- INTRODUCTION

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.