Establishing Foundations for Investigating Inquiry-Oriented Teaching

摘要

The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe the experiences of mathematicians implementing the curriculum from their perspective. Second. I will describe a study that explores the mathematical work done by teachers as they respond to the mathematical activity of their students. Finally, I will discuss a theoretical paper in which I synthesize aspects of the instructional theory underlying the TAAFU curriculum in order to develop an analytic framework for analyzing student learning. This dissertation will serve as a foundation for my future research focused on the relationship between teachersu27 mathematical work and the learning of their students.