What is Mathematical Argumentation

This chapter describes the design of integrated learning spaces (ILS) for prospective teachers (PSTs) to support PSTs' learning about reform-based teaching by helping them experience, think about, understand, and position mathematical argumentation in their future classrooms. Drawing on a longitudinal research program that explored PSTs' learning about argumentation in elementary and middle school mathematics, the authors discuss the design of ILS in the context of mathematics and pedagogy with field experience courses in a teacher education program. The authors also share the visions of mathematical argumentation as a teaching-learning practice that PSTs developed in the ILS context. Finally, this chapter poses questions for future research that might explore design principles for creating effective ILS in teacher education programs and examine how PSTs' learning in the ILS context supports their content and pedagogical knowledge development. This chapter also poses questions about ongoing support that future teachers might need to implement and sustain instructional reform.