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# An Instructional Analogy Between Unitizing and Fraction Division: Seventh-Graders’ Conceptual Understandings of Division and Interpretations of Fractional Remainders

Tomaszewski, Anna (2019) An Instructional Analogy Between Unitizing and Fraction Division: Seventh-Graders’ Conceptual Understandings of Division and Interpretations of Fractional Remainders. Masters thesis, Concordia University.

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## Abstract

Fraction division is not a simple concept. In fact, both students and teachers struggle to understand and explain this operation. This study examined whether using instructional analogies between unitizing and division were effective when teaching fraction division to seventh-grade students. The extent to which the analogies were explicitly supported varied by condition. The aim was to investigate whether condition differences existed in participants’ understanding of fraction division, in their interpretations of fractional remainders, and in their understanding of unitizing. Fifty-one participants were randomly assigned to the explicit-links condition (n = 17), the implicit-links condition (n = 17), or the control condition (n = 17). Students in the explicit and implicit-links conditions were first presented with a unitizing problem in which six was regrouped using various units and then they were taught how to solve a fraction division equation. The instructor in the explicit-links condition made connections between both concepts by using gestures, spatial cues, relational language, and other cognitive supports. The link between both concepts was in no way emphasized for the participants in the implicit-links condition. Finally, participants in the control condition saw the fraction division instruction twice and did not receive unitizing instruction. No condition differences were found at posttest in participants’ division explanations nor in their understandings of unitizing. When interpreting a fractional remainder, participants in the implicit-links condition referred to the original unit significantly more than participants in the other two conditions, but no differences were observed in their uses of the referent unit when interpreting the remainder. The present study is relevant to teaching professionals as it provides new information about the ways children think of fraction division and the fractional remainder.

Divisions: Concordia University > Faculty of Arts and Science > Education Thesis (Masters) Tomaszewski, Anna Concordia University M.A. Child Studies 14 January 2019 Osana, Helena and Alibali, Martha W. and Howe, Nina 984919 ANNA TOMASZEWSKI 17 Jun 2019 15:50 17 Jun 2019 15:50
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