Learning Decimals


Pramudiani, P., Zulkardi, Hartono, Y. & Ameron, B.V. (2011). A concrete situation for learning decimals. Indonesian Mathematical Society Journal on Mathematics Education, Vol. 2, No. 2, July, (2011), 215-230.

It was found that decimals is an essential part of mathematics whose concepts need to be learned meaningfully in order to prevent students from misconception. The fact, however, showed that Indonesian textbooks could not provide such condition and neither do the learning and teaching activities which finally led the students to the lack of understanding and misconception toward the concept. RME underlying the design of context (in this case precise measurement) and activities seemed to be an appropriate solution regarding this problem. Therefore, the study was conducted, that is, to study how measurement activities promote students’ notion of decimals.

The research was conducted in three main steps, namely, preliminary design (to produce a conjectured local instruction theory containing learning goals, planned activities, and learning process), teaching experiment (involving 26 students from class 5A SDN 21 Palembang in 6 lesson hours, prior to this, 73 students were involved in the pre-assessment and pilot experiment was given to 7 of them each from high, average, and low level students), and retrospective analysis (analyzing data collected and comparing the hypothetical learning trajectory with the students’ actual learning).

During the teaching experiment, the students did activites given in 4 level structures. The first phase called situational level provides students with context, where, the students are asked to weigh duku, body, rise and to measure the volume of beverages. Next, referential level, the students were directed to display their measurement results using stripes on the number line. Using number line to determine the magnitude of decimals was done in general level and the last, in formal level, the students were guided to compare decimals without relying on number line.

The study found that: 1) measurement activities helped the students to realize the existance of numbers between two consecutive whole numbers, 2) scale visualization involving sequence of numbers led the students think of using number line as a model for placing magnitude of decimals, and 3) number line plays a big role in bridging the experience-based activities into a more formal mathematics. Finally, based on post assessment result, most students, 85%, earned a good understanding of decimals.

In conclusion, the context and activities designed is a good concrete situation which can facilitate the students develop from informal to pre-formal mathematics in learning decimals.

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