Start from “Common Sense”, End with “Understanding”

Summary of the article:
Gravemeijer, K. (2011). How concrete is concrete. Indonesian Mathematics Society Journal on Mathematics Education, 2(1), 1-8.

This might be the answer of the previous problem given in “When nine doughnuts price as much as the other ten”. The real problem is that students sometimes think that mathematics that they learn in school has no relation with what they see in everyday life.

concrete

Dealing with this problem, teachers try to provide students with manipulative which perhaps help them connect the math to the real-world context. Occasionally, those manipulative seemed very realistic for teachers, unfortunately not for students. Teachers are usually trapped with their own thinking and forget that their students are in not in their level.

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Understanding Percent using the Percentage Bar

Summary of the article:
Van Galen, F. & D. v. Eerde. (2013). Solving Problems with the Percentage Bar. IndoMS. J.M.E, 4(1), 1-8.

In an observation toward 14 Grade VII students of a achool in the Netherlands, surprising result (only 4 students could solve the problem correctly) was performed by the students when dealing with the following problem:

Soal persen

Trying to solve the problem, the students directly did calculations. None of them tried to make visual representation to see the relations between the given numbers. As the consequence, they often went wrong.

Actually, the students have tried several ways to find the answer like working with equal proportion or playing with the numbers in the question.

The former one was supposed to bring them to the expected result. However, they were stuck since they have to work with unfriendly proportion (15 out of 100) which led them to confused. While the latter one was really out of concept. The students might think that the problem must involve simpler calculation. So, they just tried to divide 600 over 15 and conclude that the answer should be 40.

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Introducing Concept of Angles with RME Based Learning

Summary of:
Bustang, Zulkardi, Darmowijoyo, Dolk, M., van Eerde, D. (2013). Developing a local instruction theory for learning the concept of angle through visual field activities and spatial representations. International Education Studies, 6(8), 58-70. doi: 10.5539/ies.v6n8p58

The notoriety of geometry among Indonesian students as one of the hardest topics is not without proof. Studies found many misconceptions experienced by the students, especially in angle representation which might impact on their difficulties in learning geometry in the higher level.

In order to deal with the problem, Bustang has designed a four-step learning activitiy for teaching and learning the concept of angle. The design has been tried out to the third grade students of a public school in Palembang, Indonesia.

At first, the students were familiarized with the real situations involving vision lines and blind spots through an activity called ‘Now you see it, now you don’t’. Here, the students were provided with three problems related to a cat’s vision over a group of mice by representing the ‘top view’, ‘side view’, and additional case if cat do a ‘movement’.

kucing

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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.

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

JOURNAL SUMMARY

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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