Examines the mathematical sense-making of eighth-grade students as they use physical devices to learn about linear functions. Suggests the concept of transparency as an index of access to knowledge and activities rather than as an inherent feature of objects. Concludes that transparency is a process mediated by unfolding activities and users'…

Summarizes research conducted within a series of professional development workshops for teachers in grades K-8 which emphasize basic reasoning skills, integrating manipulative materials, and technology. Demonstrates these principles using patterns, relations, and functions as examples. (Author/MKR)