Academic journal article Phi Delta Kappan

Talking Mathematics: 'Going Slow' and 'Letting Go.'

Academic journal article Phi Delta Kappan

Talking Mathematics: 'Going Slow' and 'Letting Go.'

Article excerpt

It is often necessary to "let go" of the planned goal or lesson in order to pursue important mathematical ideas through classroom discourse, these authors remind us.

FOR THE PAST three years 12 elementary teachers have been involved with TERC (Technical Education Research Centers) in a project called Talking Mathematics. These teachers were all interested in investigating ways to develop mathematical discourse in their classrooms (spanning grades K through 7). TERC's goals for the project were 1) to work with a group of master teachers to explore techniques, principles, and models of mathematical talk in the elementary grades; 2) to identify the difficulties teachers experience in supporting mathematical discourse in their classrooms; and 3) to document the project's effects on teachers' beliefs about mathematics and on the nature of mathematical discussions in their classrooms.

After initial interviews and observations of all participating teachers, conducted by members of the TERC staff, the project began with a three-week seminar in the summer of 1990. During this seminar the teachers worked on mathematics together and began to explore the project's research questions with project staff. Our team (the two of us, who are both mathematics educators, and Harriet Pollatsek, a mathematician from Mt. Holyoke College) deliberately focused the first two weeks of the seminar on mathematical investigations. We further decided that we would involve teachers in working on mathematics for their own development, regardless of whether the particular mathematics content and problems we chose could be used directly with their students.[1] This approach contrasted sharply with much of the professional training the teachers had encountered, in which the "activities" from a workshop on Monday could be used in their classrooms on Tuesday.

At first, teachers' discussion of mathematical investigations centered on "how I would do this with my students" or "how I would simplify this so my students would understand it." This classroom focus acted as a barrier -- and perhaps as a shield -- which kept the teachers from grappling with mathematics for themselves. By the second week, however, the teachers were eagerly engaging in mathematical investigations for their own intellectual development. A single mathematical investigation might require several hours or even several sessions because the participants insisted on continuing their work. By the end of the third week, we laughed together each morning about the "unagenda" for the day, since we all knew it would change as we became immersed in mathematics. As they gradually let go of immediate classroom application, the teachers began to be captured by the pleasure of deep involvement in mathematics. One teacher wrote in her journal, after an investigation that involved geometric relationships, "I loved doing the polyhedra problem. . . . I don't want to leave it. I wish I didn't have other plans, a house to clean, a husband, so I could work on it. Oh boy, would I like to engage children the way I am engaged."


As the school year approached, the teachers realized that they would be returning from their intense summer experience to a culture of school mathematics in which the expectations of students, parents, and administrators; the constraints of "the curriculum" and the tests; and even their own well-established routines might act as barriers to the changes they envisioned. Feeling legitimately daunted by the nature of the task ahead, the teachers agreed at the end of the summer that "going slow" in the face of such complex change was the only way they could proceed. They understood that, if they demanded fast and radical change of themselves, they would end up feeling discouraged. As one teacher remarked, "We all have changed, and I'm afraid of what will happen to us once we're back in the system. I am afraid that I'll arrive in September, happy and with beautiful ideas, and after three weeks all will be shattered. …

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