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Talk Some Sense into It #MTBoS30 12 of 30

puzzled

People joke with me and say, “You must do calculations in your head for fun.”   My instinct is to deny this accusation, but it probably is true.  Math educators run through numbers all the time.  We play numbers games in our head like would you rather, without prompt or encouragement to do so.  I see a fraction that could be written in different way, so I try.  I see a complex shape that can be broken into parts, so I do.  These instincts were fueled by years or even decades of me talking numbers in my head.

I should never assume that this is normal, even though it is one of my life’s missions to make it so for the general population.  The CCSS Standards for Mathematical Practice says to make sense of problems and persevere in solving them (among other things).  This idea of having a sense for numbers has been discussed by some awesome educators like Fawn Nguyen, and Sadie Estrella, and it’s been the hot topic of journalists and bloggers alike.  I’m in the camp that says, “Feeling comfortable with manipulation of numbers directly supports comfort with manipulating the abstract.”

So today we were talking circles, and proportions of circles.  Instead of just giving a formula…

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…we developed our own.

It started with a spreadsheet.

then a geogebra applet

then into paper practice.

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Students shouldn’t be given a formula, and then be expected to make sense of the abstract values without having developed a sense for the concrete values.

Math educators need to talk numbers with students daily.  It just makes sense.

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