Using the Model-Strategy-Application Approach to Developing Pre-Service Teachers’ Knowledge and Assessing Their Progress in Math Methods Courses

The purpose of this research was to contribute to a better understanding of how to enhance pre-service teachers’ knowledge of mathematics teaching through Model, Strategy, and Application (MSA). 153 pre-service teachers from six math methods courses (K-8) at two universities participated in this study. Both qualitative and quantitative methods were used to measure teacher learning and understanding of the MSA approach and to identify relationships between components of the MSA model. The results of this study show that using the MSA model can enhance pre-service teachers’ knowledge of mathematics teaching. It can be used as a measurable and practical model in assessing pre-service teachers’ learning progress in models, strategy, and application. In addition, the findings indicate that the three components of the MSA model are all interrelated and equally important; ignoring one or the other will result in the lack of proficiency in teachers’ knowledge of mathematics teaching. INTRODUCTION In recent years, many studies have focused on building mathematics teachers’ content knowledge, pedagogical knowledge, and pedagogical content knowledge (Shulman, 1987; Fennema, 1992; Ma, 1999; Hill & Ball, 2004; An, Kulm, & Wu, 2004). However, research has paid insufficient attention to systematically designing a repertoire of measurable and practical models of knowledge of mathematics teaching that allow pre-service teachers to not only build conceptual understanding and procedural skills, but also to be able to make connections between mathematics concepts, procedures, and applications. In order to teach effectively, pre-service teachers need to develop the knowledge of creating various representations to unpack abstract mathematics content and make meaningful and visible to students the ideas behind the concepts and procedures (National Research Council [NRC], 2001); they also need to perform computations efficiently and know when and how to apply computations and various models in real world situations. To achieve the goals above, this study explored an effective approach that comprises: 1) creating variou visual and meaningful mathematics models to convey abstract math ideas thru conceptual understanding; 2) developing various strategies to achieve fluency in computations; and 3) developing strategic competence in word problem applications. In the Model-Strategy-Application (MSA) approach, the three aspects of it form the critical components of teachers’ knowledge of mathematics teaching in this study.