Setting the Stage: A Conceptual Framework for Examining and Developing Tasks for Mathematics Teacher Education

Abstract

This book is about tasks that teacher educators might use with prospective or practicing secondary mathematics teachers. There is a substantial literature that has established the critical role that tasks play in the teaching and learning process for school mathematics classes. Kilpatrick et al. (2001), for example, claim that the quality of teaching depends on whether teachers select cognitively demanding tasks, and whether these tasks unfold in the classroom in ways that allow the students to elaborate on the tasks and learn through those tasks. The basic argument is that it is through and around tasks that teachers and students communicate and learn mathematical ideas, so the tasks used by the teachers become the mediating tools. Christiansen and Walther (1986), drawing on the work of Leont’ev (1978), argued that the tasks set and the associated activity form the basis of the interaction between teaching and learning. Other authors who have similarly emphasized the critical role of tasks in creating learning opportunities for school students as well as the significant influences tasks have on what students actually learn include Stein and Lane (1996), Brousseau (1997), Hiebert and Wearne (1997), and Boaler (2002). This book is contributing to a related literature on the important role of tasks in teacher education.