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Heather C. Hill

This article explores elementary school teachers' mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. The Learning Mathematics for Teaching project administered a multiple-choice assessment covering topics in number and operation to a nationally representative sample of teachers (n = 625) and at the same time collected information on teacher and student characteristics. Performance did not vary according to mathematical topic (e.g., whole numbers or rational numbers), and items categorized as requiring specialized knowledge of mathematics proved more difficult for this sample of teachers. There were few substantively significant relationships between mathematical knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed.

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Heather C. Hill and Jeffrey C. Shih

This “Research Commentary” addresses the quality of statistical research in mathematics education. To do so, we analyze 10 years of Journal for Research in Mathematics Education (JRME) articles based on criteria suggested by the American Educational Research Association, American Psychological Association, and National Council for Measurement in Education (AERA, APA, & NCME, 1999); the National Research Council (Shavelson & Towne, 2002); and the American Statistical Association (ASA, 2007). We find the majority of JRME articles lacking in one or more respects, and we highlight criteria for JRME authors, reviewers, and editors.

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Heather C. Hill and Deborah Loewenberg Ball

Widespread agreement exists that U.S. teachers need improved mathematics knowledge for teaching. Over the past decade, policymakers have funded a range of professional development efforts designed to address this need. However, there has been little success in determining whether and when teachers develop mathematical knowledge from professional development, and if so, what features of professional development contribute to such teacher learning. This was due, in part, to a lack of measures of teachers' content knowledge for teaching mathematics. This article attempts to fill these gaps. In it we describe an effort to evaluate California's Mathematics Professional Development Institutes (MPDIs) using novel measures of knowledge for teaching mathematics. Our analyses showed that teachers participating in the MPDIs improved their performance on these measures during the extended summer workshop portion of their experience. This analysis also suggests that program length as measured in days in the summer workshop and workshop focus on mathematical analysis, reasoning, and communication predicted teachers' learning.

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Heather C. Hill, Deborah Loewenberg Ball and Steven G. Schilling

There is widespread agreement that effective teachers have unique knowledge of students' mathematical ideas and thinking. However, few scholars have focused on conceptualizing this domain, and even fewer have focused on measuring this knowledge. In this article, we describe an effort to conceptualize and develop measures of teachers' combined knowledge of content and students by writing, piloting, and analyzing results from multiple-choice items. Our results suggest partial success in measuring this domain among practicing teachers but also identify key areas around which the field must achieve conceptual and empirical clarity. Although this is ongoing work, we believe that the lessons learned from our efforts shed light on teachers' knowledge in this domain and can inform future attempts to develop measures.