Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students

By H. Hill, Deborah Loewenberg Ball, S. Schilling. Journal for Research in Mathematics Education, 2008

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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.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9a72f2765a4e0880a413f32e0a7ddc7e53046b60

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Citations in the corpus

Expanding computer science education in schools: understanding teacher experiences and challenges (2016, background): “This is not surprising given that good teaching requires not only substantial understanding of the subject matter, but also a solid background of pedagogy and knowledge of the learners (Hill, Ball, & Shiling, 2008; Shulman, 1986).”
“Mathematical knowledge for teaching”: adapting U.S. measures for use in Ireland (2008, neutral): “1 (from Hill et al. 2007).”
Connecting changes in secondary mathematics teachers’ knowledge to their experiences in a professional development workshop (2013, background): “…of content (i.e., by solving and discussing mathematical tasks) and specialized knowledge of content (i.e., by considering multiple strategies and the mathematical connections between them, or by considering the value of different representations of mathematical concepts) (Hill et al. 2008).”
Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics (2011, background): “Hill et al. (2008) designed a test specifically assessing mathematical knowledge for teaching and found that the measure of teacher content knowledge is a significant and positive predictor of student success in mathematics.”
The Effects of Changes in Mathematical Knowledge on Teaching: A Longitudinal Study of Teachers' Knowledge and Instruction (2015, methodology): “Although recent studies utilizing well-established instruments have provided some evidence that teachers’ mathematical knowledge is related to students’ mathematics achievement and the mathematical quality of instruction (Baumert et al., 2010; Hill et al., 2008; Hill, Rowan, & Ball, 2005; Rockoff, J”