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Fifth Graders' Enumeration of Cubes in 3D Arrays: Conceptual Progress in an Inquiry-Based Classroom

Michael T. Battista
Journal for Research in Mathematics Education
Vol. 30, No. 4 (Jul., 1999), pp. 417-448
DOI: 10.2307/749708
Stable URL: http://www.jstor.org/stable/749708
Page Count: 32
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Fifth Graders' Enumeration of Cubes in 3D Arrays: Conceptual Progress in an Inquiry-Based Classroom
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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.

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