Numerical Cognition: To what extent does language processing support mathematical reasoning?
- Chantra
- Nov 7, 2021
- 4 min read
Galileo has been quoted as having said: Mathematics is the language with which God has written the universe. While I grapple with fully comprehending that statement, I believe there is a truth in those words. There is certainly a poetry in the juxtaposition of mathematics and the universe. In this earthly world, mathematics is everywhere: in the architecture that we behold, in the planes that fly in the sky, in the tips we leave waiters and in the homework we ask our children to do.
Despite its prevalence and relevance, it seems that in school children, language ability often outpaces mathematical ability. What areas of our brain are involved in mathematics? Are these areas distinct from those associated with language processing? To what extent does language processing support mathematical reasoning?
There is evidence that a “number sense” exists in humans - regardless of culture or education - that serves as a precursor to numerical ability. In fact, both humans and non-human primates have an innate primitive system for nonverbal mathematical thinking. Studies at Duke University led by Elizabeth Brannon show that monkeys can mentally add the numerical values of two sets of objects and choose a visual array that roughly corresponds to the arithmetic sum of these two sets.1 It has also been shown that infants, too, have this number sense. That is the good news for so many of us who struggle with math: we are born with the potential for numerical ability.
It is likely of no surprise for most people to discover that the pre-frontal cortex plays a significant role in numerical ability. The pre-frontal cortex is where skills of executive function are developed, i.e., skills of planning, anticipating, sequencing, categorization, and implementation of working memory. But what might be surprising is the discovery that mathematical processing primarily takes place in the parietal cortex – specifically the intraparietal sulcus. This is the area primarily responsible for sensory motor functions such as hand-eye coordination, perception of 3D objects, visual attention and visual-spatial working memory. When the brain is tasked with making a comparison of numbers and amounts, subtracting or estimating, this area becomes highly activated. In fact, studies led by Stanislas Dehaene show that this network for math does not appear in areas of the brain related to language development.2
If the areas in the brain for mathematics and language are distinct, what is the relationship between mathematical reasoning and language? A study of the Mundurucu Indians in Brazil led by Pierre Pica sheds some light on the topic.3 The Mundurucu language does not have an extensive vocabulary for numbers. They have words for 1 – 4; for the number 5, their word is translated as “one hand.” They were tested in a variety of ways to determine their ability to compute, compare, and estimate. The results were intriguing. The Mundurucus were not able to carry out arithmetic operations with quantities above five with any precision. But they showed a cognitive capacity to approximate, much like the control group (made up of French speaking men and women). Clearly, though math and language processing occur in distinct areas of the brain, language ability supports mathematical precision.
So, what happens, then, with dyscalculia? It is important first to note that dyscalculia is more than just a difficulty with arithmetic calculation. Students with dyscalculia have difficulty understanding number-related concepts (including time, speed, and distance); often don’t understand quantities or concepts like “biggest” or “smallest”; have trouble with the mechanics of both doing math and applying math; and often struggle with working memory.4 Research findings by Karin Kucian show that developmental dyscalculia is not only associated with alterations in brain activation in the intraparietal sulcus (IPS) but also with changes in brain anatomy: there is a reduced volume of gray matter. As such, dyscalculic children may rely more heavily on supporting brain areas associated with memory, attention, and finger counting by recruiting other regions to make up for the reduced activation in the IPS. The good news, however, is that the brain is highly plastic. With proper remediation and education, there is evidence of less activation in the recruited areas and more in the IPS itself.
Numerical cognition and mathematical processing involves a complex network of systems. Computation requires accuracy, sequencing, memory, alignment, and visual-spatial organization. The application of mathematics, however, involves decoding, comprehension, working memory and process recognition. Finally, mathematical reasoning is the integration of all the above-mentioned skills. Language is what allows mathematical reasoning to be integrated, sustained and delivered. Any remediation in mathematics, therefore, must also include a remediation in language. For while it may be true that mathematics is the language with which God wrote the universe, the sentiment – indeed, the metaphor itself – would be neither penetrable nor possible were it not expressed in non-mathematical language.
Reference
1 Cantlon, JF, Brannon EM Basic math in monkeys and college students; PLOS Biol 5:2912-2910 (2007)
2 Mathematics and the Brain, Stanislas Dehaene
3 Cognition and arithmetic capability: what the Mundurucus Indians can teach us; Centre National de la recherché scientifique; Paris (2004)
Research of Pierre Pica, Cathy Lemer, Veronique Izard and Stanislas Dehaene
4 Kucian, K. Changes in brain function and brain anatomy; from Dyscalculia Blog (2016)
Recommended reading and viewing
A close Look at Mathematician’s brain, S. Dehaene
Math is the hidden secret to understanding the world, Roger Antonsen
Hubbard EM, Diester I, Cantlon JF, Ansari D, Opstal Fv, Troiani V. The evolution of numerical cognition: from number neurons to linguistic quantifiers. J Neurosci. 2008;28(46):11819-24.
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