I never asked another question.

00:08:55:02 – 00:08:57:15

Jon Orr

I think that you’re right. I think that is what you shared.

00:08:57:17 – 00:09:05:22

Kyle Pearce

And it brought back a moment for me, you know, from way back then, because I haven’t thought about that specifically. As soon as you started, I was like, Oh, I do remember that.

00:09:05:22 – 00:09:08:11

Jo Boaler

That probably was because I that scarred me.

00:09:08:11 – 00:09:51:18

Kyle Pearce

I guess what I heard that you shared here is this idea of like and we hear this coming out in 290 episodes of people sharing math moments, some positive, some negative, some that just are the thing that pop into their mind. And the one thing that you start to see is that those people who are maybe thinking a little bit differently than maybe how we may have quote unquote, traditionally thought about what mathematics class is was going from this like get done subject towards a truly constructive, true, early, engaging, enlightening epiphany filled like a feeling, a moment, an energy, a vibe.

00:09:51:18 – 00:10:19:19

Kyle Pearce

And I’m wondering and I know we discussed this a little bit way back when, but as you were on this journey, were you convinced just one day you just went, It should be like this? Or describe a little bit of this journey from where you were, Because as students who are taught in a fairly, I would say, similar way, I think many of us can relate that you’re going to sit and get and you’re going to receive this information and then you start moving through.

00:10:19:21 – 00:10:40:09

Kyle Pearce

I feel like and I know for me there was like a shift in for me, it was engagement right away. I want to engage students, but I went about it, as many people do. I use a lot of gimmicky things at first and I could get them to look my direction, but like I wasn’t getting anywhere. What would you say was sort of that maybe moment for you that started to get you to go?

00:10:40:09 – 00:10:50:07

Kyle Pearce

You know, there’s something different going on here, and I’m starting to maybe see that this can look a little bit look and sound a little bit differently.

00:10:50:09 – 00:11:17:02

Jo Boaler

I don’t really have that experience. In my first years of teaching in London, when I’d had really good training at London University that encouraged us to teach kids through more conceptual maths tasks. And so I was right from my first year giving kids those more engaging tasks, and I could see the different levels of engagement when the maths was good too, when them asked us was narrow and boring.

00:11:17:04 – 00:11:48:01

Jo Boaler

But it’s really hit me. In recent years I teach a class at Stanford to undergrads, score how to learn maths and I get all these undergrads coming to me have been very successful. You don’t get into Stanford unless you pretty much excelled in school. You were completely maths traumatized and maths damaged. I think of them, even the successful ones, those who’ve done well in maths have done well by memorizing and they just see maths as a whole list of procedures.

00:11:48:03 – 00:12:09:05

Jo Boaler

And so I worked to undo that and give them these creative problems and ones where they’re talking and they’re sharing ideas and they’re writing things on the walls and we’re all talking about maths and it’s so impactful for them. They every year they’re just saying, you know, I just don’t want to go back to the other maths. This is really what it is.

00:12:09:05 – 00:12:41:23

Jo Boaler

This is where I’m getting these amazing connections happening and I’m understanding. And so definitely that experience, as I’ve gone further and further into my career, I’ve found more and more amazing tasks that I can share with others and I just see the impact of those. I also find something that’s hit me since I’ve done more work in maths that is, the best tasks are really the ones that go across many age groups, many grades.

00:12:42:00 – 00:12:50:11

Jo Boaler

I can give my undergrads tasks that fourth graders do and they get really super engaged by them and vice versa.

00:12:50:13 – 00:13:16:07

Jon Orr

It’s almost like positioning, like the questioning around the task or the scenario that kind of like keeps the learning going or keeps the thinking going and how deep you can get on a task that may resemble a third grade task, but you can get high schoolers to engage in that same depth or not the same depth, but the same task can get to different depths just because you might tweak something or you may ask it in a different way because it’s a different brain.

00:13:16:09 – 00:13:18:08

Jo Boaler

Just take it in a different direction.

00:13:18:10 – 00:13:40:12

Jon Orr

That’s true. That too. Yeah, but you I want to get into your new book, Math ish, and I’ve read all of your books and I know the first book that I read, it was, you know, what’s math got to do with it? And which was so eye opening for me because I think it was on that crux of trying to figure out how do I change my math instruction, Like what is it looking like in my class?

00:13:40:12 – 00:13:54:20

Jon Orr

And it was like your research based approach to that book gave us like almost like a nudge being like, these are the right things to be doing in my class. So I know that book well, I know the new book, and I’m going to skip over the mindset book for a sec because I wanted to kind of like think about that comparison.

00:13:54:20 – 00:14:08:14

Jon Orr

So we asked kind of the two questions and one here, which you’re not supposed to do when you interview someone. But but I’m going to do it anyway is like is like first, how are the two books different? Because that part of it’s like giving a snapshot of what are really good practices to be doing in the classroom.

00:14:08:14 – 00:14:25:12

Jon Orr

What is mass should look like. These are some of the things and you’ve got some good research in there to kind of support the conclusions. But then also like where does the name ish come from? How is that in there? Like tell us more about math ish, but then also maybe fill us in on the continuation of what’s math got to do with it?

