Episode 10: How Do Children Learn Math?

10 Nov 2023

Why do some children excel in math, while others struggle? It’s a question Dr. Stephanie Bugden has been trying to answer throughout her career. By using interactive games, and functional brain imaging methods, her and her research team from the University of Winnipeg Psychology Department are hoping to learn more about the cognitive and neural mechanisms that guide math learning to help improve math skills in children.

On this episode the research question is: “How do children learn math?”

KENT DAVIES: Today we’re at a Winnipeg daycare centre with University of Winnipeg research assistant Alyssa Wright. Wright is observing and recording data from children, who are learning the foundations of math.

STEPHANIE BUGDEN: Mathematics, it’s really the basis for everything that we carry out in this world. It is the basis of, you know, chemistry, physics and, and it is hierarchal in a way that it builds off, you know, very fundamental skills. Everything that we do and all the decisions we make are informed by some aspect of numeracy or math.

KENT DAVIES: That’s Dr. Stephanie Bugden, assistant Professor in the Department of Psychology at the University of Winnipeg. Bugden’s research focuses on how we acquire numerical and math skills. By using behavioural and functional brain imaging methods, Bugden and her research team are exploring the basic cognitive and neural mechanisms that support individual differences in math development; trying to find out why some people excel in math, while others struggle. In order to do that more effectively her research team is focusing on how young children learn the foundations of math skills.

STEPHANIE BUGDEN: And so, I’m really interested in understanding how that occurs early in development. Maybe there’s something about their early environment or there’s something about the way in which they think about number at an early age that is influencing how they learn math once they get into school. Now, this is a very ambitious research program because there are many different factors that might influence why kids are learning more easily than others. And so, I’m really interested in trying to understand those individual differences.

KENT DAVIES: On this episode the research question is: how do children learn math?

From the University of Winnipeg Oral History Centre, you’re listening to Research Question- amplifying the impact of discovery of researchers of the University of Winnipeg.


KENT DAVIES: From an early age, Stephanie Bugden was interested in the process of learning.

STEPHANIE BUGDEN: I grew up in London, Ontario. My family is from St. John’s, Newfoundland, and I was born in St. John’s, Newfoundland, but we moved to London, Ontario when I was very young. So, I spent my childhood on the mainland. And I would say that I grew up very much enjoying going to school. I loved the process of learning, the social aspect of being in school, as well as the activities that could take place, which is partly what led to my career path here.

KENT DAVIES: At first, Bugden thought this career path would naturally progress towards teaching, but after attending psychology classes at University of Western Ontario, her career path changed.

STEPHANIE BUGDEN: I had this goal in mind that I was going to pursue a teaching degree, and in particular I was really interested in working with kids who had learning disabilities. So, I was interested in kids that might not learn in the same way that other children might learn in the classroom, because I have seen how that can negatively impact one’s school experience and even sort of future trajectories. During university, I had sort of the privilege and the opportunity to take psychology classes, and I was introduced to the world of research. And so, when I did my honors thesis I was very lucky to have worked with Dr. Daniel Ansari and his passion for research and for the pursuit of knowledge sort of transferred, I think, to me. I became very excited about the types of questions; like how do children learn and that’s what led me to pursue a masters first in education, and a Ph.D. in psychology.

KENT DAVIES: After obtaining her Ph.D., Bugden furthered her research goals by pursing a postdoc at the University of Pennsylvania.

STEPHANIE BUGDEN: So that experience was sort of life changing for me. It was an experience for me to basically sort of leave the nest. During the postdoc, I was able to establish an independent research program as well. My post-doc mentor was looking for someone who was interested in understanding how children’s brains develop. She was looking for someone to work with her to develop projects, exploring the neural basis of number processing. And so that was another moment where I was like, “Yes! This is exactly where I need to go. This is the person I would love to work with and to learn from.” And so that’s when I embarked on that pathway to do my Postdoc.

After I spent about six years at the University of Pennsylvania doing my post-doc and I was looking for an assistant professor position in a Department of Psychology. And after being in the U.S. for six years, I really wanted to move closer to home. And I was lucky enough to see a position open up at the University of Winnipeg. And the members of the psychology department here share a lot of overlapping research interests with me. And so, I was very excited to join the department and I was very happy to be able to return home to Canada.

