PhD, Easy as 1, 2, 3
You were probably too young to remember when you first learned to count in your native language. You probably also don’t remember when you first understood what “one, two, three, four, five, six, seven, eight, nine, ten” actually meant. Don’t worry, Stefan Buijsman doesn’t remember either (he’s remarkable in other ways) but he is working on a theory to explain the process. Stefan is a Postdoctoral Researcher studying philosophy of mathematics at Stockholm University. Now if you live in Sweden, you might recognise Stefan. He was in the news a lot last year when, at age 20, he became the youngest person in Sweden to earn a PhD.
Despite his accelerated path, Stefan didn’t start out as a philosopher. He got very into philosophy during his undergraduate studies in astronomy and computer science at Leiden University. He then did a Master’s in philosophy, which he enjoyed so much that he decided to continue his research with a PhD at Stockholm University. “I think one of the reasons I like philosophy so much is that I think very quickly and like to work as fast as I can think. Philosophy is one of the very nice occupations where you can do that because you don’t have to do experiments or wait for colleagues.”
Stefan’s PhD research was, as he describes it, “negative,” meaning it refuted the previous 10 to 20 years of work in the field, a fairly standard approach in philosophy. Stephan found that they were very abstract theories that didn’t taking into account recent empirical work or the realities of how people learn math. After spending 300 pages criticizing everyone else’s theories, he’s now working on one of his own. His Postdoc research at Stockholm University is on how kids learn math, focusing on how they learn the numbers, how they learn to count, how they learn to do addition, and how they figure out that the numbers keep going. While there’s a lot of philosophical literature on this topic, it’s disconnected from the current empirical research in cognitive science, math education, and psychology. Stefan examines this empirical data and tries to interpret what their results could mean about the kids’ reasoning and the type of conceptual leaps they’re making.
Take how exactly children learn the first ten numbers for example. Around the world, the underlying processes seems to be the same. First children learn to just say the numerals without understanding what they mean. They need to have these words though before they can properly start learning numbers. Around the 22-month mark children start to figure out that there’s a difference between one thing and more than one thing. It always starts with the distinction between one and more than one, probably, Stefan thinks, because this is around the time children start to make the singular/plural distinction in speech. Once they understand the difference between one and more than one, kids figure out what the number one really means in exact terms. Then they can understand two as one plus one, then three as two plus one and so on. It takes approximately 4 months per number, however the more the parents talk to their children, the faster it goes. Socioeconomic factors, such as parents’ education level and quality of schooling, also have an effect on the speed at which kids learn numbers.
By age four children have learned the first 10 numbers. Stefan says that your performance on certain math tasks at age four can be predictive of your math skills later in life, although you can improve through explicit intervention. Problem is, most young adults don’t see the value in knowing some math—especially when everyone now has a calculator (i.e. a smartphone) in their pocket. Stefan is actually writing a popular science book to address this. The book explores how math applies to the world and how is it useful. On its own, math doesn’t say anything useful about the world, but Stefan shows that it gives you structure. Different parts of math talk about different structures which you can fit on parts of the world. Stefan has also written an adventure book (in Dutch) about math for kids aged 9 to 12 that will be published in the spring. He even does some consulting every now and then for math education companies.
Although he’s learned to avoid making long-term plans (“things always go faster and different from how I think they will,”) Stefan thinks he would be happy as a professor as long as he was able to continue his work outside of the academy. “Only doing academic work feels like you’re very isolated from the rest of the world,” he explains. “I like the feeling that I’m doing something concrete and actually contributing to society. I try to go outside of the academic bubble now and then.”