Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving |
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Authors: | Email author" target="_blank">Bryan?MoseleyEmail author |
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Institution: | (1) College of Education, Florida International University, Rm 241B, Miami, FL, 33199, U.S.A. |
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Abstract: | This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function
of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing
knowledge through extended problem solving with a single perspective of the rational number domain based on part-whole relations.
A second group of 14 students received a curriculum that emphasized a more conceptually diverse multiple perspective view
of the domain through problem solving with operator and ratio relations. Analyses of the students' rational number knowledge
before and after the interventions indicated that students in the single perspective group produced organizations of knowledge
that more frequently diverged from a formal domain analysis than those produced by students in the multiple perspective group.
Further, students in the single perspective group increased their focus on superficial surface features. Alternatively, students
in the multiple perspective group demonstrated an increased focus on operations that more frequently reflected the underlying
mathematical relation conveyed by the representation. The findings indicate that an early exposure to more diverse perspectives
of rational numbers assists students in developing more interconnected and viable representation knowledge for rational numbers. |
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Keywords: | constructivist curricula early rational number knowledge elementary students mathematical representation problem solving rational number perspectives |
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