KENT DAVIES: Now part of the University of Winnipeg Psychology Department, Bugden’s research has led to new collaborative opportunities with other departments on campus, something she hopes to continue in the future.

STEPHANIE BUGDEN: There is faculty members, not just in the psychology department, but in the Faculty of Education, who we share very similar interests. And I’ve had the opportunity to liaison and work with them since being here and I truly believe that good science doesn’t take just one person. It takes a team that bring together different expertise, different skill sets for us to be able to explore, really, these challenging questions about how children learn.

KENT DAVIES: So, where do we start when it comes to our research question: How do children learn math? Well, first off, it’s important to know when theoretically children begin developing basic math skills.

STEPHANIE BUGDEN: So, it’s actually a really interesting question. There’s research to suggest that infants are born with the ability and the capacity to be able to approximate sets of objects. Even within being a month old, if you show infants sets of like dot arrays, for example, and if you keep all the features constant, like the size and the location of where they are presented on the screen. And you only change the quantity. Infants can detect that. They can tell that there are differences between the quantities that you present them, suggesting that this is an innate skill. There is some research to suggest that this is potentially a foundational capacity that individuals are born with. They can do this quite simply, and that our ability to learn math might come from there. Now, that is a very contentious question within the field. There isn’t really a simple answer, of course, about whether our sense of mathematics really comes from that core system. But the evidence is pretty robust in terms of it existing. Now when we think about mathematics in the classroom, right, being able to add, you know, a written numeral three to the written numeral two, these are very human specific capacities. Those symbolic representations of number are only available to educated adults. And when children start, their first mathematical concept is counting. Learning to count objects within the environment. So, they first start with rote counting, and that occurs shortly after they learn to talk. And then in a step-by-step way, they start to learn that those verbal number words actually mean something so you can attach them to sets of quantities that they see in their environment. And that occurs between the ages of three and about four and a half, five. It varies depending on kids experiences in the home, how much they are exposed to number, how many opportunities they get to count, and to interact with items within their environment. But on average, children learn that when they count a set of objects. So, if they count six things that the last number that they count represents the number of objects within that set. And then they quickly learn how to attach those verbal number words to written numerals once they start school. It’s a very hierarchical way of learning math, right. That each concept sort of builds on it on itself.

KENT DAVIES: These are the two areas of Bugden’s research: how children understand ordinality, or the capacity to place numbers in sequence and how they understand number words. 

STEPHANIE BUGDEN: In particular, how does the brain support the process of learning the meaning of number of words? And it’s a very sort of critical window in children’s development. There’s a lot that they’re learning, right, as they are experiencing the world around them. But this is a very understudied area in development when it comes to the brain, only because we have limited technology to be able to study the brain in that age range. So, you know, to understand the functional brain. Functional magnetic resonance imaging is typically what we use. It has really great spatial resolution in order to understand, you know, what areas of the brain are engaged when doing different tasks, of course, while lying very still in a scanner. You can imagine that having a three- or four-year-old lie in a scanner is a quite challenging feat.

KENT DAVIES: That’s why Bugden and other researchers are opting to use different technology for their research. Functional near-infrared spectroscopy is a non-invasive neuroimaging technique that measures changes in brain activity and has applications in fields such as neuroscience, psychology, and clinical research. fNIRS is particularly useful for studying brain activity of infants and children because it’s safe and practical.[i]

STEPHANIE BUGDEN: It is like a cap that you can put on your head. It has optodes that uses very basically light that indirectly measures blood flow when people are doing different cognitive tasks. The added benefit of the fNIRS is that you don’t have to lie super still like you’re a statue in the scanner while trying to see, you know, a video screen projected behind you through a mirror. You can basically put on a cap in any context. So, they could be sitting in front of our computers within the lab, or we can even take that system into a school or into a daycare and we can have them do different tasks either on a computer or even just counting items on a desk in front of them. And so, I’m really interested in exploring these very early skills that children are first learning before they start school and understanding how the brain supports that process. And then we can look at, you know, where in the brain these processes are happening. But we can also characterize individual differences in, you know, what is the variability across different individuals and whether that variability predicts other math skills.

KENT DAVIES: We’re back at the daycare now with researcher Alyssa Wright. Wright is part of Bugden’s research team and is keenly observing children play a game which will test their ability to place numbers in sequence.

