An alternative route to teaching fraction division: Abstraction of common denominator algorithm

Zembat, I. O. (2015) An alternative route to teaching fraction division: Abstraction of common denominator algorithm. International Electronic Journal of Elementary Education, 7(32), pp. 399-422.

Abstract

From a curricular stand point, the traditional invert and multiply algorithm for division of fractions provides few affordances for linking to a rich understanding of fractions. On the other hand, an alternative algorithm, called common denominator algorithm, has many such affordances. The current study serves as an argument for shifting curriculum for fraction division from use of invert and multiply algorithm as a basis to the use of common denominator algorithm as a basis. This was accomplished with the analysis of learning of two prospective elementary teachers being an illustration of how to realize those conceptual affordances. In doing so, the article proposes an instructional sequence and details it by referring to both the (mathematical and pedagogical) advantages and the disadvantages. As a result, this algorithm has a conceptual basis depending on basic operations of partitioning, unitizing, and counting, which make it accessible to learners. Also, when participants are encouraged to construct this algorithm based on their work with diagrams, common denominator algorithm formalizes the work that they do with diagrams.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Zembat, Dr Ismail Özgür
• Authors: Zembat, I. O.
• College/School: College of Social Sciences > School of Education > Creativity Culture and Faith
• Journal Name: International Electronic Journal of Elementary Education
• Publisher: T&K Academic
• ISSN: 1307-9298
• ISSN (Online): 1307-9298
• Copyright Holders: Copyright © 2015 IEJEE
• First Published: First published in International Electronic Journal of Elementary Education 7(3):399-422
• Publisher Policy: Reproduced under a Creative Commons License