Mathematician John Mighton talks with Scientific American MIND editor Ingrid Wickelgren about getting math-shy kids interested, via JUMP: Junior Undiscovered Math Prodigies
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Welcome to the Scientific American podcast science talk posted on August 8th, 2013. I'm Steve Mirsky. And if you've seen the movie Good Will Hunting you've seen John Mighton. He's a Toronto-based mathematician who was an advisor to the film. And he appears in it as well which isn't that much of a stretch because he's a playwright, too. Mighton founded JUMP which stands for Junior Undiscovered Math Prodigies. It's an organization devoted to educating kids and, you guessed it, math.
Scientific American MIND™ magazine editor, Ingrid Wickelgren spoke with John by phone.
Ingrid Wickelgren: John it's really nice of you to be here. So you're a mathematician.
John Mighton: That's right. I do research in math in a field called graph theory which is used a lot in computer science and other branches of math. I also sometimes write plays. I used to spend a lot more time writing plays. But since I started JUMP it's really taken over my life - the charity JUMP Math. Now I spend virtually all of my time working for JUMP.
Ingrid Wickelgren: What's your affiliation as a mathematician?
John Mighton: Well I have taught at the University of Toronto. That's where I got my doctorate. And I did post-doctoral work at the Fields Institute where I'm now a Lifetime Fellow. That's where I do most of my research.
Ingrid Wickelgren: And the Fields Institute is in Toronto?
John Mighton: It's called the Fields - Yeah it's called the Fields Institute in Toronto. It's sort of a math research center and think tank.
Ingrid Wickelgren: But much of your time is spent at this charity that you began called JUMP Math.
John Mighton: That's right. Yeah for the first, I would say, about 13 years of JUMP I volunteered almost - sometimes up to 40, 50, and 60 hours a week. Finally I had to take a salary because I haven't written a play or taught a math course in quite a while. [laughter]
Ingrid Wickelgren: Tell me a little bit about JUMP Math and what it is.
John Mighton: JUMP is a charity that is seeking to improve the teaching of math so that all kids can really love learning math and have success with it and teachers can enjoy it also. So we now serve about 100,000 kids in Canada who are using the program as their main classroom resource. We have student materials but the most important part of the program are these online teachers guides that show teachers how to do guided discover - that is give kids a series of small manageable challenges that they can figure out and can get very excited about their success.
And the program is now being used - We've adapted the program to the Common Core state standards for the U.S. and the program is now being used by a number of boards in the U.S. also.
Ingrid Wickelgren: So this is something that was inspired by your personal experiences with math? Or what -? You weren't always a great math teacher and mathematician right?
John Mighton: No I never thought I would be helping run a charity to teach math because I sometimes struggled myself in math. I sometimes did well but I was always afraid there was a limit to my ability. And I don't think I worked very hard often because I was afraid I would meet that limit. I grew up in the '60's when everything I read made it sounds like you had to be born with some kind of talent or innate gift to do well at something. That was really -
My fears were really sort of confirmed when I tried to take a calculus course at university years ago and was basically saved by the bell curve. It brought my mark up to a C.
Ingrid Wickelgren: Okay. [laughter]
John Mighton: At that point I dropped math and didn't think I would ever do the subject.
Ingrid Wickelgren: So what happened?
John Mighton: Well it was a strange series of accidents. I also did badly in creative writing even though I'm a writer now. When I graduated I was babysitting my sister's kids one night and I found a book of letters by the American poet Sylvia Plath. They were letters to her mother. And it was clear from the letters she taught herself to write by sheer determination. So as a teenager she did everything she could to train herself. She would memorize poems, read everything she could about poetry.
And she also did something we would rarely tell young writers to do. She wrote imitations of the poems she loved. So if she liked something she'd try and figure out the style and write something in the same voice. Gradually as she learned her craft you could see her own voice coming to the poetry. And she was one of the most original poets of the century. I was shocked that someone could actually develop a gift like that through that process. I started imitating her poems and other poets.
I gradually ended up in theater. And because I was struggling to make a living I -
Ingrid Wickelgren: So at this point you were doing what with your life -
John Mighton: Well at that point -
Ingrid Wickelgren: after college?
John Mighton: After college I had gone into philosophy and was taking a Master's Degree in philosophy at that time. I didn't think I'd ever go into the sciences. But because of the influences of Plath I started writing and eventually took a job as a math tutor because I needed to support myself. I thought I could at least tutor high school because I'd passed calculus. That was a turning point in my life. By working my way back through the high school material and having to explain it over and over things that were mysterious to me because easier and easier.
