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A M odel of a M athematics Research Community in the

Context of Indonesian Higher Education

Didi SURYADI

School of Postgraduate Studies, Universitas Pendidikan Indonesia (UPI), Bandung, 40154, Indonesia

Rizky ROSJANUARDI

Department of Mathematics Education, Universitas Pendidikan Indonesia (UPI), Bandung, 40154, Indonesia

Takashi ITOH

Department of Mathematics, Faculty of Education Gunma University, Maebashi, Gunma, 371-8510, Japan

(Accepted on September 24th, 2010)

Abstract

Communities are essential vehicles in the academic world, including those related to research activities. Through communities,ideas from its members can be developed into long-term research so that original ideas are born to enrich the treasury of knowledge. The model of a mathematics research community that is discussed in this article emerges from the demand to increase the production of well-qualified research both among the students through their final assignments and the lecturers. The model offers cooperative research activities among students and lecturers, whether within or across universities. Through this model, it is expected that production as well as quality of the research outcomes could be increased.

Introduction

The research productivity of a discipline,including mathematics,can be observed from its outcomes. The number of research articles written by Indonesian mathematicians and acknowledged internationally are still low. From the first Indonesian doctorate in mathematics in 1919 up to 2006, only 163 papers have been written by Indonesian mathematicians, as observed in the Mathematical Review (Gunawan, 2007). Mathematical Review is an online database organized by the American Mathematical Society. This database contains evaluation results and synopses of mathematics articles, statistics, and theoretical computer science. By contrast, Malaysian and Singaporean scholars have published 701 and 4,741 papers, respectively.

The low mathematics research productivity in Indonesiais an indicator that the development of

pascasarjana@upi.edu rizky@upi.edu

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mathematics in Indonesiais still limited to the use of existing mathematics laws and products and has not ye moved into the field of exploring innovative concepts. Therefore, it can be concluded that the Indonesian mathematics community has not yet acquired a sufficient research culture of innovation.

As a result,an atmosphere that supports the development of research activities and of innovative concepts is necessary. At the university level,this atmosphere can be created through a research community(hereafter, RC), which consists of both students and lecturers. Through this community,lecturers research capabilities will be sharpened and will thus encourage students to enter and enjoy the research world. A review of literature reveal that innovative research requires the abilities to think creatively and critically(Suryadi,2005). Therefore,this project would construct an activity model that uses the abilities of creative and critical thinking within a research community. A combination of these thinking abilities as well as an active research culture is expected to increase the productivity of research in general.

A. M athematics Research : Why Is Community Necessary?

The development of creative and critical thinking abilities is very important in mathematics because these abilities support scholars to explore the existing information so that innovative information can be presented effectively. One of the strategies to develop both types of thinking skills can be accomplished through active involvement in a research community. The importance of a research community as a learning vehicle is based on several reasons: First, several lecturers are not yet skilled in conducting research. Second, students may not have acquired full independence in their development of new knowledge. Third, the thinking processes of research community members will always be encouraged and developed so that they can explore information more productively and be supported to develop potential ideas.

The Development of ZPD in a Learning Community

The emerging process of new knowledge (especially in mathematics) is believed to result from a process introduced by Dubinsky as Action-Process-Object-Schema (APOS) . The object that has been stored in ones memory as knowledge will be processed when an action takes place due to a certain stimulus. This process is explained by Tall (1999) through the following diagram.

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APOS is a constructivist theory about the process of learning a mathematical concept. Essentially, the theory is based on the hypotheses of the essence of mathematical knowledge and on the ways it is developed. That theoretical perspective is explained by Dubinsky(2001, p.11) who stated that,

An individual mathematical knowledge is her or his tendency to respond to perceived mathematical problem situations by reflecting on problems and their solutions in a social context and by constructing mathematical actions, processes, and objects and organizing these in schemas to use in dealing with the situations.

The terms action,process,object,and scheme involve a mental construction made in order to comprehend a mathematical idea. When one attempts to comprehend a mathematical idea,the process will begin from a mental action of the mathematical idea and will eventually reach the scheme construction about a certain mathematical concept covered in the given problem.

