Ep 1. Math & the Myth of Ability with John Mighton
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You can listen to the episode here: Chalk & Talk Podcast.
Episode 1: Math and the Myth of Ability with John Mighton
Anna Stokke: [00:00:00] Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor and your host.
Welcome to my very first episode of Chalk and Talk. This podcast is for anyone interested in education, be it teachers, parents, students, or education enthusiasts. I'll be joined by prominent educators to talk about the significance of math, best teaching practices, and to dispel common misconceptions about math and teaching.
I have some great guests lined up and I hope you enjoy the conversation.
I'm excited to announce that my first guest is John Mighton. He's a multi-talented individual - a mathematician, a bestselling author, an award-winning playwright, and founder of the highly acclaimed [00:01:00] charity and math instruction program, JUMP Math. We'll dive into a range of topics, including the myth of ability - that's the mistaken idea that some people will say are math people will say and some aren't; we'll discuss how to get good at math; how to choose effective math programs for teaching; the importance of math in creating a more equitable society; his role in the movie, Good Will Hunting, among many other things. Now, without further ado, let's get started.
Anna Stokke: My guest today is Dr. John Mighton. He's an award-winning mathematician, a playwright, and a best-selling author. He's the founder of the Canadian Charitable Organization JUMP Math. That stands for Junior Undiscovered Math Prodigies, which supplies K to 8 math teaching materials. John has written three best-selling books.
The most recent is called All Things Being Equal: Why Math Is The Key to A Better World, which I read fairly recently. He has received numerous [00:02:00] awards for his work in math education, including being named an Officer of the Order of Canada. On a personal note, John has been a great inspiration to me. I first heard him speak in 2011 and I was completely inspired by his work.
He insists that anyone can do math and that we all have a role to play in ensuring that children receive the best possible math education. I'm really excited to talk with John today. A huge welcome to you, John, and thank you for agreeing to speak with me.
John Mighton: Thank you.
Anna Stokke: So, I'll start by asking you a bit about your background. How did you become interested in math and writing? Do you think there were any events in your childhood, for instance, that led you to becoming a mathematician and a writer?
John Mighton: Yeah, I think when I was in grade three or so, I read a story about two kids who somehow used a Mobius strip to travel in time. I have no idea how they did that, but, I don't even know if it was a [00:03:00] well-written short story, but it just, it sparked my imagination and I got into reading science fiction and, and loved both literature and math, but I didn't really know if I had the talent to do work in either field.
And I, I would always give up if I encountered difficulties and I actually didn't get the confidence to become a writer till I was in my twenties and I'm going to math until I was in my thirties.
Anna Stokke: Wow. That's, that's an interesting path because often it, it's actually kind of unusual for someone to start a, a degree late in math and, you founded a charitable organization, JUMP Math, but you're, you're a mathematician, you've got a PhD in math, so it, it's kind of interesting that you ended up working in K to 8 education and that's fairly unusual. So how did this happen? Like, what led to you creating jump.
John Mighton: Well. You know, as a playwright - I'm a playwright also - and, and I [00:04:00] needed to supplement my income when I was starting out and I saw a notice for a, a math tutor at the U of T, University of Toronto Job Centre. And even though I'd struggled in math, I figured I could tutor grade six or seven.
That was before I went back to do math properly. I started doing some tutoring and that, that really changed my life because working my way back through first elementary, then high school material, things that were mysterious to me when I was younger became clear and clearer. And then I also had an opportunity to work with some very challenged students.
And one of my first students, I, I wrote about him in my book. He was, his mom was told he could never learn math, that he was just too challenged. In, in grade six, he was in a remedial class, and a few years ago we went out to celebrate the fact that he's now a fully tenured math professor. So, I saw these incredible changes in kids and that partly gave me the conf - is what gave me the confidence - [00:05:00] to go back and do math myself in my thirties, working my way through the materials again.
And then seeing these incredible changes in the students, I thought maybe I could go back and do math properly.
Anna Stokke: Oh, wow. Well, I'm glad you, I'm glad you did. So, an interesting thing is that you were actually in the movie Good Will Hunting. You played a PhD student in that movie, right? So, you, you actually convinced them to add this line: “Most people will say never get a chance to see how brilliant they can be. They don't find teachers who believe in them. They get convinced they're stupid.” So why did you have that line added? What's the background?
John Mighton: Well, cause the, I mean, I really loved being in the movie and, and, I mean, everyone was wonderful to work with. But I worried that it, it gave the impression that you had to be born with talent or you just are either a natural mathematician or not. So, I [00:06:00] asked if I could, I could have my character say those lines.
To sort of counterbalance that idea and to suggest it might be because people will say never find the teacher they need or the opportunity they need to see how smart they can be. So, they were very nice. And let me, let me say that in the movie.
