Ep 7. How to excel in math and other tough subjects with Barbara Oakley
This transcript was created with speech-to-text software. It was reviewed before posting, but may contain errors. Credit to Jazmin Boisclair.
Ep 7. How to excel in math and other tough subjects with Barbara Oakley
[00:00:00] Anna Stokke: Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor and your host.
You are listening to episode seven of Chalk and Talk. My guest in this episode is Dr. Barbara Oakley. She is an engineering professor whose work focuses on the complex relationship between neuroscience and social behavior. She's an expert on learning tough subjects, and she has written several books for educators and students that detail science-based techniques for learning.
This episode will be useful for teachers, post-secondary instructors, students, parents, and anyone who wants to become better at learning math or other subjects. During the interview, we discuss learning techniques such as chunking and deliberate practice. We explore why being a slower learner may not necessarily be a drawback, and we consider whether it's possible to catch up on math skills later in life.
Dr. Oakley shares some effective study techniques and offers strategies for overcoming procrastination. My website includes an extensive resource page for this episode, and I really encourage you to check it out. Dr. Oakley's work on helping students learn math and science is truly inspiring, and I'm excited to share our conversation with you. So without further ado, let's get started.
Anna Stokke: [00:01:38] I am delighted to introduce my guest today, Dr. Barbara Oakley. She is joining me from Florida. She is a professor of engineering at Oakland University. In addition to having three engineering degrees, including a Ph.D. in systems engineering, she has a B.A. in Slavic Languages and Literature. She co-created and teaches with [00:02:00] neuroscientist Dr. Terrence Sejnowski, a MOOC - that stands for Massive Open Online Course - offered on Coursera called “Learning How to Learn: Powerful mental tools to help you master tough subjects.” That course has been taken by more than three million students.
She is the author of more than 10 popular books, including A Mind for Numbers: How to Excel at Math and Science, Uncommon Sense Teaching: Practical Insights in Brain Science to Help Students Learn - that's a great book for teachers - and Learning How to Learn: How to Succeed in School Without Spending All Your Time Studying; A Guide for Kids and Teens, and many others.
I think we have a lot to talk about today. Welcome, Barbara. Welcome to my podcast!
[00:02:46] Barbara Oakley: Oh, it's such a pleasure being here. I'm so glad to meet you.
[00:02:51] Anna Stokke: I'm glad to meet you too. Your career progression is quite intriguing. How did you go from studying languages to [00:03:00] studying engineering?
[00:03:01] Barbara Oakley: I always wanted to learn another language, but I didn't hang around bilingual folks. It's different in the US than in Canada, where there's this nice, healthy enjoyment of having two languages, and I couldn't really find a good way to learn another language except to join the military, and I'd actually get paid to learn another language.
So I went to the Defense Language Institute right out of high school and learned Russian. I just picked it really at random and spent about a year and a half learning it, but then went on and got my first degree. I was lucky enough to get an in-service ROTC (Reserve Officers' Training Course) scholarship that allowed me to go and get my first bachelor's degree in language, in Slavic languages and literature.
But then I went on, I spent some years [00:04:00] as a signal core officer, and I found that I was working with all this technology, and I had no idea how it really worked, but boy could I ever see that there was a lot of potential and I felt so inadequate always playing catch up because I didn't really understand anything about the technology.
So when I got out of the military at age 26, I decided to see if I could change my brain and actually learn in math and science, which I always thought I could never do. There's this uncanny similarity between learning well in language and learning well in math. And it took me years to kind of uncover why that's true, and that's actually due to the pioneering work of neuroscientist Michael Ullman who has really shown that [00:05:00] importance of learning through that habitual system, which is how we can speak a language intuitively and do math problems intuitively. And that's quite different from the normal way that math is often taught through that declarative pathway so that you're consciously aware of everything.
You actually don't want to be consciously aware of everything because that'll just bog you down. And indeed, many of my colleagues who've grown up educated in systems such as those in India or China or the Middle East, where there's some emphasis on that, those habitual pathways of learning. They look at scans and at some of the techniques used to teach math in Western countries because they know it's antithetical to really producing someone who can intuitively and [00:06:00] easily grasp many of the deeper conceptual issues that challenge us as engineers and scientists and mathematicians.
[00:06:10] Anna Stokke: It's an interesting story, and we're going to get into some of these techniques today. So I recently read your book, a Mind for Numbers: How to Excel at Math and Science and wow! I mean, as someone who's taught math for many years, a lot of this just really resonated with me, and I really wish I'd read it earlier because I think it would've helped me to help my students.
Anyone who teaches math or anyone who wants to or needs to learn math should really read this book. And the book draws on insights from neuroscience and cognitive psychology, but you also connected with hundreds of math and science teachers and professors, people who have learned math and science and become successful at it, and when you were writing the book, you connected with all these people.
