New theoretical, methodological, and design frameworks for engaging classroom learning are supported by the highly interactive and group-centered capabilities of a new generation of classroom-based networks. In our analyses, networked teaching and learning are organized relative to a dialectic of (a) seeing mathematical and scientific structures as fully situated in sociocultural contexts and (b) seeing mathematics as a way of structuring our understanding of and design for group-situated teaching and learning. An engagement with this dialectic is intended to open up new possibilities for understanding the relations between content and social activity in classrooms. Features are presented for what we call generative design in terms of the respective "sides" of the dialectic. Our approach to generative design centers on the notion that classrooms have multiple agents, interacting at various levels of participation, and looks to make the best possible use of the plurality of emergent ideas found in classrooms. We close with an examination of how this dialectic framework also can support constructive critique of both sides of the dialectic in terms of content and pedagogy.

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This paper reports on efforts to blend tablet computers with collaborative workspace technologies. An underlying conjecture is that this blend, evaluated with support from Microsoft Research and the National Science Foundation, may help increase learner engagement substantially. The pedagogical logic is that if an instructor can effect a high volume of precise feedback experiences, engagement levels and learning will climb. The intervention needs to afford the teacher a vivid lens on learner processing, and to furnish learners with means to construct representations naturally but electronically. It would also need to furnish means to mediate the rapid flow of those representations and instructor responses to them. These design principles were met with two collaboration workspace technologies and a TabletPC, critical because it allows users to make handwritten representations as one would do with paper and pencil. Results show significant increases in learner engagement that resulted from the TabletPCs/collaborative software combination, based on paper and pencil measurements, electronic engagement measurements, and interviews of faculty and students.