THE INCREASING OF PROBLEM SOLVING MATHEMATICAL ABILITY OF STUDENTS THROUGH REALISTIC MATHEMATICS EDUCATION APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM TERPADU OF MEDAN ACADEMIC YEAR 2012/2013.

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THE INCREASING OF PROBLEM SOLVING MATHEMATICAL ABILITY OF STUDENTS’ THROUGH REALISTIC MATHEMATICS EDUCATION APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM

TERPADU

OF MEDAN ACADEMIC YEAR 2012/2013

By:

Selvi Septiani Harahap ID. Number 408 611 007

Mathematics Education Study Program

A THESIS

Submitted to fulfill the requirement for the degree of Sarjana Pendidikan

MATHEMATICS DEPARTMENT

FACULTY OF MATHEMATIC AND SCIENCE STATE UNIVERSITY OF MEDAN

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BIBLIOGRAPHY

Selvi Septiani Harahap was born in Medan, September 24th 1989. Writer’s father name is (Alm) Drs. H. Haridan Harahap and mother’s name is Hotnaria Daulay. She is the first child from three children. She has two brothers. In 1995, writer studied in primary school SD Inpres number 105288 Sei Rotan and was graduated in 2001. In 2001, the writer continued her study in junior high school MTS Negeri 2 Medan and was graduated in 2004. In 2004, writer also continued her study in senior high school MAN 1 Medan and was graduated in 2007.

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ACKNOWLEDGEMENT

Praise be to Allah SWT, most gracious, most merciful and master of the judgment. Thanks are to Allah who gave the strength and ability to the writer, so that this thesis can be finished. An innovation and greeting to Rasulullah SAW, who brought people from the darkness into lightness. The title of this research was “The Increasing of Problem Solving Mathematical Ability Through Realistic Mathematics Education Approach in VIII Grade at SMP Islam Al-Ulum Terpadu of Medan Academic Year 2012/2013.” as a partial fulfillment of the requirements for the degree Sarjana Pendidikan of the mathematic department, Faculty of Mathematic and Natural Science State University of Medan.

In this occasion, the writer would like to express thank you very much to her supervisor Prof. Dr. Sahat Saragih, M.Pd for his advice, motivation, suggestion and guidance to finish this thesis. To her lecturer examinator Prof.Asmin Panjaitan, M.Pd, Dr.W.Rajagukguk,M.Pd, and Dra. Katrina Samosir,

M.Pd, for their correction with valuable comments to correct the manuscript of scientific writing, to her academic lecturer Drs. Syafari, M.Pd for his advice support to her.

The writer also would like to express thank you to Mr. Prof.Ibnu Hajar,M.Si as ahead of university and staff in office of university head, to Mr. Prof. Motlan, M.Sc,Ph.D as a dean of mathematic and natural science faculty and staff in mathematic and natural science faculty, to Mr. Dr Mukhtar,M.Pd as a head of mathematic department, Mr.Drs. Syafari, M.Pd as ahead of mathematic education program, Mr. Prof.Dr.Herbert Sipahutar, M.S, M.Sc as a coordinator of Bilingual program, Mr. Drs.Yasifati Hia,M.Pd as secretary of mathematic department, Mrs. Dr. IIs Siti Jahro, M.Si as secretary of Bilingual program, and all staff in mathematic department and Bilingual program to help the writer.

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The writer also would like to express her deepest love gratitude to her father (Alm) Drs, H. M. Haridan Harahap, her mother Hj. Hotnaria Daulay, her brother Imam Al-Rasyid Harahap and Sakti Rizki Fauzi Harahap affectionately which gave birth and enlarge to writer, gave morale support, material and pray and so all her family. To her friend Angelica Pardede and lovely all friends in mathematic bilingual program 2008 thank you very much for your support, helping to finish this thesis.

The writer has effort as maximal as she can in doing this thesis. But with her humble heart, the writer hopes construct suggestion and critics from the reader for perfection this thesis. The writer hopes this thesis can be useful and give many function to the reader specifically about subject matter which was researched in this thesis.