So I'd like to discuss some of your recommendations, and [00:07:00] I think a good place to start is with the two modes of thinking that you discussed. Can you explain the two modes of thinking and why we need to take those into consideration when we're learning math?
[00:07:12] Barbara Oakley: Oh, that's such a foundational question. For me, when I was a kid, my father was in the military. He was a veterinarian, he loved animals, and we moved all the time. So what that meant was, well, mathematics is very sequential, and so when we moved from Texas to - and it was a rural school in Texas - to a school right near MIT in Massachusetts, and I was seven years old, they were suddenly way far ahead of me in the multiplication tables. And I just thought, well, “I don't have the math gene. I can't do this kind of stuff like these kids can.” And part of what I didn't know was about those [00:08:00] two different pathways that we used to perceive the world. And the first pathway is that very logical, okay, you do this, and then you step forward, and this is how you solve a math problem that's relatively straightforward.
And people think that you usually only learn by using this focused, declarative, step-by-step, sequential way of learning - and that is a very important way we learn. That's a way we learn through declarative explanations. And that learning takes place largely through the hippocampus.
So the hippocampus serves as this conduit, a pathway for us to deposit facts and information that we've learned in long-term memory. But there's this [00:09:00] completely different pathway that we can use to get information into long-term memory, and that's through that basal ganglia, what's called procedural or habitual system.
And this system learns kind of like a big-picture way. You do a lot of problems, and it kind of gets us an intuitive sense of when you see a problem; here's what you say or what you do, here's how you handle it. It's actually quite a different way of learning than through that declarative system, but this way of learning takes a lot of time, and it's also involved in just kind of stepping back and getting a new idea about things.
So oftentimes, when we're trying to learn something, we need to sit down, focus, try and use that declarative pathway. And when we get [00:10:00] stuck, we need to stop; get our mind off it. Because as long as we keep our mind on it, we're stuck! We're going to stay in that same place.
But if we get our mind off it, go do something completely different or take a shower, take a nap, or go to sleep for the night, go have dinner - something very different - what that does is it allows this different default mode network, or what I call diffuse mode, to grapple with the information in the background and make sense of it so that later when you return to focusing, suddenly it makes sense.
Well now, I didn't know this at seven years old. I would just sit down, you know, march right onto the material, focus on it, and couldn't figure out a problem. So I just would give up and say, I, you know, “I just can't do this. I'm obviously not talented at math,” and what I needed to [00:11:00] do was simply put it away for a little bit and then come back to it.
People don't all learn in the same way, and in fact, many people just need to go back and forth a couple of times. They focus, get stuck, get frustrated, step back a little bit, then return, and that default mode network will do a lot of really deep thinking in the background. Now you might think, “Oh no, it's only the smart kids. The smart kids can go right through focusing without even needing to really go to default mode network very often.”
Well, the fact of the matter is faster learners often jump to conclusions, and when they're wrong, they can find it difficult to change and admit their error and get themselves back on the right track.
So [00:12:00] slower learners like me, I didn't know it at the time, could have an advantage. And that advantage is, although I'm slower, I'm more flexible, and I can sometimes see errors that those fast learners jump right over. So even though I'm learning more slowly, I can learn more deeply.
Sometimes I equate it to some people are race car learners; they get to the finish line really fast. Others are hiker learners. They can get to the finish line, but it's much more - it's much slower. But think about what that hiker experiences. They can reach out, touch the leaves on the trees, hear the birds in the air. They, it's a completely different experience and in some ways far richer and deeper. So being aware of those two pathways of learning [00:13:00] is important to teach students even early on because it gives them, it gives them hope. And it also acknowledges that sometimes the best way to get past that frustration of something you're working really, really hard on and you can't figure out is to let go. Because that's what will unlock that other mode that can do that problem, help you with that problem-solving.
[00:13:29] Anna Stokke: Wow. I really like the way you broke that down, and I'm quite familiar with this as someone who's learned a lot of math, and I'm still continually learning math. That's what we call aha moments, right? When you walk away, you walk away from the problem, and later you're in the shower, and you have this great idea.
If you've experienced it enough times and when you've taken a break from a tough problem, and maybe you move to a different problem, and you come back to it, and you're gonna have better ideas, then you know that this happens. [00:14:00] But I think sometimes, you're right, I think that students think that if they don't get the problem right away, that means they're never going to get the problem. And another thing you mentioned there that I, I want to talk a bit about because I know this very well as someone who's worked with many mathematicians over my career. There are some people that come across as really quick. So there are students that grasp concepts really, really quickly.
