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THE TEACHERS EFFORTS TO ENCOURAGE THE STUDENTS STRATEGIES TO FIND THE SOLUTION OF FRACTION PROBLEM IN BANDA ACEH

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The Teachers Efforts to Encourage the Students Strategies to Find the Solution of Fraction Problem in Banda Aceh

Rahmah Johar and Marisa Afrina

Syiah Kuala University

Author Note Rahmah Johar and Marisa Afrina, Department of Mathematics Education, Teacher Training Education Faculty, Syiah Kuala University This research is part of my research that supported by Ministery of Education for Hibah Bersaing Grant BCHP:258/H11/A.01/APBNP2T/2010 Correspondence concerning this article should be addressed to Rahmah Johar, Department of Mathematics Education, Teacher Training Education Faculty, Syiah Kuala University. Darussalam. Banda Aceh. Indonesia E-mail: rahmah_johar@yahoo.com

THE TEACHERS EFFORTS TO ENCOURAGE THE STUDENTS STRATEGIES TO FIND THE SOLUTION OF FRACTION PROBLEM IN BANDA ACEH

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Abstract

One of the Realistic Mathematics Education (RME) characteristic is using students own construction. Teacher stimulate the student to be more active and creative for develop their ideas or strategies. The purpose of this study was to describe the students strategies and teachers efforts to encourage them. The subject is student fourth grade of the Islamic Elementary School (MIN) Suka Damai Banda Aceh, Indonesia. Data was collected via video and field note for record the interaction between student-student and student-teacher in classroom to find their own strategies for solving fraction problem. The results of the research are there are some students strategies to solve the problem, those are 1) trial and error, 2) using diagram, and 3) using pattern. Furthermore, teachers efforts to encourage the students strategies are a) giving some choices for the student to use concrete material, pictures, or calculation, b) giving some choices for the student to use any strategies as the student can, c) asking the question to stimulate the students thinking or clarification the students answer, and d) giving compliments for the students efforts. Key words: students strategies, teachers efforts

THE TEACHERS EFFORTS TO ENCOURAGE THE STUDENTS STRATEGIES TO FIND THE SOLUTION OF FRACTION PROBLEM IN BANDA ACEH

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The Teachers Efforts to Encourage the Students Strategies to Find the Solution of Fraction Problem in Banda Aceh

Mathematics learning objectives is not only to calculate, but also to develop

thinking skills, reasoning, problem solving, and communication. One of the approaches which can be used in teaching mathematics is realistic approach, known as Realistic Mathematics Education (RME). RME was introduced by Freudenthal in the Netherlands in 1968. According to Freudenthal as cited in Gravemeijer (1994), students should experience mathematics as a human activity. It is an activity of solving problems, looking for problems, and organizing a subject matter. In addition, Panhuizen (1996) suggest mathematics must be taught in the order in which the students themselves might be inventing it. Gravemeijer (2010) complements the RME tries to relate with the experiential reality of the students. About term, real in realistic has to be understood as real in the sense of being meaningful for the students. Therefore, the choice of realistic problems plays a very important role.

To develop RME in Indonesia, Indonesian mathematicians and mathematics educator was designed Realistic Mathematics Education in Indonesia or Pendidikan Matematika Realistik Indonesia (PMRI), known as Indonesian version of RME. Dutch consultants from the APS Netherland and Freudenthal Institute (FI) of Utrecht University have been involved to coaching the PMRI team. The team that consists of teacher educator and teacher started a pilot program of PMRI from 2001 until now. The PMRI team wants to change mathematics education in such a way that most children will be able to do and enjoy mathematics to develop their mathematics knowledge, skills, and strategies. Dolk (2010) suggested such changes start in classroom. Creating learning community in the classroom asks for another role of teachers and of students. One aspect of these new norms is related to the teachers expectations and beliefs about students mathematical thinking. Gravemeijer (2010) reminded RME further requires the teacher to play an active role in orchestrating productive whole-class discussions and in selecting framing mathematics issues - context problem - as topics discussion.

