Ep 61. Why students struggle in math and how to fix it with Barbara Oakley and John Mighton

This transcript was created with speech-to-text software.  It was reviewed before posting but may contain errors. Credit to Canadian Podcasting Productions.

In this episode, Anna is joined by two familiar guests, mathematician and founder of JUMP Math, Dr. John Mighton, and learning expert and bestselling author Dr. Barbara Oakley. They discuss their new Coursera course, Making Math Click: Understanding Math Without Fear, what learning science reveals about how students learn math, and why practice and worked examples play such a critical role in building math confidence.

They discuss schemas, give some cautionary advice about using manipulatives and concrete-pictorial-abstract approaches, and explain why moving quickly from concrete to abstract matters. They describe what’s at stake when math education fails, what’s lost when students don’t develop foundational skills, and what it will take to help more learners succeed in math.

This is a practical, engaging, and insightful episode for teachers, parents, university students, and anyone who has ever felt they weren’t a math person.

This episode is also available in video at www.youtube.com/@chalktalk-stokke

Making Math Click: Understand Math Without Fear: Free course with certificate: https://www.coursera.org/learn/math-click?action=showPartnerSupportedAccess

TIMESTAMPS

[00:00:22] Introduction

[00:05:40] How Barbara’s background shaped her approach to math

[00:07:00] John’s experience with math from a young age

[00:09:21] John and Barbara’s Coursera course

[00:11:07] Who is their course for?

[00:15:45] Is the course beneficial for teachers?

[00:21:54] What math and Sylvia Plath’s writing have in common

[00:23:51] Building schemas in math

[00:26:46] Getting good at math leads to liking math

[00:31:08] Kaminsky’s research on manipulatives vs. abstract representations

[00:33:39] Fading from concrete to abstract

[00:40:30] Barbara’s article in the Seattle Times

[00:42:30] Real world consequences of innumeracy

[00:49:13] Learning math takes practice and patience[00:51:38] Societal loss from kids not learning math

[00:57:13] Failed constructivist approaches

[01:00:50] Barbara’s and John’s recommendations for system improvements

[01:05:42] Final thoughts

[00:00:00] Anna Stokke: Welcome to Chalk & Talk, a podcast about education and math. I'm Anna Stokke, a math professor and your host. Welcome back to another episode of Chalk & Talk.

In this episode, I'm joined by two familiar guests, Dr. John Mighton, founder of JUMP Math, and Dr. Barbara Oakley, bestselling author and co-creator of ‘Learning How to Learn’. I've had both of them on the podcast before, and I'm thrilled to have them back together for this conversation. We talk about their new Coursera course, ‘Making Math Click’, what neuroscience tells us about how students actually learn, and why fluency and worked examples build confidence.

We also talk about schemas, using manipulatives and concrete pictorial abstract approaches, and why fading quickly from concrete to abstract matters. And we explore the bigger picture, what happens when math education fails, what's lost when students don't build foundational skills, and what it will take to ensure more students experience success in math. I really enjoyed this discussion.

It's practical, engaging, and full of insight for teachers, parents, university students, and anyone who has ever felt they couldn't do math. I think you'll come away feeling inspired and with strategies you can use right away. If you've been enjoying Chalk & Talk, please make sure to follow on your favourite podcast platform and consider leaving a five-star rating on Spotify or Apple Podcasts.

And don't forget to follow the show on YouTube, where episodes are now available in both audio and video. Your support really helps others discover the show and join the conversation. As an added bonus today, Barb gave me a link to share with you so that you can register in their Coursera course for free, a great holiday gift for you or a friend.

You can expect the next full Chalk & Talk episode on January 9th. Happy holidays! Now, without further ado, let's get started.

I am very excited because I have two fantastic guests joining me today. So, I have Dr. John Mighton and Dr. Barbara Oakley. Dr. John Mighton holds a PhD in math. He is an award-winning mathematician, a playwright, and best-selling author. He founded JUMP Math, which is a Canadian charity that provides evidence-based K-8 math materials. And he is the author of three best-selling books, including All Things Being Equal, Why Math is a Key to a Better World.

John has received numerous honours for his contributions to math education, including being named an Officer of the Order of Canada. And that's a pretty big deal. Welcome, John.

Welcome to the podcast.

[00:03:06] John Mighton: Thanks so much.

[00:03:08] Anna Stokke: And I also have Dr. Barbara Oakley here with me today. Barbara Oakley is a distinguished professor of engineering at Oakland University and holds a PhD in systems engineering. Her work bridges neuroscience, engineering, and education.

She co-created the massively popular Coursera course Learning How to Learn, taken by more than 3 million students worldwide. She's a best-selling author of books such as A Mind for Numbers, Uncommon Sense Teaching, and Learning How to Learn. She's a recipient of several major awards, including the Harold W.

McGraw Prize, which is colloquially known as the Nobel Prize in Education. So, congratulations on that. Welcome, Barbara.

Welcome to the podcast. Well, thanks for having me, Anna. And I'm really excited to have you both here today.

In fact, John was my first guest. It's just really awesome to have you back. It's kind of like full circle.

I also have Barbara on. Since then, Barbara, I have to tell you, I have been recommending your book, A Mind for Numbers, to a lot of students and even seen some students carrying it around. So, I think you're having an impact.

I thought we'd start because you have a really great project together. And I thought we could start by talking about that. You both recently collaborated on a course called Making Math Click, Understand Math Without Fear, which is available on Coursera.

Barbara, maybe we can start with you. Can you tell us what that course is about?

[00:04:42] Barbara Oakley: Well, I think John and I both have had the same experiences, which is that we sort of blundered blindly into realising more as an adult that we actually could do math, even though we had always thought we couldn't do math. We realised that we could team up together and convey some of these very simple ideas about how you can effectively learn mathematics. And yes, you can indeed learn it even as an adult and be very successful with it.

And who better than us together to kind of convey that information and that we've been through the battle together and come out successfully.

[00:05:28] Anna Stokke: That's true. Now that you mention it, you do kind of tell a similar story. Barb, you came to math later in life.

Like I think you had a background in languages before that. Am I right? Right.

[00:05:40] Barbara Oakley: I thought I grew up hating math and science. I thought I had absolutely no talent whatsoever for it. So, I enlisted in the army and picked at random a language to learn, which was randomly Russian.

