I really want to focus on students being mindful of their process. What they are doing is important, but they really need to know why they're doing it. We've been doing daily exercises, How Many Squares? that are based on Michael Fenton's activity, How Many Peaches?
We usually highlight different student strategies and have spent some time developing a continuum of strategies that looks something like:
counting --> grouping/adding --> skip counting --> multiplying --> writing/evaluating math expressions
This student's particular strategy generated a nice conversation.
I asked whether or not students thought this was a strong strategy. Responses were less than enthusiastic so it was time to move a little.
Me: Alright, if you think this is a strong strategy stand on this side of the room; if you think it's not move to the other.
It was 31-2 in favor of the strong. So I walk over to the "not strong" side and make my case.
Me: It can't be a strong strategy because the answer is 84 and this student said it was 76.
About half the class moves to my side. I figure it was an even split on who was convinced by the "right answer" argument and who was convinced by the "I'm your teacher" argument.
Two students on the strong side raise their hands.
Student 1: I think it's still a strong strategy because he probably just made a mistake.
Me: Probably? Where does that fall on our argument continuum, gut level, some reason or convincing reason?
Student 1: Some reason.
Me: Ok, great. Can anyone take it to the next level?
Student 2: I think it's still a strong strategy because he just counted 11 instead of 12 across the top. He still multiplied right, but he just used the wrong numbers. Everything else was good.
Yeah, that'll play.