Action is a transformation of mental objects in order to obtain another mental object. This is experienced by a person facing a problem and attempting to connect the aspects of the problem using prior knowledge. One attempts to focus on mental action to understand a given concept. Those with a deeper understanding about a concept may perform better or their focus may extend beyond the given concept so that the expected action does not occur.

When an action is repeated and reflection on that action occurs, it then enters the process phase. As opposed to action,which may involve exploring concrete materials,the process phase occurs internally under the control of the doer. Experiencing a process involves facing a problem, limiting ones thoughts to the mathematical idea being faced and reflecting on this idea. New processes can be constructed through a coordination and correlation of all involved processes.

If one reflects on an operation used in a certain process,one becomes conscious of the process as a totality, realizes that certain transformations could apply to the process,and makes the transformation. At this point, the individual has transformed the construction process into a cognitive object. In this case,the processes have become encapsulated as a cognitive object. One can be said to own an object conception of a mathematical concept when she or he has been able to treat the idea or concept as a cognitive object; this includes the ability to perform an action on the object and provide reasons or explanations about its characteristics. Furthermore, the individual will also be able to de-encapsulate the object to its original characteristics. A scheme of a certain mathematical idea includes a collection of actions,process,object,and another inter-related scheme so that it constructs an interconnected framework in ones mind.

If the process of schema construction is approved as in the previous explanation, the next step is performing mathematical-thinking so that a more optimum result can be achieved. One of the foundations that can be used to achieve this result is Vygotskys Zone of Proximal Development(ZPD)theory. A person s cognitive-skill development is divided into two stages, namely, the actual and the potential development stages. Actual development is derived from self-effort when solving a problem. Potential development is derived from an interaction with another who has greater ability. The distance between the two developments is called ZPD. According to Suryadi(2005),the process to reach actual development can be facilitated by the creation of a cognitive conflict. Through the implementation of an indirect learning approach, a series of

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actual and potential development steps can be encouraged ; this is called the ZPD development model. This model, developed by Suryadi (2005), is explained through the following diagram.

The development process of ZPD can begin with the creation of a cognitive conflict generated through the presentation of a problem or the exploration of concept-deepening in a community. Through discussions, which occur in that community, the process to reach actual and potential stages for every member can take place. This process is consistent with the Theory of Knowledge Creation, as explained by Nonaka (2005). He describes this model as an interaction between two types of knowledge tacit knowledge and explicit knowledge. Tacit knowledge is subjective and experiential knowledge that cannot be expressed in the form of words, sentences, numbers, or by a definitive formula. Therefore, tacit knowledge is very relative and is strongly related to the context known to the owner or to his or her prior knowledge. Meanwhile, explicit knowledge is objective and rational knowledge that can be expressed in the form of words,sentences,numbers, or by a definitive formula so that it can be stated as knowledge that is free of context. In ones knowledge development process, both types of development are strongly related to each other. For example, ones knowledge that is derived from an observation (tacit knowledge) is influenced by his or her prior knowledge (explicit knowledge). When a child is shown a certain geometrical shape, such as a rectangular area that is made from a carton,the child will describe the geometrical shape on the basis of her or his prior knowledge. Therefore, definitive knowledge can be a reference framework to construct new knowledge; meanwhile, new knowledge that is not yet definitive can be a foundation for the creation of new definitive knowledge.

Tacit knowledge, based on the result of ones observations or experiences, can grow into explicit knowledge through an individuals interactions. If several individuals are involved in a discussion,different tacit knowledge, according to the reference framework of each individual, will exist. The exchange of tacit knowledge in a discussion will force the construction of productive new knowledge, especially, if the individuals involved in that discussion have different knowledge backgrounds.

Lesson Learned from Japanese M athematical Research Community

In the process of creating a new model,it is useful for a Mathematical Research Community to first refer to Japanese history and understand the circumstances in which mathematical research was conducted. During the Edo era, Japan denied entry to outsiders for almost 260 years, up to the 1860s. During this period, the Japanese created an original culture in mathematics called WASAN. WA means Japanand SAN means Mathematics. As the Edo era ended, the new government of Japandecided to teach European mathematics, instead of WASAN, to the Japanese.

