Generalizing-Promoting Actions: How Classroom Collaborations Can Support Students' Mathematical Generalizations

Generalization is a critical component of mathematical activity and has garnered increased attention in school mathematics at all levels. This study documents the multiple interrelated processes that support productive generalizing in classroom settings. By studying the situated actions of 6 middle school students and their teacher researcher working on a 3-week unit on quadratic growth functions that can be represented by y = ax(2), the study identified 7 major categories of generalizing-promoting actions. These actions represent how teachers and students can act in interaction with other agents to foster students' generalizing activities. Two classroom episodes are presented that identify cyclical interaction processes that promoted the development and refinement of generalizations. The results highlight generalization as a dynamic, socially situated process that can evolve through collaborative acts.