By: Siti Nurrochmah Dani
10313244004
Mathematics is a living subject which seeks to understand patterns in both the world around us and our mind. Many people think that mathematics is complicated subject to learn, but there are some people think that math is easy to learn. It is depends on our mind set about mathematics. If we comprehend mathematics as part of our life and the objects are around us and our mind, then mathematics will be easy and interesting to learn.
In school mathematics is learned as subject in formal education. The students didn’t comprehend mathematics just as formal form. They need to learn mathematics as a part of daily life. That will comply the student’s requirement through realistic mathematics education, the student will understand mathematics in concept not only memorize the formal symbol mathematics like formula.
History of Realistic Mathematics Education
Mathematics realistic education was started with the reason is mathematics in Netherlands less meaning for the student. Mathematics is formal and abstract. It just like symbol. The new concept was begun by Wijdeveld and Goffre (1968) through Wiskobas project. Since 1975 until now, realistic mathematics education direct in the eyes of Freudenthal (1977). Base on his view, mathematics must be keyed to real live, close to student experiences and relevant to society, with the purpose be a part of humanism value. Instead of seeing mathematics as subject matter that has to be transmitted, Freudenthal emphasize the idea of mathematics as a human activity. Mathematics lessons should provide opportunities for learners to "guided" and "reinvent" mathematics by doing so. Meaning in mathematics education with the primary goal of mathematics is an activity and not a closed system. So the focus of learning mathematics should be on mathematical activities or "mathematization" (Freudenthal, 1968).
Then Treffers (1978, 1987) explicitly formulated the idea in two types of mathematization in an educational context, the horizontal and vertical mathematization. In the horizontal mathematization students are given the tools of mathematics can help formulate and solve problems in daily life. Mathematization vertical on the other hand is a process of reorganization within the mathematical system, for example, found a direct link from the linkages between the concepts and strategies and then applying the findings them. So, mathematization horizontal is contrast to the realm of the real realm of symbols, mathematization while moving vertically in the realm of symbols. Both forms of mathematization is really no different from its meaning and equal in value (Freudenthal, 1991). This is due to the meaning of "realistic" that derived from the Dutch "realiseren" which means not related with reality, but "imagine". Activities "imagine" this it will be easier to do when starting from the real world, but not always have to go through that way.
According Gravemeijer (1994), there are three main principles in the learning realistic mathematics, that are: 1) guided reinvention and progressive mathematization, is through the mathematical topics presented, students are given the opportunity to experiencing a process similar to the process through which the inventors mathematics in discovering math concepts, 2) didactical phenomenology, the mathematics topics being taught comes from the phenomenon daily life. The topics were chosen with consideration of the application and its contribution for the development of advanced mathematics, and 3) self-developed models, the students develop their own model when solving problems contextual. At first, students will use a model or settlement strategy the problem informally. After the interaction and discussion in class, one model or strategy proposed completion students will be developed a formal model or strategy.
Characteristics of Realistic Mathematics Education
Realistic Mathematics Education reflect mathematics view how students learn math and how math is learned. This view is reflected on six principles that differentiated from five characteristics by Treffers
- The use of contexts.
- The use of models.
- The use of students’ own productions and constructions.
- The interactive character of the teaching process.
- The intertwinement of various learning strands.
Based on five characteristics by Treffers, the six principles as characteristics of Realistic Mathematics Education will explain one by one.
1. The principle activities
Learners must be treated as active participants in the process development of all the mathematical tools and insights own. In this case the learners are faced with a problem situation allowing it to form part of the problem and develop algorithms, such as multiplying and divide by way of informal employment.
2. The principle of real
Realistic mathematics must enable learners to apply understanding of mathematics and mathematical tools to solve problem. Learners must learn mathematics so that
useful and can be applied to solve the right problem in the context of problem solving in real life. In this context, learners can develop mathematical tools and understanding mathematically.
useful and can be applied to solve the right problem in the context of problem solving in real life. In this context, learners can develop mathematical tools and understanding mathematically.
3. The principle of gradual
Learning mathematics means that students must learn mathematics through the various stages understanding, from the ability to find solutions that informal related to the context, to the creation of the various stages of relationships direct and charting; the next in the acquisition of knowledge about the underlying principles and the wisdom to extend relationship. Conditions for up to the next stage are reflected in ability shown in the task. This reflection can be shown through the interactions. The strength of this stage the principle is can guide the growth understanding of mathematics learners and direct longitudinal relationship in the mathematics curriculum.