And I actually began to get the confidence that I could maybe do math. I never felt - Because I had struggled I never felt I understood something really well unless I could break it down into the absolutely simplest steps and the simplest explanations. Or I didn’t think I understood it. And also I was dealing with some fairly challenged students. One of my students was in a remedial grade six class and they thought he could do math. He finished his doctorate about four or five years ago and is now teaching math.
For these students who were often quite anxious, who couldn't focus, and who had gaps - I had to figure out where the problem was and go back sometimes many years. But I found that if I did that and gave them a series of incrementally harder challenges that they could succeed at they started focusing more and developing more and more confidence. And the way they learned seemed to really change dramatically so that many of them became very strong students fairly quickly.
Ingrid Wickelgren: And I guess along the way your confidence also grew?
John Mighton: Yeah my confidence grew and grew. But it's interesting because when I went back to university I had a huge advantage (in my 30's) over other students 'cause I'd been tutoring for years. I would do extremely well but I remember once I bombed a test and I was almost bedridden. I thought, "I have to give up now. I've reached this limit," even as a mature student, but it was so deeply engrained me this idea that I would meet that limit. It really helped when three years later I realized I could actually teach the material on that test because I'd had a chance to practice it and get used to it and internalize it.
I really began to think that a lot of our problems, a lot of our misconceptions about ability, come from the fact that we never have the opportunity to learn things in manageable steps or to practice enough and consolidate ideas enough to get good at anything. We give up long before we ever get good at it.
Ingrid Wickelgren: Interesting. So the people who tend to excel in math would then be those - just sort of those lucky few that despite not having the amount of exposure or, I don't know, the right type of teaching they nonetheless catch on and can move forward. Does that explain those people? Or is there some other explanation?
John Mighton: Yeah it's complicated. There are some students where you wonder, "Where in the world did that ability come from?" It's so deep and mysterious. But the vast majority of the kids who are able or good and really outstanding seem to learn because they have a great mindset. They're confident. They work. They get an advantage over other students because they know more and more and can think more quickly and draw on things they know to solve problems.
I think that a lot of success is partly accidental. And I mentioned this in the article. When kids get good instruction - We did a case study where an entire class went from being about in the 54th percentile with kids as low as the 9th to being in the 98th percentile with kids as low as the 95th in a year. And that's fairly late. That's a grade five class. So if you can see that kind of radical change in abilities you have to start wondering why it is that so many kids aren't showing that potential.
And I think it's partially psychological because they convince themselves they can't (then their brains don't work efficiently), and partially the way they're taught. The challenges we give kids often aren't broken up into manageable enough steps. They're overwhelmed by too much complexity. They don't get enough assessment. They don't get enough time to practice. They don't know the basics before they tackle harder things.
I think those are the reasons we're seeing such big differences between kids, not because some have an innate ability. It's largely psychological and has to do with the way they're taught.
Ingrid Wickelgren: So what you have is sort of a combination of things that feed upon each other. You have people who sort of have a good mindset from the beginning. Then they tend to learn more and then that bolsters their confidence. And then you have other people who may - you know - struggle. But if they can get the right intervention then that will bolster their confidence. And the confidence really kind of feeds the progress.
And on the flip side when people don't believe they can understand it - And that may be what you're saying is sort of a pervasive problem in math is that these beliefs kind of stifle the process. But if you can open that door, right - that confidence door? Then you can feed the progress through the right instruction.
John Mighton: Yeah our beliefs have incredibly strong effects. We're a society that only 50 years ago or even more recently thought that women couldn't do mathematics. We see people who can't do something and we automatically assume it's some kind of innate problem that's stopping them from doing it, that they don't have the right gift to do it. We just make those judgments constantly. But what if all kids could learn math? What if it was the case? Or virtually all kids?
I mean there are some with very severe learning disabilities, but in my estimate 98 percent of kids - 99 percent - could do extremely well if they had good instruction and believed they could do well. There's research that shows as early as kindergarten kids start comparing themselves to each other and deciding who's good at a subject and who's not. And we allow those comparisons to persist because we think they're innocent and natural. But once the kids decide they're not good at something their brains just stop working efficiently. They give up and stop paying attention.
