Cross-national variations in student achievement have been the focus of much interest and reflect a pervasive policy concern across many countries for improving student outcomes. One significant factor in this is the expertise of teachers. Using an approach which accounts for social and cultural difference, we attempt to understand teacher expertise as one particular influence on cross-national variations in student achievement in mathematics; compare expertise in mathematics teaching across Denmark, England and Germany exploring similarities and differences both across and within these countries; and understand how expert mathematics teachers within these countries mediate the many influences on their practice.

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