How a problem get students engaged

The following video shows how a group of fifth graders work on a realistic problem related to time differences. The problem is adopted from PISA 2006 questions.

What is interesting?
If you listen critically to the conversations, you will find how this problem could engage students in thinking. Solving this problem, the students seems to first imagine themselves involved in the problem. They unintentionally positioned themselves to think of consequences, related to the situation, given in the problem.

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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.


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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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:

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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