And, you mentioned in the book that sometimes that means that those students actually have really strong working memories. But being quick is often equated with being clever in mathematics, and students who don't grasp the concepts as quickly notice these really quick students, and it can be really intimidating.
And I mean, as someone who teaches and I'm at the front of the room, I kind of see what's going on, and it's sometimes those students who don't grasp things really quickly that, maybe [00:15:00] they work a little harder, but they actually often do better in the class. Is there any truth to what these students think that, oh, if they're not as quick, that maybe they're not as good at math, and what would you say to a student who takes longer or has to work harder to grasp concepts?
[00:15:16] Barbara Oakley: There's plenty of evidence from an evolutionary perspective even that those who learn more quickly have trouble letting go with what they've learned. So in other words, their little dendritic spines form these relationships, form connections. “Ah, you've learned something.” And you can't, it, it's like, oh, it sticks really well, and then they think they've got it, and they can't, they can't change their minds as well.
So I'll give you a couple of examples. So, Santiago Ramón y Cajal was a very [00:16:00] slow, very, very bad learner. But he decided he wanted to become a doctor. And he, after being thrown out of elementary schools and so forth, and after much struggle, he finally became a doctor and he became a professor of anatomy.
And he eventually, won the Nobel Prize. And that wasn't enough. He's now considered the father of modern neuroscience. And he was asked, he was, you know, he was like, okay, “how'd you do it?” You know, because knowing that he wasn't really that bright of a guy and he said, “I was no genius,” but he said, “I have worked with many geniuses, and the problem with geniuses is they jump to conclusions, and when they're wrong, they can't change their minds.”
And indeed, we all have differing baths [00:17:00] of neurochemicals or that kind of bathe our neural connections. And some people's dendritic spines, which are like part of that connection, they form and they stick in place.
So, when a person goes to remember something, that connection clicks in. Which is great, and it doesn't fall away. But because it doesn't fall away, once they think they've got that idea, they can't change. And this indeed is part of why sometimes, you know, you'll see these leaders in mathematics education, for example, who are promoting ideas that are actually counter-indicated by all of today's research. But they can't change their minds because they're inflexible.
There's also, there's a phenomenon in medical [00:18:00] school, and there's a, a little slang term that everyone uses in med school for the top medical school student who's, and they call him, they call him or her the gunner. And the gunner is someone who can remember it all, and they learn really fast, and they also kind of like to show off how much they know.
So, when the uh, the doctor says, “Okay, well what's the diagnosis here?” The gunner is the first one with their hand in the air. Everything will click, click, click right through in their brain. They know exactly what the usual key items to check off to diagnose a certain disease. And they'll check it all off really quickly, form that connection - ah, they've got their diagnosis, and they won't rethink it. They won't look more deeply.
And [00:19:00] someone who's a slower learner, on the other hand, they're gonna forget things and they, they kind of had to reform, and they're more flexible about what they're thinking. And this flexibility helps them to actually grapple more closely into the truth. We can see that even with mathematician Andrew Wiles, the great mathematician who solved Fermat’s last theorem. And he said part of the reason he was successful in doing that was because he didn't have a perfect memory.
He would do something, he would take an approach, and it wouldn't work. And then he'd forget later on that he had tried something, and he'd do it again, but he'd do it slightly differently because he'd forgotten that he did it before. And when he tried it again, he'd do it differently. Then he'd succeed.
So not having a perfect memory, you know, having a [00:20:00] really good memory is terrific, but it also can lock you in unnecessarily. So, you can be really fast, and you can know, get people to marvel at you, but you can also end up being sometimes inflexible and it can be difficult for you to acknowledge when you're wrong.
[00:20:18] Anna Stokke: It would also be good if we let our students know this. Just because you see people in the class and they're answering things really quickly, and it is intimidating to students, but that doesn't mean that that person's necessarily smarter than you or that you can't learn that material.
[00:20:36] Barbara Oakley: Just telling a few of these stories, I'm just amazed sometimes at how encouraged people are when they hear that it's okay that you can actually be really, really good if you're not necessarily some super fast student. I mean, the relief is palpable in classes.
Just a few of these stories makes an enormous difference. [00:21:00] Oh, and Friedrich Hayek, the Nobel Prize winner, he wrote an essay on how important it is to be able - that there are fast thinkers, and he was a really slow and not that great thinker, but he could spot the errors because he wasn't jumping to conclusions and that's why he won the Nobel Prize.
[00:21:22] Anna Stokke: And you're an example too. You described yourself as a slower learner, and you got a Ph.D. in systems engineering. And I also don't think, I don't consider myself to be a fast learner. It often takes me a long time to learn things, and I was able to get a Ph.D. in mathematics. So yeah, we have to be careful about, about these myths out there.
