Academic journal article Journal of Teacher Education

An Empirical Study of the Dimensionality of the Mathematical Knowledge for Teaching Construct

Academic journal article Journal of Teacher Education

An Empirical Study of the Dimensionality of the Mathematical Knowledge for Teaching Construct

Article excerpt

What constitutes teacher knowledge has been the subject of many studies, particularly in the field of mathematics education (e.g., Ball, Thames, & Phelps, 2008; Blomeke, Busse, Kaiser, Konig, & Suhl, 2016; Konig, Blomeke, Paine, Schmidt, & Hsieh, 2011; Rowland, Huckstep, & Thwaites, 2005). Since Shulman (1987, 1986) introduced pedagogical content knowledge (PCK) as another domain of teacher knowledge that is specific to the subject being taught yet that differs from content knowledge (e.g., knowing the content to teach) and general pedagogical knowledge (e.g., knowledge of classroom management), many scholars in education, especially in mathematics education, have further identified important components of the content knowledge needed in the work of teaching. These efforts have resulted in various frameworks in which teachers' knowledge is represented as a multidimensional construct consisting of several theoretically distinct subcomponents (e.g., Ball et al., 2008; Campbell et al., 2014; Kersting, Givvin, Sotelo, & Stigler, 2010; Ma, 1999; McCrory, Floden, Ferrini-Mundy, Reckase, & Senk, 2012; Rowland et al., 2005; Tatto et al., 2008). Although those efforts advanced our thinking about the nature of knowledge required for the task of teaching mathematics, little empirical research has been done since then to investigate the extent to which components of the teacher knowledge construct are actually empirically discernible (e.g., Hill, Schilling, & Ball, 2004; Krauss et al., 2008; Schilling, 2007).

The question of whether teachers' knowledge for teaching is multidimensional is an important and timely one to answer. If teachers' professional knowledge consists of distinguishable subcomponents, then the role of teachers' knowledge in instruction and student learning could be estimated inaccurately by using an overall indicator of teacher knowledge. For instance, let us assume that teachers' knowledge for teaching has three district categories (a, b, and c), yet an instrument designed to capture teachers' knowledge for teaching mainly captures domain a, some items in domain b, and no items in domain c. At the same time, another instrument also designed to measure the same teacher knowledge for teaching construct mainly measures domain b, but also measures some items in domains a and c. If the relationship between teacher knowledge for teaching and student learning is different when teachers' knowledge is measured by these two instruments, then it is unclear whether all three domains of teacher knowledge (e.g., a, b, or c) are associated with student learning or whether some components differ in their predictive validity (e.g., domain c may be the most important aspect of teacher knowledge for student learning). Thus, the emerging mixed evidence on the association between teacher knowledge and student learning could be the result of different combinations of items measuring different subcomponents of the same teacher knowledge construct (cf. Hill, Rowan, & Ball, 2005; Kersting, Givvin, Thompson, Santagata, & Stigler, 2012; Ottmar, Rimm-Kaufman, Larsen, & Berry, 2015; Rockoff, Jacob, Kane, & Staiger, 2011). Therefore, investigating specifically which knowledge components are empirically distinguishable will bring researchers one-step closer to accurately estimating the role of teacher knowledge in student learning and instruction.

In addition, unlike the current conceptualization of the structure of teachers' knowledge, if the content knowledge needed in teaching is found to be made up of different levels within a single construct, this result will have important implications for teacher education. Specifically, if the mathematical knowledge teachers need is unidimensional, then teachers' knowledge as theorized in many frameworks and the relationships among the subcomponents of that knowledge may be mischaracterized. If teachers' content knowledge for teaching is unidimensional, then a general construct, such as a key developmental understanding of mathematical concepts (Silverman & Thompson, 2008), would play a vital role in every classroom situation specific to mathematics teaching. …

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