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Jennifer K. Jacobs and Eiji Morita

This article describes a novel assessment method used to examine Japanese and American teachers' ideas about what constitutes effective mathematics pedagogy. Forty American and 40 Japanese teachers independently evaluated either an American or Japanese mathematics lesson captured on videotape. Their comments were classified into over 1600 idea units, which were then sorted into a hierarchy of categories derived from the data. Next, the authors hypothesized underlying ideal instructional scripts that could explain the patterns of responses. Whereas the U.S. teachers were supportive of both traditional and nontraditional elementary school mathematics instruction and had different scripts for the two lessons, the Japanese teachers had only one ideal lesson script that was closely tied to typical Japanese mathematics instruction. The findings suggest that U.S. teachers may have more culturally sanctioned options for teaching mathematics; however, Japanese teachers may have a more detailed and widely shared theory about how to teach effectively.

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Nanette Seago, Jennifer Jacobs, Mark Driscoll, Michael Matassa, and Matassa Callahan

U.S. students' poor performance in the domain of geometric transformations is well documented, as are their diffi culties applying transformations to similarity tasks. At the same time, a transformations-based approach to similarity underlies the Common Core State Standards for middle and high school geometry. We argue that engaging teachers in this topic represents an urgent but largely unmet need. The article considers what a transformations-based approach to similarity looks like by contrasting it with a traditional, static approach and by providing classroom examples of students using these different methods. In addition, we highlight existing professional development opportunities for teachers in this area.

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Jennifer E. Jacobs, James Hiebert, Karen Bogard Givvin, Hilary Hollingsworth, Helen Garnier, and Diana Wearne

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of classroom practice—teaching—and presents the results of two studies of randomly selected, nationally representative U.S. eighth-grade mathematics lessons that were videotaped as part of the TIMSS 1995 and 1999 Video Studies. Analyses compare features of teaching found in these lessons with pedagogical recommendations for middle school teachers in the Principles and Standards for School Mathematics (Principles and Standards) in order to examine the extent to which teaching in U.S. eight-grade classrooms is standards-based. Results show that typical mathematics teaching, in both 1995 and 1999, is more like the kind of traditional teaching reported for most of the past century (Cuban, 1993; Fey, 1979; Weiss, Pasley, Smith, Banilower, & Heck, 2003; Welch, 1978) than the kind of teaching promoted in Principles and Standards.