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Realistic Mathematics Learning (RME)
1.1 AbstrackMathematics is one of the basic science, which increasingly perceived interaction with other scientific fields such as economics and technology. The role of mathematics in these interactions lies in the structure of knowledge and the equipment used. Mathematical sciences today is still widely used in various fields such as industrial, insurance, economics, agriculture, and in many areas of social and engineering. Given the growing role of mathematics in the years to come, of course, many scholars of mathematics that is needed are highly skilled, reliable, competent, and knowledgeable, both within the discipline itself and in other disciplines to each other. To become a scholar of mathematics is not easy, must be really serious in learning, but to learn mathematics, we also have to learn any other science fields. So, if already a graduate in any field of mathematics that can be so very easy to find a job.The word mathematics comes from the word “mathema” in Greek is interpreted as “science, science or learning. ‘Major disciplines within mathematics is based on the needs of the calculations in commerce, land measurement, and to predict astronomical events. These three needs can be roughly related to the broad subdivision of mathematics is the study of structure, space, and change. Lesson on a very common structure begins in natural numbers and integers, and arithmetic operations, which are all described in basic algebra. Integer nature of the more thoroughly studied in number theory. The study of space originates with geometry. And understanding of changes in measurable quantities is a matter of course in natural science and calculus.In the trade are intimately associated with mathematics because in trade there would be a calculation, in which the calculation is part of mathematics. Unconsciously turns all people use mathematics in everyday life as if there are people who are building a house then surely that person would measure in completing his work. It is therefore very useful mathematics in everyday life.One characteristic of mathematics is to have these abstract objects that can cause many students have difficulty in mathematics. Mathematics achievement of students both nationally and internationally has not been encouraging. In learning mathematics students have not been significant, so the students understanding of the concept is very weak.”According to Jenning and Dunne (1999) said that, most students have difficulty in applying mathematics to real life situations.” This is causing the difficulty of math for students in learning mathematics is because it is less meaningful, and teachers in learning in the classroom does not associate with schemes that have been owned by the students and students are given less opportunity to reinvent mathematical ideas. Linking real life experiences, children with mathematical ideas in the classroom learning is essential for learning mathematics meaningful.
According to Van de Henvel-Panhuizen (2000), when children learn math separate from their everyday experience, then the child will quickly forget and can not apply mathematics. One of the math-oriented learning matematisasi everyday experiences and apply mathematics in everyday life is a realistic mathematical learning.
Learning mathematics relaistik first introduced and developed in the Netherlands in 1970 by the Freudenthal Institute. Learning mathematics should be near her children and real life everyday.
Usually there are some students who think learning math should be a struggle in other words must learn to extra hard. It makes mathematics such as “monster” that must be feared and lazy to learn mathematics. Especially with mathematical maketh as one among the subjects tested in the national exam is a requirement for graduation students of junior and senior high school, students were increasingly frightened. As a result of negative thoughts on mathematics, it is important to a teacher who teaches math to make efforts to make the learning process meaningful and enjoyable. There is some thought to reduce the fear of students towards mathematics.
One of the only realistic way of learning mathematics in which this learning involves the linking and the surrounding environment, the real experience of students had ever experienced in everyday life, and make mathematics as a student activity. RME approach, students do not have to be brought into the real world, but in relation to any real situation existing in the minds of students. So students are encouraged to think how to solve problems that may or often experienced by students in their daily life.
Learning now is always implemented in the classroom, where students are less free to move, try to vary the learning strategies associated with the life and the environment around the school directly, as well as use it as a learning resource. Many things that we can make math learning resources, which is important choose a suitable topic for example, measure the height of the tree, measure the width of the tree and so forth.
Students learn a little better until the students understand the material, understand the material than in a lot of material but students do not understand it. Although many claim the achievement of the curriculum until the absorption but with a limited allocation. So teachers should encourage students to complete self-study before the matter further because it is intended to prevent misunderstandings in learning mathematics.
Most students, learning mathematics is a heavy burden and tedious, become less motivated students, quickly bored and tired. As for some of the ways you can do to overcome the above with the innovation of learning. Some ways that can be done, among others, give a quiz or a puzzle that must be guessed either in groups or individually, giving a numbers game in the classroom and so depend on the creativity of teachers. So in order to facilitate students in learning mathematics must be connected to real life that happens in everyday life.
1.2 Objectives of Writing
A learning math is not difficult, there are ways to facilitate the learning of mathematics is by way of Realistic Mathematics Education. Learning where it connects with everyday life. In writing this paper aims to:
1. To facilitate students in learning mathematics can be used in learning mathematics realistic.
2. Teachers in delivering the material must have a strategy in learning mathematics, so that students are not bored in learning mathematics.