When I'm travelling in former Soviet bloc countries, that's about when it comes in handy. But actually, language learning is startlingly similar to learning the language of math. And when I was 26 years old and getting out of the military and realising that all my friends who were West Point engineers were easily able to get jobs.

But me with my profound specialisation in Slavical languages and literature, nobody was knocking at my door saying they wanted to have me. And yet there were these really interesting looking jobs out there. So that's when I opened my mind and said, you know, why don't you see if maybe you could learn it?

And actually, applying some of those ideas from how I successfully learned a language to learning in math and science, voila, they work like a charm.

[00:06:56] Anna Stokke: Very inspiring. And John, you tell a similar story, right? I've heard you talk about taking calculus and almost failing calculus, right?

And you were a writer. Do you want to tell us a bit about that?

[00:07:00] John Mighton: I think one thing that was different in my experience is that I always was fascinated by math because I read a lot of science fiction. And so, I kept that sense of wonder alive, but I didn't think I could do math. And in my 20s, I discovered through an American poet, Sylvia Plath, that I could train myself to write.

I followed her methods. And I was broke as a writer starting off. So, I started tutoring at a very low level, grade six, and I worked my way up.

And that was a revelation to me, working back through the high school material at my own pace. Things that were totally mysterious to me in high school became really obvious as I kept practising. One of my first students was told he was in a remedial grade six class, and his mom had been told that he could never learn math.

He was just too challenged. He's now a fully tenured math professor. So, seeing these changes in the students gave me the confidence that maybe I could go back.

And in my 30s, I went back and eventually got a doctorate.

[00:08:03] Anna Stokke: Really interesting. Barb, do you have anything to add?

[00:08:05] Barbara Oakley: Well, just one thing that was a revelation to me was working with John in making our course. He taught me ways of looking at math. I was like, you mean that's what was really going on there?

Here I am, more senior person, and John just taught me these simple, wonderful ways of looking at and understanding math. And everybody can benefit from these kinds of ideas. It was just a revelation.

It was so fun working with John.

[00:08:44] John Mighton: And Barb taught me so much about the brain and why the things I'd seen with students were working. But I had to learn math that way myself. Because I struggled and because I still have this insecurity, even though I'm a mathematician and I've made original discoveries, I still have this deep insecurity where I don't feel I understand things properly unless I can reduce them to steps that a child could understand, even calculus.

So, I've just spent years doing that subconsciously to train myself as a mathematician. A lot of people don't know that because they don't have the luxury, the time to go back and learn it that way. But when I was tutoring, I had to.

I had years and years to see how simple math could be.

[00:09:21] Anna Stokke: I think that sort of explains your title, Math Without Fear. So, you're trying to get the message out there that people may think that math is hard and actually it kind of can be hard. But if you do work and you learn it the right way, it becomes easier.

But people may think math is hard or they may think that they can't do math. But you're saying you can do math. Don't be afraid of math.

Is that right?

[00:09:45] John Mighton: Yeah, exactly.

[00:09:46] Barbara Oakley: And more than that is people often think that only smart people learn math. But it actually goes the other way. If you learn math, it helps make you smarter.

I remember I used to look at these engineers and I'm like, oh, you know, they must be just natural geniuses. And then once I had that training, it's like, oh, wait a minute, I'm no genius, but I can do what they did. I mean, there is a magic to it, but it's like a learnable magic.

[00:10:16] John Mighton: I remember at university when I went back, I had a huge advantage over the other students because I've been tutoring for years. I knew the high school stuff inside out, and I generally did extremely well because I had those advantages. I remember I almost failed a test once in this branch of math called group theory, and I was almost bedridden for the day.

I thought I've got to give up all my dreams and hopes. That's how deep that conditioning was. And now I'm doing research in group theory.

So, it's just having the time, spending the time and developing what we talk about in the course, these deep mental representations or schemas, building those things makes you look like a genius when originally you were struggling.

[00:10:53] Anna Stokke: I teach group theory all the time, so I hope my students haven't gone through that experience. But if they do, I'm going to refer them to your class. Let's talk more about your course.

Who is the target audience for the course?

[00:11:707] John Mighton: You know, anyone who maybe has wants to learn math for some reason at a deeper level or for a job or anything, a teacher who wants to learn how the brain works and how they can help their students, even people at a higher level in math or have any kind of insecurity or trying to learn something new that want to know how they can learn more efficiently.

[00:11:27] Anna Stokke: Are you teaching actual math topics in the class or is it more like how to learn math?

[00:11:33] Barbara Oakley: I do want to say that the ideal person who we might think of taking this course is someone who is, they're majoring in psychology, they put off that one statistics course that they have to take because they're just terrified, they hate math, and they know they can't do it. This is the course for you. And similarly, it's for parents who want to learn how to coach their kids better.

And there are ideas of mathematics and how to do specific kinds of procedures, like how do you think about division and what is really going on with division? And it turns out you can really visualise it, that's simple, and the way John explains it is like, really, that's so easy, but it's kind of a mixture of how to set your mind up and look at mathematical problems and see how to tackle them without having a panic attack and also to kind of have fun with it. And part of what is going on, I think, worldwide as far as difficulties that people have with math is that teachers are never taught how your brain really learns.

They're never really taught about the two different learning systems, one of which thrives on rote repetition pattern, which allows for pattern recognition, and the other one that thrives on explanations being given by people. If you think about it, we've been told for the last, teachers have been hearing for the last couple of decades, lecture's bad, because students create their own learning. So that means that half of the way we learn, which can be through hearing and seeing explanations, has been thrown out.

People are often taught to learn math using methods that cripple their ability to learn math, and this all arises because before, like in the last century or more, people haven't known how the brain actually truly learns. And so, we are still being taught using methodologies developed over the past century by great in education like Piaget, Vygotsky, Dewey, and so forth, who had no idea whatsoever how the brain really learns. And it's time for us to turn the page and bring these insights from neuroscience, meld them into great approaches to teaching like the ideas that John shares.

And between the two of those, you can suddenly begin to realise, oh, I can do math.

[00:14:48] Anna Stokke: It kind of sounds like a crash course in learning, like a crash course in how the brain learns math, right? Does that sound right to you?

[00:14:58] John Mighton: That's right.

[00:14:59] Anna Stokke: And so, you mentioned targeted audience. I heard you mention maybe university students who are now in a position where they have to take math, and they always felt that they couldn't do it. And by the way, that's something I see all the time, right?