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The Japanese government attempted to disseminate new mathematics to the Japanese schools and sent young people to Europe (especially, Germanyand France) to study the modern mathematics. They believed that WASAN was narrow in scope compared to European mathematics; however, in some areas WASAN excelled. After returning to Japan,young Japanese mathematicians studied only modern mathematics. The level of Japanese mathematics increased greatly soon after permitting entry of foreigners to the country.

The most famous mathematician in that era Teiji Takagi, who was born in 1875, wrote a distinguished paper on number theory. In addition to writing his papers,Takagi was also famous for publishing books in mathematics written in the Japanese language, some of which include Analysis, Algebra, and Number theory . Despite these books being published more then 70 years ago, they are still read by students, researchers, and present-day mathematicians.

Japanese culture has the tendency to translate foreign books into the Japanese language and to modify them to fit Japanese culture. If one visits the library at a Japanese university, one will notice that a large number of mathematical books with subjects ranging from fundamental to very advanced levels are written in Japanese. Articles written in the mother tongue are very important even in mathematics. Japanese undergraduate students study mathematics in Japanese from the beginning. Graduate students, as well, sometimes refer to Japanese mathematics books since it is more effective for them to understand a new theory in their mother tongue. It is also helpful for researchers.

B. The M odel of a M athematics Research Community

This section will explain the components of the Mathematical Research Community and its activities, including Expert Group (EG), Interest Group (IG), and Research Milieu (RM).

Expert Group (EG)

The Expert Group (EG) will naturally be formed by subject areas such as Analysis, Algebra, Statistics, Geometry, and Computation. However, the work of the EG may actually consist of material development, material enrichment, contemporary material discussion, or science development through research. This depends on the academic culture developed in each EG.

The members of an EG naturally relate to each other because they have similar skills and knowledge. Therefore, if a problem related to a specific skill occurs, a discussion between the EG members will automatically take place because the existing problem will more likely be solved if it is handled by lecturers with the same expertise. This natural relationship is a potential foundation for developing cooperation when facing academic problems related to a particular EG subject. If the cooperation is increased to become a more functional relationship in terms of self-improvement, academic career development, and self-existence development, the EG will grow as an innovation agent in knowledge development. It has the potential to create a positive image academically for both the individual members and the institution.

In fact,a lecturer has a moral responsibility to work academically in teaching,research,and public service. Teaching is a basic aspect of academic work because through this activity, a lecturer has the opportunity to disseminate ideas to the students. Struggling to transform ideal thoughts into reality is the daily activity within the life of academicians.

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In conducting research related to the subjects of concern,it will be ideal to work within the context of an EG. It is possible that from this research, new problems would emerge that might require further research activity. If the lecturers pursue this activity, their comprehension, knowledge, and confidence will improve each time. This is the essential meaning of an EG, as illustrated in the following figure.

This illustration shows that an EG consists of three layers,namely,the inside,middle,and outside layers. These three layers will be called Level-1,Level-2,and Level-3. Level-1 tends to focus on learning about an issue. Therefore,although a member working at this level conducts material research,the research might not be substantial; however,it is limited to a search for alternative materials to improve learning processes. The second level may involve not only learning research, but also research enrichment through alternative book studies,new books,higher level books(for example,those that are labeled GTM),or contemporary issues that are usually derived from relevant scientific journals. The third level is the most ideal EG ; it includes all the activities of the previous levels as well as knowledge development through research activities. An EG with this activity is considered to be ideal because the members can develop extensive knowledge and thus the group has the potential to encourage material exploration in class lectures.

To encourage more EG activities at the third level,a program that can facilitate EG members to improve the academic situation by gradually increasing the scope of activities is necessary. The most basic aspect to encourage this activity is the availability of contemporary research material that is periodically provided by the institution. If this research material is available,EG members will be able to conduct research and fulfill the demand to improve scholarship. This allows a lecturer to provide optimum academic service, especially during the process of assisting students in completing their final papers. The research that will be conducted by the students for their final assignment will likely be consistent with national and international knowledge development. Therefore, lecturers efforts in an EG will be able to guide students to conduct third level research. This means that an EG should have a research agenda so that students with similar interests can easily obtain relevant research ideas.

