Expert mathematicians stumped by simple subtractions

This was an interesting psychological article about how the phrasing of a word problem — in particular, adding extra information that has no bearing on the solution — can affect its perception of difficulty. Money quote:

“Sarah has 14 animals: cats and dogs. Mehdi has two cats fewer than Sarah, and as many dogs. How many animals does Mehdi have?”…

“[I]n the problem with animals, we look to calculate the number of dogs that Sarah has, which is impossible, whereas the calculation 14-2 = 12 provides the solution directly,” explains Jean-Pierre Thibaut, a researcher at the University of Bourgogne Franche-ComtĂ©. …

“One out of four times, the [professional mathematicians] thought there was no solution to the problem, even though it was of primary school level. And we even showed that the participants who found the solution to the set problems were still influenced by their set-based outlook, because they were slower to solve these problems than the axis problems,” says Gros.

The results highlight the critical impact that knowledge about the world has on the ability to use mathematical reasoning. They show that it is not easy to change perspective when solving a problem. Thus, the researchers argue that teachers need to take this bias into account in math education.

“We see that the way a mathematical problem is formulated has a real impact on performance, including that of experts, and it follows that we can’t reason in a totally abstract manner,” says professor Sander. Educational initiatives are required based on methods that help pupils learn about mathematical abstraction. “We have to detach ourselves from our non-mathematical intuition by working with students in non-intuitive contexts,” concludes Gros.