I knew of Saturday morning's keynote speaker, Catherine Fosnot, from an article or two I'd read in Tolman Library at UC Berkeley, but she was just a name to me. That would change ten minutes after she began speaking.
I immediately was introduced to a part of classroom life that I'd never encountered before. She showed us a fascinating bit of film of some third graders discussing a math problem. At first all I got out of it was that one girl was pushy and the other girl was confused. Then Fosnot began doing some exegesis and I realized that both girls were doing rather high order math reasoning. They were discovering basic tenets of math (among others, the distributive properties) without anyone telling them.
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