Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to studen
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Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning Charalambos Y. Charalambous1 · Heather C. Hill2 · Mark J. Chin2,3 · Daniel McGinn2,4
© Springer Nature B.V. 2019
Abstract During the last three decades, scholars have proposed several conceptual structures to represent teacher knowledge. A common denominator in this work is the assumption that disciplinary knowledge and the knowledge needed for teaching are distinct. However, empirical findings on the distinguishability of these two knowledge components, and their relationship with student outcomes, are mixed. In this replication and extension study, we explore these issues, drawing on evidence from a multi-year study of over 200 fourth- and fifth-grade US teachers. Exploratory and confirmatory factor analyses of these data suggested a single dimension for teacher knowledge. Value-added models predicting student test outcomes on both state tests and a test with cognitively challenging tasks revealed that teacher knowledge positively predicts student achievement gains. We consider the implications of these findings for teacher selection and education. Keywords Content knowledge · Dimensionality · Teacher knowledge · Mathematics · Student learning · Teaching-specific knowledge
Introduction There is wide consensus among scholars, teacher educators, and policymakers that teacher knowledge is an important asset in teachers’ toolkits. Despite this consensus, the composition of this knowledge and its role in supporting student learning has long been debated.
* Charalambos Y. Charalambous [email protected] 1
Department of Education, University of Cyprus, Theophanides Building, Rm 508, 11‑13 Dramas St, 1077 Nicosia, Cyprus
2
Harvard Graduate School of Education, Gutman Library, Room 445, 6 Appian Way, Cambridge, MA 02138, USA
3
Harvard University, Cambridge, MA, USA
4
Center for Education Policy Research at Harvard University, 4th Floor, 50 Church St, Cambridge, MA 02138, USA
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Drawing on Shulman and colleagues’ work (Shulman 1986, 1987; Wilson et al. 1987), scholars in mathematics education have proposed different conceptual structures for this knowledge (Ball et al. 2008; Grossman 1990; McCrory et al. 2012; Rowland et al. 2005). These conceptual structures often separate pure content knowledge (CK) from the knowledge that facilitates teaching. However, some scholars (Bernarz and Proulx 2009; Huillet 2009) doubt whether CK is separable from the knowledge needed for teaching, and empirical work on the distinguishability of these two components provides mixed findings. In fact, a systematic review of 60 research papers focusing on pedagogical content knowledge (PCK, Depaepe et al. 2013) surfaced disagreements among scholars about whether CK and PCK are distinct or intertwined. Perhaps equally inconclusive is the empirical evidence on the predictive validity of teacher knowledge on student learning. Despite the accumulated
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