The availability of research material has ensured that lecturers will increase their EG activities up to the third level. Therefore, another program, which demands that an EG regularly conduct investigations, needs to be developed. Dissemination of research outcomes,such as seminar papers,journal articles,or perhaps new textbooks, will become tangible evidence of the existence of EG activities.

In the Universitas Pendidikan Indonesia (UPI, Indonesia University of Education) case, the support program to encourage this activity has been provided by the university in the form of research funds for novice researchers; these include Developmental Research Grant, Competitive Research Grant, and Doctoral and Non-Professor Research Grant. In addition, research funds from the Directorate General of Higher Education (DIKTI in Indonesia) are provided through many competitive grants and become a very positive

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element in encouraging EG activity. The universitys and DIKTI s support funds need to be used optimally by the EG to improve the academic culture and to increase its status in the national and international academic environment.

Once the activity of an EG begins, the next important step is to maintain the program and increase the productivity and quality of the research outcome. To bring about this effort, scientific forums on both the national and international scale should be established. Through the developed forums, it is possible to establish new tied-deals for the community members so that their motivation to conduct research will be renewed and that every EG member can individually fulfill the activity of the forum regularly. The scientific forums attended by the EG members will certainly the research productivity and quality of the EG. This is due to the comments, input, and critical reviews of research outcomes of forum participants. This could be followed up during the next research study so that the quality of the masterpiece can be developed and improved in time. The explanation for this process can be illustrated in the following figure of EG activities.

EG Activity

This section describes examples of EG activities,based on the experience of the Mathematics Department in UPI. The activities presented cover routine research activities such as those that deal with learning issues, curriculum implementation, inter-relationships between subjects, textbook content used in teaching, new textbook reviews, mathematical proofs, as well as basic ideas for research activities for both lecturers and students.

Discussions of Learning Issues

EG activity at the first level is a basic aspect of academic life at a university. One of the activities at this level is discussions related to learning issues. For lecturers, these learning issues may include difficulties or special aspects of the lecturing process related to students characteristics. For example,the achievements of first-year students in the subjects of Foundation of Mathematics and Calculus could be discussed as a measure of the lecturers performance and curriculum implementation. Or an investigation could be conducted comparing same year students who have good performance in some subjects but lower performance in others.

Discussion of Curriculum Implementation

The results of EG discussions may sometimes be raised to the level of department policy or decision. This kind of policy is easily accepted by several parties because it is a bottom up process. Several department policies that may be raised from EG discussion are the (1) determination and depth of subject matter, (2)

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determination of the types and evaluation process of a subject matter,(3)arrangement of subject matter groups, such as analysis,algebra,statistics,application,or computation,and (4)arrangement of the teaching schedule.

Discussion of Inter-Subject Relationships

By using a sequential course plan for offering mathematical concepts, comprehension will become complete. For example, Real Analysis could be a requirement for taking Functional Analysis because comprehension of the concepts in Functional Analysis depends on understanding the concepts of Real Analysis. In other words,one subject is a continuance of another subject; therefore,the connection from one subject to another should be made clear. In addition,the textbooks used by students and lecturers should be appropriate. For example,the textbook for Abstract Algebra is carefully chosen to connect with the concepts of Linear Algebra,Calculus,Real Analysis,Complex Analysis,etc. Sometimes a textbook does not explicitly state its connection with the other subjects; in this case,a discussion between lecturers could help to solve this problem. From this kind of a discussion, the connections among concepts in different subjects could be derived.

Interest Group (IG)

The IG allows students to gather in a group on the basis of their research interests,particularly related to the final paper that they are required to write. Based on previous experience, IGs in the Department of Mathematics Education in UPI focused on four research group areas: Analysis, Algebra, Statistics, and Computation. This is useful since the EGs in this institution also focused on the same four research areas. Students research interests may be based on several reasons, whether pragmatic or ideal, but a good quality final paper cannot be separated from the systematic and continuous efforts of their whole course of study.

