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).

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Introduction to RME

Summary of Subchapter 2.2 (Understanding RME) of the following reference:
Zulkardi. (2002). Developing a Learning Environment on Realistic Mathematics Education for Indonesian Student Teachers (Doctoral dissertation). University of Twente, Enschede.

The concept of RME is based on Hans Freudenthal’s views of mathematics as a human activity which implies that the students should be encouraged to find and reinvent the mathematics themselves. In order to reach the target, the learning process should start from the real world problem, or things which is well known by the students. Such strategy is then called ‘didactical phenomenology’.

In addition to that, Van Hiele identified three levels of learning mathematics. It starts when students can play with the pattern which is familiar to them. The next phases are when they could recognize the relationships among the patterns, and elaborate its internal characteristics.

Following the ideas, RME is resulted with five main characteristics (tenets), that is:
1. The use of context
This tenet best matches with ‘conceptual and applied mathematization’ proposed by de Lange (1987). The idea positions ‘real world’ as both the starting and final point of learning cycle. So, the students would find mathematics concept in reality, explore it, identify the related-mathematics concept, generalize, and apply it into the other aspects of life.

conceptual and applied mathematization

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PMRI: a rolling reform strategy in process (Reflection: Part One)

Summary on:

Hoven, G.H.v.d. (2010). PMRI: a rolling reform strategy in process. In Sembiring, R., Hoogland, K., Dolk, M.(Eds.), A decade of PMRI in Indonesia (pp. 51-66). Meppel: Ten Brink.

The initiation of PMRI in Indonesia, which was supported by DGHE, strengthened the reform of mathematics education in Indonesia since 2001. Many activities regarding the improvement of the concept of RME and its dissemination were done, especially after the PMRI won a grant from Dutch Government in 2006.

The so-called DO-PMRI (Dissemination of PMRI) programme was based on four basic principles, that is, bottom up development, learning through modelling, ownership at the right place, and co-creating and were supported by Indonesian Government either morally or financially.

Historical overview of the last eight years (2002-2010)

After successfully working in a small scope, PMRI team tried to extend their wings by encouraging universities and teacher educators to take a part. This leads to the initiation of P4MRI and LPTK.

There are four main objectives to focus on the second phase of DO-PMRI, are:
1. To build knowledge, skills, and practices of primary teachers regarding PMRI
2. To build knowledge, skills, and practices of teacher educators regarding the PMRI
3. To institutionalize PMRI in the LPTKs
4. To institutionalize PMRI at nationallevel

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Addition and Subtraction up to 100 Using Empty Number Lines

Reflection on Paper:
Design Research on Addition and Subtraction Up to 100
Using Mental Arithmetic Strategies on an Empty Number Line
At the 2nd Grade of SDN Percontohan Komplek IKIP Jakarta
(Puspita Sari, Dede de Haan, Zulkardi, 2008)

Innumeracy problems experienced by many students nowadays might be caused by inappropriate approach in teaching algorithm in primary schools which seems to be premature and less contextual according to some experts. In order to deal with the problems, realistic approach involving mental arithmetic strategies is suggested in advance, that is, emphasising more on number values rather than number digits.

In case of teaching addition and subtraction to 2nd grade students, an empty number line – number line with no numbers on it – seems to fit the need since it could encourage students’ informal counting strategy to develop. The use of context as demanded in RME is highly required to stimulate a meaningful learning toward the students. For the research, the context applied was celebrating the 63rd Indonesian Independence Day, due to the current d-situation.

The Use of Empty Number Lines in Learning Implementation
1. Empty number line as a model of
In this part, the number line was introduced using a string of beads which was coloured alternately every ten beads, the length of which would be measured by students using a paper strip. This would smoothly redirect the students to think of empty number lines.number lines as model of

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