We started thinking about fractions recently. The children were dividing brownies evenly between two people. The situation was serving mostly as a way for us to access our prior knowledge about fractions before we forged ahead with new ideas. The children had lots of ideas.
Several children started to think in divergent ways by cutting the brownie into four equal pieces, giving two pieces to each individual. Hmmm, interesting.
Then I headed around the room to look at the work of other students. That's when it all started. I was shocked when I saw a drawing by one child. She had decided to share her brownie between two people by cutting her brownie into 8 unequal pieces, some large some small. Yikes!!!
Just then, I started to feel overwhelmed as my mind compiled a list of all of the foundational things we would need to revisit before moving on. I decided to get started right then and there. I began to question her about her brownie in order to help her confront the misconceptions I saw in her work.
"Well, I decided that if each person got the same amount, it wouldn't matter if the pieces were the exact same size. I would just have to make sure that each person got the same number of big pieces and the same number of small pieces so that in the end both people got the same amount of brownie."
My mental jaw dropped! I had assumed. In fact, I had assumed quite a few things and now I was feeling a little bit sheepish. As it turns out, this child knew quite a bit about fractions. Actually, she even knew enough about fractions that she began to think playfully about the task.
Luckily this episode happened in a matter of seconds, completely within my own mind. But it has given me a chance to reflect. How many assumptions like mine do we make on a daily basis? Many kinds of traditional forms of assessment and testing are full of these kinds of assumptions. If it doesn't look like the few things we think fit, then it must signify a complete and total lack of understanding. And yet, could it be possible that a child choosing a "wrong" choice on a multiple choice test may have a very valid and logical reason for their thinking?
This experience reminded me of the power of a question. All I had needed to do was ask.
Thanks for sharing such sincere thoughts. Certainly, we should be more trained in listening to our children and showing more interest in what is going on in their little heads.
ReplyDeleteoh my goodness- we were talking about these kinds of assumptions in the pre-school meeting today...being careful not to assume the children don't know something and that they do know something...it's just listening without judgement, I guess.
ReplyDeleteWhat a coincidence!
This is fascinating. I think children's "wrong" answers may often - sometimes? - be the result of taking things farther, rather than - as we tend to assume - not taking them far enough. Or, they may be looking at a question or problem from a different perspective than ours. I wonder about the desire to cut the brownies into more than two pieces; do the children somehow think that more pieces means more brownie - even though at one level they understand that the two or four small pieces are equal to one larger piece?
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