In our lab, we study how the Mind/Brain does math. A bit more technically, that means we use concepts and tools from psychology, cognitive science, and cognitive neuroscience to understand how humans acquire, use and teach numerical and mathematical concepts. Our work covers a wide range of topics (please see below for specific ongoing research projects), but there are a few cross-cutting themes.
One theme is that we strive to understand the acquisition and impact of number symbols. The letters in this sentence are symbols. The numbers on your keyboard or phone are symbols. How do we learn what these (number) symbols mean? How does acquiring an understanding of number symbols change the way the Mind/Brain works? Do we see the world differently once we see it through a number-colored lens? For instance, sure, 2+2=4, but, once you think about it, isn’t it weird that 2+2 always equals exactly 4? And why do 2+2 and 2×2 give you the same answer but 3+3 and 3×3 don’t? So in other words, how do we learn to combine number symbols into more and more complex – and sometimes quite counterintuitive – patterns? Does seeing the world in a numerical way thus essentially lead us to see the world in a different way?
Thinking about mathematics makes some people really nervous. Not everyone is comfortable thinking about math and numbers and the sort of questions we asked in the previous paragraph. That brings us to another theme in our research: why do some people get kind of emotional about math, and what does that mean for their ability to do math? As it turns out, emotions have a lot to do with (how we do) math: Around 20% of the population tends to be severely math anxious: they get really tense and nervous when faced with situations where they might – or it even seems like they might – have to do math. And perhaps not surprisingly, math anxious people tend to do worse on math tests, avoid math-related situations, and even avoid entire career paths that might involve math. Why does this happen? How can we stop it? Are there certain types of people who tend to be more math anxious than others? If so, what can we do to level the playing field?
The third major theme in our work: how can understanding how humans do math inform math education, and how can math education inform our understanding of how humans do math? There is an emerging field, sometimes called ‘Mind, Brain and Education’, or sometimes just ‘Educational Neuroscience’, that strives to link behavioral and neural sciences (psychology, cognitive science, and cognitive neuroscience) with educational practice. As ‘MBE-ers’ (MBE-ites? MBE-tonians?), our lab strives to situate the questions we ask as much as possible in the context of math education. First, culture very likely plays a very big role in how humans learn math, and in virtually every modern nation, the biggest ‘cultural input’ tends to be education. If we understand how kids are learning math, we probably know a lot more about how they are doing math – everything from how they combine those weird number symbols to how they feel about doing math in the first place. Second, we believe strongly that science works best when it takes a broad view when it comes to sources of inspiration. In our case, that means taking seriously the notion that the arrow between scientists and educators doesn’t just run from the lab to the classroom, but also the other way around. We want to know the burning questions math educators have for us. We might already know the answer, but odds are we don’t; so let’s design an experiment to find out.