ROLE: Knowledge of Algebra for Teaching

Michigan State University, East Lansing MI

Investigators

Abstract

We propose to undertake work on two components of this project, which was originally proposed as having three major components. We have redesigned this effort as a 24-month project primarily aimed at framework development and initial work on assessment tools; the attached budget would adequately support this work. Our original proposal included two research questions: Question 1. What knowledge of algebra for teaching (mathematical knowledge, beliefs, dispositions and conceptions of mathematics) do secondary school teachers of algebra draw upon to support their instruction? Question 2. How do preservice teachers' experiences in mathematics and in teacher education foster the development of knowledge of algebra for teaching? For this scaled-back version of the project we will address only the first research question. We had identified the several subquestions related to this; they are included below. We will meet as a project team to refine and narrow this list, and expect to focus on some subset of these: 1. How is teachers' knowledge of algebra organized and chunked, and how does this relate to their teaching? 2. How do teachers articulate what algebra is about? How do they describe the "big ideas" that structure the courses they teach? Can they compare and contrast the approach they take with others? How does this relate to their teaching? 3. What kind of knowledge do teachers draw upon in responding to students' ideas? 4. How do more general mathematical types of knowledge (reasoning, representing, problem solving) relate to knowledge of algebra for teaching? 5. What knowledge do teachers use in keeping their sights on longer-term mathematical goals or "big ideas" while also responding to student conceptions and interests? 6. What resources and strategies do teachers draw on for deepening their knowledge of algebra for teaching? In the 24 months of this project we will undertake the development of a framework for "knowledge of algebra for teaching" by doing the following: 1. Synthesizing literature, including: theoretical analyses of school algebra, research about the teaching and learning of algebra, research about knowledge used in teaching, investigations of how algebra teachers are using curricula. 2. Examining algebra curriculum materials and teachers' manuals, and analyses of those materials 3. Interviewing developers of contemporary secondary school algebra materials 4. Examining teaching through existing videotapes 5. Gathering data from inservice classrooms selected to span a range of curricular approaches, to support the framework development. In addition, we will begin the development and piloting of an assessment tool to assess and describe teachers' knowledge of algebra for teaching. Resources will not be available for full scale item development, piloting, and analysis. Rather we will design prototype tasks, probably in a relatively narrow content band within algebra, and conduct limited piloting efforts. The products of this work will be an analytic and empirically-derived framework describing algebra knowledge for teaching, and a set of prototype tasks that can be used as a basis for more extended task design in a subsequent project. In addition, we will use the framework as a basis for analysis of the algebra teaching in our teacher sample, and expect to produce a paper about teachers' knowledge of algebra for teaching as it relates to their classroom practice in a variety of curricular orientations.