Faster, better, smarter?

Our recent work with some students working to find out how they feel they are "smart" at math has me thinking of one of my kids at my school, and how he views himself as a mathematician.

I have been spending some time with him during math and am trying to explore some of his ideas about what it means to him to be "smart" at doing mathematics.  Watching him work and talking to him about what strategies he uses to get his solutions, I am often struck as how well he seems to grasp the concepts we are going over.  I have this reaction because his scores on assessments often do not prove this out.

The more I watch and probe, the more I am coming to the realization that he feels people who are "smart" at math are the fastest to complete their work.  He can explain his mathematical thinking, but is often interrupted in his explanation by the discovery of a calculating error made in haste.  This happens frequently.  It also carries over to his assessment work.

Knowing what I do about him, I am trying to instill in him two simple ideas in hopes he can alter his views of what mathematicians do: First, I am working to get him to believe that math is about his process, his strategy, and in the end his accurate results - speed has nothing to do with it.  I want him to be transparent with what he is doing on the paper so he doesn't trip himself up by going to fast and taking shortcuts.

Second, his confidence is often shaken by these errors he makes because of rushing.  He doesn't understand why he is getting things wrong when he feels he knows what to do.  I have had to do some re-building of his esteem.  I ask him: "what strategies do you know that will help you solve this?"  He takes me through his steps on a problem and we find out where things are going wrong together (almost always in simple miscalculations, not concepts).  Part of this rebuilding is to show him that a major part of doing math is knowing how to find and fix your mistakes. 

Now that I know where his struggles lie, I am often stopping by to remind him that "you know the stuff, just take your time and be accurate.  Don't worry about how long it takes you to get there, just get there carefully.  You can do this!"

It seems almost too simple, but now that I have an idea of what is tripping it up and we are addressing it, I have hopes he will do better.  It's a reminder for me that kids do tend to inherently think that faster means better in math, and it can lead to them not seeing themselves as "good at math" when they truly are.