00:14:25:14 – 00:14:46:16

Jo Boaler

I think math, well, it’s not got to do with it was I wrote that book because had been presenting research to a group of non math specialists. I’d actually been on this sort of special sabbatical place with people from all different disciplines. They weren’t in education, they weren’t in maths. And I was presenting my research and they came up to me, Oh my gosh, you have to get this out.

00:14:46:17 – 00:15:15:18

Jo Boaler

This is like, nobody knows this. We all think something different. And so what’s math got to do with it really was summarizing research and what we know. I feel the math ish. I’m at a totally different place in my career and it’s more show me examples of things that people are doing and that are really working well. But yes, I’m glad you ask me about what madness is, because I knew even as I was writing it and having that title, that some people, it would be horrible, horrific.

00:15:15:20 – 00:15:41:11

Jo Boaler

The idea of math ish instead of, you know, math precise. But what it is, I make an argument in the book that in the real world, when we use maths answers to nearly always ish answers. So I give some examples like you could be talking with people and asking how how big is the moon tonight? Or how much rain fell last night or how long is this journey or how much paint do I need to paint this wall?

00:15:41:13 – 00:16:15:03

Jo Boaler

Lots. And I can give you a million examples. All of them you would give an answer, but in maths classrooms maths is all about precision. So I was making the suggestion that we should engage kids more in this ish thinking. It’s what they do in the world and it keeps them at a conceptual level. Instead of getting into the nitty gritty of the numbers, they’re keeping their brain more conceptually, which I know teachers say they have a lot of problems with the kids jumping to number problems and come out with wild answers because they’re not thinking about really that bigger picture, what the numbers are.

00:16:15:05 – 00:16:52:17

Jo Boaler

But I soon found after people started asking kids, So I make a suggestion that before kids ever do a calculation, we should ask them to issue the numbers first because it does keep them thinking more conceptually and then they can calculate it and they can see that the same or similar. But I quickly found out that teachers who are going out and asking kids two ish numbers, it was opening the students up, kids who had been afraid of maths class and never engaging was suddenly raising their hands and sharing their issue numbers.

00:16:52:19 – 00:17:13:22

Jo Boaler

And I have a video. I started a website called Math ish dot org where there’s a video of six graders pitching together and they talk about both of those qualities. They talk about, well, this is what we do in the real world. This connects with us, with the world. This is what we do. But they also talk about, oh, when I ish numbers, it helps me.

00:17:13:22 – 00:17:45:05

Jo Boaler

And one of the students says in the video, we were always told we would do a calculation and then we’d do the calculation again. We have to do it two times to check. But now I issue the numbers and that is a much better way of checking. I don’t have to do calculations twice anymore. But the kids also said this was none of this is in the book, but the kids said to the teacher, Shelby Craig, that it was really going to help them in standardized testing and they planned to increase the numbers that they got.

00:17:45:05 – 00:18:07:09

Jo Boaler

And in the tests and it came out that the standardized testing saying they totally issue their way through it and how helpful it was for them. And they got answers quicker. And I mean, it’s just many benefits. I will say that we’ve always had this fact. We’ve always had this thing called estimation in maths. We encourage our kids to estimate.

00:18:07:11 – 00:18:15:24

Jo Boaler

But I also know that kids hate to estimate and sometimes they just like, calculated exactly Amanda off to make you look like an estimate.

00:18:16:01 – 00:18:21:16

Kyle Pearce

Probably that was me. That was as a kid. I vividly remember as a kid, you know.

00:18:21:18 – 00:18:22:18

Jon Orr

All this calculator.

00:18:22:21 – 00:18:34:04

Kyle Pearce

And then the teacher would ask me, you know, it’d be like I’d calculate it and then I’d like take to offer something. And then all of a sudden the teacher would ask me is, how did you get? I’d be like, I don’t I just, you know, And the teacher was like, okay, there was never really any.

00:18:34:04 – 00:18:51:04

Jon Orr

Sort of the teacher put the emphasis from the get go. The calculating was 100% right. So you saw part A of the question said estimate, and then you went to B and says, I’m going to calculate it anyway. And that’s what the teacher wants. So why am I doing the estimating first? So you just jump right to it and then go back and fix it.

00:18:51:06 – 00:18:55:05

Jon Orr

But it’s like because of the culture that was where the emphasis needs to be.

00:18:55:07 – 00:19:21:14

Kyle Pearce

You think about how helpful helping kids recognize and create the habit, because like a lot of things we do in school, I think the best things that we’re doing for students is giving. We’re equipping them with tools like thinking, problem solving, like all of these processes. And this is one of the pieces that I should automatically be thinking in my head about, about how much X, Y, or Z I need.

00:19:21:14 – 00:19:26:03

Kyle Pearce

You know, if it’s paint, if it’s gasoline, if it’s like whatever it is that you need, I check.

00:19:26:03 – 00:19:26:13

Jo Boaler

Look.

