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cc For some people this is a real surprise, that the School of Education would have a neuroscientist, but here at UW-Madison, there are lots of surprises and Ed is one of the most positive surprises. Ed got almost all of his education, at least beginning with a college degree, in California. He got his bachelor's degree from UC-Berkley. He got his Master's Degree in Experimental Psychology from UC-San Diego and he stayed there for a PhD in 2004 in Psychology and Cognitive Science.

Then he did a series of postdoctoral stints, one of them in France and what he says was the French equivalent of the NIH, --. Then he did a postdoctoral stint at Vanderbilt. In the last year of that which took him right up to 2012, he was a postdoctoral fellow in one of the departments at Vanderbilt and he was a postdoctoral affiliate in the Kennedy Center for Human Development at Vanderbilt. In 2012, he came to UW-Madison and began his track as a faculty member, so he's an assistant professor now.

His publication record is almost unbelievable for an assistant professor. He has 31 peer-reviewed papers. Eight of which were published when he was a student. He has 10-book chapters and he's the co-author of a book on Synesthesia.

I guess if you can pronounce it, you should know what it means. That's a real mouth-full, synesthesia, it requires a lot of tongue work. He's been invited 42 times to give lectures so this is number 43, I think, unless he snuck one in. He is an ad hoc reviewer for more journals than I was able to count from his CV.

If there's one measure about whether you're popular it's that you get tagged to do work for journals, and Ed must be one of the most popular people in neuroscience because he's ad hoc-ed for neuroscience, and for vision, and all this stuff, all over the place. Ed is extremely well-regarded and very popular. Today, he's going to talk about something which is really close to my heart and the program's heart. Because the program now has three integrated degree tracks and I am determined before I hang up my hat that we're going to have a fourth one and that one is going to be on neuroscience and education.

I hope that Ed will lay the ground work for making that go smoothly. So I proudly present you with Mr. Ed Hubbard.

applause

Thank you so much for that warm introduction. As Ron said I have been ad hoc reviewer for quite a lot of journals but it may not be a mark of popularity, it may just be a mark of the fact that I don't know how to say no, so there may be another component to it there. I'd like to tell you guys today about work that we're doing in my lab, the educational neuroscience lab, that we really see as building the foundations for new field, bridging between education and neuroscience. If you look out in the media, it seems like brain training is everywhere.

There are all these various different games, Nintendo DS. There is curricula even for elementary schools called Brain Gym. You can see this poor brain just working away there, trying to get stronger and bigger and faster. There's Lumosity which you pretty much see everywhere on the web, TV ads, these sorts of things.

There's even a commercial for Virgin Mobile. With a guy sitting in a brain-shaped chair, who looks suspiciously like MIT Steve Pinker and he wheels around and he tells you to retrain your brain. The goal is that where they get you to buy Virgin Mobile cell phone contracts. I'm not sure how retrains your brain would be, but the idea that what we are doing is training our brain in various different ways, seems to be out there everywhere.

It's not only captured the popular imagination. It also has captured the imagination of serious scientists and educators so these are a number of the books that have come out within the past few years. Some of these, for example, are written by former educators. John -- is a educator in Australia, who actually was one of the founders of the British Annual Series dedicated to looking at links between education and neuroscience.

Paul Howard Jones, this is very clearly Introducing Neuro Educational Research. Clearly a book targeted at his academic colleagues. Then there are other people like Eric Jensen who is writing really for teachers. If I'm really honest about it, Eric Jensen's book is a little mottled.

I would not recommend it but he's at least trying to get the word out there. Then there are various different, for example, edited volumes. The pope, not the current pope, but back in 2002, the pope had the Pontifical Academy of Sciences come and speak to him about what we know about education and brain. People from all over the planet that have been interested in education and brains came and talked with the pope and that then turned into this edited volume.

We can see not only the popular interest, but also the serious academic interests growing and trying to bridge between education and neuroscience. You might ask, why is that? What is the common ground that people are starting to see? The way I see it is that all three of these fields have started to recognize that they share an interest in learning in cognition at various different levels.

You think about teachers primarily what they're doing through teaching, through pedagogy, is thinking about student learning and thinking about how do I change this child's understanding of a particular topic, how do I change their cognition. Experimental Psychology similarly has been focusing on how learning and cognition take place in laboratory settings for well over a hundred years. Then when we think about neuroscience, it's focused on brain structure, brain processes that are involved in learning and cognition broadly, plasticity, so how is it that the brain changes as you go through these different learning events? These different fields then have come together to create this union of mind, brain, and education or what I really think of is educational neuroscience.