I have three of your books, and in each one of those, you address procrastination. And so, I found that really interesting because that's not often something you see addressed in a book about learning mathematics. But you mentioned that [00:22:00] procrastination is a particularly big problem when learning math.
So why is that?
[00:22:05] Barbara Oakley: Well, there is research evidence that shows when you even think about something you don't like or don't want to do, it activates the pain centers of the brain. Mathematics, from an evolutionary perspective, it's what's called biologically secondary material, as David Geary has pointed out.
In other words, it's not the kind of stuff that we pick up naturally. So, like our little three-month-old granddaughter, she can look at her face and boy, she knows, you know, different people right off the bat. She, you know, she's got this automatic facial recognition system, and she's picking up two languages quickly.
She's picking up Spanish from her daddy and English from her [00:23:00] mother. And she listens to it, and she's picking it up. And you can see her trying to go, “rrr,” and roll her R's and things. Those are natural. Our brains are geared for that, but our brains are not geared from an evolutionary perspective to learn mathematics. So we have to repurpose, we have to kind of shove in these new ideas because they're not something that naturally comes to us, and it's harder to do.
And for some people it's, in fact, for many people it's a little bit more painful. But actually, once you get over the hump of these initial, it's like, you know, learning the multiplication tables and learning, you know, how to add things and then fractions and so forth.
Once you start getting past these, you begin to see, you know, you start climbing up, and you [00:24:00] begin to start seeing the beauty of math. But oftentimes in the earlier, you know, the early parts, it's hard to see the beauty. And so you sometimes just kind of have to trudge through it a little bit, and you know, for a lot of kids, it's kind of like doing your scales with a musical instrument.
I mean, it's not fun, but it helps get you there to where you can really start working some magic.
[00:24:27] Anna Stokke: Okay, and so what are some tips for avoiding procrastinating?
[00:24:31] Barbara Oakley: The best one by far is the Pomodoro Technique. So this was invented by an Italian, Francesco Cirillo, in the 1980s. And you know, as you mentioned, we've had over three million people in our massive open online course. Actually, probably in all languages, it's something like five million.
And I get, I have gotten [00:25:00] thousands and thousands of emails saying the Pomodoro Technique changed my life. And it's such a simple, great technique. So when I tell it, when I tell you the magic words behind how to do it, pay attention because many people have found this to be sort of a game changer for them. All you have to do to do a Pomodoro is you just turn off all distractions.
That means, I mean, if need be, put your cell phone in the other room. No popups on your computer. Good luck if you've got a two-year-old at home. But just do the best you can to have no distractions. Set a timer for 25 minutes and work as effectively as you can for those 25 minutes. When your mind kinda wanders off, which inevitably will, just do this, end things and bring it back on target.
Because your goal is to spend as much of those [00:26:00] 25 minutes intently focused on whatever you are working on as you can. And then, when those 25 minutes are done, give yourself a five-minute relaxing reward break. And the idea here is truly don't pick your cell phone up and say, “Oh, I'm gonna, I'm just gonna check and see if I got a text.”
And then you pick it up, and then you did get a text. So you start responding. You're just going back into focusing. The idea here is, with those two modes that we mentioned earlier, the idea here is to get yourself in that diffuse default mode network of neural relaxation. So that means that be a little bored. Kind of look - your mind will be working in the background, consolidating and putting that information in its place so you can make better sense of it.
If you want to listen to a little [00:27:00] music or make a cup of tea or kind of walk around a little bit. A lot of times, what people will do is they'll do three Pomodoros and then with five-minute breaks that followed them. And after the fourth, they'll take a half an hour break.
So that's a, that's a good way to make use of like two and a half hours of studying. You'll get more done, surprisingly, than if you just said, “I'm gonna power through and work this entire time.” There are lots of apps that can help you with Pomodoros, and you can, you know, kind of play with them and get little medals for succeeding with Pomodoros.
But that is really one of the best tools, and especially if you have attentional syndromes, then a Pomodoro can help keep you on task. And if you have trouble coming back after the break, just set a five-minute timer for [00:28:00] that break.
[00:28:00] Anna Stokke: Yeah, that's really great advice, and I'm going to be passing that along to my students in the future. It's really easy to sit down and study for eight hours but not actually study because there are just so many distractions.
You really have to turn everything off. I actually use Forest, which is quite a good app for keeping you on task. We do need to get a lot of practice in math and make sure we get our study time in, and you really have to avoid the distractions.
So I wanted to talk a bit about chunking, and you mentioned that a common trait in professionals in math, science and technology is that they learn how to chunk and that this is really important for learning math concepts. So can you explain what are chunks and how can we create chunks in long-term memory to help us solve math problems?
