Teaching Mathematical Knowledge for Teaching: Curriculum and Challenges.

Abstract

Over the last decade, researchers have investigated the nature and scope of mathematical knowledge for teaching (MKT) and have provided evidence that teachers’ MKT plays a critical role in the effectiveness of teaching and learning. This dissertation focuses on the problem of helping teachers develop MKT. Two goals shape the research: (1) to specify the tasks of and challenges involved in teaching MKT and (2) to build knowledge about how to organize a curriculum for teaching MKT. The data sources are curriculum materials designed to focus on MKT and video recordings collected in classrooms where teacher educators and teachers were working with the curriculum materials. The analysis focuses on not only the tasks for teacher educators, especially in managing instruction where teachers as learners worked on developing MKT, but also on MKT as content in teacher education. This study then combines findings from the data with the analytic literature review. Five central tasks of teacher educators are illustrated to identify what might make the teaching of MKT difficult and what might be helpful to teacher educators. Moreover, mathematical work of teaching and knowledge about mathematics are specified as the focus in teaching MKT by developing a framework for a curriculum of MKT as well as identifying what components are involved in teaching MKT in teacher education and how they fit within a larger terrain of MKT. Results contribute to the pedagogical considerations that underlie the teaching of MKT and to the design and implementation of a curriculum to teach MKT. Moreover, this research expands into teacher education as another place to study MKT and provides the groundwork for a shared curriculum in mathematics teacher education.