We talk a lot in this field about building bridges, but in many cases the feeling is also that these bridges are incomplete. For those of you that know this is the San Francisco Bridge that is replacing the old span that collapsed partially in the 1989 earthquake. Here's this beautiful new bridge but as you can see that new bridge is not complete yet. The suggestion is that we can't actually build a single bridge directly from neuroscience especially from cellular and molecular levels of neuroscience, but rather that we're going to need to build multiple bridges.

If we think about again this San Francisco Oakland Bridge, there are really two separate bridges. One from Oakland to Yerba Buena Island and one from Yerba Buena Island to San Francisco. You might liken that to bridges from instruction to cognition, from cognition to neuroscience and then perhaps cognitive psychology being that island in the middle of that bridges between these two different spans. What we really need is this multilevel approach where we bring together people who are doing serious, rigorous neuroscience work who are doing the cognitive psychology and then who are also thinking about the instructional and pedagogical implications of this.

This is not a job that we can do with just one person, instead we need to have multiple different people approaching this from multiple different directions so that we get this bidirectional flow of information across these multiple bridges. One analogy that I particularly like is this analogy with the early days of medical science. If we think about what was happening in the late 1800s, doctors had all sorts of different methods that they could use to cure people who were sick, who were injured. Some of those methods really seemed to work but maybe they still don't even know why, especially down at this fundamental cellular and molecular type of level.

Other methods didn't really work. Sometimes the theory was sound that the method didn't turn out the way that people expected it to. Sometimes the theory was just wrong. If we look at what happened starting then in the late 1800 into the early 1900, the early 20th century, we started to see the advent of evidence-based medicine.

Along with that, we think about how biology, physiology, chemistry, physics all of these are now an essential part of medical training. As a consequence of that, we can see this dramatic rise in life expectancy. If you were born, for example, in 1897, you could have an average life expectancy of about 47. If you look now, the average life expectancy is nearly 80, so people who are born now have a life expectancy of nearly 80 years and you can see that this rise is almost continuous except for in 1918.

You know the flu that swept the entire world, the influenza pandemic of 1918, you can see what a huge impact that had on average life expectancy and a lot of that was because young children and infants would die very young and so the average life expectancy dropped dramatically in 1918. Other than that you can see this huge improvement. The suggestion is that now we have educators who through trial and error, through being in the classroom especially within the past 150 years or so that would had universal education, educators have started to develop a number of different methods. In the same way that medicine didn't really know why some of their methods worked didn't really know why some of their methods didn't work, teachers are in similar state now.

Just like medicine was becoming an evidence-based field a hundred years ago, education is now moving in that same direction and starting to have much more evidence taking into the decisions. If we think about for example the Institute of Education Sciences, which is the funding arm of the Department of Education, they're driving towards a lot more randomized control trials of the same sort that we would typically think of as being the gold standard in medicine so you see these types of changes. In the same way that we might think of biology as the foundation for what's happening in medicine, neuroscience and psychology can provide the basic science that supports education. That means that neurosciences and educators will be required to start to learn to translate between their different fields.

One thing that really highlights how far we come in terms of medical education and what we might think about as a model for what we want to do in terms of thinking about changing teacher education is to look at this Flexner report, so the Carnegie foundation funded this guy, Flexner, to basically go around the United States and look at medical schools all throughout the United States. In 1910, he visited with Wisconsin and he looked at the medical schools in the state of Wisconsin. If we look in Madison, you see that you have the University of Wisconsin, College of Medicine organized in 1907. The entrance requirement to get into medical school at the University of Wisconsin in 1910 was two years of college work including sciences and that was rigidly enforced.

There were 49 medical students here at the University of Wisconsin. "The laboratory facilities complete in number were admirably equipped with respect to both teaching and research. A successful effort has been made to provide facilities worthy of students on a two-year college basis and of teachers deserving opportunities for progressive work. The department lacks only a building which shall bring its parts together." That was in 1910 where we were at.

You compare that with Milwaukee. Milwaukee was a stock company, it was organized, now nominally, the Medical Department of Marquette. To get into medical school in 1910, the entrance requirement was a four-year high school education or its equivalent. That's all it took to get into medical school in 1910.

The summary for the state of Wisconsin I think is quite telling. Flexner says, "Wisconsin presents a simple problem. The two Milwaukee schools are without a redeeming feature. It is claimed that the examiner representing the state board enforces a four-year high school standard, but it has been impossible to procure any information at all from this official though repeated efforts have been made to do so.

Neither of the schools meets the most lenient standard in respect to laboratory outfit or teaching. As for clinical facilities, they are hardly more than nominal. A western state so admirably organized on the educational side furnishing excellent college opportunities without cost to the student is surely in position to meet Minnesota and Indiana in the matter of practice standards. The requirement of the year or two of college work as preliminary to practice would quickly leave the medical department at the state university in sole control." Here just a hundred years ago, you ask anybody who's a premed undergraduate here about their experience and it's radically different from this.

