Developing Measures of Teachers' Mathematics Knowledge for Teaching

Developing Measures of Teachers' Mathematics Knowledge for Teaching

| Heather Hill, Deborah Ball, Stephen Schilling
This article discusses efforts to design and test measures of teachers' content knowledge for teaching elementary mathematics. The authors review the literature on teacher knowledge, focusing on how scholars have organized such knowledge. They describe survey items they developed to represent knowledge for teaching mathematics and results from factor analysis and scaling work with these items. The findings indicate that teachers' knowledge for teaching elementary mathematics is multidimensional, including knowledge of various mathematical topics and domains. The constructs identified by factor analysis form psychometrically acceptable scales. In the past two decades, teachers' mathematical knowledge has become a focus of concern. New theoretical and empirical insights into teaching have led to greater attention to the role of such knowledge in teacher education and teaching quality. Studies have documented the mean and variation in teachers' knowledge of mathematics for teaching. These efforts have influenced teaching standards and assessments. Despite the development of such standards and assessments, there is a lack of agreement on what teachers need to know to teach mathematics. The authors analyze data collected to construct an assessment of teachers' content knowledge for teaching mathematics. They used elements from existing theories about teacher knowledge to write survey-based teaching problems. They then factor analyzed teachers' responses to determine the structure of the knowledge they tried to represent. The main question is whether there is one construct called "mathematics knowledge for teaching" or multiple constructs representing distinct mathematical competencies. Another question is whether reliable scales can be constructed to measure such knowledge. The authors describe their effort and results, beginning with an overview of the original literature on content knowledge for teaching. They then discuss their efforts to write items that represent such knowledge and describe initial results from a field-test of these items, including factor analyses and attempts to scale these items for statistical work. The literature review discusses the concept of "pedagogical content knowledge" introduced by Shulman, which includes familiarity with topics children find interesting or difficult, the representations most useful for teaching a specific content idea, and learners' typical errors and misconceptions. Researchers have conjectured about the potential organization of such knowledge, and these conjectures serve as starting points for this investigation. Shulman proposed three categories of subject matter knowledge for teaching: content knowledge, pedagogical content knowledge, and curriculum knowledge. Other researchers have proposed different organizations of teacher knowledge. The authors developed 138 mathematics items to represent the mathematical knowledge used in teaching elementary mathematics. These items were categorized into content areas and domains of teacher knowledge. The authors conducted factor analyses of these items and found that the constructs indicated by factor analysis form psychometrically acceptable scales. The results suggest that teachers' content knowledge for teaching is at least somewhat domain-specific. The authors also discuss the implications of these findings for theory, policy, teacher preparation, and measurement. They conclude that developing measures of teacher knowledge for teaching mathematics can contribute to ongoing efforts in educational research to answer policy-relevant questions and renew interest in the theoretical aspects of professional knowledge for teaching.This article discusses efforts to design and test measures of teachers' content knowledge for teaching elementary mathematics. The authors review the literature on teacher knowledge, focusing on how scholars have organized such knowledge. They describe survey items they developed to represent knowledge for teaching mathematics and results from factor analysis and scaling work with these items. The findings indicate that teachers' knowledge for teaching elementary mathematics is multidimensional, including knowledge of various mathematical topics and domains. The constructs identified by factor analysis form psychometrically acceptable scales. In the past two decades, teachers' mathematical knowledge has become a focus of concern. New theoretical and empirical insights into teaching have led to greater attention to the role of such knowledge in teacher education and teaching quality. Studies have documented the mean and variation in teachers' knowledge of mathematics for teaching. These efforts have influenced teaching standards and assessments. Despite the development of such standards and assessments, there is a lack of agreement on what teachers need to know to teach mathematics. The authors analyze data collected to construct an assessment of teachers' content knowledge for teaching mathematics. They used elements from existing theories about teacher knowledge to write survey-based teaching problems. They then factor analyzed teachers' responses to determine the structure of the knowledge they tried to represent. The main question is whether there is one construct called "mathematics knowledge for teaching" or multiple constructs representing distinct mathematical competencies. Another question is whether reliable scales can be constructed to measure such knowledge. The authors describe their effort and results, beginning with an overview of the original literature on content knowledge for teaching. They then discuss their efforts to write items that represent such knowledge and describe initial results from a field-test of these items, including factor analyses and attempts to scale these items for statistical work. The literature review discusses the concept of "pedagogical content knowledge" introduced by Shulman, which includes familiarity with topics children find interesting or difficult, the representations most useful for teaching a specific content idea, and learners' typical errors and misconceptions. Researchers have conjectured about the potential organization of such knowledge, and these conjectures serve as starting points for this investigation. Shulman proposed three categories of subject matter knowledge for teaching: content knowledge, pedagogical content knowledge, and curriculum knowledge. Other researchers have proposed different organizations of teacher knowledge. The authors developed 138 mathematics items to represent the mathematical knowledge used in teaching elementary mathematics. These items were categorized into content areas and domains of teacher knowledge. The authors conducted factor analyses of these items and found that the constructs indicated by factor analysis form psychometrically acceptable scales. The results suggest that teachers' content knowledge for teaching is at least somewhat domain-specific. The authors also discuss the implications of these findings for theory, policy, teacher preparation, and measurement. They conclude that developing measures of teacher knowledge for teaching mathematics can contribute to ongoing efforts in educational research to answer policy-relevant questions and renew interest in the theoretical aspects of professional knowledge for teaching.
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[slides and audio] Developing Measures of Teachers%E2%80%99 Mathematics Knowledge for Teaching