Friday, November 6, 2009

Learning Math

The brain has an innate ability for estimating quantity as seen in babies and non-humans. However, the human ability to match specific quantities with number symbols, a skill required for doing arithmetic, is a developed skill. It takes years for children to master the ins and outs of arithmetic. New research indicates that this learning process triggers a large-scale reorganization of brain processes involved in understanding written symbols for various quantities.

It is now known from brain imaging studies that the two distinct circuits are involved during math. One circuit gives names to numbers and carries out exact calculations. This shows up on brain scans as large and strictly left-lateralized activation in the left inferior frontal lobe. A second circuit operates intuitively and is used for estimating quantities and other numerical relationships. This one shows up on brain scans as bilateral activation of the inferior parietal lobule. Research also indicates that the cerebellum plays an important role in single digit addition and comparison tasks of math cognition, but the function of cerebellum in math cognition cooperates with the frontal lobe to perform the simple math task.

While this is true for adults, children, have been observed to recruit more of their pre-frontal cortex and depend less on parietal cortex for math tasks. It is generally thought that the parietal cortex takes time to mature and as it does so mental math becomes earier for children. Interestingly, we also find that math-gifted adolescents show more bilateral activation of frontal and parietal lobes. They are able to recruit the right hemisphere possibly for the imagery required in spatial math problems. The bilateral nature of this activation indicates enhanced interhemispheric connectivity via the corpus callosum. Programs designed to develop the whole brain would therefore be likely to improve mathematical ability as would programs that stimulate the frontal cortex.

The frontal areas of the brain, especially the prefrontal cortex houses cognitive skills as working memory and executive function. Both executive function and working memory have been found to be important foundational cognitive skills for mathematical ability. For instance a study of 141 preschoolers from low-income homes has found that a child whose IQ and executive functioning were both above average was three times more likely to succeed in math than a child who simply had a high IQ.

When math test scores in individuals who had higher levels of working memory with those who had less were compared, it was found that individuals with higher levels of working memory have superior memory and computational capacity. However, in a high pressure testing situation, it turns out that the subjects with higher working memory levels performed very poorly—that is, the subjects with the greatest capacity for success were the most likely to “choke under pressure”. This has important implications for assessment such as the COGAT test. Also, as more schools start emphasizing state-exam based curricula, these studies will become increasingly relevant and important for the development of exams and training regimens that will ensure optimal performance, especially by the most promising students.

The type of working memory involved in solving math problems may be affected by the way the problems are presented. When arithmetic problems are written horizontally, more working memory resources related to language are used. However, when problems are written vertically, visuo-spatial resources of working memory are used.

Resoning ability is another cognitive domain builds the capacity for logical thought, reflection, explanation, and justification. Math is about using logic to explain and justify a solution to a problem. It is the mental muscle necessary to successfully explore puzzles. It can also extend something known to something not yet known. Therefore developing good reasoning skills is also important in math ability.

The fact that executive function, working memory and other cognitive abilitiesare significantly related to early math performance, even in children as young as pre-schoolers, suggests that if we can improve the capacity for these skills, we can improve their academic performance.

Infact, this is exactly what we have demonstrated with Neuropath Learning programs. We recently showed that third grade students graduating our programs perform significantly better on state standardized test of math proficiency when compared to students who have not used our programs. Because Neuropath Learning programs build cognitive skills such as visual-spatial skills, reasoning skills, attention skills, executive function skills and working memory skills we have been able to boost mathematical acheivement without necessarily teaching third grade mathematics. Such is the power of cognitive training! For information on our programs visit us at http://www.neuropathlearning.com/ or send me an e-mail to npl@neuropathlearning.com.


References:

Clancy Blair, Hilary Knipe, David Gamson (2008) Is There a Role for Executive Functions in the Development of Mathematics Ability? Mind, Brain, and Education, 2 (2): 80 – 89.

Beilock, S. L. (2008). Math performance in stressful situations. Current Directions in Psychological Science, 17, 339-343.

Michael W. O’Boyle, et al., (2005) Mathematically Gifted Male Adolescents Activate a Unique Brain Network During Mental Rotation, Cognitive Brain Research, 25: 583-587.

Holloway, I.D. & Ansari, D. (2009) Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s math achievement. Journal of Experimental Child Psychology, 103, 17-29.

Shigang Feng1, Yaxin Fan1, Qingbao Yu1, Qilin Lu1 and Yi-Yuan Tang (2008) The cerebellum connectivity in mathematics cognition. BMC Neuroscience 9(Suppl 1):155.

S Dehaene (1997) The number sense: How the mind creates mathematics New York, NY: Oxford University Press

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