An alternative route to teaching fraction division: Abstraction of common denominator algorithm
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 s...
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| Format: | Article |
| Language: | English |
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Kura Publishing
2015-07-01
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| Series: | International Electronic Journal of Elementary Education |
| Subjects: | |
| Online Access: | https://iejee.com/index.php/IEJEE/article/view/88/86 |
| _version_ | 1797909479145078784 |
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| author | İsmail Özgür Zembat |
| author_facet | İsmail Özgür Zembat |
| author_sort | İsmail Özgür Zembat |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T11:08:54Z |
| format | Article |
| id | doaj.art-6641bc69694a4ad0bcfa77a288c4478e |
| institution | Directory Open Access Journal |
| issn | 1307-9298 1307-9298 |
| language | English |
| last_indexed | 2024-04-10T11:08:54Z |
| publishDate | 2015-07-01 |
| publisher | Kura Publishing |
| record_format | Article |
| series | International Electronic Journal of Elementary Education |
| spelling | doaj.art-6641bc69694a4ad0bcfa77a288c4478e2023-02-15T16:19:16ZengKura PublishingInternational Electronic Journal of Elementary Education1307-92981307-92982015-07-0173399422An alternative route to teaching fraction division: Abstraction of common denominator algorithmİsmail Özgür Zembat0Mevlana (Rumi) UniversityFrom 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.https://iejee.com/index.php/IEJEE/article/view/88/86Teaching fraction divisionabstracting common denominator algorithmcurriculum development |
| spellingShingle | İsmail Özgür Zembat An alternative route to teaching fraction division: Abstraction of common denominator algorithm International Electronic Journal of Elementary Education Teaching fraction division abstracting common denominator algorithm curriculum development |
| title | An alternative route to teaching fraction division: Abstraction of common denominator algorithm |
| title_full | An alternative route to teaching fraction division: Abstraction of common denominator algorithm |
| title_fullStr | An alternative route to teaching fraction division: Abstraction of common denominator algorithm |
| title_full_unstemmed | An alternative route to teaching fraction division: Abstraction of common denominator algorithm |
| title_short | An alternative route to teaching fraction division: Abstraction of common denominator algorithm |
| title_sort | alternative route to teaching fraction division abstraction of common denominator algorithm |
| topic | Teaching fraction division abstracting common denominator algorithm curriculum development |
| url | https://iejee.com/index.php/IEJEE/article/view/88/86 |
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