And also I think kids need certain kinds of challenges that adults don't understand. Kids love repetition more than adults. They love simple extensions of patterns. They love taking small steps and having small victories. They absolutely love that. I once spoke at the Aspen Brain Forum. And a neurologist told me that she had a lot of evidence that kids' brains work most efficiently when they're making constant predictions. But they also need to get instant feedback. They don't have a lot of patience to deferred gratification and they need that confirmation that they're doing well.
So what's missing I think in a lot of lessons is that maybe the kids are trying to make predictions and they might be struggling because the material is too hard. But they're also not getting enough feedback right away that will motivate them, excite them, and make their brains work in this kind of optimal zone where they're so excited they're in a flow, where they're remembering things, taking risks, and learning confidently because they're solving these puzzles.
Ingrid Wickelgren: So you sort of learned all of this through this tutoring process, kind of by experience with these kids who were struggling?
John Mighton: Yeah it's been a very organic process of learning. And I'm quite gratified because right now JUMP has the support of a lot of cognitive scientist who are either doing research with us or advising us or speaking at conferences to help us out. I'm part of a Cognitive Science Network at the Fields Institute. A lot of the scientists are saying that somehow we've stumbled on principles that seem to be well-supported by the research.
So for instance if kids need more practice that you can make practice interesting for kids, that you have to build up smaller skills and concepts before they can tackle bigger ones. But I just had to learn these things, first because we were tutoring quite challenged students, sometimes kids who couldn't even count by twos in grade six. We had to break multiplication into a series of saying a sequence of numbers. And also because when we went in the classrooms we were seeing wide ranges of ability and motivation in kids.
We had to design lessons that would allow as many kids as possible to succeed. And so we had to start using these principles because it was the only way we could help the kids. But after I got the confidence to go back to university I spent years. I eventually got my doctorate. But when I was close to finishing my doctorate I wanted to help kids. I felt I'd been very privileged to sort of have regained my sense of wonder and confidence through starting from reading Sylvia Plath's work.
I wanted to give something back to local kids. I decided to start a tutoring club in my apartment. A local principal sent kids down. My friend volunteered. At that time I was writing plays and doing math. So I knew a lot of actors and playwrights. They sometimes have some spare time on their hands while they're waiting for jobs.
Ingrid Wickelgren: Right.
John Mighton: They made amazing tutors because they're very charismatic and they love learning the math for the first time. The program grew very quickly. We placed hundreds of tutors in the schools in Toronto. And then one day some teachers asked me to come into the classroom and help them out. I had thought the kids we were helping would need one-on-one attention but I was wrong. JUMP has evolved through a series of very lucky accidents. I saw that the kids we were helping did much better and got much more excited when they could learn in a community.
When they could show off in front of their peers, come up to the board, and solve a problem they just got so much more excited that they learned much more quickly. And it was much more efficient than pulling them out for one-on-one tutorials. Also I realized that rather than having kids get one lesson a week from a tutor a teacher could reach 25 kids a day, five times a week. We started transitioning and are now training teachers and providing them with materials, like the online lesson plans.
It was quite surprising but I found that the message - As long as the challenges were incremental enough the methods could be used for a whole class. You have to differentiate instruction somewhat for students, especially at the beginning of the year because there can be a wide range of abilities. But we found if you didn't differentiate too much, if you made sure you reviewed enough and that the challenges were small enough then the class would move so quickly that the stronger kids wouldn't be bored. And you could always make small adjustments like give them extra bonus questions.
The other thing that came from my background in playwriting; I realized we only have one advantage in putting kids together in a group because you can't reach them individually. But as a group they're an audience. As a playwright I thought about that. There's a sociologist (Durkheim) who said you can never get people more excited then when they feel a collective effervesce. They all feel the same thing. They're experiencing the same thing together. And I saw that viscerally in these classrooms.
When all of the kids could succeed together I couldn't believe it. Kids would beg to stay in from recess. Many teachers have reported that.
Ingrid Wickelgren: Wow.
John Mighton: They cheer sometimes for math because it was like they were all experiencing the success in this amazing video game where they just kept getting to higher and higher levels. And they were moving together so they were excited together. I would never have anticipated that until I saw it in the classroom that they could move roughly in unison and that that movement would give a sense of momentum and purpose and excitement to the class that I think - I mean we haven't tested this yet rigorously but I think that actually helps the brain somehow reorganize itself or rewire itself in a very dramatic way.