As someone who teaches first year university, we have students all the time who have to take a math course or statistics, as I'm in a joint department, statistics they commonly have to take, and they're terrified to take the class. So, this would be a good course for them. And I heard you mention parents who have to help their children.

That's good. What about teachers? Some teachers probably didn't learn these techniques about how to teach math or how people learn math in their training.

Would this course be good for them?

[00:15:45] John Mighton: I think it's particularly good for teachers. You know, I've surveyed hundreds and hundreds of teachers over the past few years and said, if you're tutoring a kid in grade five, who's three years below, you're tutoring them one-on-one, what would you do? And teachers universally say, we'd go back to that level.

We'd try and find where the starting point is for the child. We'd break things into manageable chunks. We'd scaffold the lesson.

We'd give lots of practise and we'd expect mastery because we're teaching one-on-one. We would teach until the student understood it and we'd all change what we're doing if we had to, and we'd raise the bar incrementally to create confidence, but without pushing the kid too far outside of their zone of comfort. So, I say to teachers, well, that's kind of, a lot of that is in our course.

A lot of that is well supported by the science of learning. And you know it naturally already as teachers, but you've been pushed away from it in your training and in what you're being told to do often in districts, to do almost exactly the opposite of that, to throw out a rich problem, hope kids will find their level. Let some kids shine.

The other ones will immediately develop insecurities because they can't do the problems. Like you're doing everything that you wouldn't do as a tutor with your whole class, and so part of the course is to say that you, teachers can draw on what they already know about how to teach, and they can justify it using the science of learning and what we talk about in the course about the brain. They can actually say, this can work for a whole class.

This is how we can justify what we're doing. And this is a support in the science for this. Because a lot of teachers, their lives are being made very, very difficult.

They have classrooms of kids who don't love math. They have kids coming into their class three years behind universally in grade five, it's very difficult for them to reach all their students and they'd love to, and so it's really, we hope a gift to teachers where they will actually be able to teach in a way that makes sense to them.

[00:17:34] Anna Stokke: Barb, do you want to say something maybe about high school students and university students? What sort of advice would you give them? Some of the say, key scientific insights that they should know about how people learn math.

[00:17:48] Barbara Oakley: I think it's really very simple. The idea of retrieval practise, practising until things kind of come out automatically. One thing they've found, for example, Finland, vaunted Finland, a challenge that they're now having is of nursing students, for example, they've been taught, how do you do multiplication, but you don't really need to necessarily memorise the whole multiplication tables because you can always just look it up.

But it turns out that if you don't, that actually memorising the multiplication tables does much more than just give you some rote knowledge that is inflexible. And what it actually does is it helps you acquire a feel for the patterns of mathematics. It's much like learning another language and you practise a whole bunch with it.

And some of it, it's rote. You're just memorising stuff and you're using it over and over again in different ways. But that's what helps you learn to speak that language.

So, you want to be, when you are learning mathematics, what I would do is I would take a problem that I knew was a very important problem that I had the answer to that I knew was a correct answer. And then I would see it cannot have worked this problem myself and not just like do it in my head but actually make myself write it out. If I couldn't figure out the next step, I would take a peek.

But what I'd be doing is I would be letting that problem sort of whisper to me. What is the next step? What's the next step?

And then after I practise with that problem enough times, I could just look at the write-up for that problem. And in my mind, I go, oh, just like it was a song that I had sung many times, and it would unfold each step, whispering the next step to me. If you do that with a number of important problems, you can't do every problem, but let's say there's five or 10 really important problems in a chapter, you practise with them, so they become kind of intuitive within you.

And then you begin seeing, hey, wait a minute. That other problem is actually a mixture of this and that, and you start becoming much more creative with what you're learning. And students are not encouraged to do this kind of thing at all.

In fact, they're discouraged from practising too much because it'll kill their creativity. That's like saying, we don't want you to speak another language too much because it'll kill your creativity in speaking that other language. It's kind of kooky.

Again, the way that these marvellous teachers we do have are often being taught to teach cripples students' abilities to truly learn, particularly in math.

[00:21:18] Anna Stokke: I want to say that what you just explained, how you learn to solve problems in math, that's exactly how people should be doing it. We'd call that the worked example effect. One problem with students not realising that is it contributes to this idea that people think they can't do math because that's not it at all.

It's just that you're not actually being taught to like work through the problems, copy the way, the technique you learned. And then the other thing I was just thinking, this really reminds me of how John describes having learned to write by studying Sylvia Plath, right? John, it's similar.

[00:21:54] John Mighton: People talk about Homer and the days when people would memorise entire massively long poems and say, that's wonderful. It's part of your cultural heritage to know those things. So why not in math?

Like why not know something about number facts and so on? That's part of what allows you to see the beauty of mathematics. Otherwise, every day is a new day.

You're counting out again or you're counting on your fingers or whatever. You'll never see any patterns or connections. Like Plath, it was a revelation to me when I was reading about Plath.

I read her letters to her mother, and it changed my life because she did things we would never tell a writer to do now. She memorised poems and I learned from memorising poems that that puts all these rhythms and metaphors and ways of connecting things in your deep subconscious so you can actually draw on them. She wrote imitations of poems she loved, which doesn't sound very original, but you could see in her early poems, they were very derivative.

But as she learned her craft, as she learned the different forms that her experience could fit into, which people don't learn naturally, as she learned that, you could see how she was able to find a way to bring her own voice into those forms and that's true creativity. And that's what I learned from her.

[00:23:05] Barbara Oakley: Sometimes people will, poets will say, memorise the poem and you will understand it more deeply. But I say, why should we let the poets have all the fun?

[00:23:17] Anna Stokke: It's the same with piano, right? My daughter went quite high up in the Royal Conservatory of Piano and you memorise the piece because if you memorise the piece, then you can add in all the inflexions or whatever it is they do. It's important.

We've got to have these sort of basic number facts and things like that in long-term memory. And that kind of brings us to schemas because often hear people talking about building schemas in math. Barb, is that what this is?

Is this about building schemas?

[00:23:51] Barbara Oakley: Bingo, exactly. I mean, if I say to you, I go to the store yesterday, you instantly know that if you speak English, that is not quite right, and it's because you have a schema that's set up for like, you know, regular verbs and how to conjugate and you know, irregular ones, and you have a feel for when things are right or wrong, and that arises, it's like, when you practise enough, you get a feel for the relationships and what is right and what is not right, and that's all part of that schema. So, what I was doing when I was practising with my engineering problems was developing a very good, solid, rich schema where I could even take things that seemed quite different, and I could begin to see, oh, what's the relationships between them?

