Cognitive and Neuropsychological Models of Mathematical Processing - Essay Example

Mathematics is a powerful and resourceful symbol game and the neural pathways to perform mathematical operations are found in all animals. Researchers found that math ability is a survival instinct and its neural architecture evolved earlier than language pathways and also independent of it. Number sense may be indispensable to judge the number of predators or the quantity of food or the size of the turf indispensable for survival (Gallistel C. R., Rochel Gelman. (2003)).  Research to understand brain mechanisms underlying mathematical ability has included not only normal human subjects but infants, patients with injured brains, and even animals. While unequivocal proof is still elusive, several interesting finds have helped make progress. 

Studies confirm the mathematical prowess all of many animals like chimpanzees, birds, and even lions (Gallistel C. R., Rochel Gelman. (2003)), (Brian Butterworth.1999. ) Human understanding of mathematics is more complex and advanced as it involves the verbal pathways as well. According to Butterworth, human cognition of numbers begins from the first day of life. Studies were performed with babies by increasing or decreasing the number of dolls shown to them. A perceptible, intelligent change in their response confirmed the presence of mathematical hardware in the brain right from Birth. In fact, Butterworth calls this an “instinct.” (Brian Butterworth.1999.)

A comparative study of nonverbal counting in humans has been found to mimic that found in animals to prove that the basic foundation of the neural system is probably the same. (Gallistel C. R., Rochel Gelman. (2003)). However, the human brain’s capability to handle complex mathematical components arises from the much-evolved brain, having separate pathways for different operations and their productive interaction.    Although number skills are pre-programmed, Butterworth found that development depended on an individual predilection for practice and cultural & linguistic influences.  (Brian Butterworth.1999.)

Spelke highlighted the language factor in math processing in a behavioral study. Individuals fluent in English or Russian were tested with math problems involving approximations and exact answers in both languages. The results found that subjects performed better with exact umbers when questioned in their familiar language, proving the role of verbal memory pathways. Contrastingly, approximate calculations were found to be independent of language. (MIT News. 1999. May 6th )

Proof that calculations for exact numbers and approximations follow different pathways also comes from brain imaging studies by Dehaene's team. Visual, spatial, and analogical parts were involved in approximations while rote learning (needed for exact calculations) occurred in parts designated for verbal tasks. And the brain “assigned” the jobs to these areas instantaneously, suggestive of being processed there. (MIT News. 1999. May 6th  )

Two theories to explain brain architecture for mathematical cognition are held important for attempts to understand the mystery.

McCloskey’s Abstract Modular Model, says that numbers were processed through three separate and distinct modules that communicated through common abstract quantity codes. They are the number comprehension module, calculation system, and number production system. (Micheal McCloskey. 1992)

Dehaene’s Triple Code Model proposes an auditory area, a visual area and an analogue magnitude area working in conjunction with each other to perform mathematical tasks. The Arabic form mediates tasks like digital input and output, parity judgment and the like, the visual area deciphers magnitude and approximations and the auditory area provides for representation and recall of mathematical facts. (Jamie I.D Campbell.1994.)