Ingrid Wickelgren: What do you think accounts for that excitement?
John Mighton: I think a couple of things. I once taught kids in a grade five class to multiply numbers with lots of zeros. You just multiply the leading numbers and count up the zeros. And at the end of the lesson this boy came up. He'd multiplied two 20 digit numbers. There wasn't even room on the page for all the zeros. They were kind of wrapped around in circles.
Ingrid Wickelgren: [laughter] Okay.
John Mighton: Now to an adult that would be boring our pointless. And I think we have trouble teaching kids because we've forgotten that sense of wonder that they have.
Ingrid Wickelgren: Hmm.
John Mighton: They're almost like alien species. I mean who knows why he was so excited. I think because he'd proven he could handle these huge numbers - because he'd shown a pattern that's obvious to adults when it seemed to go on forever. There are all kinds of things that excite kids that we don't understand. And the thing that destroys excitement most quickly is failure or a hierarchy in the classroom where kids are comparing themselves to each other. Once you remove that and the kids feel safe and feel they don't have to compare themselves they develop what Carol Dweck would call a growth mindset.
They realize their success doesn't depend on just being smart or talented. It depends on their perseverance and hard work. I think that this is something that would be very interesting to test. But I think the group effect magnifies that. Carol Dweck saw a video of a JUMP class and said she thought it would really help kids develop a growth mindset because they're all meeting challenges that look hard but aren't too hard. They're kept in a kind of zone where they're taking a risk but they're constantly succeeding and seeing that it's worth taking that risk.
Ingrid Wickelgren: Right, right. But the aspect of JUMP math that may be so motivational and may put kids in that growth mindset is that it's sort of built on small challenges that kids can feel success after tackling successfully?
John Mighton: Yeah I think it's because these challenges are manageable. And because math is supposed to be a hard subject kids really do think they're taking a risk in meeting them. They feel very proud of themselves when they do meet the challenge. In math also you can gauge the size of the step to the student. You can make stuff as small and mechanical as you need to. And then as they get more confident you can start to skip steps and inflate steps.
Or expect them - We call the method of JUMP guided discovery. The teacher should explain as little as possible through a series of Socratic questions and challenges and exercises the kids should always be figuring out the answer for themselves.
Ingrid Wickelgren: Mm-hmm.
John Mighton: But the teacher is always there to guide them if they struggle and to adjust the size of the challenge, either making it harder or easier. But as long as a challenge doesn't incorporate a lot of new information or vocabulary or skills then generally most of the kids can work on the challenge by themselves independently and then the teacher can check on the few who might need the extra help. And when the kids who need the extra help see the challenges aren't too hard they also speed up so they can get their bonus questions too.
Ingrid Wickelgren: Right. So it seems similar also to the concept of flow in a way right? You make things challenging enough but not too challenging -
John Mighton: That's right.
Ingrid Wickelgren: so that you're just sort of absorbed in the process. You're not sitting there worrying about how good you are at something - where you rank.
John Mighton: Exactly.
Ingrid Wickelgren: But it's just the activity itself is fun -
John Mighton: Exactly.
Ingrid Wickelgren: Like playing baseball or something.
John Mighton: Yeah and it can have surprising effects. I once broke up a fight by telling the bully that if he didn't apologize I wouldn't give him his bonus question. And he apologized -
Ingrid Wickelgren: [laughter]
John Mighton: for a bonus question in math. Most people think math is too hard to ever use as a tool for social justice but it's actually kind of a magical tool for a couple of reasons. I could never go into a class and get grade six kids all reading at roughly the same level. But I can very quickly do that in math on a particular topic because I can figure out what are all the basic skills they need for that topic. How could I scaffold them in an interesting series of challenges so the faster kids wouldn't get bored as I review those things.
It's a very easy thing to design math lessons like that - much harder in other subjects. You can really change behavior we've seen in classrooms by letting kids succeed in math. And then the effect spills over into other subjects as well.
Ingrid Wickelgren: I wanted to get back a little bit to the story of JUMP Math.
John Mighton: We've grown really quickly and one of the most exciting things is we've begun to establish networks of teachers across Canada now into the States who are beginning to mentor other teachers and help us by creating materials, testing materials (like our new SMARTboard lessons), and also giving training. That's one of the - Teachers I think - Some people think many teachers are apathetic or have given up but I think it's only because they've been told to do things with kids in math that aren't' working for most kids.
