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Design Research on Mathematics Education: Investigating The Progress of Indonesian Fifth Grade Students’ Learning on Multiplication of Fraction with Natural Numbers

Nenden Octavarulia Shanty (2008)

IndoMs. J.M.E
Vol.2 No.2 July 2011
 
The research written by Nenden was done under design research methodology, with thirty-seven students of fifth grade at SDN 17 Palembang as the research subject. In this study, researcher concerned about multiplication of fraction with natural numbers by applying Realistic Mathematics Education.
This study aims at investigating the progress of studetns’ learning on multiplication fractions with natural numbers through the five activity levels based on RME proposed by Streefland. There are four activities designed by researcher in this study; those are:
  •  Locating flags and water posts on the running route with an expectation that students are able to make a construction of partitioning, part of a whole. The running race route context was chosen as the context to provoke the students in producing their own fractions within measurement (length) activity.
  • Notating fractions in the empty fractions cards, putting the fraction cards on the string of yarn, and describing the relations among fractions. Through this activity, students could symbolize the result of partitioning and show it on the string of yarn. Furthermore, they also could describe the relations among fractions such as equivalent fractions.
  • Math congress 1. In this activity, students shared their activities in activities 1 and 2, about their experiences in partitioning the track, symbolizing the result of partitioning, and describing the relations among fractions. Students, furthermore, came up with the use of number line as a model-of measuring situation. Such number line was proven as a powerful model to encourage students in generating equivalencies of fractions.
  • Determining who is running farther. Through this activity, students could compare fractions within a certain length. In this case, students informally use fractions as multipliers.
  • Math congress 2. In the second congress, students shared their ideas and experiences in informally using fractions as operator. Teacher guided students to discuss about different strategies and lead students come to the idea about a more efficient way to solve problem involving multiplication of fraction by natural number, e.g  .to find the answer of 4/6 of 6 kilometres by multiplying 4 by 6 kilometres then divided it by 6 (the denominator of 4/6). Through the use of students’ own creations and contributions, the use of number line as model-of has been transformed into a model-for more formal reasoning.
  • Conducting mini lesson about fraction as operator. In this activity, students were given the opportunity to use their strategies in solving the problems from the previous activity.
In conclusion, this research has shown students learning about multiplication fractions with natural numbers by conducting the five activity levels proposed by Streefland  (1991) as the steps of learning with fractions.

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