And I think John has good experiences with chess masters and chess.

[00:24:59] John Mighton: Yeah, I mentioned in the course that I've tried to play chess with the sharks who play on the streets in New York, and they just slaughter me, even though I'm a mathematician, you know, I can hold a lot of things in my head, think logically, I've never come close to beating them, and they're not even grandmasters, but they look like geniuses to me in chess, and that's because they played so many games, they can just look at a position and know what's a good move, while I'm plotting through move after move, and we gave you an example in math in the course, if you ask a kid in grade four, how many ways can you make 17 cents using pennies and nickels, they might get one way, and they have no way of telling you if they found all the answers, and just one simple strategy that you say, start with zero of the bigger unit, like no nickels, that's 17 pennies, one nickel, 12 pennies, and so on, they could make a chart, then they can apply that strategy across all problems, if you're finding all rectangles, a certain perimeter, and then eventually you teach them a few more strategies, like using alphabetic order, things like that, knowing how to list, if two things are happening, knowing how to make a list, if you've got two players in a game or something, then they can start solving really complex building problems where they have to count outcomes, and then they start looking like geniuses compared to the average kid who hasn't been taught those strategies.

[00:26:12] Anna Stokke: I think when you hear mathematicians talk about mathematical intuition, what it really is, it's having a lot of experience in that particular area and being able to look at a problem and say, oh yeah, I can sort of see in my head where this is going to go, and I'm going to solve it, and that comes from a lot of practise and a lot of exposure. It doesn't come out of thin air. It doesn't come from giving people problems to solve that they've never seen anything like before, right?

It comes from sort of building up to that point.

[00:26:46] John Mighton: I think in the people who don't understand that they're the ones who most naturally will give up and think, I'm not born with this ability. I heard a friend of mine told me about this kind of math education guru came to a school to speak, and they were talking about the game Sudoku, and one of the teachers asked him, well, would you give kids rigorous training in Sudoku, and the person said, no, just let them explore it, and they said, well, what if they're struggling, and the person said, well, then maybe it's not the game for them, and that's the kind of attitude I think is just rampant in education, that if you have to give the kid any kind of coaching or encouragement, if it's not something they naturally choose or are good at, then it's just not for them, and it's perfectly fine to have a classroom where you have kids who are far ahead of everybody, and other kids are struggling and anxious and nervous to even put their hand up.

That comes from this idea that there's nothing you can do about it, and teachers have this sense of learned helplessness by being told to teach in ways that create those hierarchies and create those differences, whereas if they knew how to train in problem solving, you just give kids some simple strategies, let them explore them, and suddenly they can do complex probability problems. Teachers need to see that, that that's possible with entire classrooms.

[00:27:57] Barbara Oakley: One thing in relating to this is that idea that you learn to like, I mean, things that you're good at, you naturally kind of tend to like them, but some things take much longer to get good at. It's like riding a bicycle. I mean, learning to ride a bicycle is not fun in the beginning.

You fall off, you scrape, but you can really see what the upshot's going to be when you do learn to ride. With math, you don't so naturally and easily see what that upshot is. All you see is sort of the difficulty, especially for some, of that gruelling kind of beginning to get into it.

And it takes a while before all of a sudden it starts to, oh, hey, you know, I'm pretty good at this. Actually, this is really interesting. But we don't give that kind of time.

We just say, oh, you're just not naturally good at it, so give it up.

[00:29:00] John Mighton: Yeah, that's a really good point. And so, I do a lot of demo lessons, including in behavioural classes. Sometimes it's kind of frightening sometimes going in with kids you've never met, and especially if they really turned off math, but I found one technique that really works to deal with the problem Barb just talked about.

If they can do anything, I try and give them a question that looks harder, but it really isn't any harder. I mean, if they can add a quarter plus a quarter in grade three or four, they can add a quarter plus a quarter plus a quarter, and to an adult, that seems like just a trivial generalisation. But to a kid who's never seen that, that looks like a harder problem.

You give them a string of fractions with the same denominator, throw a minus sign in and say, I'm going to trick you. Kids love to be in the zone where they're being stretched a little bit. And if they can do that in front of their peers and all meet these challenges together, the excitement is magnified.

And so, I think to deal with the problem that it takes a while often to see what the payoff of the math is, you can keep kids in that zone where they're constantly stretching themselves a bit using what I call bonus questions. Just make it look a little harder, and then you can create a continuum because then you can actually make it harder and harder, and it's like a ramp for the kids, they all start to want to go up it.

[00:30:10] Anna Stokke: Yeah, it's what we call induction in math. You know, eventually you're doing the hard problems, but just sort of small steps. I think I'd like to shift because I would like to talk a bit about representations in math, so concrete, pectoral, abstract, that approach to teaching math, because I get a lot of questions about it.

And John, I know you talk a lot about this. I've seen you speak many times. I've seen Barb too, and I recommend to people listening, if you ever get a chance to see either of these two, give a presentation, you've got to go because they're both great.

But John, I've heard you talk about Jennifer Kaminsky's work many times, and there is a widespread belief that children must start with concrete objects when they're learning. I'm just curious, how accurate do you think that is based on what we know from cognitive science, and where does Jennifer Kaminsky's work fit in?

[00:31:08] John Mighton: Yeah, so that's a really complicated question, and the answer is complicated, but the problem is people right now have too simple an answer. They think in any situation, even for older kids, if you want to teach them how to solve applied real-world problems, always start with some highly contextualised, detailed, lots of details, usually often lots of texts in the word problem, some kind of relevant problem, or they call them authentic. It's hard to argue against that because the opposite would be inauthentic.

First of all, if you look across North America, that has not been working because test scores on test problem solving ability are flat or declining. So, it's clearly not working. And one of the reasons is Kaminsky found that sometimes, especially for older students, it's better to start with a more abstract representation where you strip away all the details.

When we teach part hold problems and JUMP, rather than giving them problem after problem, we give them grids where they just shade in squares to represent the amount, so we talk about this in the course, and strip away any barriers in the language, you could just talk about green and blue marbles for the whole lesson, and the kids can learn all the different types of problems. There's a number of different part hold problems. You might have the total and the difference or the total or the two parts.