It is not four years of high school to go to med school. It is four years of extremely rigorous college coursework in a very competitive environment, especially to go to the top med schools. Flexner issued this recommendation. He said that we should actually reduce the number of medical schools.

He recommended which ones be closed that would then in turn reduce the number of poorly trained physicians; increase the prerequisites; train physicians to practice in a scientific manner; engage all medical faculty in research; give the medical schools control of clinical instruction in the hospitals; strengthens state regulation of medical licensure. If you look before this report, 16 out of 155 medical schools across the entire United States required two or more years, only 16 out of 155 so just over 10%. By 1920, this number had risen to 92%. One thing that that's unclear about is how much the Flexner report caused these changes rather than reflected changes that were already happening in society and captured the zeitgeist of the moment, what were people already thinking?

Where was the direction of things at that moment? As a consequence, there were number of positive things so we think about now the six plus years of formal instruction that physicians receive, that medical research adheres to the scientific protocol, that average physician quality increases, and medicine has become this highly paid and well-respected field. On the other hand and especially if we are to think about this as a potential policy implication that we might change education training, so teacher training, in the United States. More than half of all the medical schools merged or closed and the cost of medical school increased.

Many fewer women and minorities were able to attend medical school because of these changes and then there were fewer MDs which differentially impacted the underserved communities. Communities that already had too few doctors had even fewer. If we were to think about the changes that education and neuroscience coming together might have in terms of teacher training, we have to think of both about the positives and also about the potential negatives and how we might try and manage this transition to raise the standard for teacher education on the medical side and then also raise the standard for what we're doing on the neuroscience side for trying to bring in the insights from teachers, from school districts and really think about the experiences that are driving children brains in various different ways. Eventually, we might see this in the same way that we think about medicine that there are these many layers of experts.

You have, for example, people who are basic researchers in genetics, chemistry, physics, basic biological processes. Some of these people may also then engage in translational research. Some of them may for example be dual MD PhDs who engage in some basic and translational research that's inspired by their practice and then also think about various different application of the things that they're doing in the research. If we think about the majority of people, they typically end up in just one of these boxes.

Then interposed between this basic research, are all of these different things making sure that what the basic research is suggesting actually scales up If we look at for example, phase three trials, some place between 50 and 80% of ideas that look like they're possibly good ideas, potentially useful ideas. In the early development phases don't actually succeed when we get to phase three trials. There's a huge disconnect between for example biological research and what eventually ends up being evidence-based when we think about going out and helping lots of patients. Then eventually, we have the individual people who are working directly with the patients so their family members, doctors, nurses all of these people.

In the same way, we might think about education as having many layers of experts including people who are doing basic research in chemistry and biology, neuroscience, psychology, educational psychology thinking about perhaps the educational materials industry as equivalent to the pharmaceutical industry with some of the same concerns about conflict of interest that you see in pharmaceuticals. You might also be concerned about some of those in education. Then the Institute of Education Sciences, IES, playing some of the same role as the FDA and starting to think about regulation of these things but also for example school boards. And then eventually teachers, parents and TAs influencing the experience of an individual student.

As you can see here it's very unlikely to any one person ever would fill all of these roles. Either in the medical side or in the education side. We expect this on the medical side that we're going to see people who are doing more of the basic research, more of the applied or translational research and then people whose primary role is really in interacting with patients. We don't think about it the same way on the education side, that there are people doing the research, that there are teachers that some people might bridge multiple different levels and so I think that this is one of the things that as we start to grow this field we need to think more and more about.

How do we train people to be able to be effective at multiple different levels? For me, this is the big point. Education builds brains. Every time we're learning something we're changing the brain.

In my lab we're interested in three main areas so primarily thinking about math and number but also thinking about the impact of things like executive function, attention, visual spatial processes. Thinking about math and number also is something that links up with reading processes so you have to recognize those numbers on the page. We think about executive function as the domain general ability. Being able to focus and pay attention helps you to learn to read, helps the child to learn math, helps them to learn to ski or anything else that they might want to do, so being able to focus, this executive function is not specific to a specific domain of learning.

On the other hand, when we think about math and reading those are the domain specific abilities. So we can examine all three of these to contrast the general principles of learning, to start to identify what's going on for math in particular, what's going on for reading in particular and then what's going on more broadly. If we look at a lesson from lots of neuroscience studies, it suggests that frontal brain regions are driving the specialization of the posterior circuits. They are involved in math, number and also in reading but those circuits aren't coming from nothing.

