## Realistic Mathematics Learning (RME)

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**Realistic** **Mathematics** **Learning** (**RME**)

** 1**.**1 Abstrack****Mathematics** 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?

**CHAPTER II**

**DISCUSSION**

**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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