“What does it take to be good at something in which failure is so easy, so effortless?” Atul Gawande (2007) said this in his book Better referring to the medical field, but that question can be used in the context of many fields, specifically education. The question of what it means to be an expert at teaching has taken on some urgency in the effort to reform public education (Sternberg and Hovarth, 1995). Theories of expert teaching vary throughout the educational community (Shulman, 1987; Sternberg and Hovath, 1995). Sternberg and Hovarth (1995) state that a model must be developed in teacher expertise to those teachers who are expert at teaching students from those who are merely ...view middle of the document...
Shulman implied teachers’ SMK should represent a deep understanding of the material to be mastered by students when he said, “The teacher must not only understand that something is so, the teacher must further understand why it is so” (Shulman, 1986, p. 9).
The core meaning of pedagogical content knowledge is best represented in Shulman’s (1986) original definition he used in his address to the American Educational Research Association in 1985:
Pedagogical content knowledge identifies the distinctive bodies of knowledge for teaching. It represents the blending of content and pedagogy into an understanding of how particular topics, problems or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction. Pedagogical content knowledge is the category most likely to distinguish the understanding of the content specialist from that of the pedagogue (p. 4).
He goes on to define PCK as “the ways of representing and formulating the subject that makes it comprehensible to students” (p. 9 ). Merely having the knowledge of content does not mean that the teacher can effectively transfer it to students.
Research on Teachers’ SMK and PCK in Mathematics
Multiple views have been presented on what quality instruction in a mathematics classroom should look like (Leinhardt, 1986; Ma, 1999; Sternberg and Horvath, 1995; Stigler and Heibert; 1999; Zheng, Peverly, and Tao, 2006). The importance of teachers’ SMK and PCK, particularly in mathematics, to high-quality instructional practices has been discussed (Ball, 1990; Ma, 1999). From looking at qualitative data, researchers have seen that teachers who have a deep understanding of mathematical concepts tend to explain and represent mathematics content more effectively (Leinhardt, 1986; Ma, 1999; Zheng, Peverly & Tao, 2006). However, the precise nature of teachers’ knowledge remains empirically uncertain (Krauss et al., 2008).
Research on Subject Matter Knowledge
Each study in this section explored SMK and characteristics expert teachers possess with regard to SMK. Sternberg and Horvath’s (1995) research focused solely on SMK. They identified differences between an expert teacher and a novice teacher in mathematics by designing a prototype of an expert teacher. They claim that an expert teacher is more extensive, accessible, and organized for use in teaching than novice teachers. Expert teachers also solve problems more efficiently within their content area and do so with little cognitive effort. They engage more readily in higher metacognitive or executive processes, such as planning, monitoring, and evaluating efforts at problem solving. Finally, expert teachers have more insight and are able to identify information that is relevant to the solution of problems.
There is little agreement about what is meant by “subject matter knowledge for teaching,” but, discussion of prospective teachers’ amount of SMK tends to be evaluated on...