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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When nine doughnuts price as much as the other ten (A reflection)


Prior to this post, I went to a doughnut seller near my dorm. I ask the seller (her) how much the doughnut cost. She said, “It is Rp.2000,- for 3 doughnuts”. Since I brought Rp.3000,- in my pocket, then I meant to buy 4 doughnuts with the 3000. Surprisingly, she gave me 5 doughnuts.

The following day, I again visited her shop and brought Rp.5000,- for doughnuts. Still, I got 8 instead of 7 (as I expected).

I started to think, how if I bought 6000,- with twice buyings? It benefits me one more doughnut compared to buying it at at a time. So I could get 5 doughnuts in the  first buying, and the other 5 in the next buying. This means, with Rp.6000,- I could have 9 or 10 doughnuts. Just in case the whole consumers of her do this tricky actions, I do believe that the seller could be disserved.

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Does “context” only match with “Lower-level Math”?


Well, I am not going to ask you to solve nor to discuss the solution of the problem beside.

The question was taken from the ‘Examen Vwo‘ of Wiskunde B, a yearly math event in the Netherlands.

What I am going to show you from the picture is related to the title of this post, “Does context only match with lower level math?” which is rather be a common question, at least, by several Indonesian teachers. Furthermore, some of them used it as an excuse for not applying RME, CTL, or involve any context in their teaching of higher level math. As the consequence, most of our students feel less motivated in learning math since they did not find it useful for them.

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Dear Mathematician, don’t be too mechanistic! Be flexible! (A reflection)

This post is inspired by students’ (finalists of Kontes Literasi Matematika IV, Sriwijaya University) anwers to a question given by Prof. Dr. Zulkardi in the play-off session:

raja louis

Anwering this questions, two of the three finalists employed algebraic manipulation to find the answer. They argued that if Raja Louis X (10) has 16 wifes, then Raja Louis V (5) must have 8 wifes as it satisfied direct proportion.

Indeed, there should be no relation between the number of wifes a king has with its and its name order.

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Contractual Arithmetic (An Approach in Teaching Mathematics)

Presented by:
Christa Kaune, Institute for Cognitive Mathematics, University Osnabruck, Germany, and
Edyta Nowinska, Intitute for Mathematics Didactics, A. Mckiewicz University in Poznan, Poland

in a general lecture conducted in Sriwijaya University on 30th July 2013.

The issue of contractual arithmetic in Indonesia was firstly introduced by Christa Kaune and team from Osnaburck University. Prior to the proposal of this approach, researches which focused on mathematical cognition had been conducted in several secondary schools in Yogyakarta and Nusa Tenggara Timur.

As the result, the idea was formulated to transform from head-to-head learning style into teaching mathematics for undertstanding. This approach does concern on the cognitive styles with three main steps, namely, generating argumentation, explanation, and prediction and justification.

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