ALYSSA WRIGHT: So essentially the number line game is basically, I’m going to call it an active board game. Kids pull a coloured card, there’s a three-digit sequence on the card, they first decide if it’s in the correct order or not and after they’ve chosen, they go jump on the number line to confirm their guess or their answer there and then they come back and they make a new decision after jumping on the number line. So, the whole idea of the number line is if they’re jumping forward the whole time, the numbers are in the correct order. If they have to turn it around at all they’re in the incorrect order. They get it right they move forward on the game board to whatever colour the card is. They have a lot of fun with it. They really like jumping. They like picking the frogs and the turtles. It’s a whole exciting experience for them but it is very preliminary, but we are seeing very good results in terms of their order of understanding and proving.

KENT DAVIES: This is the second stream of research Bugden is interested in, ordinality.[ii]

STEPHANIE BUGDEN: We are interested in exploring, you know, how or ordinality provides sort of a foundational skill for learning mathematics. And in some of our work we’ve identified gaps in knowledge, so children. Really struggle to learn the ordinality. So, the count sequence is very ingrained for young children. They can count one, two, three, four, five, six, seven, eight, nine, ten. They know how to count really easily at a very young age. But if you present kids with two, four, six and you ask them, “is two, four, six and ordered sequence?” Many kids say, “no, it’s not.” And so, their concept of order hasn’t quite expanded past this, you know, number of sequences that are in the immediate count list. And so right now I have a line of research that’s understanding okay, why is this the case? And the interesting thing is we see this in children who have mathematical learning difficulties as well. So, these are middle school kids in grades six through eight. If you give them a sequence like two, four, six, and you ask them, is this an order? They say no. And so, this is really interesting where we’re still trying to further tease apart why we have these findings. But that’s some ongoing work that’s being carried out by a student of mine, Alyssa Wright.

ALYSSA WRIGHT: As a kid I was really good at math, which is like, “why are you doing math now?” Mostly because I knew a lot of people who weren’t good at math, and they struggled a lot and it made everything kind of worse. They didn’t have a great time in school as a whole because of math. So, if we can get these kids kind of like good at math or at least not hating it, then we can kind of change everything.

This whole thing happens in roughly the span of a week and then they get their post-test right after they play the number line game so it could be very fresh in their mind, and it might not be retained over time. So, we’d like to see if it does get retained over time or how often they have to play the number line game for it to be retained.

KENT DAVIES: Bugden is also examining how culture may shape the development of math skills.

STEPHANIE BUGDEN: In general, development and learning doesn’t really happen in a vacuum. Kids have multiple different experiences and environments that’s going to shape how they learn, what they learn when they learn it. And I’m really interested in these contextual influences on mathematical development and maybe more broadly on brain development.

KENT DAVIES: With that in mind Bugden has expanded her research to other parts of globe. Observing how children learn outside of North America.

STEPHANIE BUGDEN: I’ve had the opportunity to collaborate with Dr. Sharon Wolf at the University of Pennsylvania. She is doing some interesting work with the government of Ghana in West Africa, looking at ways in which they can improve their early childhood programs there. And so, we explored whether these early precursor skills— So, I mentioned the ability to discriminate dots, but also the ability to discriminate between numbers. So, if you’re presented with a five and a six, the speed and the accuracy for which you pick the bigger number is very predictive of individual differences in math skills. And we see that, you know, across different samples of kids in Canada and the U.S. and North America, where the ability to discriminate between a five and a six is very predictive of their math skills. So, we wanted to explore, you know, what are these early foundational skills in children in in Ghana. And we also did this in Cote d’Ivoire, which is Ghana’s neighbouring country to the west. And it’s really fascinating because we see a different pattern of results. The ability to discriminate between sets of objects is actually a more robust predictor of math skills in West Africa. And so that really highlights this need that we need to further explore how these different contexts might be shaping our cognitive representations of number. Kids are doing different things. They are using the numbers in different ways, which might be shaping how they think about number. And we’re thinking about why is this? Why do we see these different patterns of data across two different samples of individuals within North America and within West Africa? And so, this is something that I think, you know, we really like to pursue in terms of trying to understand how context might shape learning.

