(1) Learning What You’re Seeing in Math Class

The No Child Left Behind Act has placed new demands on principals for their students’ achievement in mathematics. At the same time, instructional methods, texts, and many of the high-stakes tests have been changing dramatically to reflect ideas about mathematics instruction that are based on recent research in cognitive psychology and mathematics education. Such research shows that children learn mathematics best when they explore ideas in the context of solving complex problems, thereby simultaneously building mathematical understanding and integrating their learning of facts and problem-solving procedures with that understanding. (Kilpatrick, Swafford, & Finell, 2001). The combination of new instructional methods and new accountability pressures puts many principals in a quandary. How do they evaluate the adequacy of the mathematics instruction occurring in their schools? How can they tell if teachers are using new methods well? And how can they be confident that their school has the right balance between learning mathematical facts and procedures for calculation, while also developing a good conceptual understanding of mathematics? For about ten years we and our colleagues have been studying how elementary principals think about and work to improve mathematics instruction. We have worked closely with nearly100 elementary principals from urban, rural, and suburban districts, and both large and small schools. The data collected in our studies include ethnographic observations and transcripts of discussions in our workshops for principals, extensive interviews with the principals, ethnographic observations of them at work in their schools, and interviews with some of the teachers with whom they worked. We presented our major findings i