Is this answer right?

“Ms. Placa. Is this right?” I must have heard that sentence a million times when I began teaching.

Many classrooms create a culture where the teacher has all the answers and the students seek approval from him or her. This sometimes works out well for things like learning about conventions or notations that the student has no way of knowing.

But it doesn’t work for learning what it means to do math. It creates a misconception among students that math is a set of arbitrary rules that the textbook or teacher tells them. The goal of math class becomes to figure out what the teacher wants you to do.

Children pick up on how to play this game early on. They note the teacher’s body language and tone of voice when the teacher responds to an answer. For example, in many classes, when a teacher asks, “How did you get that answer?” it is a signal that you should change your answer. You must have made a mistake. If you didn’t, the teacher would have just went on to the next problem.

What if we taught students that the goal was not to please the teacher, but rather to convince themselves and others why their answer was correct? The rules of the game would change. It would be the teacher’s role to give you tools and tasks that fostered learning but students would be responsible for determining if they solved a task correctly.

Yackel and Cobb (1996) give a great example of how to begin to do this. A student gave an answer to a question and then wavered when the teacher questioned her. She understood the question as a social cue to change her answer. Below is the conversation they had after she changed her answer:

Teacher: Wait, listen, listen. What did Mr. K.-what have I always taught
you? What’s your name?
Donna: My name is Donna Walters.
Teacher: What’s your name?
Donna: My name is Donna Walters.
Teacher: If I were to ask you, “What’s your name?” again, would you tell
me your name is Mary?
Donna: No.
Teacher: Why wouldn’t you?
Donna: Because my name is not Mary.
Teacher: And you know your name is—…If you’re not for sure you might
have said your name is Mary. But you said Donna every time I
asked you because what? You what? You know your name is what?
Donna: Donna.
Teacher: Donna. I can’t make you say your name is Mary. So you should
have said,”Mr. K. Six. And I can prove it to you.” (p. 468-9)

This is a great example of how to begin to create norms in a classroom so that students’ explanations become the focus of classroom discussions. Convincing themselves and others that their answer is correct becomes the role of the students in the class. They do not need to rely on the teacher for approval.

How might this change the way students think about doing math? How might it change the way we think about teaching math?

References

Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 458-477.