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.
Highlights
Abstrak Siswa menunjukkan pemahaman yang kurang pada materi pembagian pecahan dan mendukung pemahaman tersebut masih menjadi tantangan bagi pendidik matematika
Several aspects relate to the students' problems in learning fraction division, namely mathematics teachers’ content knowledge (Ma, 2010), the instructions which promote the conceptual understanding of students (Hu & Hsiao, 2013), and the complex nature of fraction division (Prediger, 2006; Ma, 2010)
The second point as the focus of the present study was in contrast to what we found in classroom observations as part of preliminary phase of design research wherein, for example, the learning activities were focused on procedural aspect instead of developing students’ understanding and did not start with contextual problems which facilitate students to employ their prior knowledge to solve the problem and develop mathematical knowledge
Summary
Abstrak Siswa menunjukkan pemahaman yang kurang pada materi pembagian pecahan dan mendukung pemahaman tersebut masih menjadi tantangan bagi pendidik matematika. Several aspects relate to the students' problems in learning fraction division, namely mathematics teachers’ content knowledge (Ma, 2010), the instructions which promote the conceptual understanding of students (Hu & Hsiao, 2013), and the complex nature of fraction division (Prediger, 2006; Ma, 2010). Several authors categorize unit rate as part and the result of Partitive Fraction Division (PFD) (Gregg & Gregg, 2007; Lamon, 2012; Jansen & Hohensee, 2016). The study aimed to analyze students’ logical reasoning in understanding division with decimals (partitive form). Zaleta (2006) inquired into invented computational strategies developed by the 6th graders in solving four fraction division problems, two of which are partitive problems. Muchsin et al (2014) employed three problems of partitive fraction division with a duration context to identify students’ strategies
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