SciTech

Brain function follows specific patterns while doing math

Credit: Courtesy of nelsonmania via Flickr Creative Commons Credit: Courtesy of nelsonmania via Flickr Creative Commons

Everyone's got their own tips and tricks to solving math problems. But a research team at Carnegie Mellon may have scientifically standardized the actual process our brain undergoes when thinking about math.

The researchers recently published a new report in [ITAL]Psychological Science[ITAL] that describes the various mental stages the brain undergoes while doing math. The team was led by John R. Anderson, winner of the 2016 Atkinson prize for Psychological and Cognitive Sciences by the National Academy of Sciences and R.K. Mellon University Professor of Psychology and Computer Science at Carnegie Mellon University. The study was funded by the National Science Foundation and James S. McDonnell Foundation.

The researchers used two analytical methods of functional magnetic resonance imaging (fMRI) to view different parts of the brain. These images were then used to identify different processes the brain uses to do math, which were condensed into the four stages of problem solving: encoding, planning, solving and responding.

"How students were solving these kinds of problems was a total mystery to us until we applied these techniques," said Anderson in a university press release. "Now, when students are sitting there thinking hard, we can tell what they are thinking each second."

The two analytical methods the researchers combined are called multi-voxel pattern analysis (MVPA), which identifies the momentary activation patterns in parts of the brain, and hidden semi-Markov models (HSMM), which analyzes the long-term effects of these patterns.

The next step for the team, which also included Aryn A. Pyke and Jon M. Fincham of Carnegie Mellon's Department of Psychology, was to test whether or not their predicted mapping matched up with how real people think.

The test consisted of 80 subjects, each of them provided with 88 math problems. The subjects were given different types of math problems, i.e., the problems would focus on a different stage of problem solving and feedback in the form of a light that lit up red when the answer was incorrect and lit up green otherwise.

The problems involved teaching the 80 subjects mathematical symbols, tools, and equations that were absolutely new to them, and then make them navigate the otherwise basic mathematical problems using those tools.

It was found that the specific complexity in terms of the stages of problem solving correlated with the time taken by the brain activity during that stage. For instance, if the problem was more complex in terms of the “planning stage,” the process stage of the brain while planning would be longer and proportional to the complexity of the problem.

This study not only allows scientists to understand how the brain works with math, but can also be instrumental to designing curriculums and understanding how this applies to other creative problems.

Although this is significant progress towards a greater understanding of cognitive processes, researchers still don’t quite understand how these tasks can be mapped onto other real-time tasks and fit together as a coherent whole. However, this research has opened door towards an application of these techniques to a wider range of situations and topics.