This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of pedagogical content knowledge caught on, it was in need of theoretical development, analytic clarification, and empirical testing. The purpose of the study was to investigate the nature of professionally oriented subject matter knowledge in mathematics by studying actual mathematics teaching and identifying mathematical knowledge for teaching based on analyses of the mathematical problems that arise in teaching. In conjunction, measures of mathematical knowledge for teaching were developed. These lines of research indicate at least two empirically discernable subdomains within pedagogical content knowledge ( knowledge of content and students and knowledge of content and teaching) and an important subdomain of “pure” content knowledge unique to the work of teaching, specialized content knowledge , which is distinct from the common content knowledge needed by teachers and nonteachers alike. The article concludes with a discussion of the next steps needed to develop a useful theory of content knowledge for teaching.

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. Such claims stem originally from the "educational production function literature," or research that examines the contribution of student, teacher, and school resources to student learning. As far back as the Equality of Educational Opportunity study (Coleman, 1966) scholars identified a unique contribution of teacher knowledge to student achievement (in mathematics, see also Hanushek, 1972;Hill, Rowan, & Ball, 2005;Mullens, Murnane, & Willett, 1996;Rowan, Chiang, & Address correspondence to Heather Hill, 6 Appian Way # 445, Cambridge, MA 02138. E-mail: heather hill@harvard.edu , 1997). At the same time, scholars studying teacher knowledge have also identified an impact on instruction (e.g., Borko, Eisenhart, Brown, Underhill, Jones, & Agard, 1992;Fennema & Franke, 1992;Leinhardt & Smith, 1985;Putnam, Heaton, Prawat, & Remillard, 1992;Sowder, Phillip, Armstrong, & Shappelle, 1998). Taken in combination, there is evidence for the proposition that stronger teacher knowledge yields benefits for classroom instruction and student achievement. MKT AND THE MATHEMATICAL QUALITY OF INSTRUCTION431 MillerYet despite these observations, and despite a wealth of current policy initiatives built on these observations, there is a lack of detailed understanding regarding how teacher knowledge affects classroom instruction and student achievement. Teacher knowledge presumably works through instruction to cause student learning, yet this relationship is not completely understood. Large-scale educational production function studies never peer inside classrooms to compare the practice of higherknowledge and lower-knowledge teachers. Studies in the teacher knowledge and mathematics education literatures have raised strong plausible propositions regarding how knowledge matters for teaching; but with sample sizes of one teacher per study in many cases, and few objective measures of teachers' mathematical knowledge, generalizations have to date been limited.The lack of specifics regarding how knowledge affects instruction leaves critical gaps in our theoretical knowledge, and significant holes i...

In this article we present results from a project to develop survey measures of the content knowledge teachers need to teach elementary reading. In areas such as mathematics and science, there has been great interest in the specialized ways teachers need to know a subject to teach it to others-often referred to as pedagogical content knowledge. However, little is known about what teachers need to know about reading to teach it effectively. We begin the article by discussing what might constitute content knowledge for teaching reading and by describing the survey items we wrote. Next, factor and scaling results are presented from a pilot study of 261 multiple-choice items with 1,542 elementary teachers. We found that content knowledge for teaching reading included multiple dimensions, defined both by topic and by how teachers use knowledge in teaching practice. Items within these constructs formed reliable scales. DisciplinesEducational Assessment, Evaluation, and Research | Educational Methods CommentsView on the CPRE website.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/cpre_articles/5 Phelps, G., & Schilling, S. (in press). Developing measures of content knowledge for teaching reading. Elementary School Journal. Developing Measures of Content Knowledge for Teaching Reading Geoffrey Phelps Stephen Schilling University of MichiganThe measures development work is being conducted as part of the Study of Instructional Improvement. The research group includes, Geoffrey Phelps, Deborah Loewenberg Ball, Heather C. Hill, and Stephen Schilling. This work is supported by NSF grant REC-9979873, by a subcontract to CPRE on Department of Education (DOE), Office of Educational Research and Improvement (OERI) award #R308A960003, by University of California Office of the President award #8047PCE186, and by the Atlantic Philanthropies. The opinions expressed herein are those of the authors and not of the funding agencies. The authors acknowledge Deborah Loewenberg Ball, Joshua Glazer, Heather Hill, and two anonymous reviewers for helpful comments on earlier drafts of this paper.Correspondence concerning this article should be addressed to Geoffrey Phelps, Study of Instructional Improvement, 610 South University Ave, School of Education Building #3112, Ann Arbor, Michigan 48109; e-mail gphelps@umich.edu. AbstractIn this article we present results from a project to develop survey measures of the content knowledge teachers need to teach elementary reading. In areas such as mathematics and science, there has been great interest in the special ways teachers need to know the subject to teach it to others -often referred to as pedagogical content knowledge. However, little is known about what teachers need to know about reading to teach it effectively. We begin the article by discussing what might constitute content knowledge for teaching in the area of reading and by describing the items we wrote. Next, factor and scaling results are presented from a pilot of 261 multiple-choice items wit...

