In 1973 Indonesia government implemented modern mathematics to replace arithmetic as subject matter in primary schools. The implementation of modern mathematics in primary schools has been a problematic since its beginning. For many teachers, modern mathematics was a difficult subject. The difficulty implied to the practice on mathematics teaching and learning in which teachers were relying on the mathematics textbooks. They conducted instruction by following the textbook page by page, without considering the correctness the mathematics written in the book (Somerset, 1997).
The teaching and learning of mathematics in Indonesia schools tends to be very mechanistic, namely mathematics teachers tend to narrate mathematics formulas and procedures to their pupils. For a long time this teacher-centered approach has influenced pupils’ attitude to be passive learners. They are used to be spoon-fed by the teachers. They are not used to thinking in critical way for self-learning. The impact of the situation may be seen on the achievement in national examinations and in international comparative studies. In national examination from 1990 to 1997, junior secondary school pupils’ average score in mathematics is always below 5 out of 10 scale, making it consistently the lowest scoring of all the subjects taught in school (Manan, 1998). In international comparative studies like TIMSS and PISA, Indonesian pupils perform below most other participating countries.
A transition from a more traditional, skill-oriented approach towards a problem-based, reform mathematics approach constitutes a complex innovation, because it does not only involve the introduction of new instructional sequences and new instructional activities, but also asks for new roles for the teacher and new social and sociomathematical norms. Teachers will have to foster a problem-solving classroom culture, they will have to bring students to changing their current more passive receptive role into one of more active participation, in which they take initiative and responsibility, and learn to think and reason for themselves. In addition, teachers will have to learn to guide the new learning process by choosing or designing those instructional tasks that may generate productive mathematical thinking at any given moment in time, and to organize and orchestrate whole-class discussions that help students in making mathematical process. The role of the teachers as a consequence will change from authoritarian, instructional oriented, and teacher centered, toward more supportive, more student centered, more learning condition oriented.
Consequently, key component of successful mathematics education reform will consist of in-service and pre-service teacher education, co-teaching in classrooms, and the production of supportive textbooks and teacher manuals.. Another, equally important element concerns the requirement to make sure that the intended innovation fits the Indonesian context. In this respect, an important prerequisite for success will be a sense of ownership of the teachers and teacher educators who are involved. Thus a bottom-up approach is called for, in which the Indonesian teachers and teacher educators ‘re’-invent a form of realistic mathematics education that fits the Indonesian situation and priorities. The theory of RME is useful in several countries, such as in the Netherlands and the US. However, much more important than this evident is that the concept of RME itself is in line with the current thinking in Indonesia about mathematics learning which emphasize on pupil-active learning, problem solving and application of mathematics. It is a common phenomenon currently in Indonesia that the objective of teaching and learning mathematics is to develop pupils’ reasoning and logical ability. If we carefully listen to the messages from mathematics teachers in Indonesia, then one of their concerns is how to make mathematics lesson relevant for pupils in dealing with the daily life problems. It is also argue that mathematics should be mastered as a systematic pattern of reasoning (Nasution, 1996). The (re)construction of mathematics ideas and concepts goes hand in hand with with the process of the development of pupil’s reasoning ability. This can be achieved in RME through pupils’ exposure to contextual problems within the framework of an interactive teaching and learning
process.
Examples From Practice
Primary school teachers from several cities in Indonesia use RME in their mathematics lesson. In the following two examples are given. The teaching and learning of fractions
“Students, tomorrow we will have lunch together with bread. You will be devided into groups and each of groups bring your own bread, bread-knife, and jam. Wow, they imagine that how cheerful it will be. “I don’t like jam, Mom, may I bring such butter or sugar? “Alright, You can bring cheese even everything what you like”. It is a situation rarely found in mathematics teaching session. With RME mathematics is so real and exciting. At a glance they seem to gladly play but actually they are learning mathematics since first time. It is not only easy to digest mathematics concept but also it will be strengthen their concept because of their own experiences. Learning using RME is exciting but it isn’t without risks. What are the risks?? They are two important things in learning using RME, realistic and re-invention. We can imagine if in every topic or sub topic we have to find activity that is able to bring student to the relevant material, how it will be spend time so much? Furthermore, it exclude time we need to have them build their conception until re-invention.
Obtaining the difficulties, it seems to be hard to realize RME. Nevertheless, it can believed there is problem without solution. What is that? The appropriate solution is intertwining. What is that and what about the application? Reality in life shows that a problem is actually a link of things linked each other. It is called intertwine. Link among units will make the all aspects of mathematics learning effective because a teacher doesn’t have to explain the material page to page .
