The purpose of this qualitative cross-case study was to investigate the growth and transfer of metacognitive strategies in mathematical problem solving from a university course to the classroom. In this study, six preservice teachers with different levels of mathematics achievement and experiences were selected purposively for in-depth analysis. Data were gathered over one semester through videotaped course and classroom observations, interviews with preservice teachers and their instructors, electronic portfolios, and teachers’ reflections. Data collected through electronic portfolios were used to triangulate these data sources. Data drawn from these observations were analyzed by using the analytical tool, NVIVO7, which guided the factors identified from the literature and those that emerged. The factors that affected how the preservice teachers solved problems within the context of the course and the classroom were examined through reflections and semi-structured interviews at the beginning and end of the study. These data were analyzed to understand the preservice teachers’ behaviors in terms of task analysis; selecting, implementing, and evaluating problem-specific strategies; and monitoring and evaluating problem solutions.
Analysis of classroom observations revealed that several aspects in the course and the middle school classroom potentially support teacher problem solving. Preservice teachers were given opportunities to experience success and challenges and reflect by engaging with the tasks and activities through multiple strategies. Findings from within and across case studies showed that each preservice teacher engaged with and interacted within the course and classroom differently. Their classroom practices showed differences in terms of (a) metacognitive skills, (b) reasoning about problem solving failures and successes, (c) attitudes towards math and teaching, and (d) instructional processes within the course and classroom. These differences brought about diverse opportunities and challenges for each teacher, which may have affected his or her development and transfer of problem solving skills. Furthermore, these analyses support the argument that students’ participation in classroom practices, in part, is the result of complex interactions including their self-efficacy beliefs and strategic knowledge.