Anna Stokke: Oh yeah, it's a great, great line too. And so, speaking about that, you, so you often talk about the myth of ability, that people will say underestimate their potential in math and, and that students often get labeled. And I, I also think that that happens, that people will say get labeled as, “oh, you're a math person,” or “You're not a math person.”
And you often say, though, that anyone can learn math, there are so many people will say who struggle with math or, or view themselves as as bad at math or, or hate math. So, what do you think has gone wrong?
John Mighton: A lot of things I think, I mean, first of all, we are very good at convincing ourselves we can't do things when we encounter [00:07:00] difficulties. And so I had a really - what Carol Dweck, the psychologist would call - a fixed mindset. When I was growing up, I, I thought you needed to be born with ability to do well at something and you know, both in writing and math ideas would just pour out of you.
I didn't know you could actually train and, and like learn to write one good sentence at a time, for instance, or just write one good sentence a day or, or, you know, make a little progress in learning, learning some math. I didn't learn that until I was in my twenties, really. That, that you could get better through what's called deliberate practice.
Just, relentlessly practicing, pushing yourself a little outside your comfort zone, um, and, and then moving on. So, that's one problem is that, that people will say don't understand how much you can learn through deliberate practice, how much you can train yourself in. And the research in deliberate practice also suggests that there are fields like chess, music, competition, [00:08:00] sports where over the centuries people will say have become very good at coaching and developing expertise.
And, so the research has shown that process of deliberate practice is much more efficient if you have someone to guide you. And so that's the second reason I think people will say are struggling. We don't have great coaches sometimes. Teachers are my absolute heroes. I love teachers. They're responsible for the growth of JUMP, for the improvements we've made.
But many teachers will say, well, you know, they don't have time to put together great lessons to find the materials. They may not have the expertise. And, and so that coaching that the kids need, that, that, that guidance. And that doesn't mean rote teaching. That means guiding kids to see things, to make discoveries.
It’s something that I think teachers need help with. And, they need great resources that are based on the science of learning, that can help kids develop that expertise. So those are two of the main reasons I think we're not seeing, um, we're not [00:09:00] seeing people will say realize their full potential in mathematics.
Anna Stokke: Yeah. I, I agree with you and, and something I often tell my students is that it, it does require a lot of practice to get good at math. And I think a lot of times students see, they see someone else solve a, a math problem and, and they know a little more and they have a little bit more background and they think, “oh yeah, that's, it is really hard.
And I don't, I don't have what it takes to do that.” But actually, it's often just having been, been taught well and, and having practiced a lot. And you, you talked a bit about deliberate practice. What, what does that mean?
John Mighton: Well, there's a popularization of the idea in Malcolm Gladwell's book Outliers, where he said, if you look at the Beatles or Bill Gates, or these people who, who appear to be born geniuses in their field, if you look at their childhood, or their teenage years, they did a lot of practice, relentless practice.
[00:10:00] So, psychologist, Anders Ericsson started studying this. And like he did, he did studies of elite musicians and he asked them, when did you start playing? How often, how much time do you spend reading music, playing in groups and stuff? And he found the, the number one determinant of their level of success was how much time they spent practicing.
And then when you look more deeply, you find that if you get a great coach who can help you practice efficiently, then you tend to learn much more quickly. And so, it's quite simple. When I graduated from university, I also got the lowest mark in my creative writing class and, and almost failed calculus at university the first time. And I was babysitting my sister's kids one night, and I came across a book of letters by the American poet Sylvia Plath. It was letters to her mother, and it was clear from the letters that she taught herself to be a writer by sheer determination. So, as a teenager, she would memorize poems, she'd write invitations of poems.
She read everything she could about the Syrian poetry, [00:11:00] and her early poems were pretty derivative. But gradually, as she developed her craft, she understood the stood the forms of literary that, that that experience could fall into. You know, she was able to capture her own experiences and she became one of the most original poets of the century.
And, and that's the kind of paradox people will say think, well, if you do that kind of training where you learn your craft, you're never going to become original. I actually think it's the opposite. You can't develop any real originality until you learn your craft. And so, so that's, I, that's when I realized that's my introduction to deliberate practice.
Or I read about Hemingway who tried to write one good sentence a day, you know, a day That was his task as a young writer. That was a, that was such a relief to me that, you know, I didn't have to sit in front of a blank piece of paper waiting for something to pour out of me that I could, that I could just imitate other people will say, try and write one good sentence that I could memorize poems and get those into my subconscious and, and be able to draw on that.
It was a complete change in my life [00:12:00] knowing that I could actually there was something I could do to develop a skill in an area till then, I had no idea. And it's a terrible thing that people will say don't know that it's a terrible thing. So, when you're saying the kids who would compare themselves to other kids - I did that all the time.
