This research is about how to develop a professional development program for preparing teachers in implementing realistic mathematics education (RME) in junior secondary mathematics. This research is expected to give a contribution for the improvement of mathematics education in Indonesia.

For a long period Indonesia is experiencing many problems in mathematics education as reflected by

1. low students’ achievement in Ebtanas (National Leaving Examination) from year to year (see: Akhmad, 1998);
2. the failure of our students in International Mathematics Olympiad or IMO (see: Supriyoko, 1997); and
3. slow improvement of Indonesia people in mastering sciences and technology as compared to our South East Asian neighbours (see: "Pengajaran Matematika Seharusnya Mengarah ke Logika", 1999).

RME appears to be a promising approach in the teaching and learning of mathematics. Much literature mentions the potential of this approach in increasing student’s understanding in mathematics (see e.g. Streefland, 1991; Gravemeijer, 1994, 1997; and Romberg & De Lange, 1998). The Netherlands is a pioneer on it through the work of Freudenthal Institute and others. Later on, in the United States some schools started using the approach as a result of collaboration between Freudenthal Institute and University of Wisconsin in a project called Mathematics in Context (MiC). The data indicate that this international collaboration has been a worthwhile enterprise, in that ‘the wisdom of practice’ from many years in the Netherlands has been used as starting points for curriculum development in the United States (see, e.g., Clarke, 1993; Clarke, Clarke & Sullivan, 1996; De Lange, 1994). The MiC project has resulted in curriculum materials for Grades 5 – 9. After students in several school districts from different states used the materials, a preliminary research showed that the students’ achievement on the national test highly increased (Romberg & De Lange, 1998). Furthermore, in the country where RME originally has been developed, the Netherlands, there are also positive results that can be used as indicators for the success of RME in the reform of mathematics education. The results of the Third International Mathematics and Science Study (TIMSS) show that students in the Netherlands gained high achievements in mathematics education (Mullis, Martin, Beaton, Gonzalez, Kelly & Smith, 1997).

Another international collaboration of Freudenthal Institute is with the University of the Western Cape in South Africa in a project called Remesa (Realistic Mathematics Education in South Africa). The Remesa project is aimed at developing and researching the impact of innovative mathematics learning and teaching materials based on the premise that "reality is the basis of and the domain of application of mathematics. The materials developed by Remesa are intended to form a useful resource from which teachers, textbook authors and others can develop school mathematics learning program relevant to South African situation (see: www.fi.uu.nl/remesa). Beside the USA and South Africa, RME also has been adopted in some others countries, such as Portugal, England, Germany, Spain, Brazil, Denmark, Japan and Malaysia (De Lange, 1996).

Much more important than the previous argument, namely that RME proved to be useful in other countries, is the concept of RME itself. In the concept of Freudenthal, mathematics is a human activity and should be connected to reality. RME is characterised by:

• students should be given opportunity to reinvent mathematics under the guidance of an adult (Gravemeijer, 1994); and
• the reinvention of mathematics ideas and concepts should start from exposure to a variety of "real-world" problems and situation (De Lange, 1995).

Those ideas, namely guided reinvention and starting from exposure to variety of "real-world" has their root in the concept of Freudenthal that mathematics as human activities and should be connected to reality as mentioned earlier on. In this point of view, process of learning is important. The learning route along which the student could be able to find the result by him/herself should be mapped out (Gravemeijer, 1997). The consequence of those principles is that teachers should develop highly interactive instruction and give students opportunities to actively contribute to their own learning process. Van Hiele (in De Lange, 1996) divides the process of learning that proceed through three levels:

1. a pupil reaches the first level of thinking as soon as he can manipulate the known characteristics of a pattern that is familiar to him;
2. as soon as he learns to manipulate the interrelatedness of the characteristics he will have reached the second level; and
3. he will reach the third level of thinking when he starts manipulating the intrinsic characteristics of relations.

Van Hiele’s level of process of learning has triggered discussion and research that result in a realistic mathematics movement in the Netherlands. This movement has developed some theories of mathematics teaching and learning like Freudenthal’s ‘didactical phenomenology’ (1983), ‘progressive mathematizing’ of Treffers (1987), ‘conceptual mathematization’ of De Lange (1987) and Gravemeijer’s ‘horizontal and vertical mathematizing’ (1994). It is relevant to say that the theory of RME is in line with the current thinking of learning, such as constructivism and students centred learning. But where a constructivist approach represents a general theory of learning, RME is a theory of learning and instruction that evolved only for mathematics. Cobb (1994) stated that constructivism and RME are compatible because to a large extent they have a similar characterisation of mathematics and mathematics learning. Both constructivism and RME contend that mathematics is a creative human activity, and that mathematics learning occurs as students develop effective ways to solve problems (De Lange, 1996; Streefland, 1991; Treffers, 1987).