So, by stripping away all the irrelevant things and all the distractors, kids learn much better and they see the deeper structure. The surprising thing is Kaminsky's done work right down to a preschool level. If you want to teach analogies, it's often better to use more generic or less appealing, like representations, because the kids get caught up, if it's a toy, they'll get caught up in the fact that it's a toy.

In grade two, she did work where she found that kids who were taught fraction concepts with colourful flowers, with petals and so on, did worse at transferring the knowledge to new situations than kids who were taught with grey and white circles, and that flies in the face of what teachers are being told, that the more engaging the thing is, the more authentic, the more it's related to their life, the better.

It's not always the case. So, kids should generally start with some kind of concrete instantiation, especially when they're younger. But often as they get older, it's better to start with a more abstract or generic representation.

[00:33:16] Anna Stokke: It kind of reminds me, I was speaking to a neighbour once and they were high school teacher and they taught geography and somehow, they ended up in a situation where they had to take over this class, and it was a middle school math class. And the way he put it to me is, the previous teacher had an unnatural affinity for manipulatives. And he said, I had to use all these manipulatives like algebra tiles and base 10 blocks, and he said the kids were just building things.

They were playing with them. So, he said, I stopped that immediately.

[00:33:39] John Mighton: It just didn't work. So can I just add one more thing, because your question is so complex. It turns out also in cases where it's better to start with a concrete instantiation or example, there's research also showing it's good to fade quickly, to fade as quickly as possible to more abstract representation.

An example of that, there's no problem with algebra tiles if they're used well, but kids can be playing with them, arguing over who had what colour. So, I do a game where I put a bag on a table at the front of the class and a couple blocks on another table. I put some blocks and I say, there's the same number of blocks on each table, what's hidden in the bag.

And that grabs kids' attention. Then I go to two bags and so on. They get quite excited.

But very quickly, I moved to just drawing a square for the bag and circles for the blocks on the board. And the kids can copy that onto their whiteboards and hold them up so I can see everybody. Within 15 to 20 minutes, they're working with way more abstract representations.

And then I can give them way more problems and more challenging problems. So, I do start in that case with a concrete instantiation, but they're not have to touch it because they've seen blocks, they've seen bags. They can all understand what the problem is just by me demonstrating it.

And then we quickly move to more abstract representation. Teachers aren't aware of that research. I don't know if I've met any educators who are aware of Kaminsky's work and it's been published in Science Magazine.

It's like as if phonics never made it into the school system. Like no one was aware of phonics.

[00:35:10] Anna Stokke: I think sort of what you said there, the fading part is a part that's getting missed. I think that sometimes people think that there's this part that has to be mastered involving concrete objects. And the thing that you actually want the kids to master is the abstract, right?

Like that's the part that they have to master. That's the part where they have to get the practise. You know, if you want to introduce something using manipulatives or concrete objects, like first of all, keep them very simple, like you said, basic chips, no flowers, no dinosaurs, things like that, because they're just distracting.

And then move quickly because you really do want to get to the abstract. That's just my take on it. But I will post some articles that you've mentioned from Kaminsky.

[00:36:00] Barbara Oakley: But psychologists have really, they're supporting everything John is saying. So, if you learn with a concrete set of manipulatives, it's like part of your neurones that are learning the concept are also sort of learning that it's related to this particular set of manipulatives.

And it's hard to like rip it away because it's affiliated in your mind. But more than that, we have to remember, why do we get manipulatives? Because people sell them to us.

Why do people sell them to us? Because they make money from manipulatives. And math is a mental sport and everyone who is trying to sell manipulatives is not necessarily, you know, they may in their mind be thinking, oh yeah, we're here to help students and so forth, but really, they're to make money for the company that's selling manipulatives.

When you have a Google scholar come and talk to you, what are they ultimately going to be kind of implying? You can always just look it up on Google, of course. Manipulatives are really; you have to be really careful in that they're often oversold because they're something that can make money.

An abacus, a simple abacus, it has been proven through dozens of generations. It teaches math really well. And it teaches it in a way that people first learn something that they can get their hands on.

But then, so for example, with flash-ons on, you learn how to use the abacus, but then you're taught to kind of put your hands away from the abacus so that you begin using your mind only, people want to be looking at manipulatives, not the way they are currently seen as concrete, tangible things, but rather does that manipulative allow for people to start like easing away and turning it into a mental sport like an abacus can do?

Because everything in mathematics, it's ultimately that's the mental sport. And we even want to have manipulatives that drive us towards that.

[00:38:38] John Mighton: That's a really great point. I can follow up with a couple of examples. First around conquering is fading.

If you do want the kids to play with tens blocks and one’s blocks, which is fine. Why not fade quickly? I say to kids, I've got a secret code.

This line is a tens block, a dot is a ones block, and a square is a hundreds block. The kids think they're little code breakers. They've suddenly moved away from having to use manipulatives and now they can represent anything.

Or if you're teaching division, if you can draw circles for the groups and dots for the objects, you can take any word problem and get a visual representation that you can carry around in your head also. And like, I think it should be a right of kids to be able to roam the universe with a pencil and paper sitting at their desk. I mean, that's Einstein discovered the deepest laws of the universe sitting at a desk.

That should be a right of every child. And the people who think the only way it root is through endless play with manipulatives, I agree with Barb, they're making money off it. I'm not saying manipulatives aren't helpful for some things, but the faster they develop a mental representation and can work with pencil and paper, the better.

[00:39:39] Anna Stokke: I definitely agree with you. I'm glad we had that discussion. That was rather interesting.

And I'm going to post those articles. So, I thought now we'd shift to Barb's Seattle Times article. And this was just a fantastic article that you recently wrote.

This was in the Seattle Times, but realistically this could apply anywhere in North America. And probably I have a lot of listeners from Australia and New Zealand too. So probably there as well.

And it was titled, Washington math education is in crisis. Here's what could help. And you write that many classrooms emphasise conceptual understanding over getting the right answer, rewarding explanations, even when the answer is wrong.

And so why do you see that as a problem?

[00:40:30] Barbara Oakley: I just got out of the hospital with deep vein thrombosis from travelling and travelling and travelling. And I really, for some reason, like it when a nurse can calculate out the proper dosage of medication for blood thinner, that will not kill me. Now you might think, well, duh, isn't that their job?

But as it turns out in some countries that have emphasised constructivist student-centred approaches, where you can always just look things up. If you mistype something in a calculator, a nursing student doesn't catch it. Like if I say to you, 12 times 12 is 299, something inside you and John recoils and says that is wrong.

