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 the development and empirical testing of measures to assess teachers’ content knowledge for teaching elementary mathematics. The authors review the literature on teacher knowledge, highlighting how scholars have organized such knowledge. They describe survey items designed to represent knowledge for teaching mathematics and the results of factor analysis and scaling work with these items. The findings indicate that teachers’ knowledge for teaching elementary mathematics is multidimensional, encompassing knowledge of various mathematical topics and domains. The constructs identified by factor analysis form psychometrically acceptable scales. Over the past two decades, teachers’ mathematical knowledge has become a focus of concern. New theoretical and empirical insights into teaching have led to increased attention on 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 standards and assessments, there is a lack of agreement on what teachers need to know to teach mathematics. Different exams assess varying aspects of teaching ability, such as solving middle-school level mathematics problems or constructing mathematical questions for students. This disagreement can be traced back to theoretical and empirical literature on teaching knowledge, where different authors propose divergent elements and organizations for such knowledge. The authors sought to shed light on this debate by analyzing 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 representing various components of the knowledge needed for teaching. Factor analysis of teachers’ responses revealed the structure of the knowledge they tried to represent. The main question was whether there is one construct called “mathematics knowledge for teaching” or multiple constructs representing distinct competencies. The second question was whether reliable scales could 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 representing such knowledge and present initial results from a field-test of these items, including factor analyses and attempts to scale these items for statistical work. The results suggest that teachers’ mathematical knowledge for teaching is multidimensional, with at least three dimensions: knowledge of content in elementary number and operations, knowledge of students and content in elementary number and operations, and knowledge of content in patterns, functions, and algebra. These findings highlight the importance of distinguishing between common and specialized knowledge of content.This article discusses the development and empirical testing of measures to assess teachers’ content knowledge for teaching elementary mathematics. The authors review the literature on teacher knowledge, highlighting how scholars have organized such knowledge. They describe survey items designed to represent knowledge for teaching mathematics and the results of factor analysis and scaling work with these items. The findings indicate that teachers’ knowledge for teaching elementary mathematics is multidimensional, encompassing knowledge of various mathematical topics and domains. The constructs identified by factor analysis form psychometrically acceptable scales. Over the past two decades, teachers’ mathematical knowledge has become a focus of concern. New theoretical and empirical insights into teaching have led to increased attention on 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 standards and assessments, there is a lack of agreement on what teachers need to know to teach mathematics. Different exams assess varying aspects of teaching ability, such as solving middle-school level mathematics problems or constructing mathematical questions for students. This disagreement can be traced back to theoretical and empirical literature on teaching knowledge, where different authors propose divergent elements and organizations for such knowledge. The authors sought to shed light on this debate by analyzing 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 representing various components of the knowledge needed for teaching. Factor analysis of teachers’ responses revealed the structure of the knowledge they tried to represent. The main question was whether there is one construct called “mathematics knowledge for teaching” or multiple constructs representing distinct competencies. The second question was whether reliable scales could 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 representing such knowledge and present initial results from a field-test of these items, including factor analyses and attempts to scale these items for statistical work. The results suggest that teachers’ mathematical knowledge for teaching is multidimensional, with at least three dimensions: knowledge of content in elementary number and operations, knowledge of students and content in elementary number and operations, and knowledge of content in patterns, functions, and algebra. These findings highlight the importance of distinguishing between common and specialized knowledge of content.
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Understanding Developing Measures of Teachers%E2%80%99 Mathematics Knowledge for Teaching