Realistic Mathematics

By : Siti Nurchoiriyah (09301244051)

Intoduction

Talking about realistic mathematics, then it will not take a mathematician to figure and education experts Prof. Hans Freudenthal. Hans Freudenthal is a German citizen who was born in 1905 in Luckenwalde. In 1930, he moved to Amsterdam, Netherlands, and in 1946 became professor at the Universiteit Utrecht. In 1971, Freudenthal Instituut establish Ontwikkeling Wiskunde Onderwijs (IOWO) or the Institute for Development of Mathematics Education, which is now better known by the name of the Freudenthal Institute. Freudenthal Institute is part of the Faculty of Mathematics and Computer Science at Utrect University, which is where the implementation of educational research on mathematics and how mathematics should be taught. Freudenthal died at the age of 85 years, exactly on October 13, 1990.

Freudenthal said that mathematics is "human activity" and of this idea was developed Realistic mathematics. Realistic mathematics brings together views on what mathematics, how students learn mathematics and how mathematics should be taught. In mathematics education, according to Freudenthal students is not just a passive recipient of the mathematical material fast food, but students need to be given the opportunity to reinvent (find) Pratik mathematics through their own experience. Realistic mathematics is a major pinsip students must participate actively in the learning process. Students should be given the opportunity to construct their own knowledge and understanding.  The subject matter needs to be real for students. This is the reason why it is called Realistic Mathematics Education. Of course not mean that mathematics should always be realistic to use real-life problems. Abstract mathematical problems can be made real in the mine (thoughts) students.

Contents

As we have seen, emphasizes the Realistic Mathematics construction of the context of concrete objects as a starting point for students to acquire mathematical concepts. Concrete objects and environmental objects some can be used as a context for learning mathematics in building mathematical connections through social interaction. Concrete objects manipulated by students within the framework of efforts to support students in the process of concrete to matematisasi abstract.Students should be given opportunities to construct and produce mathematics in a manner and language of their own. Require the reflection of social activity that can occur integration and strengthening the relationship between subject in understanding the structure of mathematics.

According to Hans Freudental in Sugiman (2007) mathematics is an activity human (human activities) and should be linked to reality. Thus when students do activities to learn mathematics is in itself a process of matematisasi. Matematisasi There are two kinds, namely: (1) matematisasi horizontal and (2) vertical matematisasi. Horizontal Matematisasi proceeds from the real world into the mathematical symbols. The process occurs in the student when he was confronted with the the problems of life / real situations. While the vertical matematisasi processes that occur in the mathematical system itself, for example: the discovery of the strategy menyelesaiakn matter, attributed relationships between mathematical concepts or applying the formula / formulas findings.

Learning mathematics in Indonesia, is generally performed with the sequence (1) the presentation of the definition / formula, (2) giving examples / sample questions, and (3)provision of training. Exercise in the form of word problems sometimes associated with the use of the definition / formula in everyday life. Thus, the tradition of learning in Indonesia is still likely to place the provision of real problems at the end of learning. This contrasts with the realistic mathematics that puts a real problem in the provision of early learning.

Realistic mathematics problem begins with the filing of the rich (rich problem), the problem can be solved in different ways.

Characteristics of the problem is rich.
1. The solution leads to the mathematical activity.
2. The solution can be done with various approaches.
3. Usually taken from everyday life problems.
4. Is essentially open-ended problems.
5. Usually involves many other disciplines.

At realistic mathematics, more emphasis on mathematics education activities, ie activities matematisasi. Matematisasi consists of two types matematisasi vertical and horizontal matematisasi. Matematisasi horizontal is the mathematics so that students can use to organize and solve problems in real situations. Matematisasi vertical is the reorganization process by using the mathematics itself. Matematisasi horizontal moves from the real world into the world of symbols, or transforming the real problem into a mathematical model, while the world moves in a vertical matematisasi symbol itself or in the process of mathematics itself.

Based on these two types matematisasi, made four classification approaches in mathematics education, namely mechanistic, empiristik, strukturalistik, and realistic. Matematisasi mechanistic approach does not use horizontal and vertical matematisasi. Matematisasi empiristik approach uses only horizontal. Matematisasi Stukturalistik approach uses only vertical. Matematisasi realistic approach uses horizontal and vertical matematisasi in teaching and learning.

Characteristics of realistic mathematics is to use the context of the "real world", models, production and construction students, interactive and linkage. Realistic mathematical learning begins with real problems, so that students can use prior experience directly. By teaching students to develop realistic mathematical concept that is more complete. Then the students can also apply math concepts to new areas and the real world.

In a study of realistic mathematics there are three key principles that can be used as a basis in designing learning.

