Saturday, November 27, 2010
When kids are first making sense of fractions, the terms numerator and denominator serve only as distractions from kids making meaning for themselves.
The idea that one-half plus one-half is a whole is something kids can construct for themselves. The idea that the denominators must be equivalent numbers so that you are adding equivalent size pieces can be constructed by children.
However, the actual word 'denominator' is not and cannot be naturally constructed. The word 'denominator' is socially constructed.
I'm not saying kids shouldn't eventually learn about the prefabricated vocabulary, but I am saying that kids can and should be afforded the opportunity to make sense of fractions before being introduced to such terminology.
The greatest risk of introducing the idea of fractions with prefabricated vocabulary is that kids will come to see the idea of fractions as something they must be told about.
Kids making meaning for themselves comes first. Prefabricated, socially manufactured vocabulary comes a distant second.