I want to talk just a bit about the importance of math more broadly. If we think about math at a national level, we can see that the United States for example is ranked number 25 on this Pisa competition, so that's international ranking. You can see Finland and Korea are performing extremely well compared to the United States, but this is something that we see often in the media, that this is a threat to American dominance in science, technology, engineering, math field, the STEM fields broadly. But it's deeper than that, so if we think about not only math skills at this level and think about individual people's lives what we can see is that people's math and number skills numerously broadly explains differences in HIV patients and their ability to actually comply with the medication instructions that they receive.

Sometimes these medications require that you take half a dose at one time, half a dose at another time, two hours before a meal but three hours after some other pill that requires food to be taken with it. HIV medication can be extremely complicated and actually following that it turns out that that depends on math and number skills in a variety of different ways. Similarly it can be shown that number skills contributed to the subprime mortgage crises, people with poor math skills were more likely to actually enter into a predatory mortgage and were therefore more likely to be in a bad financial situation. Then finally in the UK, they followed a group of people who were born in 1960 and then looked at their, basically, High School Exit Exams, they're A levels, looked at their math and their literacy skill and then look at, for example, how often had they been in trouble with the police.

The blue bars are people who struggled both with math and with literacy. The red bars are people who had good literacy skills but struggled with math. Then the two brown bars are people who had struggles with literacy but not with math or struggles with neither. What you can see here is that people who had struggles with math independent of their literacy skills were more likely to end up having been cautioned by the police, having been arrested, having been suspended from school.

These same people are more likely at age 30 to report that they're depressed. They're more likely to have actually seen a clinician for symptoms of depression at age 30. There's A level scores at age 16 in math are predicting this thing, so we typically hear in the United States think of literacy as king. Children go from learning to read, to reading to learn.

Part of what I'm suggesting is that we've been ignoring another very important component which is how much math is contributing not just to STEM fields but also contributing to all of these aspects of day-to-day living. What we can see is that there are these stable individual differences. This is a meta analysis of eight studies. There were six in the United States, one in Canada, one in the UK.

They looked at school entry math skills in kindergarten or first grade and then looked at math skills in later years. They looked at reading skills at school entry in later years. Those later years varied between about sixth grade and high school entrance. They looked at attention skills, internalizing and externalizing social behaviors and also social skills.

What you can see here is that math skills at school entry predict math skills years and years and years later. At one level this sounds fairly intuitive, math predicts math, but at another level, this is really a striking finding that children are changing what they're being asked to do in math. They're being asked initially to do basic arithmetic, to just deal with number symbols and think about the quantities that they stand for. Then they're being asked to enter into symbolic relations where X stands for some unknown.

They're then being asked to use various different visual spatial manipulations to think about trigonometry. Then finally on up to, for most high school students who are college bound, on up to calculus. We're asking children to do lots and lots of different things throughout their educational experience, so the fact that math predicts math is a really striking finding that suggests that there might be some stable individual difference. Importantly, this study then also controls for some of the other big factors that we know about.

For example family education background, family income. This study is controlled for that and when you enter into this meta analysis those have already been factored out, we still see this individual difference. The question that we've been asking is, what is that stable difference? In a number of different studies they started to suggest that number sense, or the ability to understand quantity might be the key for making this stable individual difference in math abilities.

If you look at people in cognitive neuroscience and education and even in special education, a number of different people started to converge on this idea of number sense. We can see for example that children with math difficulties have deficits in basic aspects of number sense including things like magnitude comparison, just saying, which of two sets of dots is more, which of two Arabic numerals is more, in counting even in identifying those symbolic Arabic numerals. We can be more precise about what this number sense is by thinking about what we call the approximate number system. It's this basic system for understanding quantities.

It works like other perceptual system so in the same way that you can see that something is redder or bluer, you can see that things are more or less numerous, but it only gets us a rough estimate of number. It's not an exact symbolic system and it's present even without education so we can see it in infants, we can see it in non-human animals, we can see it in people for example tribes in the Amazon that has a limited number of vocabulary. It suggests that this is a shared foundation. I'll show you guys two fairly quick videos.

In the first, this is from Liz Brannon and her group down at Duke University and what you're seeing here is a six-month old infant and you're mostly watching his eyes. The pinwheel will draw his eyes to the center and then here on the left you can see that there are dots that are alternating in number. Whereas here, it's the same number of dots repeating over and over again. As you can see he's already picked up on the fact that the number of dots is changing on this side and changes more interesting than things that stay the same.

Notice that the displays here are changing position, they're changing size. This is also changing position and size so it's not just any change. It really seems to be that changing number is attracting his attention over here and the fact that he can pick up on that change, tells us that he is sensitive to the difference between those two quantities. Interestingly, he can do this when it's a two to one ratio, so 10 versus 20 for example, but he can't do this at six months if it were 10 versus 15, so a three to two ratio.