The trend described here is in accordance with the needs for improvement of mathematics education in Indonesia, that are dominated by issues of how to increase students’ understanding of mathematics and develop students’ reasoning ("Matematika yang Menumbuhkan Daya Pikir", 1997). For instance, one of the reason of the revision of National Curriculum of 1994 by Indonesian government is because of criticism among educational professionals and within the society at large about the irrelevance and meaningless of the subject-matter content:

Santoso Muwarni, a professor of mathematics education at Jakarta State University, says that the objective of mathematics teaching and learning is not to make pupils becoming a mathematics expert, but to develop their reasoning and logic ("Pengajaran Matematika Rumit", 1999). Nasution (1996) argues that mathematics should be mastered as a systematic pattern of reasoning. However, RME not only give an emphasis to the development of pupils’ reasoning and logic, but also to their (re)construction of mathematical ideas and concepts. The (re)construction of mathematical ideas and concepts goes hand in hand with the process of the development of student’s reasoning. This is performed through exposure of contextual problems within the framework of interactive teaching and learning process. Therefore, it is worthwhile to explore whether RME is a good approach to tackle the problems of mathematics education in Indonesia.

However, RME is so new for many people in Indonesia (teachers, teacher educators, curriculum developers, supervisors, and pupils) that experiments are needed to investigate whether and how it can be translated and realised for the Indonesian context. Using the notion of ‘think big start small’ in education innovation efforts, it is important that a number of small experiments be undertaken as a contribution to the curriculum reform in Indonesia. Those experiments are needed to address components necessary for a successful innovation on curriculum and teachers’ level. Given the willingness of those who are involved in mathematics education as well as of the government to innovate mathematics education (see e.g. "Diusulkan, Guru Matematika dan IPA di SD", 1996; "Matematika di SMU Perlu Direvisi", 1997; "Matematika yang Menumbuhkan Daya Pikir", 1997), we have reasons to expect a fruitful development if we know how to adapt RME to the Indonesian context and know what a proper implementation strategy is on school level. According to Fullan (1991) a complex innovation is characterised by three dimensions, namely changing of teachers’ beliefs, introducing new teaching and learning methods, and introducing of new curriculum materials. The innovation we are talking about here pertain to all three dimensions. So, for Indonesia we are talking about a complex innovation if we want to introduce RME.

There is strong evidence from research at University of Twente for the important role of exemplary curriculum materials in the implementation of educational innovations on teacher level (see e.g. Van den Akker, 1988, 1998). Because through exemplary curriculum materials the new beliefs can be explained and operationalised as well as they can serve as a vehicle in transferring new methods of teaching and learning. So, to introduce RME into Indonesia it is not sufficient to have only new curriculum materials. Because teachers being key actors in education they need to be well trained in order to understand the philosophy of RME as reflected by new curriculum materials and have appropriate competence to put this into practice. Based on this analysis, this research focuses on the development of INSET (inservice education and training for mathematics teachers) on the basis of RME exemplary curriculum materials for junior secondary mathematics with purpose to make teachers understand RME and preparing them for effective introduction of RME in their classroom practice. For this purpose it is necessary to have some valid, practical and effective exemplary curriculum materials. Exemplary curriculum materials are being developed in cooperation with other researchers. Parallel to this study other RME related projects are being conducted in Indonesia. One of them around internet-based support system for RME training for student teacher and secondary school teachers. The development of RME-based modules for Indonesian primary education has been starting within the framework of two other projects.

Within this analysis of problems related to the introduction of RME-based mathematics education the main research question can be formulated as follows:

When we are talking about RME it is not as simple as saying that mathematics as human activities and should be connected to real life situation. There are some principles that embedded on this belief and could be viewed as an abstraction of twenty years of RME movement in the Netherlands. Those principles has been elaborated into five tenets of RME (see section 3 for a bit elaboration), namely; (1) the use of contextual problems, (2) bridging by vertical instruments, (3) pupil contribution, (4) interactivity, and (5) intertwining (see e.g. De Lange, 1987; Gravemeijer, 1994, 1997; and Treffers, 1987). From those tenets we are aware of the consequences on mathematics teaching and learning if we want to introduce RME to Indonesian schools. Those consequences are change in teaching and learning (such as class interaction and lack of authorities), change in content, and change in assessment.

Within the analysis of those consequences, the professional development program should reflect the five tenets of RME in term of how their work in reality. In order words, how to translate those philosophies into the design and practice of professional development program. In accordance with the tenets of RME, the professional development program is intended also to address the changing of teaching and learning, of content as well as assessment.

In summary, for an effort to make teachers understand RME and preparing them for effective implementation of RME in their classroom practice, a professional development program needs to reflect:

1. Five tenets of RME.
2. Changing of teaching and learning.
3. Changing of content.
4. Changing of assessment.

Because, there are, basically three problem areas here, namely adaptation of RME for Indonesian context, making teachers understand and preparing them for effective introduction of RME in their lesson, the main research question can be operationalised into three sub-research questions:

1. How to adapt RME curriculum materials for the Indonesian context?
2. How to make teachers understand RME?
3. How to prepare teachers for effective introduction of RME in their mathematics classroom practice?