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Interesting kindergarten math case study

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I've just run into something fascinating with my almost 7 year old daughter, and thought I'd report. 

She did kindergarten in public school last year, and in that class, they did area and perimeter. The way they did this is that they estimated the area and perimeter by filling up a shape with blocks to estimate area and by lining blocks around a shape to estimate perimeter. I thought this was a bit odd, because then they were measuring both in the same units, but whatever. 

OK. This year, we finally started doing a bit of geometry, and we started with area and perimeter. I defined them for her (area is "number of squares inside," perimeter is "length of the boundary") and gave her some simple shapes made of squares to calculate areas and perimeters for. I included shapes such as rectangles with missing corners, just so we could practice the idea for a while first. 

Well, she did the questions. I took a look, and almost all of her perimeters were wrong! Why? Because she was still visualizing putting the blocks around the figure! That means that she was counting something like "a missing corner of a rectangle" as a single block instead a length of 2. We fixed it easily, of course. But I thought it was a fascinating case study. Students learn what we teach, not what we THINK we're teaching, and not what's in our head as we're teaching... it's a hard thing to be mindful of! 

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