Keynote Part I

Deborah Ball

Table of Contents: Introduction Clarifying the Issue of Teachers' Content Knowledge The Aim: Improving the Quality of Teaching and Learning Seeing Teaching as Involving Substantial Disciplinary Reasoning and Problem-Solving: The Case of Mathematics Teaching Problem #1: Analyzing Errors Problem #2: Analyzing Mathematical Procedures Problem #3: Defining Terms and Concepts

---

Using Content Knowledge in Teaching: What Do Teachers Have to Do, and Therefore Have to Learn?^1-2

Deborah Loewenberg Ball
University of Michigan

Abstract

Teaching well depends on more than "knowing subject matter," understanding learning, and being able to present material clearly. Teaching is itself a specialized form of work that entails substantial content-based problem solving and reasoning. This keynote will probe examples of such work, examine what it requires of teachers, and will engage participants in considering the implications of this perspective for the content preparation and ongoing education of teachers.

In this opening keynote for the third Conference on Sustainability for Local Systemic Change, I will attempt to do three things. I will begin by redefining the issue of content knowledge for teaching -- from a problem of knowledge to a problem of knowledge use in practice. Second, I will use mathematics teaching as a site to explore the notion of knowledge use in practice, from a perspective on teaching as a specialized form of disciplinary problem solving. We'll examine some specific examples to uncover how content knowledge and reasoning permeates the actual work of teaching. I'll invite those of you whose work focuses on science teaching to consider how this perspective plays out when the content being taught is science, rather than mathematics. Finally, in part II of the keynote (to be posted on Friday, May 16th) I will draw upon this set of ideas about knowledge use in teaching and consider its implications for the professional education of teachers: What might it look like to design and structure opportunities for teachers to learn content knowledge for teaching in ways that are close to the problems they will encounter and solve in their everyday work? Together, we will explore one example of how such learning opportunities for teachers might be created using a short segment of classroom video.

Overview

Redefining the issue of teachers' content knowledge Seeing teaching as involving substantial disciplinary reasoning and problem-solving Developing a practice-based approach to learning content for teaching

Before we begin, let me say a few words about why this topic is important to the agenda of school improvement. The goals of school improvement are many, but at the heart is the aim to improve students' learning and capability. A host of theories exist about how to effect this improvement and teachers' content knowledge may not seem significant to many favored designs for change. I argue, however, that improving students' school experience and learning depends fundamentally on teachers' capacities for high-quality instruction. Such instruction, whatever forms it may take, is a product of the relationships created between students and the content - that is, the ideas and ways of reasoning and doing - to be learned. How teachers understand the content is central to their ability to connect with their students and to help them develop. By "understand content," however, I mean something quite different from what is often thought of when people refer to the subject matter understandings of teachers. As we shall see, there are mathematical and scientific understandings that are fundamental to teaching - forms of understanding that are revealed through close examinations of the actual work of teaching inside of classrooms. So whether one's preferred approach to school improvement centers on the professional culture and interactions within a school, on home-school relations, or on the development of new curriculum materials, in the end, teachers' capacity for instruction matters. And regardless of one's view of instruction, teachers' knowledge of what they are teaching plays a central role in that capacity. I have experienced this in my own work as an elementary teacher. I have also seen it over and over in my work with other teachers.

What all these words really mean will develop as we work together.

---

¹ The development of this talk was supported by a grant by the National Science Foundation (ESI-0088027). The research and ideas discussed here have been supported by grants from the National Science Foundation (REC # 0126237) and the Spencer Foundation (MG #199800202).

² I would like to acknowledge my collaborators, Hyman Bass, a research mathematician, with whom I have been studying both teaching and mathematics to develop these ideas over the past several years, and Heather Hill, with whom I am currently engaged in developing measures of teachers' knowledge in ways that both refine and test the theoretical perspective we have been taking. I thank also the members of the Mathematics Teaching and Learning to Teach Project, Mark Hoover, Jennifer Lewis, and Edward Wall, for their close work with me on studying mathematics teaching, and Kara Suzuka, who has played many significant roles in this work across many years.