Academic journal article Journal of Teacher Education

Teachers' Analyses of Classroom Video Predict Student Learning of Mathematics: Further Explorations of a Novel Measure of Teacher Knowledge

Academic journal article Journal of Teacher Education

Teachers' Analyses of Classroom Video Predict Student Learning of Mathematics: Further Explorations of a Novel Measure of Teacher Knowledge

Article excerpt

There is increasing evidence that teachers have a strong impact on student learning (Fennema & Franke, 1992; Hiebert & Grouws, 2007; Nye, Konstantopoulos, & Hedges, 2004). As more studies suggest that variance in student learning can be attributed in large part to teachers (Rowan, Correnti, & Miller, 2002; Sanders & Rivers, 1996; Sanders, Saxton, & Horn, 1997), researchers and policymakers have asked if these teacher effects might be explained, in part, by variation in teacher knowledge. In this article, we focus on understanding teacher knowledge in mathematics and the possible mechanisms by which it might affect student learning.

Teacher knowledge has been the subject of much research and discussion in recent years and of many education reform efforts. It seems obvious that one cannot teach what one does not know, but there is no consensus on what teacher knowledge is critical to ensure that students learn (Fennema & Franke, 1992). Without a doubt, the construct of teacher knowledge is far more complex than simply knowing the subject as we want students to know it. Shulman pointed this out 20 years ago when he specified the kinds of content knowledge teachers need (beyond subject matter knowledge) to teach their students effectively. Shulman, who labeled such knowledge "pedagogical content knowledge," argued that teachers needed to know the most useful representations for explaining given concepts or ideas; the most powerful analogies, illustrations, examples, explanations, and demonstrations; what makes particular content easy or difficult for learners; and common student misconceptions and mistakes (Shulman, 1986).

Building on Shulman's work, Deborah Ball, Heather Hill, and colleagues at the University of Michigan analyzed the different competencies and skills required for effective mathematics instruction and identified six distinct kinds of knowledge that teachers need. These components, which together form the Mathematics Knowledge for Teaching (MKT) construct, include general content knowledge (i.e., the knowledge teachers attempt to develop in their students), specialized content knowledge (i.e., knowledge that is only likely to develop in the context of teaching such as knowledge of nonstandard solution methods), knowledge of content and teaching (e.g., knowledge of useful representations for conveying a particular content to students), and knowledge of content and students (i.e., knowledge of common student mistakes and student thinking on specific topic areas). The latter two components were viewed by Shulman as part of pedagogical content knowledge (Ball, Thames, & Phelps, 2008; Shulman, 1986, 1987). The final two knowledge components hypothesized by Ball and Hill as necessary to teaching are horizon knowledge (i.e., the awareness of how mathematical topics are related across the curriculum) and knowledge of the curriculum (Ball et al., 2008; Hill, Sleep, Lewis, & Ball, 2007).

Items developed to measure several of these knowledge domains have, at least in some studies, been shown to significantly correlate with student learning, supporting their relevance (Hill, Rowan, & Ball, 2005). However, the level of correlation between teacher knowledge and student learning has been low. In the largest study examining the relation between MKT and student learning, a I standard deviation increase in MKT was associated with only .06 standard deviations of gain in student learning (Hill et al., 2005). (l) One possible explanation for the low correlation is what Bransford has referred to as the problem of inert knowledge. The concept of inert knowledge is used to describe at least some of the knowledge that one learns in school. Someone might "know" something in the sense that he or she can produce it on a paper-and-pencil test but still not be able to access and use the knowledge in a problem-solving situation. Thus, for example, the MKT is measuring what teachers know in one context (a multiple-choice test) but not whether they are able to activate and apply that knowledge in a real teaching situation (National Research Council [NRC], 2000). …

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