I'd, I'd look at the kids who'd write math competitions and I wouldn't work very hard because I was afraid of hitting my limits. I was very sporadic. Sometimes I'd do well in math. Sometimes I'd, I'd just do terribly and I had no control. I just felt I was waiting for the gift to kick in. So that's why that idea is so damaging to people will say.
Anna Stokke: Yeah, I, I completely agree with you. And, and what would you say to - I often hear things like, “Well, practice is boring. Making kids, making kids, do practice problems is repetitive and, and it kills creativity and, and it turns them off math.” What would you say to that?
John Mighton: Well, I'd say that there's a misunderstanding of practice - what practice can be and what [00:13:00] it, what it is. It's a really deep question. So, there's a, there's a famous cognitive scientist, Herb Simon, who also won the Nobel Prize in economics, who said that, you know, we haven't done any favors to teachers or kids by calling practice “drill and kill.”
He said the instructional challenge - he said all the research on how people will say become good at things shows you need practice. And at any level. But he said the instructional challenge is how you make practice interesting. So that's the question we should be asking ourselves. Not how to get rid of practice, but how you make it interesting.
So, we've found there are very easy ways to do that. For instance, if you give kids, if you, help kids do something, you draw their attention to something, you don't do the thinking, but you help them make a discovery or make a connection immediately. If you guide them to see that, and then if you give them a series of incremental challenges that follow from what they've just discovered, where, [00:14:00] you know, each challenge doesn't overwhelm them cognitively.
So, you might not want to introduce new vocabulary right away, or you might not want to introduce new skills or concepts right away. See if you can make what they just did look a little harder. We found kids go crazy for that. Like, like they, because one of our deepest motivators, the psychology has shown is a sense of mastery.
And we want to, we want to master things and, and meet these challenges. Yeah, at every age range. Then on top of that, if you let them do it in a group so that there's no hierarchies, everyone's doing roughly the same work. You know, some kids may do extra bonus questions, but, but everyone's doing roughly the same work.
Then you get what Durkheim called collective effervescence. We never feel anything more intensely than when we feel something together or a sense of purpose or, or fun. So that's magnified. This love of practice is then magnified when kids can do it without hierarchies, without feeling, “Oh, that kid's so much better than me.”
But just feeling they're all [00:15:00] doing the same thing, discovering the same things. So I, I've literally had kids cheer for that kind of work, asked to stay for recess to do it, and, and we've heard this from hundreds of teachers too, who, who use these methods. I even broke up a fight once by telling this bully that if he didn't apologize, I wouldn't give him his bonus question. He apologized.
So, we don't, we don't make practice fun or interesting, and practice doesn't have to be rote. It can be deeply conceptual. The kids can be figuring out every new step themselves or - there's an educational researcher, Brent Davis, in Calgary, who calls them critical discernments. The kids can be making those discernments, they can be seeing the connections and, and that just makes the practice even more fun.
Anna Stokke: And at the end of the day, it's, it's our job to make it interesting for kids and to get them to do it, right? It's not - we shouldn't be giving up on the kids - because it's an important, it's an important part of learning, right? So, it's, it's our job as the teachers to actually make sure that we can come up with ways to get them to practice and get there.
John Mighton: [00:16:00] I, can give you a really simple example. You, you might think kids in kindergarten, you know, they have limited capacity to pay attention or sit still. So, you could play a little game, you put a pair of dots on the board and you ask a child, they could be sitting at the mat.
You ask one, come up and just join the dots. So, most people will say think that's pretty boring and I'm gonna move on. But what if you, what if you really. That this incremental variation is the key to everything. And that that kids aren't adults. They love repetition more than adults. They love showing off with, with variations that might seem obvious to you.
So, I found if you just put the dots further apart, ask for another volunteer to come up, and then you, and then you're constantly impressed. You say, oh my goodness, can you join these? And you put them further apart. By the time they're across the board, the kids are just jumping up, up out of their skins wanting to come up and join it.
And then, again, don't move on. These are kids. So now do the same exercise vertically, like move them apart further and further vertically they think that's different or harder. Then the super bonuses. Do it [00:17:00] diagonally, start moving them apart, diagonally. Then you could add numbers to the dots and have them start joining them in order.
You start with, with 1, 2, 3 in a relative straight line, so it's very easy. Then you, your bonus is I'm going to disorder them a bit. So, you, and then you add more dots. Then you can start to say, uh, if I joined these dots, what letter would it make? And they might predict it's a V or a W. So, I've done those exercises with multiple kindergarten classes and the kids have sat there for over 30, 40 minutes, just want, uh, just wanting to play this game.
And when they go to their seats, they can do productive work. So, they, they can, they can draw dot puzzles for me or if they can number them, they can make more and more complex. You get length in there, you can say make the dots further apart. You get geometry, you get everything. This idea that practice can't be fun or engaging for whole groups is, is, is, unfortunately to kids and teachers.
