The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate…

An important concern in mathematics teacher education is how to create learning opportunities for prospective and practicing teachers that make a difference in their professional growth as educators. The first purpose of this article is to describe one way of working with prospective and practicing teachers in a graduate mathematics education…

To improve undergraduate mathematics learning, teachers need to recognize and value characteristics of classroom learning environments that contribute to powerful student learning. The broad goal of this special issue is to share such characteristics and the theoretical and empirical grounding for an innovative approach in differential equations…

An enduring challenge in mathematics education is to create learning environments in which students generate, refine, and extend their intuitive and informal ways of reasoning to more sophisticated and formal ways of reasoning. Pressing concerns for research, therefore, are to detail students' progressively sophisticated ways of reasoning and…