When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching

Abstract

This paper describes a research and development project in teaching designed to examine whether and how it might be possible to bring the practice of knowing mathematics in school closer too what it means to know mathematics within the discipline by deliberately altering the roles and responsibilities of teacher and students in classroom discourse. The project was carried out as a regular feature of lessons in fifth-grade mathematics in a public school. A case of teaching and learning about exponents derived from lessons taught in the project is described and interpreted from mathematical, pedagogical, and sociolinguistic perspectives. To change the meaning of knowing and learning in school, the teacher initiated and supported social interactions appropriate to making mathematical arguments in response to students’ conjectures. The activities students engaged in as they asserted and examined hypotheses about the mathematical structures that underlie their solutions to problems are contrasted with the conventional activities that characterize school mathematics.