A Concrete Situation for Learning Decimals


The research has been done by Puri Pramudiani in 2008. Together with Zulkardi, Yusuf Hartono, and Barbara van Ameron, she wrote it in a Journal on Mathematics Education, volume 2, nomor 2, page 215-230.

The aim of this research is to investigate one situation that enables the students to learn decimals in a meaningful way. It is very important because decimal is one of mathematics domains that is often used in calculation. Unfortunately, mostly in Indonesia, decimal is taught only as another notation for fractions or percentages. Students assumed that decimal is only the number with point (comma) without knowing the meaning of it. Therefore, the learning is meaningless and students can not use it in the concrete situations.

Based on that condition, Puri used RME (Realictic Mathematics Education) in her research. It was chosen because RME underlies the design of context and activities. According Zulkardi and Ilma that was quoted by Puri, the context is a main point for students in developing mathematics. It should be meaningful and real for students’ mind. In this research, Puri used measurement activities as the context, especially the activities of measurement of weighing duku, weighing the body, weighing the rice, and the volume of beverages.

The subject of this research was 26 students and a teacher for grade 5 SDN 21 Palembang Indonesia, but only 7 students involved in the series of activities of pilot experiment. She chose small group because she expected  to be more focused to the adjustment of HLT (Hypothetical Learning Trajectory). HLT is a part of planning mathematics lesson which consist of the goals, the mathematical tasks, and the hypotheses about the process of students’ learning.

The phases of students’ learning in this research are :

  1. Knowing the existing of decimal form through contextual situation (weighing duku and body)
  2. Exploring the meaning of one-digit decimals through weighing rice
  3. Using number line as a model for placing the position of one-digit decimals (partician based ten)
  4. Exploring the meaning of two digit decimals through measuring the volume of beverages
  5. Using number line as a model for placing the position of two-digit decimals (partision based tenth of tenth).

Based on the result of post assessment and interview, 69% students shows a good ability in reading the scale, 85% students have a good knowledge of decimals, and 77% students could master the idea of density of decimals on the number line, and 92% students chose number line as the tool to placing the magnitude of decimals.

Before the activities of measurement, students thought that there were no other numbers between two consecutive whole numbers. However, after the activities of measurement, students realized that decimals exist in between two consecutive whole numbers and desimals were needed to measure the things precisely. Through the series of activities, the students could develop their idea into the density of numbers on the number line which bring them into the idea of partitioning base ten and tenth of tenth.

Puri conclude that the context and activities designed (weigh and volume measurement) can become the concrete situation for learning desimals. From this research, we can show that desimals can be taught in a meaningful way. Students could discover desimals by themselves and develop their ideas to come to the number line as a model for placing their magnitude.

From this research, we can learn many things, such as :

  1. Desimals can be realized in the studends’ mind
  2. Weight and volume measurement can be a context for learning of decimal that is meaningful for students.
  3. Students able to develop their idea if the learning is meaningful.
  4. Using RME in other material can help teacher to reach the goals of the learning.

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