3. So that students know how much fun learning math.
4. To know more clearly about realistic mathematics learning.
5. To explain the theory of realistic mathematics learning.
6. For the implementation of realistic mathematics learning.
7. Realistic link between learning mathematics with understanding.
1.3 Writing Questions
1. What is a realistic learning math?
2. How can a teacher in the learning strategies so that students liked mathematics learning mathematics?
3. Why mathematics is not liked by the students?
4. What characteristics are there in RME?
5. Why do students always forget the concept has been learned?
2.1 Realistic Mathematics (MR)
Realistic mathematics that is intended in this case is carried out with school mathematics menemaptkan realities and experiences of students as a starting point for learning. Realistic problems are used as the source of the emergence of concepts of mathematics or formal mathematical knowledge. Realistic mathematics learning in the classroom-oriented characteristics of RME, so students have the opportunity to rediscover mathematical concepts. And students are given the opportunity to apply math concepts to solve everyday problems. Characteristics of RME uses: the context of “real world”, models, production and construction students, interactive and linkages. (Trevers, 1991; Van Heuvel-Panhuizen, 1998). We will try to explain about the characteristics of RME.
a. Using the context of “real world” not only as a source matematisasi but also as a place to apply the math again.Realistic mathematics learning begins with real problems, so that students can use prior experience directly. Search process (core) of the corresponding process of the real situation stated by De Lange (1987) as a conceptual matematisasi. With realistic learning math concepts that students can develop more complete. Then students can also apply konep-concept into a new field of mathematics and the real world. Therefore, to limit the mathematical concepts with everyday experiences need to be considered matematisasi everyday experience and the application of mathematics in everyday life.
b. Using models (matematisasi) the terms of this model relates to the situation model and mathematical model developed by the students themselves. And act as a bridge for students from the real situation to situation or from abstract mathematics informal to formal mathematics. This means that students create their own model in solving the problem. Situation model is a model that is close to the real world of students. Generalization and formalization of the model. Through model-of mathematical reasoning will be shifted into a model-for a similar problem. In the end will be a formal mathematical model.
c. Using the production and construction streefland (1991) emphasized that the making of “free production” students are encouraged to reflect on what they consider important part in the learning process. Formal strategies of students in the form of contextual problem-solving procedure is a source of inspiration in the development of further learning is to construct a formal mathematical knowledge.
d. Using interactive. Interactive between students and teachers is fundamental in learning mathematics realistic. Forms of interactive between students and teachers are usually in the form of negotiation, explanation, justification, agree, disagree, question, used to achieve a formal form of informal forms of student.
e. Using realistic linkages in learning mathematics. In learning there are linkages with other fields, so we must consider also the other areas because it will have an effect on problem solving.Normally required in applying mathematical knowledge is complex, and not only arithmetic, algebra, or geometry but also in other fields.
2.2 Realistic Mathematics Education
Learning mathematics is a realistic theory of learning and teaching in mathematics education. Realistic mathematical learning theory was first introduced and developed in the Netherlands in 1970 by the Freudenthal Institute. Freudenthal believes that mathematics should be interpreted with reality and mathematics is a human activity. From the opinion of Freudenthal’s true it would be nice in learning math should be something to do with reality and everyday life. Therefore, people must be given the opportunity to discover mathematical ideas and concepts with the guidance of adults. Mathematics should be near her children and everyday life. This effort is viewed from a variety of situations and issues of “realistic”. Realistic is intended not refer to reality on realitias but on something that can be imagined.
As for the view konstruktifis learning mathematics is to allow students to construct mathematical concepts with their own capabilities through a process of internalization. Teachers in this role as facilitator. In learning mathematics teachers must give students the chance to discover their own mathematical concepts to students’ own abilities and teachers continue to monitor or engage students in learning while the students themselves who will discover mathematical concepts, at least the teacher should continue to assist students in learning mathematics .
According to Davis (1996), in view of constructivist-oriented mathematics teaching:
1. Knowledge is built in the mind through the process of assimilation or accommodation.
2. In mathematical work, every step of what students are faced with.
3. New information must be associated with the experience of the world through a logical framework to transform, organize, and interpret their experiences.
4. Centers of learning is how students think, not what they say or write.
The Davis opinion, in learning mathematics students to have knowledge in thinking through the process of accommodation and the student should also be able to resolve the problem to be faced. Students learn new information associated with everyday experience in a logical, in this study should be able to understand and think for themselves in solving the problem, so it does not depend on the teacher, students can also have its own way to solve the problem.
This constructivist criticized by Vygotsky, who claimed that students in constructing a concept needs to pay attention to the social environment. Constructivism is by Vygotsky called social konstruktisme (Taylor, 1993; Wilson, Teslow and Taylor, 1993; Atwel, Bleicher, and Cooper, 1998). There are two important concepts in the theory of Vygotsky (Slavin, 1997), the Zone of Proximal Development (ZPD) and scaffolding. Zone of Proximal Development (ZPD) is the distance between the actual developmental level that is defined as the ability of solving problems independently and the level of potential development that is defined as the ability of problem solving under adult guidance or in collaboration with more capable peers.Scraffolding is providing some assistance to students during the early stages of learning, then reducing the assistance and provide an opportunity to take over greater responsibility after he can do (Slavin, 1997). So the Zone of Proximal Development there are students who solve problems by itself, and there are students who solve the problem must be with the consent of adults. While scraffolding have stages of learning, students assisted in the initial learning, but the aid was gradually reduced.After that students are given the opportunity to resolve the problem yourself and have a greater responsibility after the students can do it. Scraffolding is the assistance given to students to learn to solve problems. Such assistance may include guidance, encouragement, warning, outlining the problem into solving steps, provide examples, and other measures that allow the student to learn independently.
