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Achmad Nizar
Faculty of Mathematics and Natural Science, Surabaya State University
Mathematics

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A Learning Trajectory of Indonesian 12-years Old Students Understanding of Division of Fractions Achmad Nizar; Siti Maghfirotun Amin; Agung Lukito
Southeast Asian Mathematics Education Journal Vol 7, No 2 (2017)
Publisher : SEAMEO Regional Centre for QITEP in Mathematics

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (424.595 KB) | DOI: 10.46517/seamej.v7i2.52

Abstract

The purpose of this study was to describe mathematical hands-on activities that can support students to gain better understanding of dividing fractions. This preliminary research phase was started by testing, analyzing, and refining the initial hypothetical learning trajectory (HLT), then in the pilot experimental phase the revised HLT was implemented, and ended with the teaching experimental phase by developing a learning trajectory for 12-year old students in understanding division of fractions. In developing the trajectory, a design research methodology was employed by using four contextual-based learning series (sharing biscuit, sharing remaining chocolate bar, arranging bedroom mats, and running around school yard), including providing some concrete materials or pictorial models as manipulative tools. Seven mathematics experts and twenty five 12-year old students were involved during the research. The four designed learning goals were determining the quotient of division of integer by proper fraction, proper fraction by integer, two proper fractions, and two fractions. Students succeeded in demonstrating their understanding and stated that 16:1/2 = 32; 25/36:5 = 5/36; 24/64:1/2 = 6/8; and 15/2:3/4 = 10 respectively at the end of each designed activity. The interesting results of this study are not a proof, so that a much larger study is needed to determine if the results are due to this approach or due to the teachers’ enthusiasm or what is known as the Hawthorne Effect.
Co-Authors Agung Lukito Siti Maghfirotun Amin