00:19:26:13 – 00:19:52:10

Kyle Pearce

Yeah, exactly. And it’s like we’re in school doing all of these random problems that a whole other tangent is about who wants to actually calculate these things. Anyway, that’s a different discussion. But when it comes to building in almost the automaticity that every time you are about to calculate something that you actually look at the problem and I mean you look at a problem solving model and it tells you to do these things, but it’s easier said than done, right?

00:19:52:10 – 00:20:12:06

Kyle Pearce

Nobody wants to follow the steps, but you create a habit where you go, Oh, and I think about standardized testing and how valuable that is for students to go, Well, it’s not even remotely close. It’s like, just get that one off the board. And right there you’ve just increased your ability to because we’re still going to make mistakes.

00:20:12:06 – 00:20:45:17

Kyle Pearce

We’re still going to maybe think too quickly or whatever it might be. And just to have that tool in your back pocket is so helpful and so important. And when it comes to something that we’ve learned over our time in the classroom was and I think we got the idea originally from Dan Meyer, we used to follow his work quite a bit early in our journey was the idea of withholding information, which helps you to kind of snap that habit a little bit of I was the kid that if you gave me all the information, I would just skip right over it and I’d go and.

00:20:45:19 – 00:20:45:23

Jo Boaler

Not.

00:20:45:24 – 00:21:12:13

Kyle Pearce

Do that. But if I don’t have all the information now, we’re all kind of brought to like a common level. We can all be on the same playing field in that Joe is not going to get the answer before John does because there’s not enough information. It’s like we can get some estimates and then we can try to use math to maybe make it a little more precise, more, well, say your math is shit, but then eventually you’ll try to narrow it down a little more.

00:21:12:13 – 00:21:21:13

Kyle Pearce

How can we get a little more precise? A little more precise? And that’s sort of the beauty of mathematics and sort of why we were doing what we’re doing in the André.

00:21:21:15 – 00:22:00:06

Jo Boaler

Exactly. And I think with Ish it is exactly as you say, It’s a tool that’s going to help us in lots of situations. But what I’m also getting from teachers is it’s helping them open up their classroom and have more kids participate, really by using it for that reason. And what’s math got to do with it? Talking about book, I share a question that was given in the standardized test, and the question was 7/8 plus 12/13 and kids were asked, Is it one, is it close to 1 to 19 or 21, 12/13 plus 7/8.

00:22:00:06 – 00:22:11:07

Jo Boaler

They’re both close to one. So and it’s two. The most common answer given across the US was 19. The second most common answer was 21.

00:22:11:09 – 00:22:47:11

Kyle Pearce

And there’s two thoughts that obviously cross your mind about I’m following a blind procedure that I know nothing about or that I truly have absolutely no conceptual understanding of what a number over a number. And I use the word over on purpose because we talk about the fact that it’s not even talking about the size pieces. We could say 7/8 of a whole or whatever it is, and it’s like our language sort of allows us to get almost to procedurally too quickly instead of thinking about what is it that we’re actually dealing with here.

00:22:47:11 – 00:22:49:00

Kyle Pearce

When we look at these numbers.

00:22:49:02 – 00:23:09:22

Jo Boaler

I’m sure the kids are just jumping to, oh, fractions, what do I do to abstract? I add nominators. And I’m also sure they’ve never issued numbers because that would give you an easy answer to that question. But they probably have never thought that’s allowed to do right. Yeah, Math mass is all about precision.

00:23:09:24 – 00:23:36:03

Jon Orr

Yeah. I want to come back to what you just said there allowed because that’s a very interesting thought that I continually think about about math education. But I wanted to talk about more issues in because where I feel like the power of ish is in it has to do with the estimation process is you’re really getting students like what Kyle was saying is like holding back the information, getting them to kind of like dispersed you as a teacher.

00:23:36:03 – 00:23:58:11

Jon Orr

If you’re using that technique. And if you listen for the right things, you’re going to hear problem solving strategies just naturally show up, right? You’re going to hear different thinking, which is like complete formative assessment. Goldmine For you as a teacher to hear where you think students are on, say, this lesson or this task or this topic because you’re going to go late.

00:23:58:11 – 00:24:20:04

Jon Orr

Let’s ish through this and then people are going to have like, imagine that like reminds me of like sometimes these number of word problems where if you issue a through it, you built your whole problem solving technique and then now it’s like, put some numbers in or like, let’s we can be precise whenever we want. But the really important part is figuring out what the problem solving techniques should be.

00:24:20:08 – 00:24:21:19

Jo Boaler

Yeah, totally agree.

00:24:21:21 – 00:24:38:02

Jon Orr

Now, to go back to what you said about permission, this is the idea that I constantly think about about you hear this all the time, right? Like you hear your kids say, That’s not the way I’m supposed to do it or that’s not what I’m allowed to do. I didn’t know that you could do that. And then teachers say it, too.

