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All Journal Journal on Mathematics Education (JME) Beta: Jurnal Tadris Matematika Journal on Mathematics Education
Kuzu, Taha Ertugrul
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Education Mathematics Social Sciences Other

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PARTITIVE FRACTION DIVISION: REVEALING AND PROMOTING PRIMARY STUDENTS’ UNDERSTANDING Wahyu, Kamirsyah; Kuzu, Taha Ertugrul; Subarinah, Sri; Ratnasari, Dwi; Mahfudy, Sofyan
Journal on Mathematics Education Vol 11, No 2 (2020)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (332.454 KB) | DOI: 10.22342/jme.11.2.11062.237-258

Abstract

Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students’ understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related graphical representations. In a design-research study, forty-four primary students were involved in three cycles of teaching experiments. Students’ works, transcript of recorded classroom discussion, and field notes were retrospectively analyzed to examine the hypothetical learning trajectories. There are three main findings drawn from the teaching experiments. Firstly, context of the tasks, the context-related graphical representations, and the sequence of fractions used do support students’ understanding of PFD. Secondly, the understanding of non-unit rate problems did not support the students’ understanding of unit rate problems. Lastly, the students were incapable of determining symbolic representations from unit rate problems and linking the problems to fraction division problems. The last two results imply to rethink unit rate as part of a partitive division with fractions. Drawing upon the findings, four alternative ways are offered to support students’ understanding of PFD, i.e., the lesson could be starting from partitive whole number division to develop the notion of fair-sharing, strengthening the concept of unit in fraction and partitioning, choosing specific contexts with more relation to the graphical representations, and sequencing the fractions used, from a simple to advanced form.
Language in mathematics education – On the epistemic and reconstructivistic facet of languaging processes in linguistically heterogenous groups of learners Kuzu, Taha Ertuğrul
Beta: Jurnal Tadris Matematika Vol. 16 No. 2 (2023): Beta November
Publisher : Universitas Islam Negeri (UIN) Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20414/betajtm.v16i2.474

Abstract

[English]: In this article, languaging processes in mathematics education will be reflected from a theoretical and methodological viewpoint. Language is not just a tool for language learning: It is a highly complex medium for transporting meaning. It plays a key role in explaining and fostering as well as reconstructing and interpreting cognitive processes – not only in mathematics education, but due to the abstract nature of mathematical objects in a particularly important way. Thus, language as a mediational dimension is essential in the learners’ as well as researchers’ processes of understanding, be it in interpretational processes or in verbalized, deictical, either explicit or implicit explanations and actions. In this article, this dual-sided perspective will be explained by giving insights into language-related processes of interpreting and understanding mathematical relations in Substantial Learning Environments (SLE’s) as well as relational strategies such as the ‘Auxiliary Task.’ [Bahasa]: Artikel ini membahas proses berbahasa dalam pendidikan matematika dari perspektif teoritis dan metodologi. Bahasa bukan saja sebuah alat untuk pembelajaran bahasa tetapi juga sebuah medium yang sangat kompleks untuk menyampaikan makna. Bahasa memainkan peran penting untuk menjelaskan dan memelihara serta mengembangkan dan memaknai proses kognitif - tidak hanya dalam pendidikan matematika, tetapi karena karakateristik objek matematika yang abstrak sehingga peran bahasa diperlukan. Oleh sebab itu, bahasa sebagai sebuah dimensi mediasional sangat penting dalam proses pemahaman siswa dan peneliti baik itu dalam proses interpretasi atau dalam penjelasan dan tindakan yang diverbalkan, deiktis, baik eksplisit maupun implisit. Dalam artikel ini, perspektif dua sisi ini akan dijelaskan dengan memberikan wawasan ke dalam proses yang berhubungan dengan bahasa untuk menafsirkan dan memahami hubungan matematika dalam konteks Linkungan Belajar Substansial (Substantial Learning Environments, SLE) serta strategi relasional seperti Tugas Tambahan (Auxiliary Task).
Partitive fraction division: Revealing and promoting primary students’ understanding Wahyu, Kamirsyah; Kuzu, Taha Ertugrul; Subarinah, Sri; Ratnasari, Dwi; Mahfudy, Sofyan
Journal on Mathematics Education Vol. 11 No. 2 (2020): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students’ understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related graphical representations. In a design-research study, forty-four primary students were involved in three cycles of teaching experiments. Students’ works, transcript of recorded classroom discussion, and field notes were retrospectively analyzed to examine the hypothetical learning trajectories. There are three main findings drawn from the teaching experiments. Firstly, context of the tasks, the context-related graphical representations, and the sequence of fractions used do support students’ understanding of PFD. Secondly, the understanding of non-unit rate problems did not support the students’ understanding of unit rate problems. Lastly, the students were incapable of determining symbolic representations from unit rate problems and linking the problems to fraction division problems. The last two results imply to rethink unit rate as part of a partitive division with fractions. Drawing upon the findings, four alternative ways are offered to support students’ understanding of PFD, i.e., the lesson could be starting from partitive whole number division to develop the notion of fair-sharing, strengthening the concept of unit in fraction and partitioning, choosing specific contexts with more relation to the graphical representations, and sequencing the fractions used, from a simple to advanced form.
Co-Authors Dwi Ratnasari Kamirsyah Wahyu, Kamirsyah Mahfudy, Sofyan Sri Subarinah, Sri