The main issues in mathematics learning is how to solve math problems themselves. Sometimes it makes a dread of theoretical notion about mathematics education. To deal with these problems required the existence of an appropriate method that can help teachers in teaching and learning activities in schools. One of the method is a realistic approach to mathematics or realistic mathematics education.
Realistic Mathematics Education (RME) is a mathematics learning approach developed by Freudenthal in Netherlands. Gravemeijer (1994: 82) said Realistic mathematics Education is rooted in Freudenthal's interpretation of Mathematics as an activity, such as problem-solving activities, find and organize the subject problem. Learning mathematics means doing mathematics, of which everyday life problem solving is an essential part.
Other concept in realistic mathematics education is state by Treffers (in Fauzan, 2002: 33-34). The key idea of RME is Children should be given the opportunity to reinvent mathematics under the guidance of an adult (teacher). In Addition, the formal mathematical knowledge can be developed from children's informal knowledge.
The statements above describes a perspective of mathematics learning placed as a process for students to find their own mathematical knowledge based on informal knowledge they have. In this view of mathematics is presented not as “a finished good" that can be moved by the teacher into the minds of students.
Freudenthal (in Panhuizen, 1996: 11) mentions two types of Mathematization in mathematics learning:
1. Horizontal mathematization, involves going from the world of life into the world of symbols, the examples are identification, formulation and visualization problems with different ways by students.
2. Vertical mathematization means moving within the world of symbol, the example of vertical mathematization are presentation of the relationships in the formula, refine and adjust the mathematical model, using different models, the formulation of mathematical models and generalization.
According Soedjadi (2001: 3), there are five characteristics in the learning of mathematics:
1. Using the context, means that the environment around us or the knowledge that has been owned by students can be used as a part of contextual learning materials for students.
2. Using the model, means that the mathematical problems or ideas can be expressed in the form of model from the real situations that lead to the abstract level.
3. Using the contributions of students, means that the concept of problem solving or discovery is based on the idea of students' contribution, in this case the students play a full part in the learning process.
4. Interactive, means that learning activities are built by the students' interaction with students, students with teachers, students with the environment and so on, so that communication or interaction among class members to stay awake and facilitate the learning process because there is no boundary or divider that prevents them to interact.
5. Intertwin, which means that teachers can use the different topics that can be integrated so as to bring an understanding of a concept at once.
In realistic mathematics learning, someone can build their own knowledge through the process of active learning. A concept does not instilled through the process of transferring, but someone who is learning should be given the freedom and encouragement to express their thoughts and construct knowledge for themselves. In addition, it is also necessary for interaction in the realistic mathematics learning, both among students, teachers and students, and so on.
The implications of the social aspect that is high enough in the learning activities of students, then teachers need to determine appropriate teaching methods and in accordance with those requirements. One method of teaching that can meet these objectives is the inclusion of a discussion in the learning activities of students. Discussion activity is deemed able to encourage and to expedite interaction between students. In addition, the negotiation and evaluation between students and teachers are an important factor in this constructive learning.
The method of realistic mathematics learning is often considered to be commensurate with the cognitive learning theory, as presented by Piaget and Vygotsky. Piaget (in Atkinson, 1999: 96) explains that in the stages of intellectual development of a child are involved in the process of thinking logically and considering their life. Thinking processes take place in accordance with the child's developmental level. In order to optimalize intellectual development of children, then they need to be motivated and facilitated to build theories that explain the world around them. Piaget (in Ibrahim, 1999:18) argues that a good education is education that involves the child to experiment on their own, in a sense: a) Try everything to see what happens; b) Manipulate signs and symbols; c)Asking the question; d) Find their own answers; e) Match what they had found at some point with they found at the other; f) Comparing the findings with the others findings.
Realistic mathematical learning is one approach to learning that is consistent with Piaget's view. Realistic mathematics learning developed based on constructivist philosophy, looking at knowledge in mathematics is not as something that is already finished and ready to be given to students, but as a result of construction of students who are learning. Therefore, in realistic mathematics learning, student is a central of the learning process, while teachers act more as facilitators. The implication of this view is a must for teachers to facilitate and encourage students to engage actively in the learning process. Students should be encouraged to construct knowledge for themselves. For this purpose the students should have greater freedom in expressing his thoughts in solving the problems. To realize the situation and conditions of this study is to manage the learning teachers need to pay attention to some of the views of Piaget. Among them are teachers should encourage students to dare to try a variety of possible ways to understand and resolve the problem. In this activity students construct knowledge is realized by providing a contextual problem. Contextual problem is designed such that allow students to construct knowledge independently.
Meanwhile, according to Vygotsky, one of the characteristics of realistic mathematics learning is the discovery of concepts and problem solving as a result of ideas of the students. Contribute ideas can be realized through a learning process in which there is interaction between students and students, between students and teachers or between students and their environment. Thus, in addition to any mental activity that is personal, in a realistic mathematics learning teachers need to encourage the emergence of social interaction between members of the class in construct knowledge. Through these social interactions are more able students the opportunity to convey the understanding that it has on other students who are weaker.
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