4. The principle of establishing mutual
Intertwined principles are found in every line of mathematics, for example among topics such as awareness of the numbers, mental arithmetic, estimates (estimate), and algorithms.
5. The principle of interaction
In realistic mathematics learning mathematics is seen as an social activity. Education should be able to provide opportunities for learners to share their strategies and findings. By listening to what other people find and discuss these findings, learners get ideas for improving the strategy. After all interactions can be produce reflections that allow learners reach the stage understanding of higher
6. The principle of guidance
Teacher and educational programs have important roles in directing learners to acquire knowledge. They control the learning process to show what that must be learned to avoid false understanding through memorization process. Learners need the opportunity to form insight and mathematical tools themselves, so teachers must provide learning environments that support the ongoing process. That means they must be able to predict when and how they can anticipate the understanding and skills directing learners to achieve learning objectives. In this case the difference in the ability of learners must be considered, so that all learners have the opportunity to develop knowledge in a way most suitable to them.
Ice berg Phenomenon as RME Approach
Realistic mathematics education develops to be better concept to teach mathematics. In the development of RME, there are many methods to teach mathematics with RME approach. One of them is Ice berg Phenomenon. In this case, learned education is like an ice berg.
The phenomenon of ice berg in the mathematics learning consists of (1) concrete, (2) scheme, (3) model, and (4) formal. There are three of the four parts of the phenomenon of ice berg in the mathematics that are rarely touched and explored in more depth, whereas it is very close and real.
To develop a mathematical approach to the concept of real is not easy, let alone see math in a concrete and then connect it to formal symbols in mathematics. It happened because of the distance between them. Then as a teacher of mathematics that is more oriented to the world of mathematics should be directing students to understand mathematics as a whole that is formally and informally. That the purposes of informal mathematics here include mathematics in everyday life and everything that is real is not shown directly in mathematical symbols.
Basically informal mathematics can be extracted by opening the students' horizons to the environment surrounding the ice berg as the phenomenon of the first "concrete". By looking at all the students something concrete will be easier to understand. After discovering the problem concrete problems of the scheme will be established with the imagination to connect the existing information with the math. The next model is shaping up according to the information received. This model is a representation of the problem to be solved. And the last is a formal mathematical notation, which students should be able to change the information received through the concrete things in a formal mathematical notation. Then the students will understand mathematics easily.
The role of teachers in this study is also needed in building and motivating students to solve concrete problems into formal mathematical symbols. Teachers can also assist students in connecting from each phase to another like from concrete problems to the scheme or schemes to model and beyond by providing teaser questions. A big challenge for teachers is pointed student to see the concrete problems that exist in life.
Learning mathematics with the concept of ice berg it opens students to understand mathematical thinking as a whole, not just a symbol but also a real problem in life “realistic”. This will encourage students to think critically in solving a problem and understand conceptually. In addition students can learn that mathematics is close to life and essentially mathematical objects that are inside the human mind and that is beyond the human mind.
References:
Anonymous. 2011. Sejarah dan landasan filosofis serta karakteristik Matematika Realistik http://yubaedisiron.blogspot.com/2011/02/sejarah-dan-landasan-filosofis-serta.html
Mahmudi, Ali. 2009. Mengembangkan Kemampuan Berpikir Siswa melalui Pembelajaran Matematika Realistik
Marsigit.2010. The Iceberg Approach of Learning Fractions in Junior High School: Teachers’ Simulations of Prior to Lesson Study Activities. http://staff.uny.ac.id/sites/default/files/penelitian/Marsigit,%20Dr.,%20M.A./Marsigit_Paper_APEC%20Conferen_Chiang%20Mai_Thailand_November%202010.pdf
Marsigit, dkk. 2007. Lesson Study: Promoting Student Thinking On The Concept Of Least Common Multiple (LCM) Through Realistic Approach In The 4th Grade Of Primary Mathematics Teaching http://www.criced.tsukuba.ac.jp/math/apec/apec2007/progress_report/specialists_session/Marsigit.pdf
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