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.
Sources:
