Long day! Eight graders can really pump out some algebraic thinking skills if they can just have a little support. I'm convinced lack of confidence is one of the only reasons they don't finish problems. They just stop part way through and say they don't get it. I ask why and they respond that they don't know. You don't know why you don't get it? Its funny, because then they do the next step, and the next step, and the next step and then they stop and look up. I nod yes, and they say that's it? Yup, I say. They always look surprised and satisfied. I didn't really do anything!
PS I read the first three chapters of the Principles and Standards for School Mathematics today. Uhg. Great ideas...but so so so so so boring! The funniest thing I saw in there was a child's representation for 5 1/2. The child wrote the number five in pencil. Then, next to it, the child started writing another five, but stopped after they finished about half of it. How cute, and sensible!