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Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments

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Title: Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments
Language: English
Authors: Zhang, Xiaofen, Clements, M. A., Ellerton, Nerida F.
Source: Mathematics Education Research Journal. Jun 2015 27(2):233-261.
Availability: Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Peer Reviewed: Y
Page Count: 29
Publication Date: 2015
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Grade 5
Intermediate Grades
Middle Schools
Descriptors: Mathematics Instruction, Elementary School Mathematics, Grade 5, Mathematical Concepts, Teaching Methods, Interviews, Mathematics Skills, Pretests Posttests, Intervention, Mathematics Achievement, Achievement Gains, Concept Formation, Problem Solving, Instructional Effectiveness
DOI: 10.1007/s13394-014-0133-8
ISSN: 1033-2170
Abstract: Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children's understandings of the unit fractions, 1/2, 1/3, and 1/4, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes' (1960) dynamic principle, the students' performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students' newly found understandings had, in most cases, been retained.
Abstractor: As Provided
Number of References: 60
Entry Date: 2015
Accession Number: EJ1059859
Database: ERIC
FullText Text:
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  Data: Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Xiaofen%22">Zhang, Xiaofen</searchLink><br /><searchLink fieldCode="AR" term="%22Clements%2C+M%2E+A%2E%22">Clements, M. A.</searchLink><br /><searchLink fieldCode="AR" term="%22Ellerton%2C+Nerida+F%2E%22">Ellerton, Nerida F.</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Mathematics+Education+Research+Journal%22"><i>Mathematics Education Research Journal</i></searchLink>. Jun 2015 27(2):233-261.
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  Data: Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
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  Data: 10.1007/s13394-014-0133-8
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  Data: Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children's understandings of the unit fractions, 1/2, 1/3, and 1/4, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes' (1960) dynamic principle, the students' performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students' newly found understandings had, in most cases, been retained.
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  Data: 2015
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  Data: EJ1059859
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        Value: 10.1007/s13394-014-0133-8
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      – TitleFull: Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments
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