By the time he's nine months old, he'll be able to reliably do three to two and you and I as adults can reliably do about 10 versus nine. This system becomes much like our other perceptual systems becomes more precise with age. Then we can show that even monkeys can perform basic non-symbolic operations over these quantities and so this is Liz Brannon one of her students Jessica Cantlon, they presented these monkeys with videos. For example, six dots and then four dots are taken away and the monkey has to choose how many dots are left behind the screen.

One dot, one dot, two and you can see on some trials the number of dots that is correct is very different from the number of dots at the-- That's the incorrect trial. The ratio between the correct and the distractor is very large and so that makes it pretty easy for the monkey. On other trials, you can see that the two are pretty similar and so that makes it very hard for the monkeys. Monkeys, when it's hard, will be less accurate not surprisingly and will also take more time to make their decision, but then the kicker is that Jessica and Liz had undergraduate students at Duke do exactly the same thing.

When they made sure that the Duke undergraduates weren't able to count, Duke undergrads and these monkeys performed essentially the same. As it got harder, Duke undergrads did worse, they also took longer in the same way that the monkeys do. This suggests that there's a shared system that's not just doing quantities but really doing mental operations on those quantities that we inherit as big primates. Then we can even start to drill into what is the neural system that supports this.

Andreas Nieder when he was a post doc at MIT with Earl Miller, got a very simple study. He just presented monkeys with a set of dots, say for example, four dots and asked them to remember how many dots they had been presented with over a delay of one second. Then they were presented with either a non-match stimulus, so three dots after seeing four or stimulus that matched in number. Here you can see again the position of the dots varies, the size of the dots varies so it's not just a simple perceptual matching.

It really isn't some sense recognizing the sameness of the number. Then if the number matched, the monkey released the lever and got a juice reward. If the number did not match, the monkey would hold that lever for the entire duration then the match stimulus appears and then they release the lever to get the juice reward. Then they recorded from individual neurons in parietal cortex in particular the in the fundus of the intraparietal sulcus and also in prefrontal cortex.

What you can see is that there are individual neurons that have become either were there already or through the training paradigm we weren't really clear on in these early studies. More recent studies have suggested that they were there but they become much more precise with tuning with that-- In their tuning with practice, but they respond to number. You can see for example here is your standard firing rate histogram for this shaded period where the number was actually presented. This neuron fires some for one, fires more for two, more for three, four and then back down for five.

You start to see this really nice tuning curve where this neuron is tuned for four items. Then he introduced various different controls for example controlling for the area of the number. Here's a neuron where you can see that in fact it fires less than its baseline firing rate for all of the numerosities. What you can see is that that decrease occurs for one, two, three, four, five so you see there's a decrease in fire rate.

You again see this tuning function. This neuron would seem to be tuned for one. If you look across lots and lots of neurons and you start to average across those populations, what you can see is that there's a bank of these neurons in the intraparietal sulcus that show these tuning functions. Critically, if you plot this on a log scale, you can see that these tuning functions are actually symmetrical, which is just what we see when we think about that ratio behavior that the infant was showing us, that it's not the absolute number, it really is a ratio and again the same ways that we think about for other perceptual systems.

Then if we start to look at what we see not only in monkeys, this parietal-frontal system but in three-month old infants, in a study that I'll tell you more about where we looked at translating between quantities and symbols in children, even doing approximate subtraction in adults and integral calculus in adults, these same parietal networks are recruited over and over and over again. This suggests that when we think about math and number, we're really thinking about this approximate number system as a foundation. This foundation down here is what we share with animals, what's present already in infants and then we start to build on that. We link that up with various different other cognitive and neural systems, the spatial systems, language systems, body representations for example, finger counting, Arabic numeral symbols and so on and so forth.

Obviously, some of these types of things fit well in the constraints of an fMRI environment. For example, if we wanted to do an fMRI study of Andrew Wiles' solving Fermat's Last Theorem that might be something that wouldn't fit into the constraints of the MRI environment. We have more information about some of these basic processes and much less about for example the understanding of the complex plane or people doing various different topological proofs. This would be interesting to start to explore but they don't lend themselves well to the neuroimaging environment.

I'll tell you more about some of these basic things. The fundamental idea is that we take that approximate number system that we have and we start to link that with other systems. Primarily today, I'm going to focus on these two, thinking about linking quantities with number symbols and then thinking about linking quantities with the spatial system, a sort of mental number line. The big goal is to understand, how do we go from this to this?

To break this down into a more manageable chunk, we might look at the acquisition of number symbols in young children. There's a computational model that suggests that exactly the same neurons or the same artificial neurons in this model that respond most to, for example, three items in the world, also through training come to respond to three as a number symbol. If we see this prediction, we can actually start to design a test for this. I can't record some individual neurons in parietal cortex in kindergarten through third grade children.

