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.

What do you want to know?

Grand Valley started this week. And, as usual, I began my Introduction to Learning and Assessment course with a workshop called "A Piece of Me" (handout). This involves an activity that was introduced to me over 14 years ago during an Integrated Thematic Instruction class. I wish I could remember the presenters so I could give them credit but that information has long since vanished from my memory and my files. If anyone knows the origin of this activity, please let me know so that I can give credit where it is due. Anyway, here is how I implement the activity.

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Goal: The learner will ask questions in order to get to know the instructor/course.

Schema Activation: Whole Class Discussion
When you meet someone, What do you want to know about him or her?

Focus: Expectations - Small Group

• Develop one personal and one professional question to ask the instructor.
• During the activity, keep a record of each question that is asked.

Activity: Asking and Recording Questions

I begin this portion by saying something like, "I reserve the right to decline answering any question. I have been doing this for many years, in K12 and college classrooms, and I have never had to refuse answering a question. Now this is not a challenge for you to be the first group to come up with the unanswerable question. It is intended to demonstrate that this can be used at any level - even with middle schoolers who are known for their inappropriate questions."

We then move on to the groups asking their questions. I respond providing answers and other related information that I think they'd like or need to know. After all the groups have asked their questions, if time permits, I ask if there's anything else anyone would like to know about me or the course.

Reflection: Looking Back - Small Group Analysis

• From your list of questions, pick one that you think was an effective question. What made it effective?
• If you finish early, pick another effective question and describe what the two question have in common or consider an ineffective question and rewrite it or ... (What comes next for you?).
• How engaged were you during this activity?

I end the workshop by getting some feedback from the participants. The consensus seems to be that this activity is much more engaging than what they imagine it would be like for me to talk at them for forty minutes about what I think they need to know. They appreciate that they control the activity with their questions. They acknowledge that they are much more interested in my points because I am responding to their questions.

Because they are teachers in training, I let them in on a few secrets behind the activity: 1) I am still in control of what I share and usually get to say what I think is important regardless of what they ask; 2) I use the questions they ask as a formative assessment that provides data on what they find interesting; and 3) The activity is much more engaging for me as well because I do not know what I will be asked. (One time it was what my favorite sandwich was.)

I follow this workshop up with a home workshop where they apply the same strategy of asking questions to reading the course syllabus (handout). This is another activity that I have decided I won't waste time doing in class. They post their questions on our course Blackboard site and I address them directly on the discussion board or during subsequent class meetings.

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Now it is your turn. Any questions?