Extending use of instructional exchanges to research on teacher education

Abstract

This article considers what teacher education candidates can show their instructors as evidence that they are learning what they are supposed to learn, and how that might be described as like what happens in mathematics classrooms in compulsory settings. To support this effort, the article extends the use of the construct of instructional exchanges from the analysis of mathematics instruction to the analysis of mathematics teacher education. We describe four ways in which teacher candidates exchange their work for teacher educators' assessments of their learning of mathematics teaching and illustrate how such exchanges are a subset of a more general kind of activity, a transaction of practice. Section 4 looks at ways in which the theorizing in the study might have practical implications. The examination of teacher education closes by looking back at what the attention to the transaction of practice might suggest as ways to develop a greater range of tasks for use in mathematics teaching in compulsory settings; the use of a wider range of tasks might allow mathematics teachers in compulsory settings to make a wider variety of claims about what it is that their students have learned. The article also highlights ways in which technological tools can be considered as an important infrastructure to develop to support instructional exchanges in mathematics teacher education.