What can I do is indirectly measure the average of their population response. Let's say that I've got a neuron in this case this is from a study that Manuela Piazza did in 2004, 16. This neuron responds really strongly to 16. You show it's 16 dots.

Because it responds strongly, it also adapts a lot. Its adaptation is proportional to firing rate, a neuron that fires strongly to 16 will adapt a lot. A neuron that responds most strongly to 20, also fires a little bit to 16 and therefore will adapt a little bit. A neuron that responds most strongly to 24, won't respond at all to 16 so it doesn't adapt.

You present 16 over and over and over again and the responses to neurons that are tuned for 16 will decrease and the fMRI signal will then correspondingly decrease. Then you can present for example 16 dots again which would give you a small response. You could present 12 dots which should give you an intermediate response, eight dots which would give you a large response and then vice-versa for 20 and 24. Then you can search the whole brain for regions that show stronger responses to far deviants than to same or close deviants.

When Manuela did this, she found that these parietal regions bilateral were exactly those regions that were responding more to the far deviants than the close deviants. Then in other runs instead of adapting to 16, you can adapt to eight or 32 so that you can show that it's nothing specific about eight or 32 or 16, it really is something about the history of adaptation. That type of method now has been applied to show that four-year-old children also show this and they respond more strongly to number changes than to shape changes in parietal cortex, more strongly to shape changes than number changes that change from, for example, from circles to triangles down in ventral visual areas that are involved in shape and object recognition. Similar sorts patterns even in three-month-old infants.

Then you can look to see whether or not you can test the link between quantities and symbols by, for example, showing adults in this case 17, 18, 19 and then you show them 20. 20 is close so you'd expect a small brain response. 50 is far so you'd expect a large brain response. The key trick here is that sometimes 17, 18, and 19 are presented as Arabic numerals and then you're presented either with Arabic numerals or dots, so digits or Arabic.

Sometimes you're presented with the dots and then the Arabic. What you can see is that in all four cases, the same parietal region show this rebound effect where they respond more strongly to the far deviants than to the close deviants so independent of notation we see this link between quantities and symbols. We use this in kindergarten through third grade children to start to explore this but we showed them something that was slightly more child-friendly, six dots or eight dots. We told them that they were helping Sally the scientist and our team to get back to earth and so all they had to do was press the button when they saw the planet.

These were our kids, I won't go into all of the details here but suffice to say they were fairly typically developing. They were private school kids and actually if anything they're slightly doing better than the standardized test would predict for their grades. The key thing is that we found exactly what we predicted. We found this crossover interaction where after seeing say, for example, eight a bunch of times the response to nine was small, the response to five was large and vice-versa after seeing six a lot of times the response to five was small and the response to nine was large.

That was in this intraparietal sulcus region especially in the left hemisphere here so just where we'd expect it to be. There's some additional complications that I think are really interesting. I won't have time to get into those because I want to make sure that I talk a little bit about some of the math,the mental number line stuff. But if we look at this, we can show that there's a nice relationship between the response to the close deviants, so the precision of their quantity system and years of schooling but that's then mediated by behavioral test of how they do just on comparing non-symbolic quantities.

And that's true for the digits and for the dots. It suggests that these links between schooling experience and how the brain responds are then mediated by another individual difference measure that we can start to link. This tells us how the brain is starting to build these links between that quantity system and that Arabic numeral system, it's mediated then by the precision of the system. I'm going to skip these two questions because I want to make sure that I get also into this number line stuff.

At a higher level, we might start to think about making links not just between quantities and symbols but also between quantities and space. We typically think of numbers along a mental number line. Small numbers are on the left, in our culture where we read from left to right, large numbers on the right. You can actually show that that direction shifts in different cultures, but the idea that there's this link seems to be fairly universal.

If we start to compare brain regions that are involved in calculation with brain regions that are involved in eye movement, we see the strong overlap between those systems. We also see a system that's perhaps involved grasping so this might be a part of the finger counting link although I won't talk about that today. On the education side, there's really nice work that's been done for example by Bob Ziegler and one of his students, --, where they looked at taking children from low SES background so these were Head Start children who haven't had a lot of experience playing board games. They looked at their number abilities and they did really poorly.

One test that they asked the children to do was simply to place numbers at their appropriate position along a line. If you ask them where five went, they sent five went in the middle, but if you ask them where one went, they also said that one went in the middle and that nine went in the middle. They basically had no idea about organizing number spatially. Then they played one of two games and this was a fairly brief period.

I think it was 20 minutes a day for one week. They played this game in the schools and children who played this linear game showed a marked improvement. Children who played the circular game did not show this improvement. They also did it in a version of the game where they had numbers and the child had to move a certain number of spaces based on a spinner or game more like candy land where they just had the colors and they had to move for example from the blue square to the next green square and they didn't think about numbers so they had exactly the same experiences except for they were focusing either more on numbers or more on colors.