Anna Stokke: So, let's talk a little bit more about some [00:18:00] specific in instructional techniques and, and before we do that, I wanted to ask about working memory, and if you could say a bit about the role of working memory in math instruction.
John Mighton: Yeah. So, you know, our working memory is very limited. Um, there have been some studies that suggest we can only remember a string of seven digits when we first see them for the first time. And if you haven't committed really basic knowledge to long-term memory, then you really struggle to solve problems because you, you just can't hold very much in your short-term memory.
So there's one famous experiment in reading in the nineties where, where, uh, weak readers outperformed stronger readers on a test of baseball knowledge because on a reading comprehension test, because they knew more about baseball. And that's now a part of a slew of, of studies that have shown that foundational knowledge, basic knowledge or domain specific knowledge is critically important for [00:19:00] problem solving. You just can't, usually, you can't be a great problem solver unless you have some domain specific knowledge. So that's why it's important, you know, to commit basic facts and knowledge to long-term memory.
And if you look at, for instance, times tables or multiplication facts, uh, it's not just that a kid who has doesn't can't calculate is reliant on a calculator, won't, won't even know if the answer's correct, but it's much more serious. They can't see patterns or make connections or make estimates or guess and check or do anything that's involved in problem solving.
If they don't have that knowledge, I mean they, you know, some people will say came up with strategies to quickly find those numbers, which is fine, but you know, as long as the kids can quickly recall numbers and or find, compute and see connections. And they can't do that unless all that, all that, [00:20:00] that knowledge is really stored in long-term memory.
So again, you don't have to do times tables in a boring way. It's important that they see those things, but for example, I just noticed a pattern, the six times table, if you multiply six by an even number, so two times six is 12. Four times six to 24, you, you put a chart up on the board and ask the kids to see what patterns they see. They see all kinds of patterns. For instance, whatever you're multiplying six by is the same as the ones digit of your answer. So, six times six, it's 36. It's, you already know the ones digit of your answer, and the tens digit is half the ones digit.
So, when kids discover those things, they can suddenly, you know, put six four facts together. Well, it's actually eight facts because multiplication, it doesn't matter what order you do it in a, in a couple minutes say they can easily see a connection between eight facts that help them remember them. And I name the patterns after kids.
I say, that's your pattern. They also feel a sense of of [00:21:00] ownership because they discovered it.
Anna Stokke: Right. And I mean, it does take some time to actually memorize the times tables, but as you say, it can be fun and there are some, there, there are some fun computer programs that will help kids memorize times tables too. But, it's really empowering when they do know their times tables.
John Mighton: That's right. And, you know, most people will say think it's wonderful, for instance, that oral cultures like the Greeks would memorize entire sagas or poems. Why is that a bad thing? If you, if you memorize or know deeply some, some mathematical facts that are really a heritage - our heritage - is a, uh, you know, this is a rich part of, uh, of what human beings have created, why not learn it or know it?
Anna Stokke: And I think everyone can do it too, right? Have, have you ever met anyone that wasn't capable of memorizing their times tables?
John Mighton: Some adults have told me they aren't. [00:22:00] I want to take that seriously, but I, I haven't really found many kids who, if they, I haven't found any really in my practice, if they don't get enough practice and they see these patterns and stuff, who can't learn them.
It takes a lot of work though. It can take some work and it should start early.
Anna Stokke: I also think just in the times that I've worked with kids, I noticed that it does take some people will say longer than others, and I think that also contributes to sort of the, you know, “you're a math person, you're not,” but at the end of the day, they're all gonna know them and they're gonna be the same. It's just getting everyone to that point where they've all memorized the times tables.
John Mighton: I also think it's, I think it's kind of a psychological question too. So I was, I once taught a kid who had real attention deficit in grade four. He didn't know any of his doubles at all. So, I just got him to read big. He could read numbers in the hundreds, so if you can read numbers in the [00:23:00] hundreds, you can read numbers in the hundred, in the millions and billions and stuff.
So, he loved reading big numbers. Then I had them, him double them by just doubling the digits and I didn't put any regrouping. So, he, he would just, you know, the digits were anywhere between zero and four. He memorized that very quickly because he wanted to double these numbers. So, I think there are keys for some kids, like there are ways to make them want to engage in that work and we need to find that for each kid what is gonna inspire them to do that work.
Anna Stokke: So, I wanted to talk a bit about, using concrete materials, because that's, that's a very common thing that you see in, in today's elementary classrooms and, and even up into to high school actually. So, are you familiar with the research on, on using concrete materials like blocks to teach math concepts?
So I, I'm just kind of wondering what you think the balance should be for things like, say you're, you're adding two, three digit numbers together, you know, [00:24:00] 325 and 756, and, and you write out, you represent each number using hundreds, tens, and ones blocks, and then you regroup versus using the numerals and lining them up and, and adding and carrying. What do you think the balance should be like?
