Why should We Change Mathematics Teaching?

This is the question that I proposed to my teacher in one of my course. In the discussion, we discussed about the percentage and its relationship with decimal, fractions, ratio and proportion. I argue that we have all been taught about percents and other topics of mathematics in the traditional way, with an emphasis on learning the correct calculation procedures, and very little or not on understanding. Still we all understand what percentages, fractions and decimals are and how they are related. So why should we change the way these topics are taught? Or in any case, why should we not teach the calculation procedures first and let understanding develop later? These questions are the paraphrased ones done by my teacher.

It is an issue that we should discuss, because we hear this argument quite often. Then, my teacher proposed his own question relating to my own question: what arguments do we have for wanting to change the way mathematics is taught traditionally? What data could be used to argue against teaching the procedures, in stead of teaching for understanding?

Mathematics as a human activity

I try to give an answer to my own question, why should we change the way these topics are taught? In my perspectives, I think we have to change the way mathematics has been taught because when we teach students in the traditional way of teaching, I can be really sure that they will not make sense of what they have been learned. Moreover, as Freudenthal said in his wonderful book, Revisiting Mathematics Education, mathematics is a human activity and therefore it must be connected to reality, stay close to children and be relevant to society in order to be of human value. So, in this sense, the focal point is not mathematics as a ready-made subject full of procedures, formulas or whatsoever. Instead, the focal point is on the activity. Education should gives students a guided opportunity to reinvent the mathematics.

why should we not teach the calculation procedures first and let understanding develop later?
I think, if we do it in this way, students will not develop their understanding of mathematics. Instead, what they get from this way of teaching is that they know the procedures and formulas but they do not know how to use it in their life. It can be seen from the test such as PISA or TIMSS, that many Indonesian students fail to answer questions that dealing with complex situations and asking for advance mathematical thinking and reasoning. Even, I argue that students will not develop their understanding after they know the procedures and formulas. It is because, they will always looking for the formulas and procedures when they want to solve the problems.
what arguments do we have for wanting to change the way mathematics is taught traditionally? What data could be used to argue against teaching the procedures, in stead of teaching for understanding?
As Freudenthal said that learning processes, or at least part of them, can be more essential than their products (Cited from Revisiting Mathematics Education book). The focus of the teaching of mathematics is the process of learning it, not the product. In RME, the use of context is very important. In contrast with the traditional way of teaching, RME use the context problem both as a source of learning and to apply mathematical concepts. The students, in RME class, can develop mathematical tools and understanding while working on context problems. In the first time, they develop strategies or models that are closely related to the context. Later on, certain aspects of the context situation can become more general which means that the context can get more or less the character of a model and as such can give support for solving other but related problems (http://www.fisme.science.uu.nl/en/rme/).
One of a good example is the experience of a college professor who experienced the change in her son’s understanding of mathematics after following the RME class in the Netherlands. You can read her story in this link: http://mathematicallysane.com/realistic-math-makes-sense-for-students/

Teaching and Learning Greatest Common Factor (GCF) and Least Common Multiple (LCM) at Grade V Using RME Approach


This observation report explains about the process of teaching and learning Greatest Common Factor (GCF) and Least Common Multiple (LCM) at SD Negeri 98 Palembang, South Sumatera, Indonesia by using Realistic Mathematics Education Approach. This activity involved 33 pupils in two days.

In the first meeting, I was a teacher in the classroom. The teaching and learning activities ran about 60 minutes which was helped by Mrs. Maryani and Novita Sari for documenting and guiding the students to follow the instruction. In this meeting, we introduced the concept of Greatest Common Factor (GCF) to the students by giving the realistic problem.

In the Second meeting, in the second day, Novita Sari acted as a teacher and helped by Mrs. Maryani and me to guide the students and document the teaching and learning process. In this chance, we introduced the concept of Least Common Multiple (LCM) by using the realistic problem as we did in the first meeting.


The goal of this research is to make students understand the concept of Greatest Common Factor and Least Common Multiple by using Realistic Mathematics Education Approach.

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Lesson Study and Realistic Mathematics Education: A Conceptual Overview

Along with language, mathematics has always been at the core of education in all civilized societies. In the school context, as Latterell (2005) said that most students (and many adults) view mathematicians, and even students who are good in mathematics, as probably smart, but socially inept. Being good in mathematics is not something many students strive to be.

Mathematics education researchers try to offer solutions for this case and other problems in the teaching and learning mathematics. In fact, mathematics education is not just simply a discipline or a body of knowledge, but much more than that, it comprises things that people do. Now the didactics and the design of mathematics education become more and more develop. The focus is on theory of mathematics education. This paper explains a comparison between two approaches in mathematics education.

Lesson Study

Lesson study is a collaboration-based teacher professional development approach that originated in Japan (Murata, 2011). Lesson study gain an international attention in the past decade and in 2002 it was one of the foci for the Ninth Conference of International Congress on Mathematics Education (ICME) held by International Commission on Mathematical Instruction (ICMI). Began in the late 19th century in Japan, lesson study refers to a process in which teachers progressively strive to improve their teaching methods by working with other teachers to examine and critique one another’s teaching techniques.

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Pembelajaran Matematika Realistik, Sebuah Pengantar

Sistem pendidikan nasional yang telah dibangun selama tiga dasawarsa terakhir ini, ternyata belum mampu sepenuhnya menjawab kebutuhan dan tantangan nasional dan global dewasa ini. Program pemerataan dan peningkatan kualitas pendidikan, khususnya pendidikan matematika yang selama ini merupakan fokus pembinaan masih menjadi masalah yang paling menonjol dalam dunia pendidikan kita.

Upaya meningkatkan mutu pendidikan, khususnya pendidikan matematika di Indonesia telah banyak dilakukan oleh berbagai pihak yang peduli pada matematika sekolah. Namun, upaya-upaya tersebut belum juga mencapai harapan secara optimal dengan berbagai alasan teknis di lapangan. Kesulitan belajar matematika bukan hanya dialami oleh anak-anak Indonesia, tetapi juga dialami oleh anak-anak di berbagai negara lain. Dengan demikian, akan mudah dipahami bahwa kesulitan belajar matematika kapanpun selalu ada. Oleh karena itu, upaya untuk mengatasi kesulitan belajar tersebut harus dilakukan secara terus menerus dengan penuh kesabaran.

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A Summary of Designing A Mathematics Curriculum By Lee Peng Yee


The development of curriculum in Indonesia has changed many times through the ages. Relating to the issue of mathematics curriculum reform, the government of Indonesia has implemented at least six different mathematics curriculums since the 1970s. These curriculum reforms are Curriculum before 1975, curriculum 1975, curriculum 1984, curriculum 1994, curriculum 1994 revised and Competence based curriculum. Generally speaking, curriculum is defined as the package of a syllabus together with the implementation tools such as textbooks and other resource materials for teacher training. In Indonesian context, although the mathematics syllabus did not change, the mathematics curriculum has changed by the movement of PMRI. Normally, the next interested topic is the design of mathematics curriculum embracing PMRI.

The discussion in this summary was based upon Lee Peng Yee’s article with the same title. The summary covers several important factors in designing curriculum, some practices and the most recent trends.

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