This study explores the potential of networked handheld computers to support collaborative problem solving in small groups. Drawing on data from a middle school mathematics classroom equipped with a wireless handheld network, I argue that the sharing of mathematical objects through interactive devices broadens the Fbandwidth_ of classroom collaboration, expanding the range of participatory forms through which students might contribute to the work of a group and enhance their own learning. The analysis focuses on the participation strategies of those students in two focus groups who were most able to demonstrate posttest score gains from relatively low scores on a pretest. In particular, the device network provided those students with a set of collective, dynamic objects through which they supplemented and coordinated discursive forms of participation in the joint work of their respective groups.
This article explores ways of conceptualizing the design of innovative learning tools as emergent from dialectics between designers and learner-users of those tools. More specifically, I focus on the reciprocities between a designer's objectives for student learning and a user's situated activity in a learning environment, as these interact and codevelop in cycles of design-based research. Recent investigations of technology-supported mathematics learning conducted from an 'instrumental' perspective provide a powerful framework for analyzing the process through which classroom artifacts become conceptual tools, simultaneously characterizing the ways students come to both implement and understand a device in the context of a task. Similarly, design-based approaches to investigating instructional activity offer epistemological grounds for treating the process of designing artifacts to support learning as unfolding in concert with rather than concluding prior to situated student use. Drawing on each of these perspectives, I describe the design and initial implementation of a set of software artifacts intended to support students' collaborative problem solving through locally networked handheld computers. Through detailed analyses of three classroom episodes, I report on the ways one student group's innovative and unexpected use of these tools served as an opportunity to both examine student learning in the context of that novelty and to refine the software design. This account provides an empirical example through which to consider the potential for instrumental genesis to inform design, and for design research epistemology to broaden the scope of instrumental theory.
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