John Mighton: Yeah, I'm, I mean, I'm not an expert. I'm aware of some of the research, and I think it's a complicated issue. Um, so I have to be careful in what I say because it's a really complex issue, but, kids definitely need to touch things, to play with things when they're young to see things. But, but there's some research suggesting that you might wanna move them to more abstract representations earlier, and to guide that, that to guide very carefully the transition from concrete to abstract.
So one example, there's a, there's one researcher, Jennifer Kaminski, who's a hero of mine, [00:25:00] She did a, she did a study with I think, grade one or two kids where some kids, uh, had representation representations of flowers that were colorful with petals, colorful petals and so on, and they were asked, they were taught fractional concepts, like what fraction of these are blue and so on. Others had gray white circles and they were out taught the same concepts. The ones with the gray white circles did better than the ones with the colorful objects in, in learning and transferring the fraction concepts. And her work has shown that right up to university level. So, I'd recommend people will say look at Jennifer Kaminsky’s work.
So that's a case where she did a similar study with bar graphs and so on. Sometimes, uh, colors or pictures can be distracting and sometimes all the details of the concrete materials can stop the kids from actually seeing the math. So, you, you have to, you have to move away from, from. Overly contextualized overly detailed materials to more abstract [00:26:00] representation.
So, she found, for instance, just very simple gray and white bar graphs or gray and black bars or whatever were better than bar graphs with pictures embedded them, things like that. So, so that's one thing. There's another stream of research around concreteness fading, which suggests also that you need to introduce concepts concretely, but quickly fade to the more abstract representations, like number lines or abstract pictures and so on.
And I think teachers aren't aware of that research. And, you know, there's a, there's a lot of money to be made selling concrete materials. So, so I think you need to, you need to be aware of that research and you need to know when to move away. From the, the concrete materials to more symbolic methods or representations.
Anna Stokke: Right. And I think it's almost the opposite of what people might think, like people will say think if you make things more colorful and more cluttered and, and there, and there's, there are more things to play with that that's [00:27:00] gonna make it more interesting for kids so that it'll make it easier for them to learn. But it's actually the opposite because, and it's goes back to working memory, right? It just can overload working memory.
John Mighton: Yeah. And, and it can distract from where they should be seeing the math. Like, uh, like the flower example, they weren't seeing the fraction concepts. They were too caught up in the colors of the pedals and things like that. So, so it's a complicated issue, but I, I'd recommend teachers look at that.
And also not underestimate the importance of abstract representations of, of numerical representations and things like that, and moving kids to those, earlier than people will say typically do.
Anna Stokke: Yeah, definitely. So what do you think about - you know, it's, it's very easy to actually find a math program that will - like a software program that'll just essentially do everything for you? I mean, and we have calculators and. And, [00:28:00] and Wolfram Alpha – or whatever - and a lot of people will say might say, you know, why are we spending all this time teaching basic mathematics? Should kids even learn basic arithmetic anymore? Because they can just look it up. I mean, people will say, well, shouldn't we be spending that time instead on teaching kids critical thinking? What do you think about that?
John Mighton: Again, a really complicated question. So, if you, if you teach them to do the computations and, and see the, you know, know the, the connections between numbers. Um, I believe you're actually teaching critical thinking in a deep way if you're allowing the kids to figure things out. And also you're teaching them something about the structure of numbers that they need to know that, that if they're ever gonna have a chance.
When they're older of knowing if a claim is right or being able to do a simple, you [00:29:00] know, estimate or using ratios or anything like that. I've taught a lot of high school math, for instance, the, and I find that the, it's not the high school math that kills the kids. It's the knowledge of fractions, ratios, percents, decimals, things simple computations.
The abstract stuff is easy for them. It's, it's when they actually have to deal with a fraction in an equation, which is, which is a much deeper knowledge, like a much, much deeper in some ways than the algebra. Um, that's where they really struggle and why they need a great foundation in those things early on.
Because if you have just a part to go back to really simple example, kids at a really early age can skip count by twos 2, 4, 6, 8, because, but if you ask them to do the same thing by the odd numbers, It's very rare that they know that it's not because it's any harder. They just never hear it. Just going up by the, even numbers is a kind of useless scaffold for the number line if you're missing the odd numbers.
But if a kid can just visualize, [00:30:00] if I'm at 27, the next odd number is 29, or the previous one is 25, they can move up and down the number line effortlessly. Uh, you know, they can add two to anything. They can add four to anything. and they can get that very early. You might think, why should they bother to learn that?
It's because then they can actually later on, they, they actually know what a sum means. They know they can see patterns and numbers when you skip counting, um, all that pays off later. And it's, it's the same for just basic fraction knowledge. For basic computational knowledge. You can't even be a functioning citizen.
