Jesse Orrico

These Are The Four Stages of Your Brain on Maths

No calculators allowed.

2 AUG 2016

Ever wondered how your mind deals with complex sums and multiplications?

A new study has imaged how the brain's activity levels change while taking on serious maths problems, and reveals for the first time that there are four distinct neural stages involved in coming up with a solution.


Two different brain imaging techniques were combined for the study - one that looks at the actual firing of neurons in the brain, and one that focusses on how those patterns shift over time as participants nut out the calculations.

This is the first time that the mental stages of the brain activity have been mapped in such detail, and the results could give us a better understanding of how the brain works – not just when figuring out sums.

"How students were solving these kinds of problems was a total mystery to us until we applied these techniques," said lead researcher John Anderson from Carnegie Mellon University. "Now, when students are sitting there thinking hard, we can tell what they are thinking each second."

Anderson and his team identified four distinct stages: encoding (reading and understanding the problem); planning (working out how to tackle it); solving (crunching the numbers); and responding (typing in the correct answer).

If we can better understand how students are solving problems, says Anderson, we can improve teaching techniques too.

neuro-scansThe four stages of maths. Credit: Carnegie Mellon University

As the 80 students were figuring out the maths problems, the team worked on accurately mapping each brain scans to the four different processes.

Although the problems weren't that difficult, the participants were sometimes shown unfamiliar equations and symbols to highlight the encoding part of the process.

On other occasions, the team presented problems that required more planning, enabling them to identify each part of the cognitive process separately.


"Typically, researchers have looked at the total time to complete a task as evidence of the stages involved in performing that task and how they are related," says Anderson. "The methods in this paper allow us to measure the stages directly."

In the past, neuroimaging techniques have shown us much about how different cognitive processes work, but the aim of this study was to tie some of those processes together in a distinct order.

The research is part of an effort to work towards a 'unified theory of cognition', which is exactly what it sounds like: the idea that all types of mental processing have the same fundamentals underneath. But to make any further progress, Anderson told Benedict Carey at The New York Times, we may need to develop better imaging equipment.

For now, scientists have a much better idea of how our brains go from reading through a maths exam question to coming up with the right answer, and if you want to give yourself a challenge, here's a mind-bending problem for you.

The results have been published in Psychological Science.

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