The principle of the invention may be inspired by pemcahan informal procedures, while the re-discovery process using the concept matematisasi. There are two types of matematisasi diformlasikan by Treffers (1991), namely the horizontal and vertical matematisasi. Examples of horizontal matematisasi is identification, formulation, and penvisualisasian problems in different ways and pentransformasian real world problems into the world of mathematics. Matematisasi example is the representation of vertical relationships in the formula, repair and completion of the mathematical model, the use of different models and generalizing. Both types are balanced attention, since both these matematisasi have the same value. Based matematisasi horizontal and vertical, the approach in mathematics education can be divided into four types namely mechanistic, empiristik, strukturalistik, and realistic.
Adala mechanistic approach and the traditional approach based on what is known and the experience itself. Empiristik approach is an approach where mathematical concepts are not taught and students are expected to find themselves through horizontal matematisasi, strukturalistik approach is an approach that uses a formal system, for example, in the sum of the length of teaching need to be preceded by the value of the place, so that a concept is achieved through matematisasi vertically. Realistic approach is a realistic approach that uses problems as a starting base of learning. Through horizontal and vertilal matematisasi activity is expected students can discover mathematical concepts.
Philosophy of social constructivist view of mathematics is not absolute truth and identify mathematics as a result of solving the problem and a proposed issue by the man (Ernest, 1991). In learning mathematics, Cobb, Yackel and Wood (1992) call with socio constructivism. Students interact with teachers, and based on informal experiences students develop strategies to respond to a given problem. Characteristics of socio konstrutivis approach is very suitable to the characteristics of RME. The concept of ZPD and Scraffolding socio constructivist approach, in the so-called realistic mathematics learning with guided rediscovery. According Graevenmeijer (1994), although both these approaches have in common, but both approaches are developed separately. The differences are both socio-constructivist approach to learning is an approach of a general nature, while learning mathematics is a particular approach that is realistic only in learning mathematics.
2.3 Implementation of Realistic Mathematics learning
To give an idea about the implementation of realistic mathematics learning, for example, given the example of teaching fractions in elementary school (SD). Before introducing fractions to students learning fractions should be preceded by the numbers the same division as the division of the cake, so that students understand the division in the form of a simple and happens in everyday life. So that students truly understand the students understand the division after division into equal parts, newly introduced term fractions. This learning is very different to learning instead of realistic mathematics where students are fed by the term since the early fractions and some fractions.
Learning math begins with realistic real-world, in order to facilitate students in learning mathematics, and students with the help of teachers are given the opportunity to discover their own mathematical concepts. After that, applied in everyday problems or in other fields.
2.4 Relationship Between the Definition of Realistic Mathematics Education
If we look at the teachers in the teaching of mathematics always came out the word “how, what do you understand?” Students hurried to answer to understand. Students often complain, as follows, “sir … when I understood the explanation in class father, but when I got home I forgot,” or “sir … when I see an example in class that you gave, but I can not finish practice questions ”.
What is experienced by students in the illustration above shows that students do not understand or do not have any conceptual knowledge. Students who understand the concept can rediscover their forgotten concept.
Mitzell (1982) said that, the results of student learning is directly influenced by the experience of students and internal factors. The learning experience of students affected by the performance of teachers. When students in meaningful learning or place a link between new information with the network representation, then the students will gain an understanding. Develop an understanding of the purpose of teaching mathematics. Because without understanding one can not apply the procedures, concepts, or processes. In other words, mathematics understandable that mental representation is part of a network representation (Hieber and carpenter, 1992). Mathematics is not only understandable but should really understand the issues at hand. Generally, since the children of people have been familiar with mathematical ideas. Through experience in their everyday lives to develop ideas more complex, for example about numbers, patterns, shapes, data, size, and so on. Children before school learn mathematical ideas naturally. This suggests that students come to school with your head is not “empty” ready to be filled with anything. Learning in school will be more meaningful if teachers relate to what is already known to the child. Student understanding of mathematical ideas can be built through the school, if they are actively linked with their knowledge. Hanna and yackel (NCTM, 2000) says that learning with understanding can be enhanced through classroom interaction and social interaction can be used to introduce linkages between ideas and organize knowledge back. In learning to be teachers interact with students, for students more easily understand what has been taught, of course, in learning must be linked to real life to facilitate students in learning.
Realistic mathematics learning provides the opportunity for students to discover and understand mathematical concepts based on realistic problems given by the teacher. Realistic situation in the problem allows students to use the informal ways to resolve the problem. Informal ways students who are student production plays an important role in the rediscovery and understand concepts. This means that the information provided to students has been associated with child scheme. Through class interaction linkage scheme children will become stronger. Thus, realistic mathematical learning will have a very high contribution to the understanding of students.
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