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.
Joe,
ReplyDeleteWhenever I read your blog posts, I find myself agreeing with them, and then becoming conflicted by them.
I teach kids with moderate to intensive special needs- mostly kids with autism spectrum disorders and cognitive disorders- in Ohio.
I absolutely agree with what you write here, and yet, I am charged so much of the time with teaching this "prefabricated vocabulary" so that my students can even just function in this society we've constructed for them.
I am challenged by what you write and often have to consider and adapt it to fit my needs and the needs of my students.
Thanks for the challenge. :)
Thanks for the great post. I agree with Morgan about being a little conflicted as eventually they need to know the vocab, I guess the question is when to introduce it. With my students (I'm a college physics teacher) I like to make sure they learn things in their gut. I'll ask them at the beginning to check their gut and when I'm doing that I'm asking them about their own constructions, sometimes when they haven't even put words to it yet. I like how you talk about numerator and denominator here as social constructs. I'm curious, at what point would you say "ah, and just so you know, other people call this the numerator and this the denominator"?
ReplyDelete@Morgan I see what you are saying. In special education, it is even harder to balance teaching thinking skills versus coping skills.
ReplyDelete@Andy I'm glad ive instigated some conflict for you. Real learning is often born out of a situation where you've been dislodged from contentment.
Seems to me that the other side of this conversation includes how to connect or relate terms or vocaulary in ways that are meaningful. In the csse of demoninator and numerator, links to money (for the young ones) and religious affiliations (for the more sophisticated) is imperative. The only reason I choose to ensure terms are known is because we still have the grade before and the grade after, and my students need to know the terms to operate or use the terms to connect or make sense of what they are learning. Isn't this still the best job in the world? We get to think all day long . . .
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