Medan, February 2013 Writer

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THE INCREASING OF PROBLEM SOLVING MATHEMATICAL ABILITY OF STUDENTS’ THROUGH REALISTIC MATHEMATICS EDUCATION

APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM TERPADU OF MEDAN ACADEMIC YEAR 2012/2013

Selvi Septiani Harahap (ID. Number 408 611 007) ABSTRACT

The purpose of this research to know increasing problem solving ability of students that taught realistic mathematical education approach is better than the mathematical problem-solving ability of students taught expository approach in VIII grade at SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013. This type of research is quasi-experimental research on first (odd) semester of VIII grade SMP Islam Al-Ulum Terpadu Medan academic year 2012/2013. The population in this research is all students of VIII grade SMP Islam Al-Ulum Terpadu School of Medan consisting of 118 students. Sample was taken by using random sampling; it means that each class had the same chance to be sampled. The sample in this study consisted of two classes. The experiment class in VIII-A was taught by applies Realistic Mathematics Education (RME) approach and the control class in VIII-B was taught by applies Expository approach. Research instrument in collecting data in this study were a test and an observation sheet.

The kinds of test is essay test, contains four questions for pre-test and four questions for post-test that related to the problem solving about Linear equation two variables system. The instrument that arranged have legalized by expert validator namely lecturer and mathematic teachers. Before hypothesis that will be test must be done normality test and homogeneity test. For normality test used Liliefors normality test and for homogeneity test is used F-test. From test can get the sample is distributes normal and homogeneous. Data analysis technique that used T-test formula.

The average of pre test in experiment class is 26.0714 and the average of pre test in control class is 26.0714. The average of posttest in experiment class is 85.1785 and the average of post test in control class is 72.5. Analysis result of gain for problem solving using t testing with significant level α=0.05 for the hypothesis is tcalculate =

3.9861 and ttable = 2.0048 so that -2.0048 < tcalculate < 2.0048, Because of that, the criteria

t-_α/2 < tcal < tα/2 is rejected. It means H0 is rejected. So can be concluded, The increasing

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ii

TABLE OF CONTENTS

Page

Sheet agreement ... i

Table of contents ... ii

Table list ... iii

List of appendix... iv

Figure list ... v

CHAPTER 1: INTRODUCTION ... 1

1.1 Background ... 1

1.2 Problem Identification ... 7

1.3 Problem Limitation ... 7

1.4 Problem Formulation ... 8

1.5 Research Objectives ... 8

1.6 Operational defenition ... 8

1.7 Benefit of Researh... 9

CHAPTER 2: LITERATURE REVIEW ... 10

2.1. Theoretical Background ... 10

2.1.1 Mathematical Problem Solving Ability... 10

2.1.2 Understanding of Realistic Mathematics Education approach 17 2.1.3 Principles and Characteristics of RME ... 19

2.1.4 Steps of Realistic Mathematics Education ... 24

2.1.5 The Excess and Complexity of RME ... 27

2.1.6 Expository Approach... 29

2.1.7 The Difference of RME and Expository ... 33

2.1.8 The lesson material... 34

2.2 The Relevant Research ... 40

2.3 Conceptual Framework ... 41

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iii

3.7 Instrument Analysis Technique ... 50

3.8. Data Analysis ... 52

4.1.2 Post Test of Experiment and Control Classes ... 57

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TABLE LIST

Table 2.1 Cooperative Learning Phase

Page 12 Table 2.2 Approaches to Cooperative Learning 14 Table 2.3 The Steps of Think Pair Share (TPS) 19 Table 2.4 Calculating of Gaining Score 21 Table 2.5 Example of Giving Gaining Score 22 Table 2.6 Technique of Giving Score For Each Step in Problem Solving 24

Table 3.1 Research Design 33

Table 3.2 Criteria of Student Mastering Level 44 Table 4.1 Pretest result of the first and second experiment classes 46 Table 4.2 Post test result of the first and second experiment classes 47 Table 4.3 Gain of the first and second experiment classes 48 Table 4.4 Result of Normality Testing 50 Table 4.5 Result of Homogeneity Testing 50 Table 4.6 The Result of Hypothesis Testing 52 Table 4.7 Description of Student Misatake for number 1using jigsaw

approach

53

Table 4.8 Description of Student Misatake for number 2 using jigsaw approach

54

55

56

Table 4.11 Description of Student Misatake for number 1using TPS approach

58

59

61

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approach

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FIGURE LIST

Page

Figure 2.1 Jigsaw Teams 15

Figure 2.2 Jigsaw Steps 17

Figure 2.3 Example of prism 26

Figure 2.4 Triangular Prism and its nets 27

Figure 2.5 Dividing Cuboids become Two Triangular Prisms 28 Figure 3.1 Research Procedures Scheme 36 Figure 4.1 Average of pre test, post test and gain 48

