The mathematics class as a mathematizing complex system

Abstract

In this study, I investigated three middle school mathematics classrooms from the complex perspective, a theoretical framework that redefines classrooms as potentially complex phenomena. A mathematics class can become a learning system when individual students form a collective mathematizing entity. Such entities parallel the type of communities mathematicians learn and work in. This perspective suggests that student learning can be augmented by attending more closely to cognizing classroom collectives. Questions abound, however, about how such complex entities emerge and are sustained. I selected and studied three classroom episodes that demonstrated complex formation through fine-grained videotape analysis. My study demonstrated the existence of mathematizing complex systems that jointly created mathematics and regulated themselvesÐÐall at the class level. I describe a variety of underlying principles for teacher action that provided for the emergence of mathematizing complex systems in these classes, although the method of each varied. Such research can help teachers and teacher educators augment individual learning in their own mathematics classrooms by occasioning similar collective behavior.