Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students’ positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students’ positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.

We examined the codevelopment of mathematical concepts and the mathematical practice of defining within a sixth-grade class investigating space and geometry. Drawing upon existing literature, we present a framework for describing forms of participation in defining, what we term aspects of definitional practice. Analysis of classroom interactions during 16 episodes spanning earlier and later phases of instruction illustrate how student participation in aspects of definitional practice influenced their emerging conceptions of the geometry of shape and form and how emerging conceptions of shape and form provided opportunities to develop and elaborate aspects of definitional practice. Several forms of teacher discourse appeared to support students’ participation and students’ increasing agency over time. These included: (a) requesting that members of the class participate in various aspects of practice, (b) asking questions that serve to expand the mathematical system, (c) modeling participation in aspects of practice, (d) proposing examples that create contest (i.e., monsters), and (e) explicitly stating expectations of and purposes for participating in the practice.

Our aim is to discuss how school mathematical activity is modified when students’ everyday situations are brought into the classroom. One illustrative sequence—7th grade classes solving problems that required proportional reasoning—is characterized as a system of interconnected activities within the theoretical perspective of activity theory. We discuss the tensions and contradictions that evolve when a generic school procedure emphasized by the teacher meets the specific procedures applicable to everyday situations proposed by the students. We evaluate the modifications that we perceived in the power relationships and other components of the school activity and the expansion of the meaning of those procedures as positive outcomes of how everyday situations were dealt with in school mathematics.

MasterClass in Mathematics Education: International Perspectives on Teaching and Learning. Paul Andrews & Tim Rowland (Eds.). (2014). London, United Kingdom: Bloomsbury Academic, 240 pp. ISBN 978-1-4411-7235-8 (hb) $140.00, ISBN 978-1-4411-7975-3 (pb) $42.95, ISBN 978-1-4411-7608-0 (e-book) $36.99.