Space and time in classroom networks: Mapping conceptual domains in mathematics through collective activity structures

This paper reports on a design-based research project in which we are developing collaborative activities for classroom networks. Research in generative design has explored classroom activities that analogize the many participants in a classroom with an often-infinite family of mathematical objects. By contrast, our project focuses on classroom activity structures that support interactions among two to four students, each aligned with different components of a shared mathematical object. In each case, these network-based relationships among students are intended to serve as resources to support learners' efforts to jointly navigate the conceptual territory delineated by their corresponding mathematical relationships in the space of the network. We compare the kinds of exploration of mathematical terrain respectively supported by whole-class and small group activities in classroom networks in order to examine the distinctive learning opportunities provided by each, and consider the potential of these different activity structures for providing mutually supportive instructional experiences.