I believe - especially with all the claims that are being thrown around now - you can't even function as a citizen if, if you can't say whether a claim is, is even plausible. And then the other thing is people will say don't understand is that when you learn to think mathematically, you are actually learning to see patterns, to make inferences, to construct good arguments and proofs, to make generalizations, to make [00:31:00] connections.
You're learning it and, and you're actually learning it in a way that's accessible to every brain. people will say think math is the hardest subject. There's research now suggesting it actually could be the easiest subject for kids, and there's no other subject where they can learn to think critically so quickly to solve problems, to organize their thinking.
If a problem has more than one solution, how do you know you got them all? It's almost impossible to teach those things with dense texts sometimes in reading. You can teach critical thinking a hundred times more quickly in in math than in other subjects and problem solving. So, it's the one subject you should be focused on if you want.
If you want to have an equitable system where everyone learns to think critically, spend more time on math.
Anna Stokke: Yeah, I agree that it, it definitely could be the easiest subject to learn. The, the difficult part about it is that it is the ladder effect and oftentimes, you know, you're, you're trying to teach someone something - and this happens when I teach first year calculus - and students [00:32:00] often struggle with some of the concepts that we're doing in that class.
And it's not because of the calculus, it's because of the algebra that they didn't actually - that they don't remember - or that they didn't learn properly or that isn't solidified in their brain from grade 10. So that, that's often the difficult part, is just the, the ladder effect - that often in math, a concept that you're trying to teach someone depends on a whole bunch of other concepts that they should have learned beforehand.
John Mighton: Now the good news in math though, at the earlier grades, if I could just say like, so we had a teacher who took a grade five class where, where, when she when she tested them, the kids were as low as grade two level. And so there was a wide range of marks a year later when she retested on these standardized tests.
The lowest score was in the 95th percentile. Like the kids look like a gifted class within a year. And then they wrote the math competition a year later. And, and all but three got awards of [00:33:00] distinction. So that's the kind of plasticity that's in kids' brains in grade five. But you might think, well, it's kind of late to catch a kid up from grade two level.
The very first thing the teacher did was teach the kids how to count the distance between two numbers on their fingers if they had to, because she couldn't assume they could subtract. The minute they can count the distance between a pair of numbers. They can do pattern work. They can say what the next number is.
When they know what the, the gap is between the numbers, they can do T tables, which is grade five work. If you just make sure every kid can count the gap between a pair of numbers on their fingers if they have to, you can bring them to grade five level in one lesson or two lessons. They can be doing curriculum-based work. It's not too late to catch kids up if you do a, a task analysis of what they need and, and you build those skills and concepts very quickly.
Through the year, you can work on getting them off their fingers. You can do all kinds of mental math work, but if you want to make the whole class feel that they can actually participate at grade level and suddenly wake up the brands of the ones who've been, who've been shut down, you can do it in a day or [00:34:00] two.
I do demo lessons all the time, and in one lesson, I can close a gap in grade seven and have everybody work on the same stuff. So, the, the ladder effect you need to take account of it. But thankfully in up to grade nine, 10 or so, I would say they can scale the parts of the ladder, they need to very, very quickly - if you've got well designed lessons,
It gets harder as they get older.
Anna Stokke: Yeah. That, that sounds quite promising. So, so on that note - and this is a really big question - and you might have a lot of things you want to say, so just, , maybe hit the high points, but what, what would you say are the main components that you should have for a math instructional program to be successful based on, your experience and, and what you know about the cognitive science research that you've certainly looked into a lot.
John Mighton: So, so I think first of all, you need to be, careful that it's aligned with the science of learning. There is [00:35:00] now a growing body of rigorous research on how kids learn. There's a famous reading consultant in the states who recently apologized to teachers publicly because she said some of the things she's been telling teachers to do in reading are not well supported by the science of learning, and that's wonderful.
That she'd admit that - like it's very rare. So, I really respect that. But on the other hand, a lot of teachers have been doing what, what she said they, they should do, and it's had, you know, it's had an impact on kids. So, whether it doesn't matter what your program you're using, look to see if there's some evidence and not just by their claims, but other studies and, and is it, does it seem to be aligned?
Teachers should familiarize themselves with the research like Jennifer Kaminsky. They should look up her work. Her articles are very easy to read. Just get familiar with articles that are published in scientific journals. That's the first thing. And be familiar with the science of learning. Before you pick a program, like make sure it's [00:36:00] aligned with that.
The other thing is if, if it is aligned with the science of learning, then it should probably introduce problem solving more gradually. For instance, like if you want to teach kids to play chess, the research suggests it's better to start with mini games that have been designed by experts so they can play a position and see that's a weak position, that's a strong position, here's how a piece moves.
