From fractions to proportional reasoning: a cognitive schemes of operation approach

Four seventh grade students participated in a constructivist teaching experiment in which manipulatives within a computer microworld were used to solve fractional reasoning tasks followed by tasks that involve concepts of rate, ratio and proportion. Through a retrospective analysis of video tapes, t...

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Bibliographic Details
Published inThe Journal of mathematical behavior Vol. 22; no. 2; pp. 133 - 179
Main Author Nabors, Wanda K
Format Journal Article
LanguageEnglish
Published Elsevier Inc 2003
Subjects
Cognitive schemes
Fractions
Proportional reasoning
Teaching experiment
Fractions
Teaching experiment
Proportional reasoning
Cognitive schemes
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Summary:Four seventh grade students participated in a constructivist teaching experiment in which manipulatives within a computer microworld were used to solve fractional reasoning tasks followed by tasks that involve concepts of rate, ratio and proportion. Through a retrospective analysis of video tapes, their thinking processes were analyzed from the perspective of the types of cognitive schemes of operation used as they engaged in the given problem situations. One result of the study indicates that the modifications of the students’ available schemes of operation when solving the fractional reasoning tasks formed a basis for the cognitive schemes of operation used in their solutions of tasks involving proportionality.
ISSN:0732-3123
1873-8028
DOI:10.1016/S0732-3123(03)00018-X