Students' Understanding of Three-Dimensional Cube Arrays: Findings from a Research and Curriculum Development Project
Michael T. Battista Kent State University
Douglas H. Clements State University of New York at Buffalo
As part of our work in developing the geometry strand in the Investigations in Number, Data, and Space elementary mathematics curriculum project, we developed three-dimensional geometry instructional units for each of Grades 3, 4, and 5 ( Battista & Berle- Carman, 1995; Battista & Clements, 1995a, 1995b). A major portion of these units focuses on exploring three-dimensional configurations of cubes, especially enumerating cubes in three-dimensional rectangular arrays. Concurrent with our curriculum development, we conducted a research program investigating students' understanding of three-dimensional configurations of cubes (see Battista & Clements, 1996). This chapter gives an overview of both our research and our curriculum development efforts.
We first describe the various conceptual structures that students construct in enumerating three-dimensional cube arrays and suggest the mental operations that underlie these constructions. We then describe instructional activities that target the development of these conceptual structures, as well as the rationale we had in using these activities. Finally, we illustrate how learning occurs in students using these instructional activities.