How would you describe someone successful at math?

I try to start each semester with some activity that brings to light my preservice teachers' beliefs about mathematics. This typically entails using a modified version of a Simile Survey used in my doctoral work, but last August I attended a session at the Michigan Council of Teachers of Mathematics Conference that introduced me to some new tools. This is one of the tasks that Shannon Sweeny shared with us during the session:

Shannon gave me permission to use this instrument in my teacher preparation  courses, and I combined it with an article from Educational Leadership to create a productive workshop that got at beliefs about success in mathematics.

The teachers picked the five words their "elementary-self" would have chosen to describe someone who was successful at math. Then I asked that they write out the experiences they had during elementary math lessons that might have contributed to their choice of words. Next, I had them read the first part of the article, Afraid of Looking Dumb, that includes the following exchange between the author and a second grade student, Brenda.

Brenda: I feel like I'm not good in math, and I get scared. I feel like I'm the dumbest in the class in math.  

Me: In just math or other things, too? 

Brenda: Other things, too. 

Me: Why do you feel that way? 

Brenda: I can't do as much as other people. 

Me: When you start math, what do you tell yourself? 

Brenda: I can't do it. I'm scared. 

Me: What if you couldn't do it? 

Brenda: I wouldn't be smart in that subject. I should be able to do it. I'm scared that people will tease me. 

Me: What would it look like if you were smart? 

Brenda: I'd be a fast thinker, quick learner. The first time I try things, I'd get it right. 

Me: What do you tell yourself when I tell you that you're better than you think in math? 

Brenda: I don't believe you. 

Me: Do you want to change? 

Brenda: Yes, but how? How are we going to change our thinking? 

I asked the teachers to: (1) predict the five words Brenda might have selected regarding success; (2) identify the evidence in the dialogue that supports their choices; and (3) infer what experiences Brenda might have had that fostered her beliefs. As an example, I said, "I think Brenda might pick 'arrogant' because of the line, 'I'm scared that people will tease me.' This might be the result of having experiences where kids or teachers teased her or her peers when they made math mistakes." A fair number of the teachers remarked that they thought Brenda would have picked a lot of the same words as their "elementary-self." Consequently, in predicting the experiences that might have contributed to Brenda's view, many shared their own experiences in elementary math classes as possible reasons for Brenda's perspective.

This awareness that not much has changed in the teaching math since they were elementary students is an important step if we are going to begin doing things differently. I told them that I do not want to be having this same conversation with their students when they get to my class in 20 years. Don't get me wrong, it's an interesting discussion, but the semester would get off to a better start if everyone entered class believing they could be successful in math.