[00:28:57] Barbara Oakley: Chunks are a little hard to explain because they can be as [00:29:00] big or small as you want them to be. So first, let's look at learning to play a song on the guitar. So, your first chunk is probably going to be one note that you learn, where you put your finger on, and then after you learn, you'll learn maybe a chord.
So you've got four fingers, and you learn where to place them for the chord. So now, instead of, you know, there being four different chunks - one for each finger - you kind of learn one position for that chord, and that becomes a chunk. So now let's say you learn to play three chords together, “da, da, da.” And as you're playing those chords, you play it a number of times, and it can become one chunk as you [00:30:00] gradually kind of get used to just doing it together.
So, similarly in math, when you're learning any concept at first, it's like the simplest part of that concept that you can grasp. Absolute simplest. And then, you're going to start grasping the nuances of it.
Someone who is really well practiced with the multiplication tables, it is, in essence, the multiplication table; it becomes like a chunk for them. If you grasp that, those essential relationships between the numbers of the multiplication table, it becomes much easier for you to grasp in your head. Not in a computer or in a calculator, but in your own head. Then when you're faced with things like, “Well, what's two divided by four?”[00:31:00]
Oh, you can easily simplify because you already have those intuitive relationships in your mind. It does make me laugh sometimes because some of the biggest proponents of “you don't need to memorize it, you can just look it up” are those who are actually working for technology companies that, you know, that have math analysis programs and so forth. And it's like, of course they're saying that; they want you using their programs!
This relates to what we were just speaking about before, as far as - let's say that you're trying to learn some concept. Let's say that it relates to the binomial distribution, and you're really trying to grasp that idea. “What is the binomial distribution?” And a good trick is right before you go to sleep at night, [00:32:00] pull to mind, “What is the binomial distribution?”
Can you remember that relationship? And just take two minutes, pull to mind that relationship that you're trying to understand, or a concept you're trying to grasp, or something you're trying to remember. Take two minutes right before you go to sleep and pull it to mind. What this will do is signal your brain.
This, whatever this thing is, it's super important, and we better practice it during sleep. And indeed we can. Researchers can actually see that hundreds of times the brain will sweep over and strengthen the very connections that you are, you have been using during the day, and especially those right before you go to sleep.
So, a good way to enhance a chunk that you're trying to develop, whether it's a [00:33:00] conceptual chunk in math or a physical chunk of how to pronounce a word in Portuguese, or how to hit a ball in a certain way in tennis. Any of these things can become a chunk, and they can be chunks that are related into other chunks to become larger chunks.
But all of these can be enhanced by simply practicing with them. And a good way to do that is to practice with them right before you go to sleep because that's when - sleep time is when the brain calms down, and it can kind of clear and make connections more easily.
[00:33:43] Anna Stokke: And this reminded me of a few things. So, first of all, it, the memory is a powerful thing, you know, so let's use it. And absolutely, things like times tables, we need to have those memorized, and everybody can do it. They just need a lot, a lot of [00:34:00] practice. And as we mentioned earlier, sometimes it will take some students longer than others.
That doesn't mean that those students are any less capable, it just means that it takes them longer. And once they know their times tables, they're the same as everybody else. And it reminded me also of teaching my daughter to drive a standard transmission, which a lot of people don't know how to do anymore.
But we happen to have a vehicle that was standard transmission, and I just know how to do it like it's in my head. So, that's also an example of a chunk. When you have a technique like that in your head, and the same thing kind of happens with math. If you get a lot of practice with problems, you start to get these problem techniques in your head. And when you see a problem, you just kind of know how to solve it.
And so, that brings me to deliberate practice. And you mentioned that deliberate practice on the toughest aspects of the material can actually lift average [00:35:00] brains into the realm of those with natural gifts.
Would you mind elaborating on that a bit? How important is practice in learning math?
[00:35:09] Barbara Oakley: Oh, practice is unbelievably important! I mean, think about it. You can't learn a language without practicing it. You can't learn to play a sport without practicing it. You can't learn, you know, how to dance without practicing it. You can't learn a musical instrument without practicing it. Why on earth would it suddenly become that mathematics is, “You can't practice math because it'll kill your creativity”? No, nothing could be further from the truth! Sometimes advanced mathematicians, and only cherry-picked few, will say,” Oh yes, practice will kill creativity.” It's because they have a preternaturally [00:36:00] good memory, and they can remember these things.
And so, then, they didn't need to practice as much to remember these things. I remember a friend of mine who was - he got his Ph.D. from Princeton. They used to ask him to go and take tests because he could come out of the test, and this was all legal to do, but he'd come out of the test - he had a perfect memory - he would write the whole test down and all the solutions to the test. And then they'd store it in the test bank of the student group that he belonged to. And he was always very keenly, “Oh, you don't need to memorize anything. Why take the time to do that?” And I'm like, “Of course you don't need to memorize things because you do it naturally without spending time on it.”
