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This study explored whether and how teachers’ mathematical knowledge for teaching contributes to gains in students’ mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders’ mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized mathematical knowledge and skills used in teaching mathematics. This finding provides support for policy initiatives designed to improve students’ mathematics achievement by improving teachers’ mathematical knowledge.

This review of related literature and research prompted the development of a framework for understanding the role of the principal as an instructional manager. A number of links between school-level variables and student learning are proposed. The discussion includes consideration of instrictional organization, school climate, influence behavior, and the context of principal management.

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This paper discusses conceptual and methodological issues that arise when educational researchers use data from large-scale, survey research to examine the effects of teachers and teaching on student achievement. Using data from Prospects: The Congressionally Mandated Study of Educational Growth and Opportunity 1991–1994, we show that researchers’ use of different statistical models has led to widely varying interpretations about the overall magnitude of teacher effects on student achievement. However, we conclude that in well-specified models of academic growth, teacher effects on elementary school students’ growth in reading and mathematics achievement are substantial (with d-type effect sizes ranging from .72 to .85). We also conclude that various characteristics of teachers and their teaching account for these effects, including variation among teachers in professional preparation and content knowledge, use of teaching routines, and patterns of content coverage, with effect sizes for variables measuring these characteristics of teachers and their teaching showing d-type effect sizes in the range of .10. The paper concludes with an assessment of the current state of the art in large-scale, survey research on teaching. Here, we conclude that survey researchers must simultaneously improve their measures of instruction while paying careful attention to issues of causal inference.