In both of those cases, they were able to show that this little bit of board game experience, changed how they did on this behavioral tasks and that then generalized to a number of other math abilities. We think about this mental number line where numbers are represented with more similar numbers close together, smaller numbers on the left, larger numbers on the right. What I think is happening here is that there's actually the evolutionary precursor. In monkeys we already see these networks for number and for space intermingled in the intraparietal sulcus.

Then education is basically taking those retraining it and building on it. Bob Ziegler talks about what he called the Wisdom of Culture. Educators through lots and lots of experiences have found things that work and they passed those along. Those things that work are the things that are easiest for our brain to acquire because the way that our brains are setup.

Educators have done it on one side. We're coming at it on the other side but these two ideas then mean that we see this convergence across neuroscience and education to think about spatial representations of numbers. We can even start to then do various different behavioral tasks that show that there this is this spatial link between numbers. One simple version is that we ask people simply to indicate whether a number is odd or even.

In one block, they indicate that the number is odd with their left hand and the other block they indicated that it's odd with their right hand. Then unbeknownst to the subject what we're really interested in is, how big is the number? One is a small number, nine is a large number and then we just take the amount of time that it takes them and subtract the right hand from the left hand. If you're faster with your left hand then right minus left is going to be positive.

If you're faster with your right hand, then right minus left is going to be negative. You can see this very clear relationship where people are faster with their right hand for big numbers, faster with their left hand for small numbers. It turns out it's not just hands, so if I had you crossed your hands, you're now faster with your left hand on the right side of space for big numbers. If I ask you to move your eyes to the left or to the right, you're faster to move your eyes to the left for small numbers.

If I ask you to do it with foot pedal responses, you're faster with your left foot for small numbers so it seems to be independent of what affecter you're actually using. So it's not just for example typing experience. It's something much deeper than that. We started to look at exactly this.

I'm going to skip a couple of this setup slides. We started to look at exactly this by having people in the scanner do exactly that SNARC and also have them make eye movements in the scanner so they either move their eyes to the left or to the right. In some blocks, we had them respond with their right hand on the right side of space. Some blocks they responded with their left hand on the right side of space.

In this way we could actually disentangle the hand that they were using to press the button in the side of space that they were responding on. We could then define three different spatially selective regions along the intraparietal sulcus. We can define a region that is selective to the hand and that's in the more anterior portion of the IPS and so for example here you're seeing in the left hemisphere right greater than left, left greater than right in the right hemisphere. This is not a surprise.

Here we can see that the side of space matter so left versus right and right versus left. It's hard to see but there is a little blob right there and then finally we can see this for eye movements leftward versus rightward eye movements. Once we define those regions we can then ask, how does, for example, left hand versus right hand responses impact brain activity? We do the same thing that we've done before with that subtraction right minus left.

So in the left hemisphere, not surprisingly we expect right hand activity. Right hand movements to illicit greater activity, that's what we, see vice-versa. In fact, that should not be a surprise because that's also how we define that region. Same thing here with space, same thing here with eye movement.

The real kicker though is that when we look at number magnitude and what we can see here is that there's a small but significant effect, a small but significant interaction between magnitude and hemisphere in the same direction as these eye movements. This tells us that the same brain systems that are involved in moving your eyes around in space are also involve when you're dealing with numerical magnitudes. This effect was, as you can see in terms of the effect size, in terms of the actual signals, about the same as what we saw for actually moving your eyes but the variability here was much less. The variability here was much larger.

We look at this, we only had 12 participants in the study. But we did look to see if there was a correlation between their behavioral measure and their fMRI measure and we did see that those too went in the same direction but it was not significant, probably just the 12 subjects. Then we wanted to dig into this further. I won't tell you about the ERP study because I really want to talk about this one.

What we did here is we had people in the scanner and they had a little rest period and then they were warned, you're going to do an addition task. You're going to see this set of dots for example for 300 milliseconds then there's a delay. They're reminded that they're doing addition. Another set of dots 300 milliseconds and then they're asked to mentally add these two.

Then once the delay period is done, we asked them to indicate which of these is the correct one. We did that for small and large quantities with arrays of dots, also for small and large quantities with symbolic numerals and then we also had some colored trials where they just saw blue, blue and picked blue so the stimuli were identical. Critically, what we did is we trained up a classifier on leftward versus rightward eye movement, so this was a support vector machine and we just trained the classifier to discriminate leftward eye movement versus rightward eye movement. What you can see here is that not surprisingly, the classifier could do this.