“You don't know how someone like me thinks,” and I think more like typical students do because a lot [00:37:00] of times, those who are very naturally gifted, they don't get used to these ideas of having to work at it.
It all comes easy for them. So, what can happen, for example, when they are in high school, it's all easy. So they don't learn skills about how to tackle procrastination, for example.
So one thing that can happen, like when a big problem at schools like MIT, is that these super smart students will arrive and they have no good study skills. And some of them just wash out because they're really smart, but then they get there, and they, they haven't really learned how to study well. And you know, and so, there are students who go through MIT that are not as gifted, you know, if you wanted, however you [00:38:00] define gifted, as some, but they also, they know how to practice.
They know how to really bring out the best that's in their brain. I know a fellow who is in the top 100 of most cited scientists ever, and he has dyslexia. And it was very difficult for him to learn. But he developed this technique where he would go and take a textbook, and he would just open it at random and try to find a problem to solve randomly, you know, so he wouldn't know what technique or what part of the book it was in.
This is a form of interleaving. Sort of randomly picking problems out and practicing with them. So you don't really, like, a lot of times students will know what that problem involves. “Is this a perimeter problem, or is it a [00:39:00] volume problem?” And they already know kind of what formulas to use, but if you don't know what type of problem it is, you aren't told that right ahead of time, and you practice that way, you can really develop your skills.
So he developed these really great practice techniques so that, even though he was not a superstar student, he could do really well. And even if you look at Freeman Dyson, who was sort of Einstein's go-to mathematician. What did Dyson do? He would spend his holiday breaks working problems.
He just loved it. And so, he would work. Hundreds and hundreds of problems, and the other students weren't doing that. So people will say, “Oh, Dyson's a genius. He's just a natural.” But that seemingly natural ability actually came out of a lot of [00:40:00] hard work.
[00:40:01] Anna Stokke: Hard work is really important in math, and practicing's really important. And you mentioned that it, it is a bizarre thing that, yeah, there is this sort of movement, I guess we could call it, where people are saying that practice kills creativity. But it's exactly the opposite. I mean, to be a creative thinker, you need to have knowledge.
You need to have things sort of seared in, in your brain so that you can draw in those techniques and facts and knowledge to actually be a creative thinker. And the other bizarre thing about it is that disparaging practice, it actually hurts the struggling students the most because they need the practice more than anybody; practice with feedback to get good at math or many subjects really.
Along those lines, I always say math can be relentlessly hierarchical. And what I mean by that is it's, it's sequential. So it's like a ladder. So, if you're missing [00:41:00] some step early on, that will impact you later on because it follows along this string. And you have a quote in your book, which I really loved, and I'm gonna read it, read it out.
And so you wrote that “math can also be a wicked stepmother. She is utterly unforgiving if you happen to miss any steps of the logical sequence--and missing a step is easy to do. All you need is a disruptive family life, a burned-out teacher, or an unlucky extended bout with illness - even a week or two at a critical time can throw you off your game.”
And you kind of experienced this as a young child. You missed some part of the math sequence, and so you're quite familiar with this. But my question is, can a person catch up on math facts and mathematical techniques later, say as a teenager or even later in life? And is it harder as you get older?
[00:41:57] Barbara Oakley: Oh, that's a great [00:42:00] question. I think I'm living testimony to the fact that it is possible to do it later in life. I started with remedial high school algebra when I was 26 years old. I think part of what I did that was really good was I didn't have this cocky sense of, well, “I'm just gonna land kind of high, and I'll catch up with everybody.”
No, I just started at the bottom, acknowledged that I needed to be humble intellectually and then slowly begin climbing my way upward. In fact, one math program that I really like is called Kumon Mathematics. And part of their, you know, it's a Japanese-based program, that's careful interleaving.
It always makes me laugh when some reformed mathematicians will be like, “Oh, it's, it's the sign of the devil.” I mean, Kumon Mathematics because they have you practice. And it's like, [00:43:00] well, it is the equivalent of practicing in order to learn a musical instrument. Except in this case, the instrument you are practicing with is your mind.
This wonderful program starts kids out by, it tests them, and it starts them below the level they actually should be starting at. So then kids get going, and they're like, “Hey, you know, this is pretty easy. I can do this.” And so they, they start out very naturally. But we have two sons who we adopted from Kosovo, who were refugees. And they were college students, or about to be college students, so they were in their late teens, early twenties.
And we put them in the Kumon program in order to help them get kind of caught up with some maths because they weren't allowed to study, you know, with the dictatorship that had taken over in Kosova. [00:44:00] So, it's absolutely possible. Does it become more difficult as you get older?
