Stroup, W. M., Kaput, J., Ares, N., Wilensky, U., Hegedus, S. J., Roschelle, J., Mack, A., Davis, S., & Hurford, A. (2002). The nature and future of classroom connectivity: The dialectics of mathematics in the social space. Paper presented at the Psychology and Mathematics Education – North America, Athens, GA.
Introduction
New theoretical, methodological, and design frameworks for engaging classroom learning are provoked and supported by the highly interactive and group-centered capabilities of a new generation of classroom–based networks. This discussion group situates networked learning relative to a dialectic of (1) seeing mathematical and scientific structures as fully situated in socio-cultural contexts and ( 2) seeing mathematics as a way of structuring of our understanding of and design for group-situated teaching and learning. Acknowledging (1), significant classroom examples are then used to illustrate the reciprocal process (2) of mathematics structuring the social sphere (MS3). The mathematically informed ideas of space-creating play and dynamic structure are then used to update our ideas of generative teaching and learning and to situate these classroom examples. Then, returning again to the dialectic, this current work is critiqued from a socio-cultural perspective (1). Participation and agency are highlighted in this critique. The session closes with a discussion of future possibilities for classroom connectivity.
The highly interactive and group-centered capabilities of a new generation of classroom-based networks are helping both to support and to provoke the development of new theoretical, methodological and design frameworks for engaging classroom learning. This discussion group situates networked teaching and learning relative to a dialectic of (1) seeing mathematical and scientific structures as fully situated in socio-cultural contexts and (2) seeing mathematics as a way of structuring our understanding of and design for group-situated teaching and learning. The idea is that if mathematical and scientific structures are seen to fully participate in the social plane, then not only are they structured by the social plane (i.e., (1)) but they also structure social activity (i.e., (2)), including learning and teaching. Due to the group-focused interactivity and data collection capabilities of next generation networking, we now have a new tool to explore the dynamics of—and design for—classroom learning. A number of projects have responded to the challenge of learning in a network space by using mathematical/scientific ideas to organize and analyze classroom activity. Some of these recent projects focus on student learning and one is focused on teacher understanding. All of these projects have begun to use mathematics itself to organize their classroom-based work. This use of domain-related “big ideas” to organize and analyze group learning is what is meant by mathematics structuring the social sphere (MS3). The mathematically informed ideas of space-creating play and dynamic structure are then used to update our ideas of generative teaching and learning and to further situate the previous classroom examples. Our argument is that to take full advantage of these notions, and of the new classroom tools, researchers and educators must acknowledge explicitly the dialectic that exists between the domains of mathematics or science as structuring agents and the structuring functions of the social, cultural, historical milieu in which classroom learning and teaching in the domains exist. Returning again to the dialectic, this current work is then critiqued from a socio-cultural perspective focusing on ideas of participation and agency. Consistent with this dialectic framework, an overall notion of what is called generative teaching and learning is clarified in a way that both draws on previous work and uses the mutually constitutive relations captured by the dialectic for extending the prior analyses.
This paper is not about technology per se, but rather about a specific instance of the interaction and coevolution of design, technological affordance, and cognitive theory (Dewey, 1938; Hickman, 1990). Networks and ideas of generative teaching and learning can be and have been discussed without specific reference to technology (Wittrock, 1978, 1991; Learning Technology Center [LTC], 1992). The idea is that next generation networking can better support or “resonate” with generative practices and also, in iterating back to theory, allow us to further develop our ideas of what generativity is. To start this conversation, we may need to understand first how these new network designs are functionally evolved, and thus distinct, from the kinds of networking that has been with us for a long time. In this section the question becomes: What might be said to be “new” about next-generation network functionality in classrooms?