Running Race Road for Learning Multiplication of Fraction with Natural Numbers

running route

The title of this research is Design Research On Mathematics Education : Investigating The Progress Of Indonesian Fifth Grade Students’ Learning On Multiplication Of Fractions With Natural Numbers. The research has been done by Nenden Octavarulia Shanty in 2011. Together with Yusuf Hartono, Ratu Ilma Indra Putri, and Dede de Haan, researcher wrote it in Journal on Mathematics Education, volume 2, nomor 2, page 147-162.

The aim of this research is to investigate the progress of students’ learning on multiplication of fractions with natural numbers through the five activity levels proposed by Streefland. It is very important because most of the learning on multiplication of fraction in Indonesia was meaningless. Students only memorize formulas and tricks in calculating to solve the problem. Teachers don’t know whether the students know and understand the meaning of the procedures and algorithms lay behind it. Unfortunately, according to Stafylidou and Vosniadou that is quoted by Nenden, fractions are not consistent with the counting principles that apply to natural numbers to which students often relate. It makes students confuse.

In this study, thirty-seven students of grade five of SDN 179 Palembang as the subject. Researcher designed the HLT (Hypothetical Learning Trajectory) as a research instrument containing five activity levels based on RME (Realistic Mathematics Education) approach proposed by Streefland. As the starting point of learning, researcher chose measurement of length activity (running race route) as the context.

Students activities in this study consist of :

  1. Producing fractions by locating flags and water posts on the running route, notating fractions in the empty fractions cards, putting the fraction cards on the string of yarn, and describing the relations among fractions.
  2. Generating equivalencies by mathematics congress 1
  3. Operating through mediating quantity by determining who is running farther
  4. Doing one’s own production by mathematics congress 2
  5. On the way to rules for multiplying fractions with natural numbers by minilesson

Through the sequence of activities above, students gain more insight in multiplying fractions with natural numbers. It is obvious that students’ learning progress through the five activity levels based on RME approach proposed by Streefland.

This research has shown 5 tenets of RME. Measurement of length activity (running race route) is a good context to start the learning (use of context). The use of string of yarn here was as a bridge to the number line model which was in more abstract level (use of model). The use of number line as a model of  measuring situation transformed into a model for more formal reasoning (use of students’ own creations and contributions). The classroom settings was elaborated where the students could share their thinking in the class discussion by mathematics congress (interactivity). The last, we found the close relation between proportions and fractions during the learning process (intertwinement).

In conclution, through 5 activity levels and the connection with RME approach, this study has taken an important initiative to improve education in Indonesia.


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