Yeah, so, but it's still quite doable. I think part of the challenge is simply the older you are, the more life stuff you've got going on. And so, you know, it can become a challenge just finding the time to practice enough so that it seems very familiar and comfortable. And you're, you're not just getting those declarative links in long-term memory, but also those habitual procedural links, which takes time.
[00:44:37] Anna Stokke: So I wanted to talk a bit about some of the study techniques that students use that may not work as well as others. I'll give you an example. So I'll sometimes have a student does poorly on a test, and they'll say, “How did this happen? I mean, I watched 24 hours of YouTube videos,” or “I read through the solutions that you [00:45:00] posted to the problems.”
What's the issue with that? If a student's reading through work solutions, is that enough to create understanding so that they'll be able to do the problems themselves?
[00:45:13] Barbara Oakley: Well, think of learning, I mean, learning math; it really does relate very much to learning a language. If you sat there reading a list of vocabulary words in Japanese, would you be learning Japanese? Obviously not. It's just, it's gonna skim right over, and it's not going to create any neural links in your long-term memory.
The challenge is, so the World Economic Forum, this is fascinating, they have plans that in the years to come, so for 2025, they are planning to begin rolling out that they're going to examine schools to see if schools are [00:46:00] teaching students, not just the things that they're supposed to be learning with subjects, but they are also learning how to learn.
Can you imagine that kids have 12 to 16 years of higher education and they never get a course in how you learn effectively? It's unconscionable because there's, well things like, students just don't understand that skimming their eyes over material is in no way helping them to actually, or very little way, is it helping them to create the links in long-term memory.
Those links are best created by what's called retrieval practice. And that's, it's basically a mild form of self-testing. So it's low stakes or no stakes, as Pooja Agarwal calls it in her wonderful book, [00:47:00] Powerful Teaching, about retrieval practice. You're basically, you're trying to pull ideas from your own mind.
So, what I would do is I would teach myself. I would look at a problem, and I would have practiced that problem so many times that all I had to do was look at that problem. And I didn't practice it from the sense of, I'm memorizing the solution. You know, it's not, it's not this sort of humdrum plastic understanding.
It was, okay, “I see this problem. What's the first step?” Now it's whispering to me what the second step is, and that step whispers to me. “What's the next one?” When I'm learning in this way, this intuitive way, so I can look at a problem, and it whispers to me how to solve it. Then when you do that with enough problems, you gain this intuition so that even when you see problems you haven't seen before, you have an [00:48:00] intuition of how to go about solving it.
Using retrieval practice oftentimes poets will say, “Memorize the poem, and you will understand it more deeply.” I always say, why should we let the poets have all the fun, you know? But what we can do is when we look at problems, you know, you work it. And you make sure that you could work that problem. You can retrieve it from your own mind, and you're not cheating yourself by just looking at the problem going, “Yeah, I know how to solve it,” but actually step through it with your mind.
And afterwards, after a while, when you do this enough you feel like a master musician. You know, it's like, “Oh, I'm, I'm not playing a chord, but I'm doing something even better. I'm playing with the, with the concepts in my mind.” And it's a really cool feeling.
[00:48:59] Anna Stokke: [00:49:00] Precisely, and we can facilitate this as teachers too. So the idea is, we wanna make sure that students are actually working through the problems themselves. Sometimes that might be looking at a work solution and then actually putting it away and, and trying to do the problem yourself. As university professors we give, we try to give lots of homework.
But with young children, you probably do want to guide that practice. Your book contains so many helpful things for students and for teachers. And you have one specifically for teachers that's also really helpful. And one thing that came to my mind, and we often talk about this when we're giving students tips or some students did poorly on the test, and we go back to class afterwards, and we give them tips for how they can do better the next time.
Or, on the first day of classes, I'll tell my students, “You need to [00:50:00] study at least eight hours on your own outside of class.” And we always say the issue is that the students who were going to take our advice, probably would've done this anyways. And they maybe didn't even need me to say that.
And the ones that really need to hear it are the ones who just don't hear it, or they don't listen. So how can we get these messages through to our students so that they use these techniques that are recommended in your book?
[00:50:32] Barbara Oakley: Oh, that's a great question. It, it all boils down to the question of motivation. And, you know, there's, you cannot motivate everyone. I mean, much as we would love to, with current technology, we can't scramble into people's brains and change their motivation. So you, one way that can be helpful, and it's, [00:51:00] this is just shockingly underrated or not discussed, is the importance of your own extraordinary enthusiasm for the subject you're teaching.
If you think back on all of your favourite teachers, usually they were really, really enthusiastic. And what happens is when you are very enthusiastic, your face gets all excited, your hand gestures are all excited. You are making surprising motions that are just enhancing what you're trying to teach.