And so it's very hard to manage classes when that's happened. You get exhausted and maybe discouraged. But we've found that the vast majority of teachers, when they're given tools they can use to reach all their students, get incredibly excited. And they volunteer for us. They help us any way they can. That's one of the most exciting things. In one board in Canada I'm actually going to be training 12 master teachers who will keep data on their students. And then at the end, if that goes well (which we hope it will) we'll start to train other teachers in the board.
JUMP will be self-sustaining in the board. We won't always be having to go back because there will be a network of teachers in the board who can train and support other teachers. We've also been engaging more and more deeply in research. We've involved in a two-year randomized, controlled study in over 100 classrooms that just is finishing its first year. We just finished a study in New York that went very well.
Ingrid Wickelgren: What were the results of that?
John Mighton: I can't say yet but it went well. [laughter]
Ingrid Wickelgren: Got it.
John Mighton: It's preliminary but they were very positive and that is now going into its second year. We're very concerned that programs are being in schools that aren't being tested rigorously enough. That's why we're engaging in all this research. First of all, not only to document the effects of JUMP but to also make sure it's working and to see if we could improve it in any way.
Ingrid Wickelgren: Is most of the data so far in support of JUMP anecdotal or are there some studies that have been completed so far?
John Mighton: Much of it is anecdotal but we did participate in a randomized controlled study that's complete and the researchers have announced that the JUMP students - their math knowledge grew at twice the rate of students in the control group on measures of fluency, computation, and quantitative concepts. That's the most rigorous piece of evidence we have.
Ingrid Wickelgren: Right.
John Mighton: And that was strong enough to convince the U.S. Department of Education to fund the second study. It's quite strong evidence. We do have some large pilots like the one I mentioned in the article in Lambeth in England that year after year showed that a very surprising percentage of kids who were far behind caught up and passed the national exams. And then we've got a lot of anecdotal evidence from teachers.
Ingrid Wickelgren: If this were expanded across the board what would that mean for progress in math for students? I know that the U.S. doesn't expect quite as much as some other European countries in math. What's standard in seventh grade here might be standard in sixth grade somewhere else. Would that mean we could all move faster - "all" meaning students? That the U.S. could be more competitive and kids could be a year ahead? What do you see happening?
John Mighton: Yeah I have a short-term and long-term answer. In the short-term the new Common Core state standards that are coming out in the U.S.; we're adapting our materials so those standards. We find they're quite good and they are quite advanced. And they focus on important things.
Ingrid Wickelgren: The new standards?
John Mighton: Yes. So I think the U.S. is going to have an advantage over a lot of countries because they're going to have very good standards. Now the fact that they're at a high level we've had to do a lot of work making sure we've constructed the materials so that kids would have enough support to meet those standards. That will be something of a challenge but the standards are extremely good. In the longer term I never saw myself as a textbook developer or a developer of materials for kids.
We're more concerned - Even if people don't use JUMP we hope that the research we're doing and the data we're gathering will help raise the bar and the expectations in school so that whatever program they're using we're not going to be satisfied with leaving so many kids behind and that we will know the significant majority of kids could not only do much better in math but could love it a lot more and could really enjoy it.
Ingrid Wickelgren: I just wondered if you could convey your feelings about math in terms of - or what kinds of feelings you want to impart to students about the wonder of math.
John Mighton: We would think that kids were stunted if they didn't see any beauty in a mountain or a star. But we think it's natural for the vast majority of people to graduate from high school with no appreciate of the invisible beauty of the world, the incredibly elegant connections that permeate all of nature and that you can only really understand and appreciate or see through mathematics. That's a huge loss. There's also a kind of loss of potential as a sustainable society. We don't have a lot of sense of risk or how our actions add up.
That's why we've had so much trouble dealing with climate change or developing sustainable economies because we don't really know what risk means or how to gauge the effect of the things we do. So on all levels I think we suffer a great deal because of these myths that only certain kids can do math or enjoy math.
Ingrid Wickelgren: Mm-hmm.
Steve Mirsky: Look for the article about John Mighton and JUMP in the upcoming September/October issue of Scientific American MIND™ magazine. That's it for this episode. Get your science news at your web site: https://www.scientificamerican.com. And check out the collection of Scientific American e-books available for Kindle, NOOK®, and iBooks. You can find them by going to our web site then clicking on “Products” on the right near the top and then on Scientific American e-books.
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