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Recent studies of elementary teachers' knowledge about reading have been built on the premise that teachers need thorough knowledge about language and reading processes, but these studies have provided only limited evidence that teachers' performance on tests of such knowledge contributes to their students' reading achievement. The present study was designed to examine the contribution of first-through third-grade teachers' knowledge about early reading to their students' improvement on tests of word analysis and reading comprehension, controlling for socio-demographic characteristics of students, their prior reading achievement, and teachers' educational attainment, professional experiences, and socio-demographic characteristics. Preliminary analyses indicated that the test of teachers' knowledge had adequate psychometric characteristics. However, performance on this measure of teachers' knowledge did not significantly explain students' improvement on the two reading subtests. The complexity of the factors that influence teachers' knowledge acquisition and the context in which the study was carried out offer possible explanations for these results. In addition, teachers' content knowledge about reading might not be closely associated with the practices they use in reading instruction, and therefore might not be significantly related to their students' improvement in reading over a year.Keywords Reading Á Elementary Á Teacher knowledge Á Reading achievement Purpose of the studyThe federal goal of improving the quality of teaching (U.S. Department of Education, 2002b) has made it critical that there be means of identifying more and Order of authors is alphabetical.

We examine the impact of teacher professional development on knowledge growth and subsequent knowledge retention. Specifically we use English Language Arts teacher content and pedagogy assessments to determine whether the California Professional Development Institutes significantly improve teacher content knowledge and whether teachers retain that knowledge six months after the institutes are completed. The results indicate that teachers vary significantly in pre-institute knowledge on the four assessed domains, demonstrate significant knowledge growth, but only retain about one half of what was gained during the institute. Further, pre-existing knowledge gaps are not systematically reduced and teacher perceptions of institute quality are not related to knowledge growth and knowledge retention. Current No Child Left Behind (NCLB) legislation requires that all students are taught by highly-qualified teachers (NCLB, 2001). The logic of NCLB and related state and district policies is straightforward; to make adequate progress towards proficiency in the core subjects of English language arts and mathematics, students need to receive instruction from teachers who are well-prepared to teach these subjects. Teacher professional development is widely viewed as the most promising intervention for improving teacher quality in U.S. public schools. Nearly every state and district provides inducements for teachers to participate in professional development and these are increasingly supplemented by federal programs such as Reading First. Districts often add requirements on top of these, either in the form of mandatory programs for all instructional staff, or by requiring time investment beyond state requirements. The

Despite recent shifts in research emphasizing the value of carefully designed experiments, the number of studies of teacher professional development with rigorous designs has lagged behind its student outcome counterparts. We outline a framework for the design of group randomized trials (GRTs) with teachers' knowledge as the outcome and consider mathematics and reading knowledge outcomes designed to assess the types of content problems that teachers encounter in practice. To estimate design parameters, we draw on a national sample of teachers for mathematics and a state Reading First sample to estimate for reading. Our results suggest that there is substantial clustering of teachers' knowledge within schools and professional development GRTs will likely need increased sample sizes to account for this clustering.

Debates persist over the knowledge needed to teach elementary reading effectively. In one commonly held view verbal ability is what matters most and the best approach to improving teacher quality is to recruit teachers who themselves are good readers. Others argue that teachers need special forms of professional knowledge that differ substantially from common adult reading and verbal ability. These different assumptions about what teachers need to know are directly relevant to whether teaching reading demands specialized professional knowledge and they have lead to radically different policy recommendations for both teacher preparation and induction. This study presents preliminary evidence that elementary reading teachers can hold a special knowledge of language, text, and reading process that differs substantially from common reading and verbal ability. Implications for the measurement and study of teacher quality and related implications for teacher evaluation and teacher development are discussed.