Developing Preservice Elementary Teachers Awareness Of Mathematical Teaching Knowledge
Historically, teacher knowledge in mathematics, as measured by teacher certification, courses completed, major, grade point average, and scores on standardized exams, have not shown a significant relationship to student achievement, especially at the elementary level (Grossman, Wilson, & Shulman, 1989; National Mathematics Advisory Panel, 2008). These results imply that traditional mathematical content knowledge, although necessary, is insufficient for teaching mathematics (Hill & Ball, 2009). Similarly, knowledge of general pedagogical strategies in the absence of content area knowledge is insufficient for teaching. Shulman (1986) described this as the missing paradigm and proposed that, in addition to subject matter knowledge, teachers must also develop pedagogical content knowledge (PCK).
Shulman (1987) acknowledged that his conception of teacher knowledge was incomplete and encouraged researchers to formulate a clear framework for teacher content knowledge. Ball and colleagues set out to determine what successful teaching necessitates in respect to mathematics content knowledge and PCK (Ball, Thames, & Phelps, 2008). They identified domains of knowledge required for teaching mathematics and developed items to measure this knowledge. Findings indicated that knowledge for teaching mathematics extends beyond simply knowing the mathematics in elementary curriculum (Hill, Shilling, & Ball, 2004). Teachers also must be able to quickly identify errors and the sources thereof, understand students’ misconceptions based on particular errors, evaluate nonstandard approaches to determine mathematical correctness and generalizability, explain conceptual underpinnings of procedures, identify benefits of different ways to represent content, and determine appropriate sequences of examples. Ball et al. (2008) developed a framework, Mathematical Knowledge for Teaching (MKT), comprised of Subject Matter Knowledge and PCK, expanding on Shulman’s (1986, 1987) components of teacher knowledge.
Research findings on teachers’ MKT have shown a significant relationship between teachers’ MKT, the mathematical quality of their instruction (Hill et al., 2008), andstudent achievement (Hill, Rowan, & Ball, 2005; Rockoff, Jacob, Kane, & Staiger, 2008). However, much of the MKT research has been geared towards informing teacher educators about MKT, its different components (Ball et al., 2008; Hill & Ball, 2009), and means to improvethe MKT of teachers via professional development (PD) or university coursework (Ball & Forzani, 2009; Hill & Ball, 2004). Therefore, preservice teachers (PTs) are often exposed to MKT implicitly through the structures and content of mathematics coursework.
Ball et al. (2008) called for studies on the effects of different methods used in mathematics teacher education on teachers’ MKT and development of support materials for university coursework and PD related to MKT. In this presentation, we describe the results of a research project addressing both aspects of this call in the context of a two-semester mathematics methods course for elementary PTs who were explicitly exposed to MKT through purposively designed class activities and assignments. Specifically, a case study was used to promote the PTs to consider the importance of teacher knowledge. PTs analyzed and discussed the case study identifying strengths and weaknesses in the teacher’s instruction and knowledge needed by the teacher to effectively teach the lessons. Drawing on these discussions, the PTs developed an initial teacher knowledge framework. Throughout the mathematics methods courses, PTs refined the framework as they engaged in class activities, readings, journal responses, evaluation of their and other teachers’ practice, and assignments in which the framework was integrated. The results of this process demonstrate that providing PTs the experiences and support in considering the importance of teacher knowledge in teaching mathematics can increase PTs awareness and development of MKT.