Contextual Research and Large Empirical Research? Developing the Theory of Mathematical Knowledge for Teaching by Investigating its Nature, Measurement, and Growth

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This large empirical study by a research team at the University of Michigan Ann Arbor is developing the theoretical foundations for mathematical knowledge for teaching (MKT) in three strands of work. The primary focus is on preservice and beginning teachers in the area of mathematics. The first strand includes a set of theory-building studies analyzing current understandings in the literature and current classroom practices. For this strand researchers map MKT by identifying the different aspects that constitute the construct. The second strand is an instrument-development project that began with some prior developed multiple-choice measures. The focus of this strand is developing new alternative assessment items and instruments using different formats that will be valid and reliable measures of MKT at teachers? different stages in their career. In the third strand, researchers are articulating a description of teachers' learning progressions over their careers as they develop mathematical knowledge for teaching. The project is guided by three goals: (1) to systematically map the terrain of mathematical knowledge for teaching; (2) to develop alternative measures of MKT and analyze the data obtained; and (3) to conceptualize the trajectory of teachers? acquisition and use of MKT. Multiple methods are being employed to achieve the project goals. Three teams of researchers are working concurrently, each one devoted to addressing one of the three strands. All research teams are doing an extensive review of reported research and are drawing heavily from analyses of video records of mathematics lessons. Data from surveys administered nationally are being analyzed to help identify a trajectory of MKT for teachers? careers. In Years 1-3 nine beginning teachers and their classrooms are being observed and video tapped for five consecutive days at three points during the school year. Researchers are administering new assessment items and conducting cognitive interviews of 60 teachers to analyze the validity of and refine the items. Eight camps of multiple days are being conducted of multidisciplinary experts to review materials being developed (e.g., items and proposed trajectories) and to work collaboratively and independently to produce supportive materials. An external evaluator is collecting, analyzing, and reporting data to the research teams for both formative and summative purposes. The evaluator is guided by specific questions and will review products, video analyses, and the camps of scholars. The main products that will be produced are a map of MKT, alternative assessments of MKT, and a professional learning trajectory for MKT. These products and findings are to be disseminated through peer-reviewed journals, conference presentations, and multimedia content guides. As evidenced by the large dissemination and use of prior materials produced by this research team, this work will reach and influence a significant number of those in the mathematics education field.