The teaching and learning of mathematics in Indonesia schools tends to be very mechanistic, namely mathematics teachers tend to narrate mathematics formulas and procedures to their pupils. For a long time this teacher-centered approach has influenced pupils’ attitude to be passive learners. They are used to be spoon-fed by the teachers. They are not used to thinking in critical way for self-learning. The impact of the situation may be seen on the achievement in national examinations and in international comparative studies. In national examination from 1990 to 1997, junior secondary school pupils’ average score in mathematics is always below 5 out of 10 scale, making it consistently the lowest scoring of all the subjects taught in school (Manan, 1998). In international comparative studies like TIMSS and PISA, Indonesian pupils perform below most other participating countries.
A transition from a more traditional, skill-oriented approach towards a problem-based, reform mathematics approach constitutes a complex innovation, because it does not only involve the introduction of new instructional sequences and new instructional activities, but also asks for new roles for the teacher and new social and sociomathematical norms. Teachers will have to foster a problem-solving classroom culture, they will have to bring students to changing their current more passive receptive role into one of more active participation, in which they take initiative and responsibility, and learn to think and reason for themselves. In addition, teachers will have to learn to guide the new learning process by choosing or designing those instructional tasks that may generate productive mathematical thinking at any given moment in time, and to organize and orchestrate whole-class discussions that help students in making mathematical process. The role of the teachers as a consequence will change from authoritarian, instructional oriented, and teacher centered, toward more supportive, more student centered, more learning condition oriented.
Consequently, key component of successful mathematics education reform will consist of in-service and pre-service teacher education, co-teaching in classrooms, and the production of supportive textbooks and teacher manuals.. Another, equally important element concerns the requirement to make sure that the intended innovation fits the Indonesian context. In this respect, an important prerequisite for success will be a sense of ownership of the teachers and teacher educators who are involved. Thus a bottom-up approach is called for, in which the Indonesian teachers and teacher educators ‘re’-invent a form of realistic mathematics education that fits the Indonesian situation and priorities. The theory of RME is useful in several countries, such as in the Netherlands and the US. However, much more important than this evident is that the concept of RME itself is in line with the current thinking in Indonesia about mathematics learning which emphasize on pupil-active learning, problem solving and application of mathematics. It is a common phenomenon currently in Indonesia that the objective of teaching and learning mathematics is to develop pupils’ reasoning and logical ability. If we carefully listen to the messages from mathematics teachers in Indonesia, then one of their concerns is how to make mathematics lesson relevant for pupils in dealing with the daily life problems. It is also argue that mathematics should be mastered as a systematic pattern of reasoning (Nasution, 1996). The (re)construction of mathematics ideas and concepts goes hand in hand with with the process of the development of pupil’s reasoning ability. This can be achieved in RME through pupils’ exposure to contextual problems within the framework of an interactive teaching and learning
process.
Examples From Practice
Primary school teachers from several cities in Indonesia use RME in their mathematics lesson. In the following two examples are given. The teaching and learning of fractions
“Students, tomorrow we will have lunch together with bread. You will be devided into groups and each of groups bring your own bread, bread-knife, and jam. Wow, they imagine that how cheerful it will be. “I don’t like jam, Mom, may I bring such butter or sugar? “Alright, You can bring cheese even everything what you like”. It is a situation rarely found in mathematics teaching session. With RME mathematics is so real and exciting. At a glance they seem to gladly play but actually they are learning mathematics since first time. It is not only easy to digest mathematics concept but also it will be strengthen their concept because of their own experiences. Learning using RME is exciting but it isn’t without risks. What are the risks?? They are two important things in learning using RME, realistic and re-invention. We can imagine if in every topic or sub topic we have to find activity that is able to bring student to the relevant material, how it will be spend time so much? Furthermore, it exclude time we need to have them build their conception until re-invention.
Obtaining the difficulties, it seems to be hard to realize RME. Nevertheless, it can believed there is problem without solution. What is that? The appropriate solution is intertwining. What is that and what about the application? Reality in life shows that a problem is actually a link of things linked each other. It is called intertwine. Link among units will make the all aspects of mathematics learning effective because a teacher doesn’t have to explain the material page to page .
The following example is one of in intertwine implementation in fraction
By simple activities teacher gives stimulant and direction to the students. They are able to re-invent and learn several fraction materials in intertwine all at once as follows:
- Fraction as division (in activity-1)
- Fraction as part of a whole. (in activity -1&2)
- Comparing fractions with the same denominator(in activity-2)
- Putting fraction with the same denominator in the right order. (in activity-2)
- equivalent fraction and simplifying fraction (in activity-3)
They have sliced bread and spread it with jam and the end of the activity they have
eaten it together. Unconsciously,they have learnt mathematics joyfully.
eaten it together. Unconsciously,they have learnt mathematics joyfully.
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