Sunday, November 11, 2012

Math and Cognition

If you are interested in cognition, language, and mathematics, you will enjoy reading The End of Ignorance: Multiplying Human Potential by JUMP Math founder John MightonDr. Mighton cites recent research in cognitive psychology that "suggests that it is not only the words we use to name physical  objects and quantities, but also the formal and grammatical structures of our language that help to determine our perception of the physical world."   

Interestingly, the grammatical structures of language affect a child's developing sense of number.  (Coexeter Theory: The Cognitive Aspects by Alexandre Borovik)In English, children begin with a "one-knower" stage, where they perceive sets of one accurately but seemingly randomly name sets of more than one with any greater number...two, three, four, etc.  In English, adults say one horse, and then our plural forms - two horseS, three horseS, four horseS, etc.  In other words, the grammatical difference is between one and more than one.    

In Russian, the plural forms are different.  There is a unique plural form for one object, a plural form for sets of two, three, or four objects, and a plural form for sets of five or more.  Instead of a "one-knower" stage where an English speaking child develops the ability to accurately distinguish between sets of one, a child who speaks Russian develops the ability to distinguish between three sets--sets of one, sets of 2-3-4, and sets of 5 or more.
Doing symbolic work can help a child perceive (and also be more motivated to perceive) the concrete world more clearly, just as an unconscious awareness of the grammatical structures of a language can make a difference to the age at which a child can perceive certain sets of numbers...Learning to understand math symbolically is as conceptual as learning to understand it concretely.
The implications are fascinating. Teaching children the symbolic language of math---rules, operations, logic--- builds and strengthens their ability to perceive, classify, and understand the world around them.  When working with children who seem confused by manipulatives, instead, develop their understanding of math symbolically.  

I have had the opportunity and pleasure to work with many individuals who have delays in the structure of language.  Delays in grammar typically affect one or more cognitive tasks such as comprehension in reading and listening, completing multi-step processes from long division to organizing, and speaking or writing to the point.  Excelling in the language of math can be a route to help develop the organization of the brain, and the understanding of how we organize language for meaning - with grammar.