Without suffering from cognitive overload, they can learn to play the game in chunks and, and then build up to the, the full game. I think a good math resource should do that. You shouldn't be throwing complex, multi-step, language dense problems at the kids in the first month, because it's bound to fail with, with most of the kids and convince them there's no point engaging for the rest of the year.
The research suggests that's the worst way you can teach problem solving, but teachers are told “you've gotta do this right from day one or it's not a conceptual program.” That's probably the worst idea I've come across in [00:37:00] education. It mistakes the end for the means. The end is to have them do multi-step rich problem solving. The means to get there is to start more incrementally and have them solve problems in chunks and build up.
So that's the second thing. Look at the program. If it looks from day one, if the kind of problems kids are asked to engage with look exactly the same in the first term and the second term, it's a pretty good sign it's not aligned with the science of learning . Um, it should, the program should, equalize the class. It should make the kids feel equal from the beginning. Otherwise, there's research showing as early as grade one a kid can tell if a teacher has different expectations, no matter how good the teacher is.
Kids decide very early if they're in the talented group or the inferior group. Once they've decided the, they're in the inferior group. The research has shown their brains stop working. So, if your program is doing that, it's probably not aligned with the science of learning and not gonna be very productive. So I, I think those are some of the things that teachers need to think [00:38:00] about in choosing programs.
Anna Stokke: One problem though is that a lot of times teachers actually don't get to choose the program. It's sort of handed to them either by the principal, the maybe the school board, sometimes even maybe the province. So, what can a teacher in that situation when they're being told to use a program that they know doesn't work?
John Mighton: Well, I would - that's hard, hard question, but one thing they could do is, is find some articles on the science of learning. I wrote an article for Scientific American Mind, called For the Love of Math. Find some article. There's another great article they can just Google and get, it's, called “Principles of Instruction.”
Anna Stokke: It's Ro, it's Rosenshine, and I can put a link to that.
John Mighton: Yeah. So that has, that was sent to me actually by a cognitive scientist, because she [00:39:00] said this, this are, these principles are, are very well supported by the research on how kids learn.
They're - you know this, this article has great references in it and, so she thought that it was all of the references that the articles were published in very good scientific journals, so that's why she sent it to me, and it's very simple. Right on the first page, it lists 10 principles of effective instruction.
Like, basically, ask lots of questions, assess constantly, teach in chunks. All those things that we're talking about today, are in that article. So, if I was a teacher, you, you know, I might find some articles like that and bring them to the principal and say, are you sure that what we're doing is aligned with this?
The, the irony though is because, because, test scores have been going down or flat across North America, like in Ontario, they, they've gone down precipitously over the past decade. There was a bit of a loss of faith in textbook programs and people will say started saying, well, maybe teachers [00:40:00] should be allowed to create their own programs.
But I, I saw a study from the Fordham Institute recently that rated material that teachers are pulling off the internet, and according to this rating, they found only about 10% of the material that teachers were pulling in math were very high quality. So, we've gone from trusting textbooks that were not aligned with the science learning to now expecting teachers to pull programs together with very little time or expertise.
So the good thing is there's a little more freedom now for teachers, I think in many schools. And I think teachers to, to take advantage of that, to really look for evidence-based programs. And in reading too, like there's just so much evidence that phonics is critically important, critically important, things like that.
I think teachers have the, have more power now. To actually insist that they, they be able to pull materials or [00:41:00]find materials or, or get programs that are aligned with research and real research, like, I mean, research published in scientific journals by cognitive scientists or educational researchers who, who are, who are using rigorous methods.
Anna Stokke: So you, you actually, mentioned the science of reading a little bit, and I want to just discuss something about that because instructional programs in math actually don't always take into account the science of learning. And, actually a lot of the research results have been around for some time and we've seen this play out in, in both reading and math.
And, for anyone who's listening, I would recommend listening to Sold a Story, Emily Hanford's podcast. And, she investigated authors in publishing companies that made millions, actually, selling reading instructional materials to schools based on methods that had been shown years ago not to work.
And when [00:42:00] evidence about learning is ignored, children suffer. So why do you think that, like, why would instructional designers or prominent educators disregard evidence on the science of learning?
John Mighton: I don't know why people will say don't have more exposure to the science of learning. I think they're, I think first of all, the, the whole industry of textbooks and everything have been very good at finding out what people will say want, what's popular, and then giving them that. And, and so whatever sounds good to people. And usually - I'm a very progressive person - extremely progressive. Like I started JUMP as a charity because I want to help create an equitable world.
But sometimes the most progressive ideas, do a lot of damage. And so, you know, “kids should solve rich problems.” Yeah, I [00:43:00] agree a hundred percent. They should be rich problem solvers, but you may want to get to them in a more incremental way and, guide them to that point. They're still doing the thinking, they're making the discoveries, but guide them, guide that learning and practice.
