Learning Percentage through Role-Playing ‘Surveyor-Respondent’

One of the very-closed mathematical concepts to us is percentage, of which the idea is represented in such common forms as discount, interest in bank, battery, polling result, and some other social activities. This familiarity would be a great potential to bridge students to learn the concept using PMRI (Pendidikan Matematika Realistik Indonesia) learning approach.

Therefore with, my friend and I have tried to design a set of activities to encourage students’ understanding regarding the concept. The design has been tried out to Grade V-E students of SD Pusri Palembang.

The first activity was conducted to identify how closed the concept of percentage to students is. To begin with, we showed a tagged paper ‘50%’ and asked the students where they use to meet such writing. Almost all the students answered ‘discount’. Several other answers like ‘battery’ and ‘polling result’ was also mentioned.

Capture quickcount
Representation of percents in real life

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Teaching Multiplication of Fractions with Natural Number

Summary on:
Shanty, N.O., Hartono, Y., Putri, R.I.I, de Haan, D. 2011. Design research on mathematics education: Investigating the progress of Indonesian fifth grade students’ learning on multiplication of fractions with natural number. Indonesian Mathematical Society Journal on Mathematics Education (IndoMS. J.M.E), 2.2, 147-162.

The difficulties of students in learning fractions, according to researches, is caused by two main factors. The first one due to teaching method which emphasizes only on technical procedures. As the consequence, the students see the algorithm as meaningless series of steps. Hence, they often forget the steps or might change the procedures with the incorrect ones. The problem is also called ‘algorithmatically based mistakes’. Another factor is the concept of the fraction itself which is NOT consistent with counting principles as it is in natural numbers.

In order to deal with the problems, remodeling mathematics by developing sequence of activities which are RME based seems to be appropriate. Here, we might design learning activities by combining 5 activity-levels in learning fraction (proposed by Streefland) with the 5 tenets of RME. In addition, the 4-level emergent modelling (by Gravemeijer) was also being concerned.

A design, covering the aforementioned needs, has been implemented by Shanty toward the 5th Grade students of SDN 179 Palembang. Here, the following, describes the activity she conducted and its effects to the students.

1. Producing Fractions
The activity employed contextual problems in order to stimulate students’ informal knowledge of partitioning, as meant to be a situational activity. The problem given was about ‘locating flags and water posts on the running route’ and delivered in form of story related to the celebration of Independence Day. In the story, two people were preparing running competition from PIM (Palembang Indah Mall) (A) to Palembang District Office (B). On the way from A to B, 8 flags and 6 water posts were installed, each of them with equal distance among its kinds. The students were, then, asked to locate and label the positions of the 8 flags and the 6 water posts in the provided running map.

The running route from PIM (A) to District Office (B)
Picture is available on https://www.google.co.id/maps

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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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