Figure 4.2 Level of Problem Solving 64

Figure 4.3 Students Mistake in Understanding Problem Number 2,3,1,and 4 using Jigsaw

69

Figure 4.4 Student Mistake for arranging Strategy using Jigsaw Approach 70 Figure 4.5 Mistake in calculating using Jigsaw 71 Figure 4.6 Mistake in Putting Some Values 71 Figure 4.7 Student’s Mistake for Understanding Problem using TPS

Approach

73

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APPENDIX LIST

Appendix 1 First Lesson Plan for Experiment Class A

Page 81 Appendix 2 Second Lesson Plan for Experiment Class A 88 Appendix 3 First Lesson Plan for Experiment Class B 95 Appendix 4 Second Lesson Plan for Experiment Class B 101

Appendix 5 Student Work Sheet I 107

Appendix 6 Student Work Sheet II 113

Appendix 7 Latticework of Pre-test 119

Appendix 8 Latticework of Post-test 120

Appendix 9 Pre-test Question 121

Appendix 10 Alternative Solution of Pre-test 123

Appendix 11 Post-test Question 126

Appendix 12 Alternative Solution of Post-test 128 Appendix 13 Observer Assessment Scale 131

Appendix 14 Validator Assessment Paper 133

Appendix 15 Validator Names 134

Appendix 16 Observation Paper of Learning Process Using Cooperative

Learning Jigsaw Approach

135

Appendix 17 Observation Paper of Teacher Activity for cooperative learning Think Pair Share (TPS) Approach

137

Appendix 18 Technique of Giving Score For Mathematic Problem Solving

139

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Appendix 26 Post Test for the Second Experiment Class 154 Appendix 27 Pre Test and Post Test Mark for the First and Second

Experiment Classes

156

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CHAPTER I INTRODUCTION 1.1. Background

Education is one of very important aspects of life. Giving the role of education is an effort to form a high quality human, then the problem of education in the spotlight, especially in Indonesia. One of the goals of national development in the field of education is the intellectual life of the nation and to improve the quality of Indonesian human. Through improving the quality of education at all levels of education, which enables its citizens to develop themselves as whole human beings Indonesia. To realize the national development in the field of education needed improvement and refinement of education in accordance with the development of science and technology (Science and Technology).

Mathematics is one of the basic sciences in school curriculum and must be learned in educational institutions. Based on the data above, Indonesia ranks are located in 39th of the 41 states and this must be very worrying. This problem must be improved immediately and be seriously handled because the usefulness of mathematics and very important both in development thinking, mastery of science

and technology and its role in several other scientific subjects. It is also expressed by the Daniel Muijs and David Reynolds (2008: 332) which states mathematics is

the main means for developing the ability of logical thinking and higher cognitive skills in children and plays an important role in several other scientific fields such as physics, engineering, statistics and others. Therefore, it is necessary teach students to mastery the mathematics early on creating, face and master modern technology for globalization era. Then, Cornelius in Abdurrahman (2003: 253) show several reasons for studying mathematics, namely:

1. Means of a distinct and logical thinking 2. Means to solve problems of daily life

3. Means to know the patterns, relationships and generalization of experience 4. Means to develop creativity

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Based on the above quotation through the learning of mathematics is expected that students can develop the ability to think, reason, develop creativity, communicate and present ideas and information and solve problems in daily activities. According to the National Council of Teacher Mathematics (NCTM) and its agenda for action in Alfred S. Posamentier Jay Stepelman (1990: 109) state that problem solving as primary goals for mathematics education and teacher are urged to:

1. Create a classroom environment and develop appropriate curricular materials in which problem solving can flourish

2. Give priority to identification and analysis of specific problem solving strategies

3. Develop examples of good problem

4. Encourage students to question , experiment, estimate, explore and suggest explanations

KEMDIKNAS 2006 in http://pmat.uad.ac.id/perkembangan-pembelajaran-matematika-di-indonesia.html then stated:

