The phrase “mental math” has a whole new meaning.
Patterns in brain activity are giving Carnegie Mellon University researchers a glimpse at the stages of thinking involved in solving complex mathematics.
“It’s hard to know what people are thinking while they’re solving problems. We decided to explore how brain imaging data might provide a window to gain insight on the internal stages of problem solving,” said Aryn Pyke, psychology research fellow at CMU and study author.
Pyke and her colleagues observed the brain activity of 80 participants as they completed complex math problems, which varied in length and difficulty. Functional MRI neuroimaging indicated that in each situation, four specific activity patterns indicated four distinct cognitive stages: encoding, planning, solving and responding.
The study investigated how variances in math problems affect each stage's duration.
“Certain problems take a long time to plan, but a short time to solve, where other problems take the same total time, but a short time to plan and a long time to solve," Pyke said. "We didn’t know that even though these problems take the same amount of total time, the internal process is very different.”
In the study, participants were first taught that specific operations symbolized arrows that function in the way an addition or subtraction sign might act within an equation.
Half the participants were provided a formula for the arrow operation; the other half had to solve using addition alone. As they worked, a functional MRI scanner, which measures blood flow through the brain, monitored their mental activity.
Specific problems were manipulated to test whether the length of specific stages changed. Some problems were designed to contain a longer planning period while others needed extended effort to complete the algorithms, Pyke said.
After each problem was completed, participants completed an unrelated activity to distract their brains between questions.
It’s an exciting beginning, Pyke said.
"It’s been a real challenge in cognitive research up until the present time to see what people are thinking while they’re solving any kind of problem," she said. "This technique provides a new window to these internal stages we couldn’t otherwise see behaviorally.”
Math is among the first applications for fMRI study. Pyke said she hopes to develop a unified theory about how the brain solves problems so students can better learn to ignore outside thoughts and focus on the task at hand.
“This technique has the potential to provide insight on the different stages that a person is going through and that’s not just for math problem solving, but for any problem solving or thought process,” she said.