High school, numbers and the brain.

Of all things the human brain learns, few fascinate me more than numbers. It starts with kids counting, one by one, elements that they care about. How many gifts are there under the tree, how many oranges are there in the bag? 1, 2, 3, 4 … For a long time counting will be the process by which kids navigate through the endless series of numbers. At some point, the problem of addition kicks in. How much does 6 + 5 give ? Let me check … 7, 8, 9, 10, 11. The answer is 11.

Counting and subitising

An illustration of numbers 1 to 10, counted as small circles.

Photo by Nevit Dilmen, released under the Creative Commons License.

Eventually, we develop tricks to go faster, sometimes exploiting the number representation system with base 10. How much does 16 + 13 give ? Well, 6 + 3 = 9 and 1 + 1 = 2, so the answer 29. By then we can jump from number to number, omitting the long path that sometimes separates them. Later, during elementary school, we are expected to understand multiplication. Suddenly the numbers throw each others forward at a much faster rate … 3×3 = 9, 9×9 = 81, 81×81=6561. It begins to be hard to find the mental processes that could handle those calculations. For 1 to 12, people often get trained through repetition to know the results by heart. Ask me what 6×7 gives, I’ll tell you 42, because a teacher of my elementary school has been making me recite this until I knew it. I still have the visual memory of that small mathematics mini-book, and the whole class going through every possible combinations, speaking out loud: 3×3 = 9, 3×4 = 12, 3×5 = 15…

Although the learning process described above is what we wish for everyone, the ability to learn mathematics and the speed at which people learn is highly variable. Presumably, the variation in mathematics performance observed in high school are due to multiple factors including genetic ones and life history. Ultimately, however, these various processes have to affect the brain in some way to exert their influence on learning. There have been efforts for a couple of decades to understand the brain processes underlying numerical abilities in humans and in non-human animals, but the link between the brain areas identified in the laboratory and real-life math learning remains to be determined. A recent study published by Gavin R. Price, Michèle M. M. Mazzocco and Daniel Ansari1 has investigated this by looking at the brain areas activated during the solution of simple mathematical problems in the laboratory and combining those measures with performance at a math test known as the Preliminary Scholastic Aptitude Test (PSAT) math subtest.

The subjects who participated in the study solved simple equations such as 3+5 = ?. Therefore people performed very well at the task, relatively independently from their mathematical aptitudes. But the interesting finding is that although everyone was successful at solving the equations, some brain areas were more or less activated based on the mathematical aptitude of subjects. These activations were measured using functional magnetic resonance imaging. Two brain areas were found to be more activated in subjects with higher PSAT scores: the left supramarginal gyrus and the anterior cingulate gyrus. Another area, the intraparietal sulcus, was found to be activated more in subjects with lower PSAT scores.

It remains to be determined why these areas are differentially activated in individuals with different mathematical aptitudes. For now, the authors of the study propose that subjects with more mathematical aptitudes might recruit brain areas that are related to storing mathematical facts (one could think of those as responsible for memories that are simply recorded and retrieved). People with less mathematical aptitudes might rely on areas that are more involved with processing and comparing mathematical quantities. They argue that the acquisition of mathematical competence might rely, in part, on this process by which people exchange heavy numerical processing strategies to simple fact retrieval or memories about specific numbers. This hypothesis is an interesting one. However, the authors also note that some of the differences between brain area activations in the study might be due to heavier use of general working memory processes that are not specifically linked to numerical magnitude processing mechanisms.


1. Price GR, Mazzocco MM, Ansari D. (2013) Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores. Journal of Neuroscience 33:156-63

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