Making Sense of Instructional Devices: The Emergence of Transparency in Mathematical Activity

This article examines the mathematical sense-making of children as they use physical devices to learn about linear functions. The study consisted of videotaped problem-solving sessions in which pairs of 8th graders worked on linear function tasks using a winch apparatus, a device with springs, and a computerized input-output machine. The following questions are addressed: How do children make sense of physical devices designed by experts to foster mathematical learning? How does the use of such devices enable learners to access selected aspects of a mathematical domain? The concept of transparency is suggested as an index of access to knowledge and activities rather than as an inherent feature of objects. The analysis shows that transparency is a process mediated by unfolding activities and users' participation in ongoing sociocultural practices.