00:24:38:02 – 00:24:55:14

Jon Orr

This is why it’s like I feel like it’s such an important topic, because teachers will say that Kyle and I talked to teachers, talked to district leaders every single day across North America and I always hear them say, I’m not sure like I was or you hear the coach say that. The teacher said, I didn’t know you could do that.

00:24:55:14 – 00:25:09:23

Jon Orr

You know, it was like a loud to do that technique or teach that way. I feel like. And I wanted to get your take on it. Where do you think like this whole idea of permission? I didn’t have permission to do it. That way really comes from within.

00:25:10:00 – 00:25:42:06

Jo Boaler

Yeah, I mean that I definitely see that Holding kids up in math is I describe a teaching moment, which I actually have on video where great teacher has asked kids to think about what fraction of a shape something is, and it’s actually just square divided into quarters with one quarter shaded. So kids are in their groups. But on this square there is an all the lines you see the one quarter shaded and a big square with no dividing line.

00:25:42:08 – 00:26:06:02

Jo Boaler

So the kids are in their groups and they’re saying, Oh, I think it’s one too. I think it’s one. But I think it’s like they’re all over the place. And then there’s one boy who’s totally correct reasons. Really. Wow. And said, But look, if we imagine a line drawn down and across, we can see this four parts and one of them is shaded and the other kids say, but there is no line.

00:26:06:08 – 00:26:29:11

Jo Boaler

And then another one says, yes. And she didn’t tell us. She didn’t tell us to think like that. She just asked us, what is the fraction? She didn’t ask us to prove it. So I’m like, oh my gosh, these kids are so held up by these different ideas about what they’re allowed to do. Changing a shape like AD by adding lines is a really mathematical thing to do.

00:26:29:13 – 00:26:48:22

Jo Boaler

We pay a lot of attention in that math set circles to numbers sense, and I think of that as shape sense. Okay, I have this fraction question. I’m going to draw some lines so I can see it more clearly. Kids don’t think they’re allowed to do that. They think they have to work with the shape they’ve been given.

00:26:48:24 – 00:27:13:21

Jo Boaler

Can’t draw lines, same as they think. You can’t change numbers if you’re given a question like 18 times five, you have to work out 18 times five. You don’t think, Oh, I could be like 20 times five and take off two fives. So kids who do know that they’re thinking flexibly, they’re adding lines, they’re changing numbers. So many kids don’t know so many kids that think that’s not part of mathematics.

00:27:13:23 – 00:27:22:06

Jo Boaler

It’s not a question I was given that bound up by these imaginary rules that are really holding them back.

00:27:22:08 – 00:27:42:02

Kyle Pearce

And I love that because it’s exactly where I wanted to go. You talked about the imaginary rules, but the reality is, when we talk about what math is and then what math looks like in a classroom, it’s like there’s so many opportunities. John And I recorded an episode recently. John You’ll remember the Angles problem that my son had, right?

00:27:42:04 – 00:28:04:12

Kyle Pearce

And I never cause any parental issues with my kids and how their teachers teach or anything like that. It’s like me and my kids. We talk and we talk about what they could have been thinking or whatnot. But the example I want to give you is this example where the point of this assessment was to determine if they knew how to measure right angles.

00:28:04:14 – 00:28:23:05

Kyle Pearce

And we’re talking like this. Well, I measured it with a protractor because my son was like, this is not a right angle. And my teacher like and I put it’s not a right angle. And it was like 93 degrees. And the lines were thick enough that you could potentially, like, move the and I’m like, right.

00:28:23:05 – 00:28:23:22

Jo Boaler

Angle ish.

00:28:24:03 – 00:28:54:04

Kyle Pearce

IT service angle. It was like a perfect example of that. And so the reason that popped into my mind as this example is that it’s not actually imaginary for the kids though, because it’s like they have so many examples of where they get dinged for not following the exact question or exactly what they were said. And you think about a word problem that says one thing that’s slightly maybe not intentionally there to trick, but it could easily trip someone up.

00:28:54:04 – 00:29:10:03

Kyle Pearce

And when you zoom out on it all and we go and I said to my son, I was like, Do you know what a right angle is? Tell me everything you know about a right angle. And he tells me all he knows. And I said, So I’m like, Could you see why your teacher might think that this is a right angle or not?

00:29:10:03 – 00:29:31:22

Kyle Pearce

Yeah, I understand. At the end of the day, the thought that he had was he didn’t know what he actually knew, and it was based on the fact that it was not flexible enough when in reality we I think as educators, we really have to be aware of what is it that we’re trying to learn about our students, What do we want to know that they know or don’t know?

00:29:31:22 – 00:30:00:06

Kyle Pearce

Because I want to know that, too. Because I want to help them to get better at it. But how do we do it in a way where students don’t start making up a game in their mind because they’re just trying to follow the rules of the game? And for me, I don’t know. I mean, I have one way of making math more math ish is going to help with that, because what that allows educators to do is maybe to zoom out just a little bit and say, I don’t think it was that important.

