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
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. 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 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 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
