Studying Secondary Teachers' Knowledge for Teaching Mathematics

• In Event: 70.043 - Investigating Knowledge for Teaching Secondary Mathematics

Abstract

In recent years, mathematics teacher education policy documents (e.g., NCATE, InTASC) have contained a hypothesized or theoretical perspective on what mathematics teachers should know and there have been extensive reviews of literature that provide evidence that we have an empirically-based depiction of mathematics teachers’ practices (e.g., Franke, Kazemi, & Battey, 2007), what influences mathematics teachers’ practices (e.g., Sowder, 2007), and the connections between certain teaching practices and students’ learning outcomes (e.g., Hiebert & Grouws, 2007). However, we know little about the knowledge that expert teachers draw upon when designing and enacting their instruction and argue that the design of mathematics teacher education can and should be based on what teachers who have expertise in the profession do know. As a result, there is a need to better understand how mathematics teachers with expertise draw on their knowledge when designing instruction and provide empirically-based thick descriptions of that knowledge.

Shulman (1986, 1987) conceptualized pedagogical content knowledge (PCK), the specialized knowledge of content-area specialists that is necessary for effective teaching, and described it as a “special amalgam of content and pedagogy that is uniquely the province of teachers, their own special form of professional understanding” (p. 227). Magnusson, Krajcik, and Borko (1999) built upon and extended the work of Shulman. In their PCK framework, Magnusson and her colleagues delineated PCK for science teaching into four components: knowledge of science curricula, knowledge of students’ understandings of science, knowledge of instructional strategies, and a new PCK component – knowledge of assessment of scientific literacy.

In this presentation, we will articulate a more finely delineated framework for studying mathematics teachers’ knowledge for teaching mathematics than is currently available in the literature—drawing upon how expert secondary mathematics teachers thought through and designed an introduction lesson on linear relationships. We will share explicit examples of both pedagogical content knowledge and pedagogical knowledge across four strands of teacher knowledge identified by Magnusson, Krajcik, and Borko (1999). These descriptions and examples of teachers’ actions that correspond to each knowledge strand contribute to the mathematics education research community by enhancing our abilities to characterize teacher knowledge beyond earlier efforts (e.g., Hill, Ball, & Shilling, 2008). Furthermore, we provide an in-depth description of knowledge for mathematics teaching at the secondary level.

In previous work, we have described beginning teachers’ development of PCK over a 2-year span (e.g., Authors, 2013). However, in doing similar analysis with both beginning and experienced secondary mathematics teachers, we are struck by the non-integrated nature of beginning teachers’ knowledge when compared to their more experienced and professionally active colleagues. The findings from this research demonstrate and document that expert secondary mathematics teachers think in complex and integrated ways. And, as the authors of How People Learn: Brain, Mind, Experience, and School (National Research Council, 2000) argue, “the study of expertise shows what the results of successful learning look like” (p. 31). When we study expert mathematics teachers’ thinking, it can provide important directions for mathematics teacher education that is grounded in empirical research.

Authors

• Cynthia E. Taylor, Millersville University of Pennsylvania

• Fran Arbaugh, The Pennsylvania State University