That doesn't sound as progressive as just, you know, give kids some strategies and let them deal with rich problems. This idea of low floor, high ceiling problems, where you give kids a very complex problem where they can find their level. Some kids might be in the basement, some in the higher level. Um, problems with multiple entry points. Very, you know, usually with real world applications and kids can find all different ways of doing it.
That's great. But if kids are in the basement, the research in psychology suggests they're going to stay there cuz they know they're in the basement and that's going to affect the way their brains work. So, you might not want to use that kind of problem until they're all confident, strong math learners.
So I think that people are sold by [00:44:00] slogans and catchphrases that sound good? And they, there's there's not an instinct to say, “what's the evidence? Do you have a rigorous, rigorous evidence behind this?” And that that's got to really change in the system. And I don't, I think education faculties have a responsibility to expose teachers to those.
And, and I know lots of educators like Brent Davis in Calgary, who are now pushing the system to move that way. And so I'm, I'm optimistic that there are changes, but that's, but I think we're a really ignorant species when it comes to, you know, thinking about ourselves. We, we've accepted fact that so many kids struggle and fail in math because we just assume it's some kind of innate problem rather than looking at what we're doing cause that problem.
Anna Stokke: Yeah. And we'll keep hoping that that things get better and I, think they gradually are. The premise of your book, [00:45:00] All Things Being Equal is that society would be more equitable if everyone had a better understanding of basic math. Can you elaborate on that?
John Mighton: Yeah. Well, first of all, if everybody actually learned math properly, they, they would be, they would learn thinking skills and, and developmental capacities that would transfer into any subject across all subjects. Like to see patterns, to make connections, to create, you know, really well-structured arguments.
All these things would transfer and so, so if they just knew math deeply, we'd have much better results in other subjects. There's studies showing that math for young kids is the strongest predictor of success at school. Academic success stronger than reading even. It predicts reading success more strongly than reading does.
So there's all these benefits you get from math. Also, on top of that, like kids are born with this incredible sense of wonder and curiosity, [00:46:00] and we would think kids were stunted if they graduated from high school without any appreciation of the visible beauty of the world or of nature, but we think it's natural for them to graduate with no appreciation of the invisible beauty of the world that you can only see through mathematics.
So, kids will solve problems. They'll, they'll work on puzzles and things like that endlessly if, if they're not afraid of failure and they have a right to keep that side of their brain open and to, to really maintain their sense of curiosity and wonder about every part of the world. So, I think that should be a right of kids to, to think mathematically, to see the world scientifically, to see the beauty of the world.
And finally, you know, almost all fields now require math on some level. There would just be so many more opportunities for kids if they could choose whatever they wanted to go into, including fields that involve math. and certainly, uh, no economist would doubt that it would [00:47:00] be better for our economy to have an educated workforce, which is, you know, that's important to me.
But there's all those other things too. The loss of wonder, the loss of our capacity to think deeply, to think critically, those are the things we lose when we don't teach math well.
Anna Stokke: Very well said. And, and I agree especially about the beauty of mathematics and we need to expose more people will say to that.
John Mighton: I think we'd have a much happier society if people will say actually had, could use every part of their brain. I think we're born to learn, basically. That's one thing that's innate in us – we’re born to learn, to make connections, to make discoveries. And if we could do that with every part of our brain, we would be much happier people and we’d be much nicer to each other too.
Anna Stokke: You're quite right about that. So, what do you think the future holds for math education?
John Mighton: Well, I'm hoping, I'm hoping there'll be a shift towards the science of learning and much higher expectations of kids, knowing what kids can do and what they love to do. [00:48:00] As a charity JUMP, what JUMP is trying to do is, is at least find some schools where we can demonstrate, you know, across whole schools that virtually every child can learn math and love learning math, and you know, which it should be expected.
Once people will say start seeing that, then I, I think there'll be a shift, a much wider shift. I hope there'll be a kind of tipping point when people will say start to apply the science of learning and see what kids are really capable of.
There'll be a tipping point we'll never go back from, once people see it on broad scale, that it's possible for everybody learn math.
Anna Stokke: Well, that sounds promising. And thank you for everything you do to help kids learn math and to create a more equitable society. And thank you for talking to me today.
John Mighton: Oh, thanks so much and thanks for everything you do too.
[00:49:00] I hope you enjoyed today's episode of Chalk and Talk. Please go ahead and follow on your favorite podcast app so you can get new episodes delivered as they become available. You can follow me on Twitter for notifications or check out my website www.annastokke.com for more information. Technical support and social media support was provided by Rohit Srinath. This podcast received funding through University of Winnipeg Knowledge Mobilization and Community Impact Grant funded through the Anthony Swaity Knowledge Impact Fund.