To implement RME in Indonesia, teacher educator and teacher in primary school collaborate to design the context problems for Indonesian Primary School students, it is use to develop the students thinking/reasoning in mathematics. Context problem in RME must be accessible, inviting, and worthwhile solving, also challenging and it must be obvious to the students why an answer to a give question is required. In short, problem must be meaningful. The emphasis on higher-order reasoning implies that the problem situations should be fairly unfamiliar to the students. In other words, problem solving in RME does not mean simply conducting a fixed procedure in set situation. Consequently, the problems can be solved in different ways (Panhuizen, 1996). This problem we known as non-routine problem because the mathematical procedures that children must use to solve them are not obvious (Reys, et.all, 2007), they dont know how to solve comfortably with routine or familiar procedures (Schoenfeld, 1983).

The problem likes this one: suppose mother baked 1 cookie. If she has 2 children (or 4 or 6) and each child gets the same number of cookies, how many cookies does each

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child get? It is a routine problem for Indonesian Primary School students at fourth grade. Because they can be solved by applying a mathematical procedure in much the same way as it was learned about simple fraction for share topics. But, the problem 15 kg meat for 20 poor people is as a non-routine problem for them, therefore context problem in RME. The student didnt know yet about the fixed procedure they can solve, so they want to develop their own strategies.

Student at grade 4 in primary school need to discuss with the other student to solve the context problem and teacher play the role to stimulate them. Teacher encourages the student to be more active and creative for develop their ideas or strategies. In general, Horn et.all (2005) proposed the strategies for creative instruction, those are 1) student-centered learning, 2) Use of multi-teaching aids assistance, 3) Class management strategies, 4) Connection between teaching contents and real life, and 5) Open questions and encouragement of creative thinking. These research objectives are describing the students strategies and teachers efforts to encourage the students strategies to solve the fraction problem at fourth grade of the Islamic Elementary School (MIN) Suka Damai Banda Aceh, Indonesia.

a. Context Problem in Realistic Mathematics Education

Context is one of the prominent characteristics of RME. Borasi defined context as a situation in which the problem is embedded (in Panhuizen, 1996). In other word, context means the situations to which they refer. In the learning process, context gives meaning to the content (Johnson, 2007). The context need not necessarily refer, however, to real life situations. The important point is that they can be organized mathematically and that students can place themselves within them. Panhuizen (1996) offered two requirements of problem in RME, problems must be meaningful and informative. In order for problem to be meaningful, the context problem must be obvious to the students why an answer to a give question is required. Meaningful also respect to subject matter, it cover the entire breadth and depth of the mathematical area. Another requirement is informative. It means the problem must be as clear as possible to the student and the students must have the opportunity to give their own answers in their own words. They can solve in different ways/strategies and different levels.

About problem itself, Lester (in Zawojewski and Lesh, 2003) defined a problem as a task which: (1) individual or group confronting it wants or needs to find the solution, (2) there is not a readily accessible procedure that guarantees or completely determines the solution, and (3) the individual or group must make and attempt to find a solution. In this line teacher have to stimulate the students to find their own strategies to solve the problem. b. Teachers Efforts to Stimulate the Students Strategies to Solve a Context

Problem Problem solving-it means solving the non-routine problem or context problem- is a

primary goal of mathematics teaching and learning and is considered to be the essence of mathematics (NCTM, 2000). However, some students fail in solving problems typically

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defined as non-routine and teachers encounter difficulties in supporting the development of the students problem-solving competency (Kolovou, et al. 2009). The teacher has to play an active role in orchestrating productive whole-class discussions and in selecting framing mathematics issues - context problem - as topics discussion (Gravemeijer, 2010, Gravemeijer and Cobb, 2006). The teacher not only asks the student to explain your strategy but also show how you got your answer (Panhuizen, 1996).

In general, the initiator of how to solve the problem is the Hungarian-born mathematician George Polya. He, in general, proposed four-stage model

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