00:30:00:12 – 00:30:30:18

Kyle Pearce

He knew that if it was around 90 degrees that we’re going to call it right angle And if it’s not anywhere, you know, and I just wonder when you’re thinking about educators and the teachers that you’re working with, the pre-service teachers, for example, how do you help them to maybe gain the confidence, to help break free from some of these practices that I think are just they’re kind of built in because we went through a very similar system, sadly.

00:30:30:20 – 00:30:56:03

Jo Boaler

And what makes me sad when I hear this example is I feel like often in maths, kids feel they have to follow somebody else’s rules and their own thinking is inside it. They don’t think it’s their job to figure it out themselves. They think it’s their job to follow some rule that’s been given to them. And that’s not true of other subjects.

00:30:56:03 – 00:31:29:16

Jo Boaler

When they’re sitting in English class or history class, probably think I’ll figure it out. I’ll use my thinking to reason about this situation. But in maths class, it’s not that it’s not a part of the equation for kids. When I did my Ph.D. study years ago in England and I wrote about this in message, I mean in what the kid said, the difference with maths and other classes was maths class was not about thinking in other classes.

00:31:29:16 – 00:31:35:08

Jo Boaler

You have to think for yourself about things. Wow, that’s kind of tragic, really.

00:31:35:13 – 00:31:36:08

Jon Orr

I see it too.

00:31:36:10 – 00:32:02:08

Kyle Pearce

Do you know what’s really sad about that? That I just had this little mini epiphany for myself? It’s not a good one either, is that? I think that’s why I actually did well in math as a student, is that actually I didn’t have to think and I didn’t enjoy the other classes. I think for the exact opposite reason that thinking is hard, you know, And it was about stuff I didn’t want to think about at the time.

00:32:02:10 – 00:32:26:23

Jon Orr

And I think, I don’t know, help me on this part. But it’s like I think I heard this too, is like thinking actually burns more calories. Your body’s job is to actually try to conserve calories, to stay alive in a way. Right. So it’s kind of like doesn’t want to think. And teenagers especially don’t want to think. And it’s like so kind of like you not enjoying the other classes because you’re forced to think and liking math more because you didn’t have to think like it makes sense.

00:32:26:23 – 00:32:34:06

Jon Orr

Like your body’s saying do that more than that because that’s burning more calories than that and we want to keep you alive longer.

00:32:34:08 – 00:33:05:10

Jo Boaler

We also have adolescents, and I’ve interviewed these kids, too, who as they get into their teenage is particularly and they’re 14, 15, 16, they start to resent being controlled by other people. They want to have their own thoughts and their own values respected in class. I know lots of kids who reject maths because of that, and I was doing kids in calculus classes some years ago and there was one set of kids.

00:33:05:10 – 00:33:27:08

Jo Boaler

They spoke very eloquently about this, but they were saying, My calculus, my math stats, it’s all about control. I just have to do what I’m told to do. And he didn’t like that. He was like, you know, basically when you sit down and you follow what you’re told to do and it was very much about wanting his own agent.

00:33:27:10 – 00:33:57:16

Kyle Pearce

That is so interesting. And I see a lot of myself in my son. My son is ten and my son, I would say a very intelligent child. And he’s like a perfect example and a nice kid doesn’t get in trouble or anything, but he does not enjoy school. And I mean, part of it, I’m sure that he wants maybe more control, but it’s like the whole day, I think, to him, and I think I can relate as a student that it was I just had to get it done.

00:33:57:18 – 00:34:16:10

Kyle Pearce

And I think I looked at all subject areas that way and I think that’s why I landed on what’s the easiest subject to just check it off the list. And for me it was math because I was, I’ll call it just lucky that I was able to memorize enough in the patterns to put in minimal amounts of effort and get a result.

00:34:16:10 – 00:34:46:14

Kyle Pearce

Whereas if I was a student in my own classroom in the last, say, ten years, where I actually am pushing for productive struggle and I’m pushing for thinking and I’m pushing four ish, as I will now call it, I, I would have been my own worst nightmare as a student, at least at first. But it’s like when you see kids like me or like my son when they’re actually challenged to think, and this is specific to math, that’s the only area of education that I actually taught.

00:34:46:16 – 00:35:05:19

Kyle Pearce

When you see that shift from a student who is like me, it’s like, I love it. Like I just love seeing the light bulb go off where they go. I had one student, for example, John, I’ve told you this story. I think I’ve mentioned it on the podcast where all of grade nine, this student was a me and she memorized her whole way through.

00:35:05:19 – 00:35:27:24

Kyle Pearce

She won the math award in grade eight and all through grade nine she pushed so hard and that on it just she was like, it wasn’t as easy and it was like the teaching style was obviously different. It was in grade. It took that entire year. In grade ten, she stopped me in the hall and said, Thank you for making me think, because she said, I have no clue what I’m doing right now.

00:35:27:24 – 00:35:48:12

Kyle Pearce

And it feels worse than ever. And I was like, erm, you know, sad for her at the time that she was lost because now it was back to rules and back to whatever. But it was like it took that experience for her to get to a place where she went. I guess it was worth it. I guess it was worth doing the calorie burning and the thinking.

