Teacher Learning and the Mathematics Reforms: What We Think We Know and What We Need to Learn.

The work of professional development is as uncertain as practice itself, Ms. Ball points out. Our challenge is to experiment, study, reflect on, and reformulate our hypotheses. All of these are necessary if we are to successfully engage a wider community - to "scale up" reform by sowing ideas. These are times of ambitious efforts to reform curriculum and instruction in mathematics. Reformers have invested time and energy in the creation of new mathematics standards and state curriculum frameworks. (1) A host of innovative curriculum projects are under development, and many states are in the midst of changing their state assessments. (2) Now there is increasing talk of "scaling up" the reform effort, of developing ways to reach more teachers. (3) As one who has been engaged in mathematics reform at several levels - as an elementary teacher, as a district-based resource teacher, as a teacher educator, as a researcher, and as a contributor to the Professional Standards for Teaching Mathematics, published by the National Council of Teachers of Mathematics (NCTM) - I suggest that we take a closer, more skeptical look at what we think we know about teacher learning and about the teaching envisioned by the reforms and that we consider what "scaling up" might mean. A central tenet of my argument is this: because the mathematics reforms challenge culturally embedded views of mathematics, of who can - or who needs to - learn math, and of what is entailed in teaching and learning it, we will find that realizing the reform visions will require profound and extensive societal and individual learning - and unlearning - not just by teachers, but also by players across the system. (4) What might such ambitious learning entail? In this article I focus on the learning of teachers. I examine four questions: 1) What do we think we currently know about how teachers learn? 2) What do we know about the thing to be learned - this new approach to the teaching of mathematics? 3) What do we know about teachers and what they bring to learning about such teaching? 4) What don't we know about teaching and teacher learning that might matter in trying to "scale up" the mathematics reform effort, and how could we go about learning more? What Do We Think We Know About Teacher Learning? Over the past decade, research and practice have yielded a mass of working ideas about teacher learning. (5) Some of these ideas have been investigated in studies of teacher learning and teacher education. Some have emerged from the practice of experienced teacher educators. Others are part of the current ideology. I use words like "ideas" and "beliefs" deliberately here. To call these tenets "knowledge" seems problematic, for they are unevenly inspected and warranted. For example, the proof of some of these ideas about teacher learning is circular. That is, professional development projects are designed with these ideas in mind; then, when the project is judged "successful" by some standard, this result is taken as validation of the ideas. Other ideas about teacher learning are not supported with evidence at all but are advanced as moral positions. They are seen as an inherent good. This does not automatically reduce their potential value, but it should shape our understanding of what they represent. I am not saying that any of the ideas we currently have are wrong. But I am urging that we be more skeptical of what we think we know. Some of the ideas in the following list are so vague as to need considerably more development, while others may be true only in certain ways or in some situations. Despite their varied genesis, a small number of ideas about teacher learning show up repeatedly - in discussions, in professional development projects, and in the literature. They concern teachers, what teachers need to know, and the conditions and arrangements that support teacher learning. * Prior beliefs and experience. What teachers bring to the process of learning to teach affects what they learn. …