The idea of “teaching for understanding” at first seems obvious. Of course we want students to understand; what else is school about? Magdalene Lampert (p. 26) puts the matter in perspective.
I first heard of Lampert and her colleague, Deborah Ball, from Lee Shulman, who talked with me several years ago (Brandt 1992) about a wholesale change in the ways researchers in the 1980s chose to study teaching. Shulman explained that most researchers were no longer doing “process-product” research (systematically observing the behaviors of large numbers of teachers to find relationships between certain behaviors and unusually high achievement) because they had learned about as much as could be learned that way. He mentioned a variety of new forms of research, including studying one's own teaching, and spoke admiringly of Lampert and Ball.
Maggie Lampert isn't teaching elementary school on a regular basis this year, because she recently moved from Michigan State to the University of Michigan and she wanted a little time to get settled. But for several years, as a professor, she taught 5th grade mathematics. She believes she needs to teach the same group of youngsters every day to develop a classroom climate in which students feel secure enough to freely offer and discuss conjectures about mathematics.
Even though, as she acknowledges, Lampert does not teach the full range of classes that most elementary teachers must handle, she says that teaching mathematics her way—the way envisioned in the Standards of the National Council of Teachers of Mathematics—is very difficult. She sees her role as trying to establish what good teaching of elementary mathematics can be. It's like the heart transplant in medicine or the four-minute mile in athletics. Someone must first set the standard by demonstrating that a thing can be done; only then can it be practiced more widely. Doing it is still no easier; I can't teach mathematics as Magdalene Lampert does any more than I can run a mile in four minutes or do a heart transplant. But her work is contributing to development of a vision that will enable us to describe with greater clarity the kind of teaching we want for every learner.
A crucial point is that teaching for understanding begins with understanding by the teacher. That becomes painfully clear in a courageously candid account (in Cohen et. al. 1993) of the collaboration between Ball and teacher Sylvia Rundquist, which Rundquist confesses made her feel “... less competent. Often during the first year, she was amazed and chagrined to see that her knowledge of mathematics was even more tenuous than she had thought. She ... was afraid to let other teachers know how inadequate she felt” (p. 19). The story ends happily, with Rundquist “... able to pursue her excitement about a piece of mathematics with confidence and eagerness” (p. 27). It's an inspiring story, truly moving—but Sylvia Rundquist began the journey as a comparatively open, risk-taking person, an experienced teacher embarking on a graduate program to become a teacher of teachers—and the change in her took four years!
No doubt about it, the kind of teaching envisioned in this issue is not typical, is not readily learned or easily practiced, and may in fact be impossible under current conditions in some classrooms. Even so, we must not be satisfied with anything less.