Towards the end of their studies at a university, students will naturally gather in accordance with their interests in their chosen subject areas; however, this process is not enough to develop an IG as a research-orientated group. In fact,until the end of their studies,several students are worried about choosing the correct subjects rather than choosing research topics, therefore many students do not finish their studies punctually. Consequently, the academic situation outside the lecturing process should be set up so that students are involved in an RS from the very beginning of their studies. That RS could be developed in the form of local, national, or international forums, or the dissemination of students and lecturers research in journals, proceedings, or yearbooks.

If we look closer at the journey of students from their freshman year until they finish their studies at the undergraduate level, it can be divided into three phases, namely the orientation phase, basic phase, and development phase. In the orientation phase, students are generally still making many adjustments,whether how to learn,how to socialize,or how to live independently away from their parents and family. In this phase of academic life,students continue with orientation by choosing general courses that relate to the development of social knowledge and personality. After going through the orientation phase,students come into the basic phase by choosing several basic science subjects that provide a foundation for further knowledge development. The last phase of their study journey is the development phase, which usually leads to specialization ; here, students opt for several subjects in line with their interests. In this phase, students focus on conducting research to meet the requirements of their study.

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Essentially,the research situation can be introduced to students in the orientation phase and continue into the basic phase. In the former phase, they are introduced to the investigation of research outcomes through many formal and informal forums organized by EGs or IGs and the exhibition of written research and investigations. In this phase, the involvement of students in academic forums is still passive so we may call it passive research. As they enter half way into the basic phase, students may begin to actively enter the research forum. Active research means that students posses sufficient basic knowledge to explain mathematical ideas in an IG on the basis of their interest. At the same time,several students will also be in the basic and development phases. Students in the development phase are now expected to take initiative and conduct active research,while students in the other phases have just begun to conduct passive research. The situation can be illustrated in the following figure.

In the orientation and basic phases, the students have only conducted passive research,but this does not mean that they do not conduct active research as well. Active research is related to the course materials. Therefore, students activities can start by examining basic ideas derived from the course materials and be followed with advanced mathematical ideas that lead to the research activity of the final assignment. Therefore, the students IG activities are essentially the same activities as the lecturers EG, as shown in the following figure.

This illustration describes IG,which consists of three layers level-1(the inside),level-2(the middle),and level-3 (the outside). The focus of IG in level-1 is on the course material issues. For the second level, in addition to research on course materials, they also conduct research related to enrichment materials such as alternative source books, new textbooks, higher level books (such as those labeled GTM) or contemporary issues usually derived from relevant scientific journals.. The third level is the most ideal IG in which the members not only research course materials and enrichment materials,but also conduct research activities. An IG with this activity is considered to be ideal because the members are developing extensive knowledge so that

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when they enter the last phase of their studies, they will easily finish their final assignment.

To encourage the emerging activities of an IG at the third level,a program that systematically facilitates the IG members is necessary. The most useful way to encourage activity improvement is by using contemporary materials that are periodically provided by the department. Facts reveal that the demand to continually improve knowledge and ability is a natural part of academic life. This research can be conducted internally in an IG environment or in other relevant I where students could possibly be involved. Students who are working on their final assignment research can be involved in the EG by giving a presentation of their research to receive critical advice. The research conducted by the students could be a part of the EG s wider research so that their existence in EG activities is natural and useful.

The availability of research materials and the occurrence of scientific forums in the university does not guarantee that the students improve IG activities up to the third level. Therefore,another program is needed, which consists of the expectation for an IG to regularly conduct research. The research may be conducted on a small scal or on a large scale involving many people. The research results could be used as evidence of the existence of IG activities, such as research outcome reports, seminar papers, or journal articles. Research funds from the institution or government are a positive aspect if they involve students who are completing their final assignments. Several research grants, in fact, require that students be involved in the research activity. If it is well organized, the effort to improve research productivity and quality can be realized quickly.

