Erasing = Learning

I think that the best learning is hidden in the things that we erase. I’m not saying that the best final product is a rough draft, or a sketch of a future painting, or the initial musical concept that leads to a masterpiece.  I’m just saying that erasing indicates a change of mind… it points to learning.

Have a listen to this:

In this demo we get a pretty powerful picture of what will become “Don’t Stop ‘Til You Get Enough” .  The “erasing” is the refining that leads to Michael’s final product.  If I think about the changes that happened and all of the thought that went into those changes, it’s hard for me to describe that process as anything other than learning.

… And that makes me think about my learning at school.

I can vividly remember my high school English teachers asking for multiple drafts of essays, “with all edits made using a  different coloured pen”.  Apart from writing assignments in English, I struggle to remember any other kind of drafting/iterative process in school.

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Maybe that’s why I was so happy when I read Jo Boaler’s ideas about editing in math.  I loved how she contrasted math in schools with math in the world:

…“they have learned, wrongly, that mathematics is all about precision, not about making estimates or guesses.  Yet both are at the heart of mathematical problem solving.
After making a guess, mathematicians engage in a zigzagging process of conjecturing, refining with counterexamples, and then proving.  Such work is exploratory and creative”…

Today I saw such a beautiful example of math editing and thinking in one of my SWST classes. 

A teacher had given her students a substantial assignment to work on with a set of partners.  When the questions were finished, groups gave each other feedback on their responses.  Their teacher gave them feedback too. Next, students had to use their drafts to create a larger scale version of the problem. Then they had to redo the assignment. 

I sat with one group of students for their entire math block.  Their erasings (the original ideas and feedback) were fascinating.  Still more fascinating was all of the erasing that was required to create a larger version of the problem.  Students had to rely on a pretty huge skill set to change the sizing of the shapes (all to scale) and then re-answer the question.

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As I sat there listening, and chatting with the students, time slipped away.  We debated about the best tools for measuring/drawing.  We debated about how reasonable our answers were.  We talked about ways to check and re-check work…  At the end of the math period, they had technically produced nothing.  No final product.  No polished item.  However, all of the conversations and the thinking that had come out of what they had erased would have filled three textbooks. 

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