"The goal of learning mathematics, namely: (1) understand math concepts, explain the relationship among concepts and apply the concepts or algorithms in widely, accurate, efficient, and appropriately in problem solving, (2) using the pattern and characteristics of reasoning, mathematical manipulations in making generalization, arrange evidence, or explain mathematical ideas and statements, (3) solve problems that include the ability to understand the problem, design mathematical model, complete model and interpreting solution obtained, (4) communicate ideas with symbols, table, diagrams, or other media to explain the situation and problem, (5) respect of the usefulness of mathematics in life, which has the curiosity, attention, and interest in studying mathematics and a competent attitude and confidence in problem solving.”

From the above statement, one of the aspects emphasized in the goal of learning mathematics is problem solving ability. It is very important because in solving the problem usually involves some of the concepts and skills in new

situations or different that in the process possible the students’ learning gain experience in using knowledge and skills to be applied in problem solving.

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students become passive. More emphasis on learning outcomes (product) in which students live using formula rather than emphasizing the process. Thus some actives to learn mathematic is to be trained in order to solve the problems.

This is also reinforced one of them by the results of The Third International Mathematics and Science Study (TIMSS) that the junior high school students in

Indonesia are very weak, but pretty good problem solving in procedural skills. (Al-jupri & kartika). In addition Hudojo (2003: 152) states that teaching students to solve problems allow students to become more analytical in taking decisions for life. In other words if a student is trained to resolve problems, the students were able to make decisions for the students to have skills on how to gather relevant information, analyze information and realize the need to re-examine the results already obtained. But most of mathematics educators are concerned about the narrow focus of many schools programs, the limited treatment of content that they view as important for students, and the lack of attention given to developing in reasoning and problem solving (Lindquist, 1980: 9).

Furthermore, Tarwiyah (2011) explains that solving problems in

mathematics learning is an approach and goals to be achieved. As an approach, problem solving is used to discover and understand the material and mathematical

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problem-solving is an activity in the learning process has not become a major activity so that there are many students who find it difficult when faced with problem solving.

Mathematical problem solving ability has get attention because it is a necessary capability in learning. Mathematical problem solving ability to encourage students in meaningful learning and togetherness, but it can help students in dealing with mathematical problems and issues of everyday life in general. Weak student math problem-solving ability is not out of lack of opportunity and not frequently students do problem solving. Mathematical problems presented in the classroom tend to routine problems. So that the students are not accustomed to solving problems in determining what is known and what is asked on the matter and to what to use.

The Causes of low mathematical problem-solving ability is due to intake of students who have previously not met the standards. Knowledge and experience of the material previously learned material will affect the learning process further. This is reinforced by Herman Hudojo statement that: "Studying the concept B is based on the concept of A, that person may not understand the

concept of B. This means, learning mathematics should be gradual and sequential, and then based on their learning experience."

From the observation of the junior high school Al-Ulum Islamic Terpadu Academic Year 2012/2013, students tend not to like math because of lack of delivery of material related to everyday life so that academic concepts are difficult to understand. The teachers still teach and learn conventional learning models as a center of learning where the teacher (teacher cantered). Conventional learning gives effect to the inactivity of learning actors. Thus resulting to a total mastery of Mathematics and ultimately affect the competences and learning outcomes of students in mathematics.

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less able to translate the linear equation of variables system itself in everyday life. As the initial observations by the author on Islam Al-Ulum Terpadu in VIII class academic year 2012/2013 that most of the students were unable to resolve the problem concerning the complete linear equation of variables system. One problem, the ratio of rika and rido’s money is 3:2, if the amount of their money is Rp.20.000, their money is the difference? Of course the problem can be regarded as a social arithmetic. But it would be better if we look as a problem in linear Equation of variables system. In linear equation of variables system, the problem above can be seen as a problem with two equations and two unknown variables. But in fact most students are not able to solve algebra problems thoroughly.

Based on these observations it can be identified that many mistakes which made by students at SMP VIII Al-Ulum Islam Terpadu Medan for solving problem of linear equation two variables system. caused by the weakness of students in aspects of pouring, declaring, disclosing, or making a model of ideas, mathematical concepts, and relationships among them into a new mathematical form variety in the form of words (written text), graphics, tables, diagrams, drawings, equations (mathematical expression), or a form of concrete (props) and

use them in solving problems with the sort of things are known, asked, then answered.

