I read Diane Ravitch (skimming past a majority of the numerous posts) so I can stay aware of what's happening to public schools across the nation. This may be the first time I've seen math discussed in depth on her blog. Gary Rubenstein wrote a great post on Common Core Standards, and how they affect math class. He used the Pythagorean Theorem as his example, describing some of what he'd do with 8th grade students. (My college students would have fun with this, too, and would learn some valuable math from a lesson like this.)

His take on how to assess was refreshing. See if you can explain the group of pictures below after reading the article.

The idea is to shade the bottom two pictures with the blue, yellow, and
brown from the top pictures to show what's the same. I got something
algebraically, but what I did wasn't nearly as elegant as the shading he
showed.

## Thursday, February 7, 2013

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I love this diagram (Bhaskara's dissection) and included it in the history chapter of my book. Some of the things I would look for in a discussion of the diagram:

ReplyDeleteWhere did the white square come from? How is it related to the triangle?

Do the students realize that it's important to explain how they know the lower shapes are square?

Can they explain how they know that the conclusion doesn't depend on the shape of the original triangle (except that it needs a right angle)?

What would happen if we drew different shapes on the side of our right triangle -- say, other triangles, or semi-circles instead of squares? ...