This article presents an "evidence-based" program improvement effort that sought to strengthen student teachers' implementation of subject-specific pedagogy for teaching mathematics in a K-8 multiple subject teacher education program. We report the process of how we used a research-based approach to gather evidence about "status quo" of the mathematics student teaching component that prepared elementary level teachers, changes that were made in the program to better prepare pre-service teachers to be reflective mathematics teachers who plan and implement effective subject-specific pedagogy, and how we measured levels of effectiveness. Specifically, we investigated whether mentoring strategies and materials designed to engage student teachers in applying aspects of mathematical knowledge for teaching (MKT) during the lesson planning/teaching/feedback cycle of student teaching would impact pre-service teacher reflective practice and teaching performance. In addition, we studied how we should change the supervision process used to develop the reflective thinking of student teachers as they engaged in teaching mathematics.
What Student Teachers Need to Know about Teaching Mathematics
Recent studies have identified the need for improved classroom practices in teaching mathematics as a condition for improving K-12 pupil achievement in mathematics (Ball, Hill, & Bass, 2005; Ma, 1999; National Mathematics Advisory Panel, 2008; Stigler & Hiebert, 1999). To improve classroom practices, pre-service methods classes should focus not just on teaching general methods of instruction, but should engage pre-service teachers in learning how to successfully teach subject matter content using highly specific strategies that are specialized to that discipline (Shulman, 1987). We focused on three important components in the current literature base on teaching mathematics to guide us in developing a pre-service preparation program that develops mathematical proficiency in teachers: (1) Deborah Ball and her colleagues' work on Mathematical Knowledge for Teaching, (2) process standards formulated by the National Council of Teachers of Mathematics(NCTM), and (3) the National Research Council's (NRC) work on mathematical proficiency.
There are four common themes in these works: (1) Problem Solving--being able to pose good mathematical questions and problems that are productive for students' learning; (2) Explanations--communicating mathematical ideas, justifying reasoning, interpreting strategies of others, and responding productively to questions; (3) Representations--carefully choosing the best diagrams, examples, symbols, for maximum understanding; and (4) Mathematical Connections--making explicit how mathematical ideas are related to each other and applied to the real world (Ball, Hill, & Bass, 2005; Hill, Rowan, & Ball, 2005; NCTM, 2000; NRC, 2001). Our elementary teacher preparation program chose to emphasize problem solving, explanations, representations, and mathematical connections as four important subject-specific strategies that student teachers need to be able to implement to effectively teach mathematics.
Applying What Student Teachers Need to Know about Teaching Mathematics to the Student Teaching Experience
For years now, teacher preparation programs have been challenged with reforming how new teachers are prepared for teaching (Carnegie Task Force, 1986; Darling-Hammond, 1999). The student teaching experience has been identified as one of the most influential factors in preparing beginning teachers (Koehler, 1988; Lemma, 1993). Zeichner and Conklin (2008), in their description of characteristics of exemplary teacher education programs, cite dimensions of field experiences that can contribute to a program's success, including the need to closely connect supervision during student teaching to content of courses so that faculty and curriculum experiences reflect one vision of teaching and learning. …