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Realistic Mathematics Education

A brief overview of RME in Indonesia

Before we go to what RME is, let me remind you about your mathematics subjects when you were at elementary, secondary or high school; do you still remember who taught you math and can you solve some mathematical problems of elementary student’s level when your little brother or sister ask for your help to solve his or her homework? Did you hate mathematics or even do you still hate mathematics?

In Indonesia, not only was the problem of mathematics informed formally (Marpaung, 1995) that most pupils in a number of selected primary schools in Yogyakarta were afraid of mathematics, but also the result of mathematics education for 16 different urban and rural secondary schools in several provinces was very low based on finding from two diagnostic test carried out by Suryanto (1997) and Somerset (1996). He pointed out that mathematics teachers less confident and lack of smile so the classroom situation have no interaction and pupils have no chance to communicate their solution ( Zulkardi). Seeing mathematics like an evil or monster makes it difficult to learn mathematics due to the feeling of scary toward mathematics. However, lacking of understanding of teachers on the contents and pedagogic of mathematics is also one of factors that make pupils hard to learn mathematics. Too many exercises and homework to be solved, rules to be proved and lack of applications in their daily life get pupils had poor attitude toward mathematics. 
In an attempt to combat the low achievement and poor attitude toward mathematics, hence, a new approach in mathematics education that can overcome those problems is needed. one of the promising approaches toward the teaching and learning of mathematics thought to address these problems is realistic mathematics education (RME).

The philosophy of RME
Mostly determined by Freudenthal’s view on mathematics (Freudenthal, 1991), two of his points of views on RME are: mathematics must be connected to reality; and mathematics should be seen as human activity. Firstly, mathematics must be close to children and be relevant to everyday life situations. However, the word ‘realistic’ refers not only just to the connection with the real-world, but also to the problem situations which are real in students’ mind. Secondly, the idea of mathematics as a human activity is stressed. Mathematics education organized as a process of guided reinvention, where students can experience a similar process compared to the process by which mathematics was invented. Concepts of mathematization as a guide are used in this reinvention process and later it is categorized by Treffer (1991) into horizontal mathematization and vertical mathematization.
Principles and Characteristics of RME
 the characteristics of RME are historically related to three Van Hiele’s levels of learning mathematics (de Lange, 1996). Assuming that the process of learning process, it proceeds through three levels: (1) a pupil reaches the first level of thinking as soon as he or she can manipulate the known characteristics of a pattern that is familiar to him or her; (2) as soon as he or she learns to manipulate the interrelatedness of the characteristics,  he/she will have reached the second level; (3) he/she will reach the third level of thinking when he/she starts manipulating the intrinsic  characteristics of relations. Traditional instruction is inclined to start at second or third level, while realistic approach starts from first level. Then in order to start at the first level dealing with phenomena that are familiar to students, Freudenthal’s didactical phenomenology that learning should start from a contextual problem, is used. Furthermore, by the guided reinvention principle and progressive mathematizations, students are guided didactically and efficiently from one level to another level of thinking through mathematization.

The combination of three Van Hiele’s levels, Freudenthal’s didactical phenomenology and Treffer’s progressive mathematization result in five basic characteristics of realistic mathematics education or five tenets of RME (de Lange, 1987, Gravemejer, 1994). In brief those are:
  1.     Use of contextual problems (contextual problem figure as application and as starting points from which the intended mathematics can come out.
  2.    Use of model or bridging by vertical instruments (broad attention is paid to development models, schemes and symbolization rather than being offered the role or formal mathematics right away).
  3.    Use of student’s contribution (large contributions to the course are coming from student’s own constructions, which led them from their own informal to the more standard formal methods).
  4.     Interactivity (explicit negotiation, intervention, discussion, cooperation and evaluation among pupils and teachers are essential elements in a constructive learning process in which the student’s informal strategies are used as a lever to attain the formal ones).
  5.     Intertwining of learning stands (the holistic approach implies that learning strands cannot be dealt with as   separate entities; instead of intertwining of learning strands is exploited in problem solving.

Strategies for introducing RME in teacher education in Indonesia
In the country where RME originally has been developed and implemented for about 3 decades in the Netherlands, there are also positive results that can be used as indicators that RME might be promising to increase  the quality of mathematics education. For instance, the results of the Third International Mathematics and Science Study (TIMSS) showed that pupils in the Netherlands gained high achievement in mathematics education which was ranked 6th in 38 participating countries and the gap between smart pupils and weak ones was very small, while Indonesia, the achievement of pupils in mathematics education was ranked 34th out of 38 participating countries (Mullis et al., 2000). Thus, “mathematics for all’ which is only a slogan for some countries including Indonesia has been achieved in the Netherlands. Still, these positive results could be achieved not in short-term but in the long term endeavor.

Based on the explanation above, RME looks promising to be introduced and implemented in Indonesia because it could increase pupil’s understanding and motivation toward mathematics. For instance, RME content materials are developed using the contexts that are experimentally real to the pupils. Pendidikan Matematika Realistik Indonesia (PMRI) is an adapted RME founded by PMRI team promoted by Prof. R.K Sembiring and officially launched in 1998 to reform mathematics education in Indonesia. This team results in cooperation between Directorate General of Higher Education (DGHE) or DIKTI and NESO Indonesia that is an International Master Program on Mathematics Education (IMPoME). This program is under collaboration with between Freudenthal Institute Utrecht University and Sriwijaya University and Surabaya State University.

Reference : Zulkardi. Developing a 'rich' learning environment on Realistic Mathematics Education (RME) for student teachers in Indonesia. Matematika FKIP Unsri.

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