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The Set Model: A Flexible Approach for Dividing Fractions

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Title: The Set Model: A Flexible Approach for Dividing Fractions
Language: English
Authors: Terri L. Kurz, Makayla Mendonca, Tirupalavanam Ganesh
Source: School Science and Mathematics. 2026 126(2):189-197.
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 9
Publication Date: 2026
Sponsoring Agency: National Science Foundation (NSF)
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Secondary Education
Higher Education
Postsecondary Education
Descriptors: Elementary School Mathematics, Secondary School Mathematics, Preservice Teachers, Preservice Teacher Education, Mathematics Skills, Fractions, Evaluative Thinking, Mathematical Concepts, Mathematical Models, Division, Algorithms, Knowledge Base for Teaching
DOI: 10.1111/ssm.18396
ISSN: 0036-6803
1949-8594
Abstract: The set model for fractions is a way of representing fractions using sets of objects where the whole is represented by a set of items, and the fraction indicates how many of those items are being considered. It is a flexible model because the whole can be redefined, addressing limitations often faced using standard linear or area models. Two-sided chips are an adaptable tool often used with the set model; the whole can be easily redefined. Preservice teachers explored the concept of dividing fractions using the set model, moving beyond the traditional algorithm and the more common models used in the elementary and middle school classrooms. The set model for fractional division can be used in conjunction with linear and area models to support rich learning experiences that encourage sense making while exploring what the division of fractions conceptually represents. The research question was: How does integrating the set model into teacher education affect preservice teachers' ability to explain and justify the process of dividing fractions? Even though there were some initial challenges, preservice teachers were able to justify their observations and connect mathematical concepts. Ready-to-use activities for elementary and middle school classrooms or university classes are provided.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1502666
Database: ERIC
FullText Text:
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  Data: The Set Model: A Flexible Approach for Dividing Fractions
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  Data: <searchLink fieldCode="SO" term="%22School+Science+and+Mathematics%22"><i>School Science and Mathematics</i></searchLink>. 2026 126(2):189-197.
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  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
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  Data: 9
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  Data: 10.1111/ssm.18396
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  Data: The set model for fractions is a way of representing fractions using sets of objects where the whole is represented by a set of items, and the fraction indicates how many of those items are being considered. It is a flexible model because the whole can be redefined, addressing limitations often faced using standard linear or area models. Two-sided chips are an adaptable tool often used with the set model; the whole can be easily redefined. Preservice teachers explored the concept of dividing fractions using the set model, moving beyond the traditional algorithm and the more common models used in the elementary and middle school classrooms. The set model for fractional division can be used in conjunction with linear and area models to support rich learning experiences that encourage sense making while exploring what the division of fractions conceptually represents. The research question was: How does integrating the set model into teacher education affect preservice teachers' ability to explain and justify the process of dividing fractions? Even though there were some initial challenges, preservice teachers were able to justify their observations and connect mathematical concepts. Ready-to-use activities for elementary and middle school classrooms or university classes are provided.
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        Value: 10.1111/ssm.18396
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      – Text: English
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      – SubjectFull: Mathematical Concepts
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      – SubjectFull: Division
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