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| The Triple-Header Run-On |
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| The Vertical Right Side Equal Sign |
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| The Upside Down Double Flip |
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| The Order Of Operations Parenthetical |
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| The Multi-Operational Spectacular With Arrow |
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| The It Works For Every Other Operation So Why Not Division? |
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| The Double Division Combo Special |
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| The Fraction Run-On, Whiteboard Edition |
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| The Wait a Minute, I Get To Write On the Table? |
"Mathematics is the language with which God has written the universe," said Galileo. These first attempts at using that language, while not always perfect in their grammar or usage, deserve to be celebrated. If we look only for what's wrong, we'll miss the creativity, ingenuity, and inventiveness our students gift us as they themselves try to make sense of the universe around them.
It's funny isn't it: when a child learns spoken language, we find the funny things they say delightful. Sometimes we even start calling things by the same name. When my son was very little, he couldn't say scorpion, so he said "gumpsy" instead. We started calling them that! And were a little bit sad when he learnt to say scorpion!
ReplyDeleteWhen it comes to writing equations we go the other way. Shock horror if they write them wrong. They might be establishing wrong habits. Quick annotate their work or something before the contagion spreads!
So true! And sometimes what they call it is even better than the actual name.
DeleteThanks, Joe, and thanks Simon as well. Wise words, I think.
ReplyDeleteI very much wish we used an arrow or something to indicate "what I have so far" so we could do "run-on" equations without any confusion. I am completely in sympathy with kids who don't want to start and write the whole expression again just to satisfy someone else's idea of what = means, when they can follow their own work easily.
ReplyDeleteAgreed! I think we can model good equation writing habits, just as we model good patterns of speech, in a way that honors student thinking. What's interesting is that what's OK when stacking vertically and keeping a running total is not OK when writing equations horizontally. That must be confusing for many.
DeleteThis reminded me of how "we" embrace invented spelling as students lear not write..."just get your thoughts down"!
ReplyDeleteHow can "we" encourage the same love of sense making in math...the correct representation will come...if the T shows them in a sense-making convo...