The more that I teach, the more I think that I really don’t know anything about teaching. Take group work, for instance. Over the years, I have had students work in a variety of group structures on a wide variety of tasks — quizzes, routine class work, challenging problem solving, discussion and development of new ideas, projects, and more. Students sometimes hate it and sometimes like it. But I have always been sure that it was “obviously” the right thing to do in the classroom, even when students resisted. Today, I’m not so sure.
Why am I not so sure? The real reason is a paper I read yesterday that seems to say that mathematical discourse is not always unequivocally positive. The recent article by Jessica Pierson Bishop* features a pair of students, Bonnie and Keri. Bonnie is “bad at math” and Keri is “good at math,” and when you look at the interactions in the article, their interactions serve to reinforce both of their identities. Keri holds power in the relationship and uses that power to keep her position as the “smart one” and to control the relationship. Bonnie, for her part, willingly submits to this and holds her negative mathematical identity almost as a protective shield against risk. I am sure that I have had pairs like Bonnie and Keri in my class, and I am now questioning whether having them work together is actually productive.
Of course, you can argue that instead of throwing out joint problem-solving and discourse, I should instead be thinking about how to structure those working relationships so that they are more positive than the relationship in the article. In other words, don’t throw out the baby with the bath water. You are right, and I’m thinking hard about how to do that very thing this semester (I would be grateful for ideas!), but it’s in my nature to question things, and I’m now questioning how I got this idea that working together is a positive. Like most of my ideas about teaching, this one wasn’t born of research or careful investigation of best practices, but instead on my own intuition, the vaguely constructivist philosophy that rubbed off on me while I was getting an undergraduate degree in math education, and my practices as a mathematician. These don’t always serve as perfect guidance.
Actually, I don’t question the importance of discourse, because one of my goals in the classroom is communication about mathematics. Students and teachers need to know how to talk about mathematics, and, like most things, practice is necessary to become a good communicator. Of course, I too often neglect the fact that practice alone doesn’t make a person a great communicator; feedback and reflection are crucial to developing good communication skills. But I am less sure that group problem solving work is important. Students give it mixed reviews, and I think I need to do a better job of understanding why some students in some classes enjoy this kind of work and other students do not. For instance, is it possible that the students with high status and relative power in the classroom are the students who enjoy group work, and that the group and pair work in my classroom may actually be reinforcing status inequalities, as it does in the Bishop article that started me on this question?
In other words, I’m asking a question I find myself asking a lot lately: Is it possible that the negative feedback I have gotten (in this case regarding group work) is valuable feedback with important pedagogical merit? Could it be that when I hold fast to my belief that I know better than my students what is good for them that I am simply wrong? Everything I have been reading and thinking lately has been telling me that I need to listen more to my students, and I have been trying to open new lines of communication with each semester.
So this semester I will be trying to not just open up communication between me and the students, but also try to truly understand the student-to-student communication that is happening in this classroom, and I will be doing some assessments to try to discover what is going on between students in the classroom and to listen carefully to what the students say. Wish me luck!
* Jessica Pierson Bishop, “‘She’s Always Been the Smart One. I’ve Always Been the Dumb One’: Identities in the Mathematics Classroom,” Journal for Research in Mathematics Education 43, no. 1: 34-74.