But imagine a person who has not internalised the multiplication tables. There's nothing inside them. When you mistype something, it's like, looks pretty good to me.

And then off they go. And they inject me with something that I could end up not being here today. So, I am a bit believer in the right answer actually matters.

And I bet you that anyone who sits there and goes, they can always just look it up. Probably would want a doctor and a nurse who could do fundamental calculations themselves. And they really just haven't thought about it that way before.

[00:42:14] Anna Stokke: Everybody's concerned about real world problems. And I mean, you just mentioned some real-world consequences of not being fluent in basic math, right? I mean, it should clearly be an issue.

John, did you have something to add?

[00:42:30] John Mighton: Yeah, I can give you an example. The teachers are my absolute heroes. They're not respected enough.

But many teachers will admit that they don't understand the math. Well, they don't have resources that they can actually learn the math from. And so, we do a problem-solving session with teachers where there's a town with four girls for every five boys and there's 36 kids.

And this is from a provincial test before people were sensitive to gender. So, we use it. But the assumption is all only girls and boys in the town.

We asked teachers like, what's the fraction of girls? So, four girls for every five boys. And some teachers are very proud to say 80% or four over five, because they don't understand they've got to find the hole.

There's nine kids, four of them are girls. And it just shows that if you've become afraid of math or haven't had access to it, you're not even thinking because it couldn't be 80% because that's more than half, like it's four to five, there's less than half the kids are girls. So, some teachers have developed this just as guessing instinct.

They'll do a calculation or something and they won't even try and estimate or have any sense of whether it could be right or not. And then they pass that on to their students. And not only is that a threat to people who are going to the hospital, it's a threat to our economy, but it's also a threat to kids' development as human beings.

We think it's natural for kids to graduate. We think kids were stunted if they didn't see any beauty in a mountain or a star. But we think it's natural for them to graduate from high school and have no idea of the invisible beauty of the world that you can only see through mathematics or science.

And it should be a right of them to actually know four to five, it's actually four ninths are girls. That should be a right of every child. And it's not just a rote thing.

It's, it opens up a world of wonder to them that they can't see unless they have the mathematics.

[00:44:22] Barbara Oakley: You know, I think part of all of this has arisen because back in the day, let's say 80 years ago, there was a lot of practise and that was a big part of how people were thought to learn. And indeed, it really is part of how people learn. It can be really boring, and it can turn people off.

And so, I think well-meaning educators went, you know, all this extra practise and this rote memorisation, we'll get rid of that, and they'll find math more fun. And so, it was all for good intentions, mostly I think, but it's just that they had no idea how the brain really learns. And they didn't realise that they were throwing the baby out with the bath water, that you can't have your cake and eat it too.

Sometimes you just do have to have some practise and so forth. And I'm not saying that means that every child's life needs to be this endless rote practise, but 20, 30 minutes of practise with math and with other critical topics that helps develop that automaticity and fluency that is essential to become an expert in virtually anything.

[00:45:45] John Mighton: There was a great article in Science Magazine, Nature Communications, about six years ago, called the 85% zone for optimal learning. We talk about it in the course. 85 is an exact number, but it turns out we're happiest as learners and we learn most efficiently when we've almost got something, like we're about 85% proficient, we have to stretch ourselves a little bit.

And also called the Goldilocks zone, not too easy, not too hard. And so, I've literally taught tens of thousands of children across the world in demonstration lessons. And it's the most universal phenomena ever, that when you keep them in that zone, especially when they're in a group, they get really excited and they will choose to work, and they'll choose to practise.

They actually think the practise is fun, but it can't be too easy. You've always got to be stretching them a bit, but you can't push them outside that zone because then they also don't like it and they start misbehaving and distracting class. We're not taking advantage of that.

And Barb actually told me, I learned so much from the course about the brain, but Barbara actually told me that when you're in that zone, you're actually even getting a dopamine reward. Like we are wired to love to be in that zone. As a playwright, the one thing I bring to this is I see the kids as an audience, and they'll never get more excited than as a group.

And if you can take away the hierarchies in the class and the anxieties and let them all stay in that zone together, you get what Durkheim called collective effervescence. We never feel anything more intensely than as a group. And so, we throw away that advantage when we don't keep kids in that zone, and we don't allow them to show off in front of their peers.

We're not exploiting the way the brain works and the things that I learned from Barb in the course of doing the course.

[00:47:21] Barbara Oakley: There's something else that John does that I think is kind of magical. And what's cool is we can understand the neuroscience now of why what he's doing is so successful. What he will do is he will just ask a seemingly simple question.

He might have a good visual and be pointing to something, but he'll ask a question. There's 100 trillion possible connections in the brain. So even if you're focussing kind of on one problem, you're talking about millions of potential connections, almost all of which are wrong.

When John asks a question, what he's really doing is he's narrowing that high dimensional set of possible answers to a much more tractable space where students can suddenly begin to see before they were just like, I'm lost, I have no one. And then John will ask a question and they'll begin, they're in that 85% space. So, they're looking around, but it's a much smaller space.

And here's the real magic is he makes them think they found the solution. And they did, but he cleverly narrowed that space so they could see where the solution was with a little bit of looking around. So, they got that practise that in looking around for solutions, which leads to creativity, but they also got that aha dopamine hit of, oh, I got it.

It's actually John leading them there to think that they did it themselves, but it all works, that's great teaching.

[00:49:13] John Mighton: We make this mistake also, that zone, the 85% zone, it has a very narrow diameter with novice learners or kids who are learning something for the first time. You have to make sure you're only varying one or two concepts at a time or skills. But the other thing people, the big mistake is we keep mistaking the end where we want to get kids to.

We want them to be resilient, struggle with rich problems. Yeah, that's great. If you keep them long enough in that zone, it starts to expand and they can handle more steps or variations.

They can struggle more, but the vast majority of kids need to be kept in that zone for quite a while to develop the confidence and the schemas and the knowledge they need for you to expand that zone, but constantly the biggest mistake we make in education is when I hear people talk about 21st century learners or we have to develop resilient problem solvers, I know we're in trouble because they're going to start by overwhelming the kids rather than having a more gradual path to that. If we've done studies in JUMP where kids have done better in problem solving, but when people look at our materials and see how gradual the development is, they think, oh, that's not possible because they keep mistaking the end where you want to get kids to for the method to get them there. Novice learners need a lot more support in scaffolding than experts do.

