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Jeremy A. Kahan and Harold L. Shoen

Problems and problem solving have a long history in mathematics education (Dewey, 1910; National Council of Teachers of Mathematics [NCTM], 1980; Pólya, 1945; Schoenfeld, 1992; Stanic & Kilpatrick, 1988). The Curriculum and Evaluation Standards for School Mathematics asserted, “Problem solving should be the central focus of the mathematics curriculum” and placed it as Standard 1 (NCTM, 1989, p. 23). The 1990s saw the development of school mathematics curricula based on various interpretations of these Standards. In most of these curricula, the mathematics emerges from the solution of problems, and there is a growing body of research evidence supporting the effectiveness of these curricula (Senk & Thompson, 2003). Teaching mathematics through problem solving also continues to be a focus of mathematics educators independent of the curriculum that is used (Schoen & Charles, in press).

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Harold L. Shoen, Kristen J. Cebulla, Kelly F. Finn and Cos Fi

We report results from a study of instructional practices that relate to student achievement in high school classrooms in which a standards-based curriculum (Core-Plus) was used. We used regression techniques to identify teachers' background characteristics, behaviors, and concerns that are associated with growth in student achievement and further described these associations via graphical representations and logical analysis. The sample consisted of 40 teachers and their 1,466 students in 26 schools. Findings support the importance of professional development specifically aimed at preparing to teach the curriculum. Generally, teaching behaviors that are consistent with the standards' recommendations and that reflect high mathematical expectations were positively related to growth in student achievement.