Elementary preservice teachers' mathematical knowledge for teaching: Using situated case studies and educative experiences to examine and improve the development of MKT in teacher education.

摘要

This study examined pre-service teachers' development of mathematical knowledge for teaching (MKT) over their final year in a university based teacher education program. This was done through analyzing written reflections, focus group interviews, individual interviews, teaching observations, and post-observation interviews as well as through the use of a quantitative measure, the MKT test (Learning Mathematics for Teaching, 2005). The study design employed situated case studies, in which tiered participation resulted in extensive data for three focal pre-service teachers as well as a comparison to larger groups of their peers through interviews (n=8), focus groups (n=11), and written reflections and the MKT test (n=35). A new protocol for coding elementary pre-service teachers' mathematics lessons was developed to extend Rowland et al.'s (2009) work on the Knowledge Quartet (KQ) model.;The study investigated pre-service teachers' definitions of MKT, demonstrations of MKT in their teaching, and educative experiences that contributed to their development of MKT. Insights were gained into pre-service teachers' definitions of MKT, the development of which was dynamic, non-linear, individual, and shared similarities to the aggregate definition only at the end of the year. The KQ category of foundation tended to dominate the pre-service teachers' definitions of MKT, the transformation category remained vague, connection was an inconsistent category in their definition, and contingency arose late in the year and at a relatively small proportion.;Insights were also gained into pre-service teachers' demonstration of MKT in their teaching of mathematics. Dimensions of MKT were most often demonstrated at a minimum level, growth on a dimension as indicated by scores that improved over time was extremely rare, scores were more variable than predicted across the four observed lessons, and the connection category was particularly challenging.;This study used the theoretical lenses of cognitive views of learning and Dewey's (1904/1964; 1916/1985) philosophy of educative experiences. These foundations enhanced this study and led to more substantial suggestions by which to improve teacher education in order to better develop pre-service teachers' development of MKT through the methods course, initial field placements, student teaching and content-based discussion groups such that pre-service teachers' can better develop MKT via educative experiences that encourage conceptual rather than procedural teaching knowledge.