And those teachers are being forced to teach their classes like they're experts.

[00:53:33] Anna Stokke: And you have to be patient. Learning takes time and getting good at math takes time. And you can certainly waste a lot of time if you are giving students problems that they're not equipped to solve.

We have to do this the right way and then we can get there. I wanted to mention something else to you, John, because I thought of you a couple of weeks ago and I recently was at an event and what was happening at this event is the findings of a human rights investigation into how reading is taught in Manitoba were being presented. So similar, you had a similar report in Ontario.

And so, the investigators were talking about some of their findings and talking to students and parents. One of the investigators said that the most tragic part of failing to teach children to read is really the enormous loss of human potential, like all the contributions that those students might have made if they'd been properly taught to read. So, do you see a similar loss of human capital from failing to teach math well?

[00: 51:38] Barbara Oakley: You know, I mean, really, as I mentioned before, it's not just that smart people learn math, it's that learning math makes you smarter. And every time I go to a university that's trying to get more people to pass math courses and so forth by dumbing down their material, and they don't realise that they think they're doing a favour for students and what they're actually doing is making dumber students. Because math helps you.

It's like a cognitive exercise. And I mean, there's even some good theoretical underpinnings to underscore the idea that if you have some kind of cognitive damage, say from a concussion or something, one of the best ways to work on it and try to start getting things back in order is do math because you're sort of reestablishing critical circuits for cognition. I think math is quite beautiful and it's really important, but it's also really important for societies in the modern day to have well-educated population that isn't so easily hornswoggled by people who come up and say, yeah, you can just kind of, I don't know, excuse my French, but bark your way into whatever budgets you want and it sounds believable if you don't know math.

There's just so many ways to mislead people and so forth when they don't have a good cognitive underpinning in this vital life skill.

[00:53:22] John Mighton: I was invited to give a talk to the Education Writers of America last year in Texas, and one of the academics there said that if you don't get some kind of college level certification within six years of leaving high school in Texas, you have a less than 20% chance of earning a living wage, which is just frightening. And they also said that the number one barrier to getting any kind of college certification, whether it's community college, university, is the math courses. We did a study at one community college where the kids had trouble even getting into carpentry, into culinary arts, because they couldn't pass the math courses.

And so, there's a huge economic drain, but I care less about that. I mean, that's very important. But as Barbara said, we have a population that doesn't understand risk, doesn't understand what's happening with the climate or these financial disasters that keep happening, but then even deeper, the math, as Barb said, rewires the brain.

It builds your ability to focus, to concentrate. There's even evidence now it builds executive function in the part of the brain that strategizes and plans and so on. And then the deepest loss to me is I once taught a behavioural class in Brixton in a very violent school, grade six kids, and I just taught them how to read binary codes.

And if you can count on your fingers, you can read binary codes. But the kids thought they were a little code breakers, like they wanted longer and longer codes. And they figured out how to go backwards.

They could go from the code to a number and the number backwards. They figured that out themselves. And then it did a mind reading trick and it's connected to the code.

And when the kids figure that out, they all want to come up and do the mind reading trick. And within three lessons, these kids are cheering when we're coming in for math and they're the most violent kids in the school. Like that is the biggest tragedy to me that we just throw these kids away.

We're born with this sense of wonder that they lose through failure. That's just a tragedy.

[00:55:09] Barbara Oakley: In Taiwan in the 1990s, they did an experiment where they brought constructivist approaches to teaching math. And within six years, it was an absolute disaster. No, Taiwan is right next to mainland China.

And so, they can easily do a comparison. And when their students are falling behind, they really are aware of what's happening. Of course, constructivists said, you just didn't do it long enough.

You didn't do it right. It, you didn't put enough money. There's, I'm working on a paper now on the non-falsifiability of constructivist approaches because there's always excuses.

But the thing is, so Taiwan just said after six years, they were like, that's it. We were going back to traditional approaches. New Zealand, on the other hand, they just sailed ahead for 30 years.

Now you compare those two countries. Now, Taiwan is, they have plenty of well-educated populace. They have some of the best fab labs in the world, and it's easy to find people who can work in a very highly, you know, it's a very analytical environment.

In New Zealand, on the other hand, they cannot even find elementary school teachers to teach because they're so afraid of math. So, what happened was Taiwan kind of got rid of this before the entire generation was kind of washed away. But New Zealand didn't.

And those two countries have such different trajectories.

[00:56:57] Anna Stokke: It, it's really sad to see. I think they're trying to make changes now in New Zealand though, right? They're bringing in some big curriculum changes.

And certainly, there's lots of changes in Australia too, from what I understand.

[00: 57:13] Barbara Oakley: You know, think about it. If you're a teacher and kids love how you teach, you're going to say, hey, but my kids love how I teach. Now, the thing is, it's like me going up and teaching kids air guitar.

They get on the stage, they clown around, they have a lot of fun. They applaud each other and they love it. And when I asked them about how I'm teaching guitar, they go, oh my gosh, I just love how we're learning it.

They're actually not learning guitar. And it's often quite like that for math. You know, teachers will say, oh my goodness, kids just love how I do it.

[00:57:51] Anna Stokke: But they're not learning math. I've heard you say that too, John, that it seems like people think that you make people like math by teaching math that doesn't actually involve math, right?

[00:58:04] John Mighton: Yeah, I think that one thing I learned from Barb and some other researchers, a lot of educators think that you do anything you can to get kids engaged in math, let them do a skateboarding project that involves some math or something. So, they'll eventually have success. And researchers like Barb have said that the arrow actually goes much more the other way.

If you have success at something, which Barb said earlier, if you're good at something, you like it and you'll naturally engage in it. And so, we're doing everything but giving kids success at math, learning it deeply.

[00:58:35] Anna Stokke: And you don't have to like everything at every moment all the time, right? That's another problem in my opinion. There's a lot of hard work sometimes to get to a point where you're good at something, and if we rogue people of that, if we rogue kids of the opportunity to see that, that you do lots of hard work or practise, and at the end, look, look how much you've learned, like, look how much you've gained, you know, we're really robbing them of something when we take that away too.

[00:59:04] John Mighton: I agree with that. And kids have to learn the power of practise and that it can be gruelling and so on. But I have a weird take on that with math.