Once the activity of an IG has begun,the next step is to maintain its continuance and improve the quality and productivity of the research outcomes. To bring about this effort,student involvement in scientific forums should range from local, regional, and national, up to international levels. Through the development of forums,it is possible to provide new inspiration for students so that they gain increased motivation to continue in the field of research. If scientific forums engaged in by the IG members are at various levels, it would trigger the productivity of students research,which would influence their study completion. If students have an opportunity to present their research through scientific forums, they will receive comments, input, and critical views that can be followed up with further research so that the quality of the developing work will improve over time. This explanation will further be illustrated in the following figure.

The Relationship between EG and IG

As previously explained,there are three activity levels that would take place in EG and IG circumstances, namely,the investigation of learning and enrichment materials,the discussion of advanced textbooks or journal articles, and research. However, basic differences exist between the groups functions, as shown in the following table.

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EG Activity IG Activity Course material research is conducted to fulfill the

following purposes: finding more effective ways to achieve learning goals, finding didactical designs that help students to study better, enriching learning materials by adding contemporary issues, investigating the relationships of various subjects so that the implementation of the curriculum will be more synergistic

Course material research is conducted by students to fulfill the following purposes: understanding the concepts being learned, practicing problem solving regarding the learned material, solving the difficulties in the learning process, expanding the material

Investigating new issues to enrich learning materials, increase knowledge that is consistent with the expertise, find inspiration to develop basic ideas into expertise

Investigating new issues in order to find basic ideas to use in the final assignment research

Conducting research in terms of knowledge development

Conducting research to fulfill the final assignment that also develops knowledge

Although the research characteristics of the two groups are different,the implementation of the activities creates a synergy between them so that students gain benefits from the developing academic circumstances. In accordance with the activity level in each group, the level of relationship could also cover the three levels of course material research, enrichment research through discussions of advanced textbooks or journal articles, and research activities. Therefore, the relationship between these two groups can be illustrated in the following figure.

#

A small group seminar conducting continuous(ex.once a week)and intensive discussion on specific topics deeply

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Research M ilieu (RM )

A community would be easier to organize if the tasks are clear and its membership is definite. However, if certain communities include research,a new aspect must be considered : how does each community develop long-term activity to insure that the productivity and quality of the research output will improve over time? To achieve this expectation, a community model needs to be develope to guarantee the occurrence of sustainable activities. One of the ways to encourage the expected activity is to develop a RM. Research Milieu is a community model whose existence depends on an RS created by community members individually or collectively. Therefore, this RM will automatically be developed when the RS in the community is maintained. On the other hand,if there has never been a RS,the RM will automatically disappear. A clearer picture of this research milieu may be found in this illustration.

This illustration shows that community (1) creates an RS in their community so that a response to the situation occurs. The interaction that occurs with community members will motivate the occurrence of deep thinking,especially,for(1)but also for others so that RS will grow dynamically in line with the critical ability of the community members. The productivity and quality of research outcomes are,in fact,influenced by the productivity and well-qualified research that are developing in an institution. In order to obtain the goal,an RM culture should be developed as soon as the students begin their study at the university. Several stages are necessary so that students will be able to contribute to creating a qualified RM : (1) introduction,(2) finding basic ideas,(3) formulizing the issue of a research idea,(4) developing and elaborating,(5) socialization,and (6) publication.

A RM will be evident in all stages. Students in the introduction stage are those who enter the orientation phase. In this stage, students involvement is not based on interest, but rather on a primary introduction to investigation. As a novice RM member, students can learn from senior members how to present a mathematical idea that could create RS, what kind of mathematical ideas are appropriate to raise, where the inspiration is from, how to provide comments to the expanding RS, how to raise a question, and how to critically elaborate the ideas and comments that emerge in a dynamically-expanding RS. Students will come to understand the characteristics of every discipline more deeply so that eventually they will discover an interest in one of the disciplines. By the time they reach half way into the basic phase,they are ready to choose one of the IGs.