00:35:48:17 – 00:36:10:00

Jo Boaler

You know something, You remind me of the students who don’t want to do this deep thinking work. I was asked a few years ago to teach an incoming class of undergrads at Stamford Calculus, and they were all students who were in a program where you get to come early because of various things that first generation, they’re different things.

00:36:10:02 – 00:36:33:15

Jo Boaler

But anyway, so we had these hundred students. We taught them like conceptually through thinking and giving them tasks and saying, okay, you found the rule, now figure out why and really pushing them to think conceptually. And there was a group of resistors who hated it and just wanted to be told what to do, and they communicated this to us.

00:36:33:15 – 00:36:55:03

Jo Boaler

Just tell me what to do. I don’t want to think about why and when. We did deep analysis of the data we collected on them over the next year or so, we found that they were the lowest achieving students and they what we realized was happening was they’d go far as far as that got by, like memorizing and not really understanding.

00:36:55:09 – 00:37:06:06

Jo Boaler

And now here we were saying you need to understand. And that made them insecure and then push back on it.

00:37:06:08 – 00:37:08:04

Jon Orr

Yeah, yeah.

00:37:08:06 – 00:37:10:03

Kyle Pearce

Forcing them to be vulnerable.

00:37:10:05 – 00:37:16:09

Jo Boaler

Little But I thought it was really interesting that it certainly the lower achieving kids who are most pushing back.

00:37:16:11 – 00:37:38:14

Jon Orr

I’m going to I’m going to stretch the limits here in thinking about math ish and the ideas that you present in the book and thinking, where do you see? Because you continually talk about changing instruction so students have these experiences. Is a big chunk of the book that you talk about metacognition and how it’s so important in learning mathematics.

00:37:38:16 – 00:37:59:24

Jon Orr

We think about the experiences we want to be providing for our students. You are a huge part of the new California framework and what do you see math going in ten years in classrooms? We talk a lot about like what we want it to look like. But if we start to think about how do we actually see these changes taking effect, like sometimes I get worried.

00:38:00:03 – 00:38:15:23

Jon Orr

You talk to you how many years ago, five or six years ago, and it’s like things are spreading, but it’s like the rate is so slow. So now it’s like imagine ten years from now and I want to think about ten years and I want to think about these students that were experiencing some of these things that some of our teachers are putting into place.

00:38:15:23 – 00:38:26:15

Jon Orr

Some of them are going to become teachers, and then the cycle should get easier. But I mean, do you see it soon? What does ten years look like if we’re moving in the way that we’re trying to move?

00:38:26:17 – 00:38:46:02

Jo Boaler

I think if we were moving the way we were trying to move, we would see classrooms where kids for more of the time were working on deeper problems, not just these short questions that they don’t care about, where they were working on, problems that they did care about, and where they got to think and reason to talk to each other.

00:38:46:04 – 00:39:13:21

Jo Boaler

And I certainly see those happening in more classrooms now than I ever have before. And now we’ve actually managed to get that approach into policy in California is pretty amazing, particularly given all the pushback. And I am seeing leaders in districts already putting the ideas into place. In fact, we’ve already got some data back from leaders who as soon as we started the process of the framework.

00:39:13:21 – 00:39:40:11

Jo Boaler

So it’s like three years ago started doing work with teachers and now their kids achievement has shot up. So we’re seeing it in place. We’re seeing the evidence of it in place. But you’re right, it’s so hard to change and it’s particularly hard when people fight the changes. I mean, I know we have just so much research showing that kids can learn in a better way and in other professions.

00:39:40:11 – 00:40:05:02

Jo Boaler

I mean, if you look at the medical profession, we wouldn’t be in the place where doctors are like, I’m just not looking at that research. I’m going to keep using. Right. Get blood out of patients. They would be disbarred. No, that’s lawyers. But they are not doctors any longer. But we have this in education that we know what works and it’s hardly happening anywhere.

00:40:05:04 – 00:40:35:02

Jo Boaler

So change is tiny, very, very, very slow. And then I do think it has been made slower by the people who try and block it and the people who try and block it. I have learned over the last few years can be very well organized and funded by very wealthy people who are very invested in blocking change. And you talked about how, Kyle, you were saying that maybe it’s people who have never thought conceptually, so they don’t know what it is.

00:40:35:04 – 00:40:56:11

Jo Boaler

And I think it’s partly that. But then we have a system in the U.S. so I don’t know how similar or different this is in kind of it, but where kids are basically pushed out of high levels at every opportunity and what the framework was supposed to do is change that system and not be pushing kids out, but having more kids go forward.

00:40:56:13 – 00:41:26:23

Jo Boaler

So there were people who weren’t very happy about that because they know how to play the game. They’ve done it. They know how to get their kids to do it, and if you’re taking away their advantage, then they are going to fight that. They said that to me or about me to people that super wealthy CEOs in Silicon Valley said, she’s going to stop my kids, get into the highest boats.

00:41:27:00 – 00:41:32:15

Jo Boaler

And of course, we’re not stopping their kids getting to the highest levels, but we are making it so that more kids camp.