So, Andrews Erickson, who wrote the book Peak, who did a lot of the research on deliberate practise, he said, even though deliberate practise can turn you into an expert in spectacular ways, he said, many people won't do it because it's gruelling, lonely, takes a lot of time. So, in the end, it's turning all things being equal, I argued that that's actually not the case in math, because when you let kids succeed in math together, they actually love it. And they'll actually beg for more work.

It takes the gruelling out of it. And then there's tonnes of time in school. If you use the time well, like kids could be doing calculus or very advanced math by grade nine, if the time was used well, and it's not lonely and there doesn't seem to be a cutoff like in basketball or some experiments that they've done on perfect pitch.

If the kids aren't taught these techniques by age seven, it's hard for them to learn perfect pitch. Or if you're very short in basketball, you generally won't be as successful. But I've never seen any barrier in math at any age.

Like there's no cutoff to math. It's accessible to every brain. So, all the things that make deliberate practise hard, math is actually the ideal subject for that.

And we could see that instantly if we changed the way we taught math, that kids could be practising at a very deep level and having a lot of fun daily. If we would just turn more to the science of learning.

[1:00:26] Anna Stokke: You've both spent years studying how students learn math and what actually works in classrooms. So, let's say you have the ear of every education minister in Canada or the U.S. or whatever you call them in the U.S. or every superintendent, say the teacher preparation programmes. What are the key changes that you'd urge them to make?

Barb?

[1:00:50] Barbara Oakley: I'm going to punt on this one because the answer is so obvious is point them all towards JUMP Math. That's kind of what I do too. Yes, but really, I mean, John has got some wonderful approaches together.

We've given a good sense of the underlying neuroscience, which shows why these approaches are so effective. And I think the path forward is really quite clear. I couldn't recommend John's approaches and JUMP Math more highly.

[1:01:28] John Mighton: If you're not doing better, if things aren't, and I mean a lot better, I don't mean just having a few more kids pass the state test, but if almost all your kids aren't thriving in math, then you got to ask why. You have to ask, do you have the right consultants? Do you have the right leadership?

Do you have people who know something about the science of learning? Are they compromised by having taught the same thing over and over again or being gurus or whatever? And then finally, why are you only running one programme always?

Why do you just adopt and dump one programme on teachers without ever testing it? Run several programmes and try and pick some programmes that are aligned with the science of learning and actually run them properly. If you're not doing better, then it's not the kid's problem.

It's your problem because the kids can learn math.

[1:02:11] Barbara Oakley: I think one important point to add is that major meta-analyses have shown that in education, 0.13% of all education studies are replicated. That means like nobody ever really goes and checks when somebody publishes something without naming names. There are so many shysters out there who come up with these things that sound really good.

And hey, they got a published study that shows it and they can even be very famous and well-known. And yet when you really look, there's a lot of very well-placed criticism. And so just be very, very careful because there's a lot of stuff that sounds great that from people that are really well-known and they actually are kind of the road to perdition.

If you really care about your students' success.

[1:03:16] John Mighton: With the research ed movement driven by teachers, I'm starting to meet people who are running pilots and they're finding ways to really improve education. And it becomes a grassroots movement among teachers, among consultants. Like my recommendation is look to that movement and see what people are doing in that movement, because I'm very optimistic, never been more optimistic about education since I've seen what's happening in that movement towards the science of learning.

[1:03:44] Anna Stokke: Were you more optimistic than you were when I met you, which was about 15 years ago?

[1:03:51] John Mighton: Oh yeah. I couldn't help it. That was a dark time.

[1:03:54] Anna Stokke: Yeah.

[1:03:55] John Mighton: As you recall.

[1:03:56] Anna Stokke: I do remember that. And I was just kind of getting started and I was really keen and I was very optimistic. And you were saying, no, you're not going to get anywhere.

It's just, it's impossible. I do remember that. And then I kind of ended up being like that because over time, you realise that it's pretty tough to make changes and to get people to see that there are some serious problems.

And you mentioned replication and it's more than that. I mean, there are programmes used in schools. There's no been no study on that programme at all.

And you might be told that there's a study on that programme. And then you look at the study, and the study didn't actually measure learning. Like it didn't measure whether anyone learned.

Anyway, is there anything else you want to add?

[1:04:42] John Mighton: We've sprung and partly your advocacy has been part of my optimism. Like, I mean, this podcast, for instance, and this growing movement of people who want to try to do better. I'm really much more optimistic now.

[1:04:55] Barbara Oakley: Think about medicine and where medicine was 200 years ago. You couldn't even get surgeons to wash their hands because they were clean and they knew that they knew how to do it. But you look at medicine today and for all, it's a difficult field.

But I would be much happier being under today's medical care than 200 years ago. I truly believe that right now in the field of education, we're sort of like medicine was 200 years ago with a lot of quackery and a lot of stuff, but that we are, as John, as you're both saying, turning a corner and people are becoming aware that truly there are problems and that actually these educational surgeons, so to speak, really do need to wash their hands. And because people outside of education are becoming so aware of the problems, I think it is finally beginning to foment much needed change.

[1:06:02] John Mighton: You said we had a researcher at SickKids Hospital. We did a randomised control trial with them, said you should write a play about that Doctor Barb just mentioned. And so, I did some research and it turns out historians think the number one reason people didn't believe that doctor, even though he did experiments where he showed he could bring down the death rates, is because doctors would have to admit they were harming their patients.

Subconsciously, they just could not. They could explain away his data. And so, we all have to be aware of that in education.

That's why change is so slow. If all kids can learn math and you're a teacher and you're thinking, well, not all my kids are learning math. You might think, what have I been doing to the kids all this time?

But heroic teachers will then say, well, I've got to try something different, even though I may not have served my kids in the past. I've got to change as quickly as possible because all kids can learn math.

[1:06:54] Anna Stokke: Thanks to both of you for all the work you're doing. And that's my reason for optimism is because of people like you. I really enjoyed getting to know both of you.

And I loved hearing about your course today. And I'll put a link to that, too, on the resource page. So, thank you so much for joining me today.

It's been a pleasure.

[1:07:18] John Mighton: Thank you so much. Thanks for the work you do.

[1:07:20] Anna Stokke: Thank you.

[1:07:22] Barbara Oakley: Thank you.

[1:07:23] Anna Stokke: All links are in the show notes and check out my website, annastokke.com for more information. This podcast is funded by a grant from La Trobe University and from the Trottier Family Foundation through a grant to the University of Winnipeg to fund the Talk & Talk podcast.