1.      Reinvention and Progressive Mathematization ('guided discovery' and the process of growing matematisasi). According Gravemijer (1994: 90), based on the principle of reinvention, students are given the opportunity to experience a process similar to the current process of mathematics is found. History of mathematics can be used as a source of inspiration in designing the course material. Besides the principle of reinvention can be developed based on informal resolution procedures. In this informal strategy can be understood in order to anticipate the completion of formal procedures. For this purpose it is necessary to find the contextual issues that can provide a variety of procedures and indicate the completion of the learning routes that depart from the real level mathematics to study the level of formal mathematics (progressive mathematizing).

2.      Didactical phenomenology (which contains the charge didactic phenomenon). Gravemeijer (1994: 90) states, based on this principle of mathematical presentation of the topics contained in realistic mathematics learning is presented on two considerations: (i) led to various applications, which 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 to be answered is: how do we identify phenomena or symptoms relevant to the concepts and mathematical ideas that students will learn, how we should know the symptoms mengkonkritkan phenomenon, what didactic actions necessary to help students gain knowledge as efficiently as possible.

3.      Self-developed models (Establishment of a model by the students themselves), Gravemeijer (1994: 91) explains, is currently working on the principle of contextual problems students are given the opportunity to develop their own model that serves to bridge the gap between informal and formal mathematical knowledge. In the early stages of developing a model that students become familiar. Furthermore, through generalization and finally pemformalan model into something that actually exists (entity) owned by students. With a 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. Eventually will become knowledgeable in formal mathematics.

Learning characteristics of realistic mathematics approach are:
1. Using a real problem as a starting point to learn.
2. Using the model as a bridge between the real and the abstract.
3. Using the contribution of students in the learning process.
4. Learning takes place in a democratic and interactive.
5. Learning is integrated with other topics.

Conclution

Realistic Mathematics emphasizes the construction of the context of concrete objects as a starting point for students to acquire mathematical concepts. Concrete objects and environmental objects some can be used as a context for learning mathematics in building
mathematical connections through social interaction. Concrete objects manipulated by students within the framework of efforts to support students in the process of concrete to matematisasi abstract. Students should be given opportunities to construct and produce mathematics in a manner and language of their own. Require the reflection of social activity that can occur integration and strengthening of relations antarpokok discussion in understanding the structure of mathematics.

Learning characteristics of realistic mathematics approach are:
A. Using a real problem as a starting point to learn.
2. Using the model as a bridge between the real and the abstract.
3. Using the contribution of students in the learning process.
4. Learning takes place in a democratic and interactive.
5. Learning is integrated with other topics.

Traditional Teaching Vs Innovative Teaching

By: Siti Nurchoiriyah (09301244051)

Introduction
To teach students according to their way of learning styles so that goals can be achieved with optimal learning there are different models of learning. In practice, the teacher must remember that there is no learning model most appropriate for all situations and conditions. Therefore, in selecting appropriate learning models must consider the condition of the student, the material properties of materials, available-media facilities, and conditions of teachers themselves. So in learning activities digunakanpun method is not enough with just one method alone, but must be more innovative and interesting.

Contents

Without us knowing it was education in our country is still very traditional, the mark by using a single method that is expository with delivery method, positioning the teacher as the main actors and students are positioned as passive learners. Assuming the material to packing as much as possible to the students, then the traditional learning, teachers are forced to perform various control activities so that students cooperate and pay attention to the teacher. Control is done through a variety of ways even if necessary when the teacher asked a question though. This is because not understood as a paradigm of educational needs of students and the absence of the scheme for it. In addition, teachers also have not been able to develop a learning scheme to serve a wide range of academic needs of students.
Teachers in learning activities demonstrate how students' work and working on math problems individually to produce what has been shown to the student teacher. Activities of daily student learning consists of watching his teacher solve the problems on the board and ask students to work alone in a textbook or worksheet students have been provided. Based on what we know in schools, it seemed expressions of dissatisfaction from traditional teaching methods such as this.
To that needed to be taught how to change from traditional to modern or constructivist. This method would also demanding teachers to be more creative in providing instruction. Effective teachers are teachers who menstimlasi siwa learn math, so teachers do not make the student as a spectator or listener only, but students must participate actively in learning. Education findings from cognitive psychology and mathematical education show that optimal learning occurs when students actively assimilate new information and new experiences and construct their own meaning.
To understand what they learn, students must act with their own work through the math curriculum, testing, state, transform, resolve, implement, demonstrate and communicate. This generally occurs when students belaja in groups, engage in discussions, making presentations, and responsible with what they learned themselves.

Conclusion

To improve the quality of education, changes in the traditional way of teaching from a constructivist or a modern must begin immediately. This change would also demanding teachers to be more creative in providing instruction. Effective teachers are teachers who menstimlasi siwa learn math, so teachers do not make the student as a spectator or listener only, but students must participate actively in learning. Education findings from cognitive psychology and mathematical education show that optimal learning occurs when students actively assimilate new information and new experiences and construct their own meaning.