Mathematical Knowledge for Teaching Teachers: The Mathematical Work of and Knowledge Entailed by Teacher Education.

Abstract

This dissertation investigates the mathematical work and knowledge demands of this work to teach mathematics to teachers. The last 20 years have seen progress in the study of the specialized knowledge of mathematics needed for the work of teaching, as well as much discussion about the importance of strengthening teachers’ mathematical preparation. However, less attention has been paid to the mathematical work and the knowledge demands of the work for those who must teach the courses, write textbooks, or develop programs to help teachers learn mathematics. This study investigated the work of teaching teachers and the mathematical knowledge entailed by that work. The overarching question of the study is: What is the work of teaching teachers mathematics and what are the mathematical knowledge demands entailed by this work? Two sub-questions are: • What are some of the key tasks of teaching mathematical knowledge for teaching that are involved in teaching teachers mathematics? • What are the mathematical knowledge demands entailed by teaching teachers mathematics? This study examines the teaching of two mathematics teacher educators, educators significantly different in professional training. Their students are different. One teaches in-service teachers. The other teaches student teachers. The contrasting sites provided data to probe recurrent tasks and demands of the work of teaching mathematics to teachers. First, I identified several task domains within the work of both teacher educators. Three appeared to be central: selecting interpretations and representations, selecting examples, and managing mathematical tasks. Four cases of teaching, two from each teacher educator were analyzed for elements of these task domains. Based on my cross case analysis I differentiate elements that seemed to be consistent and idiosyncratic across the cases. I proposed a framework for the study of the work of teacher education. Second, I examined the mathematical work of these cases for the mathematical knowledge demands. I proposed a domain of mathematical knowledge, mathematical knowledge for teaching teachers (MKTT), discussed distinctive qualities of MKTT that appeared to characterize the ways MKTT is held and used for the work of teacher education.