This dissertation reports on a pilot study of a classroom network of handheld computers. The project included the development of a handheld software application called Code Breaker and a middle school mathematics unit introducing the topic of algebraic functions through the applied context of cryptography. The unit was implemented over a five-week period in two summer school math classes. This research poses two central questions about this initial deployment of the Code Breaker system: (1) What kinds of mathematical learning does the Code Breaker technology and pedagogy support? (2) In what ways and to what extent is access to that learning differentially distributed among students?; Close examination of video data of collaborative problem-solving in two student small groups suggested that groups learned to break codes by employing successive strategies that drew on increasingly sophisticated ideas about mathematical functions, through changing patterns in their use of representations, and by finding increasingly efficient and effective ways to align their discourse around those strategies and representations. Through engagement with these group-level strategies, representations and discussions, individual students displayed learning about algebraic functions, and about the practices of representing and communicating mathematical relationships and ideas.; Analyses of student decoding discourse revealed certain forms of participation in the work of the group that appeared consistent with greater posttest achievement gains. The patterns of student participation in each group's collaborative work showed little variation despite the rotation of group roles intended to support equitable participation. Nonetheless, certain pivotal episodes from the video data indicated ways in which both the roles and the handheld computers sometimes supported productive mathematical learning experiences for low-status and low-achieving students, and also opportunities for students to disrupt those otherwise-persistent hierarchies of participation.; These findings indicate both areas for redesign of the Code Breaker system, and directions for further research. In particular, designs for collaborative systems in complex problem-solving environments like this one must carefully balance the needs and experiences of individual learners against the distributed problem-solving agency and the labor-dividing tendencies of collaborative groups.
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