Fifth graders' enumeration of cubes in 3D arrays: Conceptual progress in an inquiry-based classroom

Abstract

In this study I utilize psychological and sociocultural components of a constructivist paradigm to provide a detailed analysis of how the cognitive constructions students make as they enumerate 3D arrays of cubes develop and change in an inquiry-based problem-centered mathematics classroom. I describe the classroom work of 3 pairs of 5th graders on an instructional activity involving predicting the number of cubes that fit in graphically depicted boxes, and I carefully explicate how the mental processes of abstraction, reflection, perturbation, spatial structuring, and coordination, along with face-to-face social interaction within pairs, brought about meaningful and powerful student learning.