You're coming up with different kinds of ways, but those, those facial expressions can be mirrored in the faces of your students. And what a face is doing, actually, it dictates what the mind is thinking. [00:52:00] You think what the mind is thinking dictates how the face looks, and that's true, but it works the other way as well.
For example, if you put a pencil in your mouth, it will force the corners of your mouth up. And it's been shown through a lot of research over the years; this actually makes you feel happier. You will answer in ways that are happier.
So anyway, mirror neurons, there's a mirror neuron system in your students, and when they see your happy, excited, enthusiastic face, they can't help but get that same sort of feeling started inside of them. So a very important thing to do to help motivate your students is to reflect it in your face, this enthusiasm, because they will pick up what on it and have an [00:53:00] expectation of your students.
I mean, not like, “Everybody in this class is going to do great, blah, blah, blah," but like each individual student, you expect that student to be a star. And there's so much research that's shown that, you know, when teachers are sort of nefariously told that certain students are actually secret superstars, those students will actually begin excelling even though they were just typical average students.
So expectations and enthusiasm can make a big, big difference for your students. It's really exhausting to be on, so when you go home, you can turn it off and relax and just like be a mental vegetable. That's what I do sometimes. But when you are in front of your classes, that is one of the best things you can do to help all of your students.
[00:53:58] Anna Stokke: That's [00:54:00] excellent advice, and that's been my experience as well. Passion, enthusiasm, and having high expectations of your students will take you a long way in helping your students to achieve. So my last question is, we have a lot of students who are forced to take math.
You know, as young students, they're required to take math at the university level they may be required to take math as part of their program, or we have students that are avoiding math, and then that actually shuts them out of certain careers. What advice would you give to students who think they're bad at math, but they're required to take it?
[00:54:39] Barbara Oakley: An analogy for me is I used to teach electrical circuits. Half my class would be electrical engineering students who wanted to be there, and half of them were mechanical engineers, engineering students who did not want to be there, did not want to be learning from some lady [00:55:00] professor at the front of the class, you know, with this subject that really had nothing to do with them getting their hands on the engines they wanted to be working with and so forth.
And so, I just had these wonderful expectations. They would always sit in the back of the classroom. And they’d, you know, mutter to one another or whatever. And I, I would learn all their names, and I'd call on them, and when they'd ask a question in a snarky, you know, kind of mean tone of voice, I’d just field it as if it was really a good question because actually often embedded within it was a really good question.
And my expectations of these students were such that I ended up being called into the mechanical engineering department because I was stealing so many mechanical engineering students into electrical engineering because they were falling in love with the discipline.
Be encouraging [00:56:00] and encompassing and excited and know their names. You don't have to be everyone's friend, but if you're, you’re just encouraging them, and you acknowledge them as human beings, even when they first look like they're going to hate you and hate your subject. It really can just change lives and change worlds.
It's an amazing and good thing. So, expectations can really matter. Even if their expectations are bad to start with, you can change it. What, you know, what can you do with counsellors and so forth? One thing that bothers me is oftentimes students are simply not told that they need to start with math early. And they need to get the calculus done in the first year or two. They can't just, like, start with it because so much builds off of calculus.
So I, I so wish that many [00:57:00] guidance counsellors were much more aware of the importance of pushing math earlier. But a real challenge is just the way that universities are often set up does not reward good teaching. And so, as a consequence, students can find it very difficult to find encouraging teachers and professors and instructors, unfortunately, when they are beginning these critical, critical early years where it's so easy to wash out.
[00:57:33] Anna Stokke: Yeah, I think that's unfortunately quite true, and I, I really appreciate your perspective on that. I really wanna thank you so much for coming on my podcast today. I just feel so honoured to have had the opportunity to speak with you today, and I really hope we get the chance to meet in person soon.
[00:57:53] Barbara Oakley: No, I'd love that, Anna. So, fingers crossed it will happen maybe this year and if [00:58:00] not the next. And in any case, thank you so much for your great work on the front lines of really helping people to learn math.
[00:58:09] Anna Stokke: And thank you for your work. So now, I'm going to go do some work, and I'm going to use the Pomodoro Technique.
[00:58:17] Barbara Oakley: Me too.
00:58:19] Anna Stokke: Okay, okay thank you.
I hope you enjoyed today's episode of Chalk and Talk. Please go ahead and follow on your favourite podcast app so you can get new episodes delivered as they become available. You can follow me on Twitter for notifications or check out my website annastokke.com for more information. This podcast received funding through a University of Winnipeg Knowledge Mobilization and Community Impact grant funded through the Anthony Swaity Knowledge Impact Fund.