Rancangan Permasalahan Matematika Berbasis PMRI (Versi Indonesia)

Untuk membuat 6 porsi ‘saus es pisang ijo’, dibutuhkan bahan-bahan sebagai berikut:esp

– 1 liter santan
– 60 gram tepung beras
– 100 gram gula pasir
– 1/2 sdt garam
– 1 lembar daun pandan

Andi ingin membuat ‘saus es pisang ijo’. Ia mempunyai 10 liter santan, 100 gram tepung beras, 1 kg gula, banyak garam, dan 10 lembar daun pandan. Berapa banyak ‘saus es pisang ijo’ kah yang dapat ia buat?

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Design of PMRI-based Mathematical Problems (English Version)



In order to make 6 portions of ‘es pisang ijo sauce’, the following ingredients are required:
– 1 litre of coconut milk
– 60 gram of tepung beras
– 100 gram of sugar
– 1/2 tea spoon of salt
– 1 piece of palm leave

Andi wants to make the sauce, and he has 10 litre of coconut milk, 100 gram of tepung beras, 1 kg of sugar, a lot of salt, 10 pieces of palm leave. How many portion of ‘es pisang ijo sauce’ he could make?

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Let’s Play Math (Colourful Necklace for Learning Number Pattern/ A Paper Based Applet)

This paper-based applet adopts the Java version entitled ‘Beads on Chain’. To access this, you may visit: http://www.fisme.science.uu.nl/toepassingen/00747/

Number pattern, or commonly known as ‘bilangan loncat’ by the lower grade students in Indonesian primary school, is first taught in the third grade.

The ‘beads on chain’ applet is actually a very good manipulative to stimulate students’ understanding on this concept. However, internet connection which does not support most Indonesian elementary schools has been an undeniable challenge. Therefore, preserving the paper-based version could be an alternative.

I have tried out the ‘Colourful Necklace’ to learn number pattern with a number of Grade III-D students of SD Pusri Palembang.

At first, I invited 2 students to play during the breaktime. Hearing that I would play with them, some other students came closer and got involved. Foto0355 It shows how this tool first impressed and be positively responded by the students.

To begin with, I told them the way to make a colourful necklace. Here, I emphasized that a similar pattern is important to make the necklace more beautiful. So, we first placed two yellow beads, then one brown, then yellow, and then blue again. Next, I tested them for the following sequence to ensure that they understood the problem. Finally, we got the first two sequences of alternating beads colour.

I, then, told them that I would love to use 32 beads for my necklace and I was worried about the colour of the last bead will be. The students were mostly confused and tried to gamble the answers. After a little repeating with emphasis to the questions, several students tried to think.

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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.

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Representation of percents in real life

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Let’s Play Math (Using Applet)

Anxiety toward mathematics has been found commonly in our students. To deal with the problem, a joyful way of learning the math is necessary, that is, to condition the students not to afraid to get involved in mathematical activities. Applet, a java based application, seems to be able to fulfill the need of the students of interesting and fun math learning. Such kind of application could help students understand mathematical concepts and processes, increase thinking flexibility, provide tools for problem-solving, and can reduce math anxiety for some students.

Using this way, the students might not realize that they have learned a crucial concept of math. In addition to that, the tool could also be employed to assess students’ thinking, procedural understanding, and build their awareness of the existence of math all around them.

The application is java-based and could only be accessed on line only. However, the idea could then be represented (adapted) into a paper-based task or games if the internet connection does not really support.

Example of applets provided freely in the internet

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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’.


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