Establishing conceptual bases for the measurement of volume
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2003
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Abstract
Fourth grade students’ understanding of rectangular solids made of small cubes was
investigated. A three-phase procedure was utilized. First, interviews were conducted individually to
assess the students’ level of functioning in cube-enumeration tasks. Second, participants were
engaged in equal sharing of spatial constructions. Last, postinterviews were conducted to probe
students’ improvements as revealed by their use of enumeration strategies. Students used three
distinct conceptualizations for the arrays of cubes depending on what they formed as unit and how
they structured the whole building. Initially, their structuring was distracted by the complexity of
buildings and none of them used the same strategies consistently across problems. During the
instruction, they exhibited the same conceptualizations and transitioned from one to the other. After
the intervention, all the students consistently used layering strategies regardless of the complexity of
the buildings. Equal-sharing situations coupled with coloring activities paved the road in establishing
units, composite units, and unit iteration.