A Concrete Situation for Learning Decimals

Decimals is important domain in mathematics. Indonesian curriculum, nevertheless, leads most teachers to introduce decimals merely as another notation for fractions or percentages. Teaching and learning of decimal is conducted in a very formal way, in which decimal is directly converted from fraction which has denominator ten or one hundred without using of concrete situations to introduce its concept to students. As consequence, many students assumed that decimal is just the number containing point (comma) without knowing the meaning of it. At the same time, they might think that there were no other numbers between two concecutive whole numbers.

The researcher, therefore, conducted this study aiming at developing an instructional program that enables students to discover decimals and get insight about their magnitude through measurement activity as a meaningful way. RME underlies the design of context and activities used in this study.  

This research was done under design research methodology, conducted in six lessons at grade 5 SDN 21 Palembang by involving 26 students and a teacher as research subject. The learning activities in this study were generally designed to help students explore the notation and the meaning of decimals. There are four activities design by researcher in this study; those are:

Activity 1

Playing come closer game with an expectation that students are able to determine the numbers between the other numbers. Through this activity, it could be known that whether students have already perceived an idea about decimals based on their daily experiences or they have no idea at all about any number between two concecutive whole numbers.

Activity 2

Measuring the weight of the things (duku and body) using weight scale and digital weight scale. Through those activities, students were encouraged to do the precise and accurate measurement so they eventually could find decimals in weighing body activity, for instance, by observing the scales that when the needle pointed to the position between two consecutive numbers there should be comma numbers (decimals) in it, e.g between 35,6 appeared on the digital weight between 35 and 36.   

Activity 3

Measuring the weight of rice helped students to invent the meaning of one-digit decimals by finding that there were ten partitions containing one digit decimals between two concecutive whole numbers which eventually lead to the idea that decimals refer to the number of base ten, i.e: 0,2 is at the second stripe from ten stripe overall (two over ten).

Activity 4

Measuring the volume of beverages aimed at developing students’ acquisition for the idea of two-digit decimals. By using model of measuring cup, the students could perceive the idea that there are decimals between two concecutive whole numbers, and between two concecutive one-digit decimals there are other decimals, namely two-digit decimals.  Furthermore, they also found the idea that decimals refer to the partitioning base tenth of tenth by noticing the stripes provided by measuring cup.

To conclude, context and activities designed (weight and volume measurement) can become the concrete situation for learning decimals. It could provoke students’ thinking about decimal idea developing from informal level to pre-formal level containing insightful mathematical ideas. Or the other word, decimals can be taught in a meaningful way by applying RME approach, however it was known as abstract for most students.