Reckoning with intangibles


David Landy and the science of learning math

IN 2007 PBS professor David Landy was a Ph.D. student at IU in computer science and cognitive science, studying the cognitive process by which people learn and perform mathematical problems. He was also the father of a newborn baby girl. Graduate research and new parenthood do not always happily coexist. But on one particular night, as Landy held and rocked his daughter into the late hours of the night, he had an idea that decisively shaped the course of his career as a scholar and scientist: a computer program that could dramatically change the way we learn and do math.

Algebra is hard. It's hard intrinsically to think abstractly, Landy observes. Making it even harder is the 500-year-old interface with which mathematicians work out a problem. This ancient interface, otherwise known as paper, has certain advantages, but it also has some unnecessary limitations.

Imagine, he explains, that you were going to learn to play chess, but you didn't have a chessboard and had to recopy the whole board each time you make a move. After five moves, you'd make a mistake. There's too much room for error. And most of your time would be spent in copying, rather than thinking.

Such is the case with algebra.

Paper is static. At each step of a problem, you need to rewrite your equation, increasing the likelihood of making a mistake. A more flexible, fluid medium, Landy suggests, would be less error prone and lessen the working memory load more generally, which simultaneously includes remembering the general rules of algebra and the variables of a specific problem.

The programs he and his colleagues have created address these issues. They also have the advantage of tracking the users’ computational moves, thereby preserving reams of data for further research into the cognitive underpinnings of math and the efficacy of their own applications.

We seem to be really good at dealing with things we can touch and see and work with. Once it gets beyond that, it gets hard.