00:41:32:18 – 00:41:56:20

Kyle Pearce

Right, right, right. Which I guess from a logical perspective, a very selfish perspective, someone like that is going, hmm, they do the ish on that in their mind. They go, Oh, wait a second, if there’s only so many spots. And my kid was basically a shoo in because X, Y, or Z, this is definitely problematic. Yeah.

00:41:56:22 – 00:42:07:09

Jon Orr

You’ve said this, Kyle, a long time ago when you started to see changes in your classroom and the kids, when the kids start to see it in their rooms and you’re trying to change the way classrooms.

00:42:07:09 – 00:42:10:20

Kyle Pearce

Where the field starts flattening instead of it being it’s like.

00:42:10:20 – 00:42:37:11

Jon Orr

You’re giving voice to kids who normally had didn’t have voice and you’re starting to reward, in a way, trying to get more thinking out into the open. Some of those students who had Kyle, you used to say like, it’s almost like this game has changed. Where I used to be like, this was my subject where I used to show dominance, like this was my thing and now it’s all of a sudden the tables are flattening and now I’m feeling threatened that no longer.

00:42:37:11 – 00:42:56:05

Jon Orr

And so then the pushback in those experiences has always been from the kids who get 90 fives because the changing instruction to be about these other things. But they’ve had a lot of success not thinking. And now you’re asking to think thinking now all of sudden maybe the success isn’t there for them anymore. And that’s a threatening happening and they’re going to push back.

00:42:56:07 – 00:43:08:22

Jon Orr

And it’s the same outside of our classroom right now. It’s like the threatening is there. We’re going to push back. Everybody thinks that they have an opinion on education because they are part of an education system at one point or the other and they think they know what’s best.

00:43:08:24 – 00:43:43:07

Jo Boaler

Exactly. That’s exactly the case. And most of the opponents, nobody really look to this, that the people opposing the changes in California were all super successful mathematicians and stem academics. Nobody. QUESTION Is this coming from the cross-section of society? No, it’s coming from a group, have been super successful. They don’t want mathematicians. I there are some I mean, obviously some apps are amazing, but there are some mathematicians who don’t like to be told that anyone can be good at maths because they’re built their whole identity.

00:43:43:07 – 00:43:49:19

Jo Boaler

On the idea that the special are some high school maths teachers in that group to.

00:43:49:21 – 00:44:30:17

Kyle Pearce

100%. And we’ve discussed that in the past as well. And our last question for guests is always about a big takeaway for the audience, and I’m wondering if I can add a little slight nuance to it here. And I’m wondering specifically for those I’m going to go ahead and say it, that if you’re listening to our podcast, whether it’s the first time or the 294th time that you’ve listened, the reality is, is it’s likely that you are on a journey and you are trying to effect change and they’re trying to follow a lead like from you there, Joe, and from others in the space who are trying to do great things in math.

00:44:30:19 – 00:45:04:10

Kyle Pearce

But you might feel like you’re on an island. So some of these people who are listening, they might be the only person in their department listening or the only person in their school on this journey, and they might feel alone. So I guess instead of the big takeaway here, I’m wondering what would you want those individuals who are feeling like they want to do the work, but they’re feeling as though they’re not sure where to start or how do they do it when they feel that they’re sort of alone looking around and they’re the only one sort of pushing this thing forward.

00:45:04:10 – 00:45:18:24

Kyle Pearce

And we know what happens if someone doesn’t do this work is nothing happens and then it slows change. So what’s sort of maybe big takeaway do you have for those who might be feeling that way or just feeling like the work is just too daunting in their context?

00:45:19:01 – 00:45:42:01

Jo Boaler

Well, one thing I suggest to teachers who are just, you know, not in this place at all and a beginning is maybe to try some of these open, creative tasks maybe once a week, maybe every Friday, kids are working on tasks that are different and richer and start with that. You don’t have to overhaul all of your teaching, but try it.

00:45:42:03 – 00:46:06:01

Jo Boaler

Maybe try once a week. And I’ve found that that can help teachers. I do think that the only one that’s really hard and one piece of advice I would give to people in that situation is find the other people online or in your region, find people who you can talk to about it and connect with. And we have a new Cubed Facebook group.

00:46:06:03 – 00:46:22:10

Jo Boaler

And I love that space. It’s got over 30,000 educators in it and there are like minded group of people and they use each other as colleagues and resources. So don’t be alone. That’s really hard to make changes when you’re alone.

00:46:22:12 – 00:46:40:24

Jon Orr

That’s a good message for sure. For sure. Joe, we want to thank you so much for joining us here on another episode of the Making Mouth Moment That Matter podcast. I know that the book Math is in all the places you get books, and I actually appreciated you recording the audio version. That’s how I listen to it. So I listen to the audio version.

00:46:40:24 – 00:46:50:24

Jon Orr

So it was great to hear your voice talk about all those things. So anywhere else you want to point people to, to kind of reach out to you or kind of learn more about the work you’re doing.