This is a fairly trivial task. For all of the participants the classifier could do it. But then we took that same classifier and we fed it the data from when people were doing the addition and subtraction tasks. What we're able to show is that the classifier without any additional retraining on exactly the same voxels that we had used previously was able to discriminate addition versus subtraction.

In the same way that we could discriminate leftward versus rightward saccades, we could discriminate addition versus subtraction. This again tells us that those same brain systems that are involved in moving your eyes around in space, shifting your attention are also involved when you're doing basic arithmetic. This suggests that there's an integration of these numerical and spatial systems to support that mental number line both when you're dealing with just individual magnitudes and when you're thinking about quantities. If you're doing an addition, it's like moving your attention or your eyes to the right.

If you're doing a subtraction, it's moving your attention or your eyes to the left. We see this in the fMRI study, also in the ERP study eye I skipped. This suggests that there's really this spatial mapping when we're dealing with numbers. This then leads me to the last thing I want to talk about which is children who struggle with math.

We all have heard of dyslexia. There's a math version of this called dyscalculia. It's about 10% of the population so it's just as common as dyslexia, but almost nobody has heard of dyscalculia even educators, teachers out there in the schools, haven't heard of dyscalculia. Scientific research is just now starting to catch up in exploring what's going on with math learning with dyscalculia.

One idea is that if we go back to that foundation, that approximate number system, there are difficulties in that approximate number system. That's supported by looking at performance on a simple task where children and adults are just asked to compare sets of dots. If you need a small difference between the set of dots to compare, then this is a small number. For example, for adults when they're comparing nine versus 10, 0.1 is the difference that they need so basically 10%.

On the other hand if you need a large difference then this is a large difference. Say for example 15 versus 10. What you can see here is that if we look at a group of five year olds, this light gray traces their distribution. A group of 10 year olds, this is their distribution and so obviously 10 year olds get better.

Adults are even better than that, but if we look at 10-year-old children with dyscalculia, with math learning difficulties, they look just like the typically developing five year olds. Those distributions are almost perfectly overlapping. Here are these children now maybe they were developing perfectly, typically until they got to age five and then their brains didn't respond to those educational experiences in a typical way, maybe they're on the same trajectory but they're just delayed for the 10-year-old dyscalculic versus the typically developing. We don't know because this is just one data point.

Then in the study that looked at comparing these arrays of dots, so non-symbolic quantities, they also found that people with dyscalculia recruited this intraparietal sulcus region less. This suggests that there's a biological difference here and we can even see that math learning difficulties are associated with for example low birth weight and fetal alcohol syndrome. Some evidence suggests also in Fragile X so all of these different things that might hit parietal systems are also associated with math. These are people who don't have any of those sorts of things and just have a specific learning difficulty with math.

The suggestion is that as we start to better understand these brain systems for math, we start to understand the approximate number system and start to understand its links with counting, with symbols and then also with space, that we might be able to not only identify but even help to effectively remediate this math learning difficulties. One attempt at this is an adaptive game that increases in difficulty and it focus along the same skills that I've been talking about today so it looks that there's approximate number system so you just have to pick the side with more so that you get to move along the game board and then try and win the race. It starts to build links between quantities and symbols, and then it even has this basically organized mental number line. You can see for higher levels for example that it even starts to involve various different numeric operations.

This game based on research of principles has been shown to be helpful for some of the children that are struggling with math learning difficulties. To wrap this up, educational neuroscience is this emerging field that's bridging the social and the biological sciences. I think that future progress in this field really will depend on bringing together educators, psychologists, and neuroscientists to find that common ground that we share when we're thinking about questions and education in neuroscience. Obviously, educational experiences are not the only one but they are an important one that is building brains.

When we look at for example the brains of students here at UW-Madison, we're inherently selecting a very non-representative sample of brains. We do all these MRI studies on college undergraduates, but they get into an institution like this because they're not the average student in the state. In fact, many of the students graduate high school and never go on to any university much less a university like this. We're always looking at these brains that have been built through educational experiences and are, some sense, non-representative.

We don't know how non-representative but we know that they must in some sense be non-representative. Turning more specifically to the things that I'm looking at, we think about how language and education build this exact concepts of quantity. Then we link that to number symbols, space, eventually even on to higher order reasoning which I haven't really had a chance to touch on, but then those same cognitive systems might be linked even in different ways to different brain systems depending on those experiences. We can show how differences in brain structure and brain function relate to differences in math ability.

Then the hope is that we can start to use these insights to explain math learning difficulties and evenly to targeted remediation to help out these children. Across the board, this type of field is leading to a number of different policy suggestions about the importance of math, about identifying math learning difficulties, and then the things that we might do, not just in my lab, but then more broadly thinking about all of these as examples of this broader field. I just want to say thank you and thank you to all of my collaborators in Paris and at Vanderbilt, thanks. Thanks.

applause