The reported exploratory study consisted primarily of classroom visits, videotaped sessions, and post-treatment interviews whereby second graders (n = 12) worked on problems in planar geometry, individually and in triads, using physical and virtual manipulatives. The goal of the study was to: 1) characterize the nature of geometric thinking found within the interrelationships of social interactions and instructional artifacts; and 2) describe this nature of thinking in terms of instructional artifact "transparency". Juxtaposing collective and individual views of mediated inquiry, we analyze interrelationships to reveal qualitatively different influences on geometric thinking for three conceptually related tasks using manipulatives. Our examination of interrelationships between social interactions and instructional artifacts leads to insights for designing and evaluating instructional technologies for early elementary mathematics, including emerging multi-touch, multi-user systems. (Contains 4 tables and 1 figure.)