00:46:50:24 – 00:47:08:05

Jo Boaler

Anybody can reach out to me. My emails secrets to find the easiest one is probably Joe BOLO at gmail.com, but I recently made math ish dot org, so you can all go on that website. There are some things in the book that I have made into beautiful glossy handouts on the website.

00:47:08:07 – 00:47:31:01

Kyle Pearce

So awesome. We will definitely put links to the resources. We won’t post the actual Gmail. We don’t want it to get scraped by. Your favorite friends that are out there these days, but those who are listening, you heard it from Joe, so don’t be a stranger and I love your message. Reach out to people relation ships is key.

00:47:31:01 – 00:47:52:12

Kyle Pearce

It’s key with our kids and it’s key with our colleagues, right? Those who are trying to do the great work with. Because if you feel alone, your mind tells you all kinds of crazy thoughts. So, you know, lean on somebody to try to get some real objective thoughts and feedback. So thank you, Joe. It is episode 290. You have to wait another 280 episodes.

00:47:52:12 – 00:47:57:23

Kyle Pearce

By the way, we would love to have you back sometime in the future and to catch up to chat all things math.

00:47:58:00 – 00:48:01:20

Jo Boaler

All right, I’ll be away. Me I don’t know if that sounds Oh.

00:48:01:22 – 00:48:03:24

Jon Orr

Yes, Kyle says it differently, but I.

00:48:03:24 – 00:48:09:17

Kyle Pearce

Say, I say, Oh, whammy. I just like pronouncing that John doesn’t like that. He’s from a different part in, the province.

00:48:09:21 – 00:48:11:16

Jon Orr

So the letters, you spell the letters, you know.

00:48:11:16 – 00:48:15:15

Kyle Pearce

So I love it. So 20, 25, then 2025.

00:48:15:15 – 00:48:16:08

Jon Orr

All right. We’ll see you.

00:48:16:08 – 00:48:18:16

Kyle Pearce

That’s looking forward to it.

00:48:18:18 – 00:48:41:07

Jon Orr

Take care. All right. I hope you enjoyed that episode with Dr. Joe Bowler. As we said in the episode, we can’t believe that she was one of our first guests that we interviewed on this podcast, Episode ten, which in this episode was 290. And it’s been a long journey that and I have been on and that we’ve learned so much from so many educators.

00:48:41:07 – 00:49:03:20

Jon Orr

We’ve talked to you here on this podcast, including Dr. Joe Bowler and the specifics from this episode. We think about our math classroom tree or our program tree. If we’re a district leader and we think about some of the moves that we’re making in our class rooms to be more ish or to get more ish out into the open, that’s our branches of the tree.

00:49:03:20 – 00:49:38:13

Jon Orr

We call those. Our pedagogical content knowledge is the teacher moves that we make on a regular basis. And if you’re going to get a little bit more ish happening in your classroom, those are the moves. Like what moves can we help with estimation? What are the moves that we can help that out into the open and try to do a little bit more estimating that allows us to kind of work with numbers in a way that makes sense and show students that they’re out there in the world can also be estimated because we use that on a regular basis, help them with those moves that we want to be using and utilizing our brains for

00:49:38:19 – 00:50:01:12

Jon Orr

when we’re working with number out in just I guess I’m going to use the term real world, but out in the world that we live in on a regular basis. So I want you to think about your key takeaway here from this episode. We talked a lot about different ways to invoke this idea in your classroom and thinking about it, but what is your big takeaway?

00:50:01:12 – 00:50:25:15

Jon Orr

We’d love to hear about it and we encourage you to share that takeaway with another teacher because we know that we the fact that you are sharing your takeaways helps solidify that takeaway into maybe more accountability into your practice. So take a moment and share that. Find this on, share the podcast, this episode with someone, and then you can share back and forth your key takeaways.

00:50:25:17 – 00:50:50:08

Jon Orr

Share the way that you found the podcast. If you found the podcast because of your subscribed, you know, share the link to the actual podcast. If you’re on YouTube, share that link on YouTube to someone else. If you’re on the website right now listening to and our website, our blog, where all of our lessons are and where all of our academy is, and where all of our resources are for teachers and district leaders in the classroom, share it over there.

00:50:50:10 – 00:51:08:13

Jon Orr

You can get more resources, more ideas. You can get a link to the book from Dr. Joe Buller on the show Notes page, which is make map moments dot com for each episode to 90. That’s mcmafia Amazon.com for episode 290. And before you go, make sure you hit the subscribe button so that you get next week’s episode, show up in your notifications.

00:51:08:17 – 00:51:15:09

Jon Orr

And if you do that, you know that next week’s episode, it’s going to be just as good. All right, folks, take care.

00:51:15:11 – 00:51:20:13

Kyle Pearce

All right. There, Math moment makers. Until next time, I’m Kyle Pierce.

00:51:20:13 – 00:51:21:14

Jon Orr

And I’m John or.

00:51:21:15 – 00:51:24:01

Kyle Pearce

High fives for us.

00:51:24:03 – 00:51:27:17

Jon Orr

And a high bar for you. Oh.

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