KENT DAVIES: Math anxiety is another factor that Bugden believes not only affects our ability to learn math but has been a factor in reinforcing some harmful stereotypes.[iii]

STEPHANIE BUGDEN: I would say that one of maybe the bigger misconceptions that is out there is that boys are better at math than girls. And even at an early age. So, there are a few robust studies that have that have shown that there are no differences between boys and girls when they’re doing very basic number of tasks in kindergarten and first grade. Now, there is some research to suggest that there might be some differences in adults, but this is some very fascinating work by Dr. Erin Maloney, Dr. Moriah Sokolowski, who have actually showed that it’s not necessarily the math skills. Any differences that we see between males and females when carrying out complex math is accounted for by math anxiety. Okay. So, these are feelings of apprehension and tension around doing math. Math anxiety tends to be higher and in females relative to males. For those individuals who have math anxiety if they’re presented with math problems, they are automatically really stressed about carrying out those operations that is really going to tax their working memory system, which would make mathematics a lot more challenging. Right? So, if you’re stressed about doing math and you don’t want to do math and you’re not going to participate in it, you might not take math classes when you go to high school or you go to university, you avoid it. And then and then you tend not to get better at it with any skill you need to practice it to get better. And if you’re avoiding it, then it’s hard to get better.

KENT DAVIES: Dr. Erin Maloney’s work also showcases how it’s not just an individual’s anxiety that can affect math learning but those around them as well.[iv]

STEPHANIE BUGDEN: And what’s really cool about some of the work that Dr. Maloney is carrying out is that we do see that there are associations between teachers’ anxiety about teaching math and their student’s achievement as well as parents. So, how parents feel about math is also associated with how children think about math. In particular, those who have who have math anxiety and that help their kids with their mathematical homework. And so there seems to be this cultural sort of influence about how we think or how we perceive individuals should, you know, perform at math. But every person can be a math person. You often hear that people will say, you know, “I’m not a math person.” You either get it or you don’t. Relative to, say, reading. Right. But there is there is no scientific data to suggest that not that there are math people and that there are non-math people. Everyone is capable of learning math.

KENT DAVIES: Back to our research question: how do children learn math? For Bugden it can be many factors, but her focus remains on uncovering the basic cognitive processes associated with learning math.

STEPHANIE BUGDEN: That is the overarching question of my research program. In particular, I’m really interested in, you know, the underlying sort of neural structure that supports math learning. So, how do children’s brains— how do they vary when they’re doing these different types of math tasks? So, even as simple as, as choosing the bigger number or adding two plus four and trying to understand a little bit about, you know, how the brain changes, even how we learn those skills, is something that I’m really interested in, in trying to, you know, focus on and to uncover.

And if we sort of go back to talking about how children learn the meaning of number words or even the ordinal structure of number, if these are really important precursor skills for mathematics, that’s one step, which is very critical for informing how we identify kids. Right. So, if we are seeing that kids when they start school and they’re not starting school with those foundational capacities to be able to count, to be able to order number, and those are the kids that end up having math learning difficulties later, then those are the types of skills that we should be assessing early to be able to pinpoint that those are the kids that might struggle.

KENT DAVIES: Recently Bugden has been part of establishing the Center for Cognitive Neuroscience at the University of Winnipeg, which is homebase for her research team, where they are equipped portable functional near-infrared spectroscopy (fNIRS) kits, a portable electro-encephalography (EEG) kit, and a magnetic resonance imaging (MRI) simulator. This equipment is essential in furthering her team’s research goals of understanding how children learn mathematics.[v]

STEPHANIE BUGDEN: We want to bring kids into the lab, or we could even go out into the schools and use our neural technology as well as collect behavioral measures before kids are starting school and we want to track them longitudinally. We want to track these skills over time, and we want to see how these kids perform so we can identify, who are learning at quicker rates, who is learning at slower rates. And this is work that I’m very excited to carry out with Dr. Amy Desroches and Dr. Steve Smith, who are experts in reading and emotional processing. So, we can track not just math development, but also reading, development and emotional development and see how these skills grow together or independently over the course of time. And track or identify what were those skills before they started school that is predicting how they are performing later in their school careers. And if we see that these skills that when they start school are associated with lower performance, then that is incredibly informative for identifying kids that might struggle and for identifying kids that might need a little bit extra help in the classroom or at home in order to help them excel or succeed at math.

KENT DAVIES: The centre is also important for training the next generation of neuroscience researchers.