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mathematics. Mathematics has its own characteristics in terms of both aspects of competency to be achieved, as well as from the aspect of the material being studied to support the achievement of competence.

Realistic Mathematics Education (RME) is a learning system based on the philosophy that one will be able to absorb the subject matter if they can grasp the meaning of learning. RME is a comprehensive system that consists of five components, namely the contextual issues, modeling, production and contribution of students, interactions, linkages. If any parts of the RME intertwined with each other it will produce effects that exceed the results given in the parts separately and involve different processes as well, when it is used together to enable the students to make connections with each other produce. Learning mathematics using Realistic Mathematics Education approach (RME), which concerned local conditions (culture or environment or context) shows that students are not afraid to express their ideas, has begun to dare to give a different problem solving with their peers, grow their creativity in doing problem solving(problem solving) together.

The purpose of Realistic Mathematics Education is to solve the problems

facing students by linking the material to the real world so that students can solve problems. This method is cooperative so to enhance cooperation among of

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1.2.Problems Identification

Based on the background of problems it can be identified some problems, as follows

1. Teachers who taught using teacher centered make students as passive objects in the study.

2. Many mistakes which made by students in VIII grade at SMP Islam Al-Ulum Terpadu Medan for solving problem of linear equation two variables system.

3. The students are not yet accustomed to solve problems in mathematics learning in the classroom.

4. Realistic mathematical approach has not been implemented in the school, in general, teachers tend to prefer the conventional approach in teaching mathematics.

1.3.Problem Limitation

Seeing the wide scope of issues identified and comparing the ability of the researcher, the writer feels the need to limits the problems that are examined for

the results in this study that can be performed and directed.

In this study the problem under study is limited to the influence of Realistic

Mathematics Education for mathematical problem solving ability of students the subject of linear equation of variables system in VIII grade at SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013

1.4.Problem formulation

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1.5.Research Objectives

Based on the above problem formulation, the objective of this study is "To know the increased problem solving abilities of students that taught realistic mathematical education approach is better than the mathematical problem-solving ability of students taught by expository approach in VIII grade at SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013.”

1.6.Operational definition

So that the terminology in this study is more clearly so that the objectives and research directions to be is specific, then the variables are defined as follows:

a. Realistic Mathematics Education is an approach to learning mathematics that has five characteristics: (1) using contextual problems as a first step, (2) using a mathematical model developed by students, (3) consider the contribution of students, (4) optimize the interaction with his students, students with teachers and other supporting facilities, and (5) consider the relationship between the topics.

b. Expository approach is a procedure commonly used by teachers in teaching. The steps are the teachers prepare teaching materials in a

systematic and organized, explaining the subject matter, students are given the opportunity to ask questions, students are given exercises that work on the problems of teachers, students and teachers discuss the exercise, then the teacher give homework.

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1.7. Benefits of research

This study is expected to be useful:

1. As input material for teachers, especially SMP Islam Al-Ulum Terpadu Medan is a way to improve students' mathematical problem solving ability.

2. As input and consideration for prospective teachers in implementing the teaching and learning activities

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CHAPTER V

CONCLUSSION AND SUGGESTION 5.1. Conclusion

Based on the result research from data analysis, can be obtained some conclusion, those are

1. By testing hypothesis using t-test of the gain average in the control and experiment classes, then can be concluded the increasing of problem solving mathematical ability students that taught realistic mathematics education approach is better than the mathematical problem solving ability of students taught with expository approach on subtopic system of linear equations two variables in VIII grade at SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013.

2. Based on the observation of the application of realistic mathematics approach and expository approach on the subject of system linear equation two variables the categorized is good.

5.2. Suggestion

Based on research result, then the suggestions that can be given by the researchers are:

1. For math teacher who want to use realistic mathematics education approach, give more attention to time allocation for each phase so that learning process can be done better.

2. For math teacher, realistic mathematics education approach can be used as alternative learning approach because it can be increase problem solving ability of student.

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4. For students, especially students in SMP Islam Al-Ulum Terpadu Medan are suggested more brave in the expressing an opinion or ideas, can use the full potential in math.

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