Learning math lately emerging discussed is Realistic Mathematics Education (RME) . RME is known as an approach that has been successful in the Netherlands. The idea of a realistic approach to the study of mathematics is not only popular in the Netherlands alone, many developed countries have been using the new approach is a realistic approach. Realistic mathematics determined by Freudenthal views about mathematics. Two important insights he is 'mathematics must be connected to reality and mathematics as human activity'. First, mathematics should be close to the student and must be relevant to everyday life situations. Secondly, he stressed that mathematics as a human activity, so students should be given the opportunity to learn to perform activities of all the topics in mathematics.
Realistic Mathematics Education is a teaching approach that starts from the things that are 'real' for students, emphasizing skills 'process of doing mathematics', discuss and collaborate, argue with classmates so they can find their own ('student-inventing' as opposed to the 'teacher telling') and in the end use of mathematics to solve problems both individually and collectively. In this approach the teacher's role was more of a facilitator, moderator or evaluators while students think, communicate, train shades of democracy with respect the opinions of others.
A. Definition of Realistic Mathematics Education (RME)
Learning mathematics is realistic or Realistic Mathematics Education (RME) is a learning approach Freudenthal mathematics developed in the Netherlands. Gravemeijer (1994: 82) which explains that which can be classified as such activities include problem solving activities, searching and organizing subject matter. Realistic mathematics intended in this case was conducted by the school mathematics menemaptkan realities and experiences of students as a starting point for learning. Problems realistically be used as a source of the emergence of mathematical concepts or knowledge of formal mathematics.
Characteristics RME uses: the context of "real world", models, production and construction students, interactive and linkages. Realistic mathematics learning begins with the real issues, so that students can use previous experience directly. With realistic mathematics learning students can develop a more complete concept. Then students can also apply mathematical concepts to new areas and the real world.
B. Components of Realistic Mathematics Education (RME)
In realistic mathematics learning there are three key principles that can be used as a basis for designing learning:
Ø Reinvention and Progressive mathematization ("guided discovery 'and the process of mathematization increasing). According Gravemijer (1994: 90), based on the principle of reinvention, the students are given the opportunity to experience the same process with the current process of mathematics is found. History of mathematics can be used as a source of inspiration in designing the subject matter. Furthermore reinvention principle can also be developed based on an informal settlement procedure. In this case the informal strategies can be understood in anticipation of a formal settlement procedures. For this purpose it is necessary to find the contextual issues that can provide a variety of procedures as well as the completion of the study indicate that depart from the learning level mathematics significantly to the level of formal mathematics learning (progressive mathematizing).
Ø didactical phenomenology (containing charge didactic phenomenon). Gravemeijer (1994: 90) states, based on this principle of presenting mathematical topics contained in realistic mathematics learning is presented on two considerations: (i) gave rise to a variety of applications that must be anticipated in the learning process and (ii) compliance as being influential in the process mathematizing progressive. Mathematical topics presented or contextual issues that will be raised in the study should take into consideration two things namely the application (usefulness) and its contribution to the development of mathematical concepts further. Related to the above, there are fundamental questions that must be answered is how we identify phenomena or symptoms relevant to mathematical concepts and ideas the students will learn, how we should mengkonkritkan phenomena or symptoms, what didactic actions necessary to help students gain knowledge as efficiently as possible.
Ø Self-developed models (Establishment of a model by the students themselves), Gravemeijer (1994: 91) explains, based on this principle when working on contextual issues students are given the opportunity to develop their own model which serves to bridge the gap between informal and formal mathematical knowledge. In the early stages of developing the students become familiar model. Furthermore, through generalization and pemformalan end models into something that actually existed (entity) that is owned by the students. With generalization and formalization of the model will be transformed into a model of the problem. Model-of will be shifted into the model for similar problems. In the end will be a formal knowledge in mathematics.
According Soedjadi (2001: 3) realistic mathematics learning has several characteristics and components as follows:
Ø The use of context (using context), meaning that in mathematics realistic everyday environment or have knowledge of the students can be used as part of a contextual learning materials for students.
Ø Use models, bridging by vertical instrument (using models), meaning that problems or ideas in mathematics can be expressed in terms of the model, both models of the real situation and the model that leads to the abstract level.
Ø Students constribution (using student contribution), meaning that the concept of problem solving or discovery is based on the idea of students' contributions.
Ø Interactivity (interactive), meaning that the activity of the learning process is built by the students' interaction with students, students with teachers, students with the environment and so on.
Ø intertwining (integrated with other learning topics), meaning that the different topics can be integrated so as to bring an understanding of a concept simultaneously.
C. Principles of Realistic Mathematics Education (RME)
There is a realistic learning principles in realistic mathematics curriculum are:
Ø Dominated by problems in context, serving two terms, namely as a source and as applied mathematical concepts.
Ø The attention given to the development of models, situations, schemes, and symbols.
Ø Contribution of the students, so that students can make into a constructive and productive learning, students produce their own and construct their own so as to guide the students of mathematics level informal toward formal mathematics.
Ø Interactive as a characteristic of the process of learning mathematics
Ø Interwinning (making braids) inter-subject or inter-subject.
According Treffers and Goffree (2004) that the contextual issues in the curriculum realistic, useful to fill a number of functions:
Ø Establishment of the concept: In the first phase of learning, the students are allowed to enter into scientific mathematics and motivated.
Ø Establishment of the model: Problems contextual foundation entering students to learn the operation, procedures, notations, rules, and they do this in relation to other models that its usefulness as an important driving force in thinking.
Ø Application: contextual problems using reality as a resource and for the applied domain.
Ø Practice and training of spesipik capabilities in applied situations.
D. Type of mathematization in Realistic Mathematic Education (RME)
According Treffers and Goffree (2003) there are two known types of mathematization in Realistic Mathematic Education (RME), namely:
Ø Mathematics horizontal
Horizontal mathematical process at intermediate stages of everyday problems into mathematical problem that can be solved or the real situation changed into symbols and mathematical models.
Ø vertical Mathematics
Mathematical process at the stage of the use of symbols, emblems rules that apply mathematics in general.
E. Stage Realistic Approach Mathematic Education (RME)
Step-by-step approach phase Realistic Mathematics Education, namely:
Give problems in daily life.
Encourage students to resolve the issue, either individually or in groups.
Provide other problems in students, but in the same context as obtained several steps in solving the problem.
Consider ways and means prescribed by examining and researching, then teachers guide students to go further in the direction of the vertical math.
Assigning students either individually or in groups to solve other problems either applied or not applied.
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