STEPHANIE BUGDEN: I’ve been very fortunate to work with really amazing students. I think it’s very important to integrate students in the research process. All of my students are encouraged to work collaboratively in a team. This is the cool part is being able to see some of the light bulbs go or see how excited they are about carrying out their research. Being able to work with these students as they come up with their own questions, as they take other classes and they say, “Hey, Stephanie, this was really interesting, and I think this makes me think this way about how children develop numeracy skills.”

KENT DAVIES: Advancing our understanding of developing brain function, so that parents and teachers can identify and intervene for children with learning difficulties is one of Bugden’s overall research goals.

STEPHANIE BUGDEN: It is very predictive of a lot of outcomes and success, right? So functional numeracy skills are very predictive of, you know, job security, you know, mental health, you know, even incarceration rates. Whether you default on your mortgage, you know, functional numeracy skills are very predictive of a lot of these sort of applied outcomes.

Often times kids that struggle, we have a hard time picking those kids out, not until about third or fourth grade when they are clearly failing. Right. When they’ve had a couple of years of math education. And they’re just not they’re not excelling. So often, children with learning disabilities are diagnosed in third or fourth grade if they’re even diagnosed or identified at all. And if we can pinpoint those skills early in development, if we can know who is going to need a little bit of extra help earlier so that we can mitigate any negative consequences of failing or struggling in math or not grasping concepts in a simple way.

KENT DAVIES: Bugden also hopes her research can inform and advance how we teach math for the years to come.

STEPHANIE BUGDEN: If we can even if we can share that knowledge with teachers or early childhood educators, that these are the types of skills that they can focus on in their classroom or they can watch out for. So, if kids are not grasping those really early concepts that they might want to spend a little bit more time making sure that they do that kind of information could be very fruitful for teachers and educators or even how best we can teach that, you know, collaborating with educators or educational psychologists who are carrying out research on best pedagogy practices. That kind of stuff would be very fascinating.

KENT DAVIES: You’ve been listening to Research Question. Research Question is produced by the University of Winnipeg Research Office and the Oral History Centre.

The University of Winnipeg is located on Treaty 1 Territory, the heartland of the Metis people.

Written, narrated and produced by Kent Davies.

Our theme music is by Lee Rosevere.

For more on University of Winnipeg research, go to uwinnipeg.ca/research

For more information on the University of Winnipeg Oral History Centre, and the work that we do, go to oralhistorycentre.ca.

Thanks for listening.


[i] Stephanie Bugden, Nicholas K. DeWind, and Elizabeth M. Brannon. “Using cognitive training studies to unravel the mechanisms by which the approximate number system supports symbolic math ability.” Current Opinion in Behavioral Sciences 10 (2016): 73-80; Wei-Liang Chen, Julie Wagner, Nicholas Heugel, Jeffrey Sugar, Yu-Wen Lee, Lisa Conant, Marsha Malloy et al. “Functional near-infrared spectroscopy and its clinical application in the field of neuroscience: advances and future directions.” Frontiers in neuroscience 14 (2020): 724.

[ii] Sylvia U. Gattas, Stephanie Bugden, and Ian M. Lyons. “Rules of order: Evidence for a novel influence on ordinal processing of numbers.” Journal of Experimental Psychology: General 150, no. 10 (2021): 2100.

[iii] Erin A. Maloney, Stephanie Waechter, Evan F. Risko, and Jonathan A. Fugelsang. “Reducing the sex difference in math anxiety: The role of spatial processing ability.” Learning and Individual Differences 22, no. 3 (2012): 380-384.

[iv] Erin A. Maloney, Gerardo Ramirez, Elizabeth A. Gunderson, Susan C. Levine, and Sian L. Beilock. “Intergenerational effects of parents’ math anxiety on children’s math achievement and anxiety.” Psychological science 26, no. 9 (2015): 1480-1488; Erin A. Maloney, and Sian L. Beilock. “Math anxiety: Who has it, why it develops, and how to guard against it.” Trends in cognitive sciences 16, no. 8 (2012): 404-406.

[v] Mieke Ruth Van Ineveld, “Neuroscience Profs Building ‘First-of-its-kind’ Research Centre,” Uniter, September, 14, 2023. Accessed October 12, 2023;  “New cutting-edge neuroscience lab opens at UWinnipeg,” UWinnipeg, accessed October 20, 2023.