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The finding of a basic idea begins when the students join one of the IGs permanently. This stage ideally begins when students reach half way into the basic phase. The activities performed include research on advanced mathematics materials, previous research results, and the latest journal articles. By following the routine activity of RM as an active member and contributing thoughts to the expanding RS,students at the end of the basic phase will have found basic ideas regarding the research issues that they would like to investigate more deeply. At that time, they have assumed their roles in RM as members who can create RS. Critical comments and other responses to RS are important aspects of further exploration until the status of the basic idea is advanced to be a hypothesis ready for further investigation. By the time students move into the development phase, ideally they have been able to form their hypothesis, although it is only the beginning. However,because of the continual relationships between students and lecturers,the hypothesis would be further elaborated through seminar forums (for example, between IG or EG) and through a larger RM that involves many IGs, so critical comments that could improve the quality of the scientific work will be made.

If the scientific work developed by the students is considered well-qualified both from the aspects of originality and content, it is possible that the work is published in a scientific journal. To obtain this goal, the role of lecturers as advisors is very important to support the possibility of publishing. Several positive aspects would be gained for both the graduate students and the lecturers. For university alumni,the evidence of scientific work that has been published in a scientific journal means recognition for the related community. This also adds good capital in the job field ; when an alumnus of a university applies for a job, this can be viewed as recognition of university quality. Published scientific research is also recognition of the writers capability and would be very beneficial if the writer is interested in continuing her or his study in universities abroad.

To encourage the growth of research activity among students, it is important to develop a conducive academic environment so that the students will become involved in the RM from the very beginning. Developing this circumstance through EG activities will lead to more research ; this will have to be programmed continually by facilitating forums and contributing to scientific publications. This will emerge automatically as a consequence of routine demands that have to be fulfilled by every member of an EG and IG. If possible,the best investigations and research from each group are displayed in the form of a yearbook or scientific journal,so that the work contributes to the pride of its members and serves as motivation for new students.

The Relationship Among RM s

Investigation of research activities does not always happen in the same community,since cross-disciplinary research is also conducted. For example, a community or group of students willing to investigate industrial and financial issues in terms of future probability may design methods to lessen the probability of unexpected events and to lessen the negative effect of future activities. This research is cross-disciplinary between mathematics, statistics, and economics, now called the actuarial discipline. The relationship among RMs could occur not only because of the exploration of an issue from different perspectives,but also the exchange of information so that academics can motivate each other. This relationship could occur through collective activities in the form of conferences or seminars that provide an opportunity for each RM to present their research. Through activities such as this,every RM could benchmark their work with each other,noting the

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improvement that has been achieved and creating a healthy competitive situation to motivate additional research.

A similar RM relationship could also occur among universities. This relationship is very important as a benchmarking effort and to create a synergy among universities. The potency could be related to the existence of human resources with different expertise,different research focuses,and different strengths so that improvement will occur with higher acceleration. Mutual cooperation, however, is necessary at every university. The following diagram illustrates the relationship of RM in a university or between two universities.

References

Borg, W.R. dan Gall, M.D. (1989). Educational Research (Fifth Edition). London : Longman.

Dubinsky, E. (2001). Using a Theory of Learning in College Mathematics Courses. Coventry: Universityof Warwick. Evans, J.R. (1991). Creative Thinking in the Decision and Management Sciences. South-Western : Thomson Publishing

Group.

Gunawan,H,(2007). Kontribusi dalam Matematika dan Pengembangan Ilmu dan Teknologi,Pidato Ilmiah Guru Besar ITB. Marzano, R.J., Brandt, R.S., Jones, B.F., Presseisen, B.Z., Rankin, S.C., dan Suhor, C. (1988). Dimensions of Thinking : A

Framework for Curriculum and Instruction. Virginia: ASCD. Nonaka (2005). Theory of Knowledge Creation. Jakarta: UI.

ODaffer,P.G.,dan Thornquist,B.A.(1993). Critical Thinking,Mathematical Reasoning,and Proof.Dalam P.S.Wilson (Ed.). Research Ideas for the Classroom : High School Mathematics. New York : NCTM.

Suryadi,D.(2005). Penggunaan Pendekatan Pembelajaran Tidak Langsung serta Gabungan Langsung-Tidak Langsung dalam Rangka Meningkatkan Kemampuan Berpikir Matematik Tingkat Tinggi Siswa SLTP, Ph. D. Thesis, PPS UPI. Tall, D. (1999). Reflections on APOS theory in Elementary and Advanced Mathematical Thinking. Haifa: PME23.

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