• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.83-102
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• 2014

The purpose of this study was to explore students' understanding on units embedded in multiple interpretations of fractions: (a) part-whole relationships, (b) measures, (c) quotients, (d) ratios, and (e) operators. A total of 150 sixth graders in elementary schools were surveyed by a questionnaire comprised of 20 tasks in relation to multiple interpretations of fractions. As results, students' performance on units varied depending on the interpretations of fractions. Students had a tendency to regard the given whole as the unit, which led to incorrect answers. This study suggests that students should have rich experience to identify and operate various units in the context of multiple fractions.

• The Mathematical Education
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• v.48 no.3
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.