Person: Hill, Heather
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Hill, Heather
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Publication Learning Lessons From Instruction: Descriptive Results From an Observational Study of Urban Elementary Classrooms(Teachers College Record, 2018) Hill, Heather; Litke, Erica; Lynch, KathleenBackground: For nearly three decades, policy makers and researchers in the United States have promoted more intellectually rigorous standards for mathematics teaching and learning. Yet, to date, we have limited descriptive evidence on the extent to which reform-oriented instruction has been enacted at scale. Purpose: The purpose of the study is to examine the prevalence of reform-aligned mathematics instructional practices in five U.S. school districts. We also seek to describe the range of instruction students experience by presenting case studies of teachers at high, medium, and low levels of reform alignment. Participants: We draw on 1,735 video-recorded lessons from 329 elementary teachers in these five U.S. urban districts. Research Design: We present descriptive analyses of lesson scores on a mathematics-focused classroom observation instrument. We also draw on interviews with district personnel, rater-written lesson summaries, and lesson video to develop case studies of instructional practice. Findings: We find that teachers in our sample do use reform-aligned instructional practices, but they do so within the confines of traditional lesson formats. We also find that the implementation of these instructional practices varies in quality. Furthermore, the prevalence and strength of these practices corresponds to the coherence of district efforts at instructional reform. Conclusions: Our findings suggest that, unlike other studies in which reform-oriented instruction rarely occurred, reform practices do appear to some degree in study classrooms. In addition, our analyses suggest that implementation of these reform practices corresponds to the strength and coherence of district efforts to change instruction.Publication Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement(American Educational Research Association (AERA), 2005-01) Hill, Heather; Rowan, Brian; Loewenberg, DeborahThis study explored whether and how teachers’ mathematical knowledge for teaching contributes to gains in students’ mathematics achievement. We used linear mixed model methodology in which first (n=1190) and third (n=1773) graders’ mathematical achievement gains over a year were nested within teachers (n=334 and n=365), who in turn were nested within schools (n=115). We found teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades, controlling for key student and teacher-level covariates. While this result is consonant with findings from the educational production function literature, our result was obtained using a measure of the specialized mathematical knowledge and skills used in teaching mathematics. This result provides support for policy initiatives designed to improve students’ mathematics achievement by improving teachers’ mathematical knowledge.Publication Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide?(2005) Loewenberg Ball, Deborah; Hill, Heather; Bass, HymanIn this article, the authors describe a program of research they have been developing for more than a decade into the mathematical knowledge and skills that are used in teaching. Their research begins with examining the actual work of teaching elementary school mathematics and noting all of the challenges in this work that draw on mathematical resources; this is followed by analyzing of the nature of such mathematical knowledge and skills – how they are held and used – in the work of teaching. Through this type of analyses, they've derived a practice-based portrait of what they call “mathematical knowledge for teaching.” This article traces the development of these ideas and describes this professional knowledge of mathematics for teaching.