THE COMPARISON OF STUDENTS’ MATHEMATICAL PROBLEM SOLVING ABILITY ON CONTEXTUAL TEACHING LEARNING AND REALISTIC MATHEMATICS EDUCATION IMPLEMENTATION ON GRADE XI IN SMAN 1 LUBUKPAKAM ACADEMIC YEAR 2016/2017.

THE COMPARISON OF STUDENTS’ MATHEMATICAL PROBLEM SOLVING ABILITY ON CONTEXTUAL TEACHING LEARNING

AND REALIST IC MATHE MATI CS E DUCAT ION IMPLEMENTATION ON GRADE XI IN SMAN 1

LUBUKPAKAM ACADEMIC YEAR 2016/2017

By:

Aida Syahfitri IDN 4123111004

Bilingual Mathematics Education Study Program

SKRIPSI

Submitted in Partial Fulfillment of The Requirement for The Degree of Sarjana Pendidikan

FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN

MEDAN 2016

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BIOGRAPHY

Aida Syahfitri was born in Sidodadi Ramunia on March 8th, 1994. Her

father’s name is Wikanto and her mother’s name is Marinem. She is the second

child from 2 children. She has old brother, his name is Rial Rinaldi. In 2000, she started her study in Elementary School at SDN No 105345 Beringin and graduated in 2006. Then, she continued her study in Junior High School at SMPN 1 Lubukpakam along three years and graduated in 2009. In 2009, she continued her study in Senior High School at SMAN 1 Lubukpakam and graduated from senior high school in 2012. After graduated from Senior High School, she was following the examination of Written SNMPTN test and become the student of University of Medan in Bilingual Mathematics Study Program, Faculty of Mathematics and Natural Sciences in 2012.

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THE COMPARISON OF STUDENTS’ MATHEMATICAL PROBLEM SOLVING ABILITY ON CONTEXTUAL TEACHING LEARNING

AND REALIST IC MATHE MATI CS E DUCAT ION IMPLEMENTATION ON GRADE XI IN SMAN 1

LUBUKPAKAM ACADEMIC YEAR 2016/2017

Aida Syahfitri (ID. 4123111004)

ABSTRACT

The aim of this research is to know whether student’s Mathematics Problem Solving Ability taught using Contextual Teaching learning is higher than Realistic Mathematics Education for Grade XI in SMA Negeri 1 Lubukpakam at Academic Year 2016/2017. Sampling techniques that is used in this research is purposive sampling. There are two samples in this research those are, Class A is XI MIA 3 taught by CTL and Class B is XI MIA 5 taught by RME. Each of class consist of 30 students. Technique of analyzing data is consisted of normality, homogeneity, and hypothesis test. Based on normality and homogeneity test, the data was taken from normal distribution and homogeneous population. Hypothesis test is done by using analysis of t-test. The result of t-test show that tcalculated = 2.878 and t(0.5)(58) = 1.672. Consequently tcalculated > ttable, then H0 is rejected. So, we can conclude that students’ mathematics problem solving ability taught using Contextual Teaching Learning model is higher than taught using Realistic Mathematics Education. Keyword :mathematical problem solving ability, CTL, RME

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PREFACE

Praise and thanks to Allah Subhanallahu Wata’ala Who has give for all the graces and blessings that provide health and wisdom to the author such that the author could finish this thesis well. This thesis which entitled “The Comparison Of Students’ Mathematics Problem Solving Ability Between Contextual Teaching Learning and Realistic Mathematic Education On Subject Program Linear on Grade XI SMAN 1 Lubukpakam Academic Year 2016/2017” is submitted in order to get the academic title of Sarjana Pendidikan from Mathematics Department, FMIPA Unimed.

In this part, the author would like to thank for all supports which gained for completion of this thesis. Special thanks to Prof. Dr. Edi Syahputra, M.Pd. as thesis supervisor who has provided guidance, direction and advice from the beginning until the finishing part of this thesis. Great thanks are also due to Prof. Dr. P. Siagian, M.Pd, Drs. Zul Amry, M.Si, Ph.D. and Dr. Faiz Ahyaningsih, M.Si as thesis examiners who have provided builded suggestion and revision in the completion of this thesis. Thanks also extended for Prof. Dr. Asmin, M.Pd as academic supervisor and also for all lecturers in FMIPA Unimed.

The author also expressed sincerely thanks for Prof. Dr. Syawal Gultom, M.Pd as Rector of Unimed, Dr. Asrin Lubis, M.Pd as Dean of Mathematics and Natural Sciences Faculty, Dr. Iis Siti Jahro, M.Si as Coordinator of Bilingual Program, Dr. Edy Surya, M.Si as Head of Mathematics Department, Drs. Yasifati Hia, M.Si as Secretary of Mathematics Education, and all staff employess which supported in helping author.

Appreciation also present to Drs. Ramli Siregar, M.Si as Headmaster in SMA Negeri 1 Lubukpakam, Drs. Geviner Harianja and Robert Purba S.Pd as Mathematics teacher who has provide guidance when the research was held and all teachers and staff employes who helped author conduction the research well.

Another thanks expressed by the author to all of students in SMA Negeri 1 Lubukpakam for cooperative and helping when the research.

Most special thanks especially would like to express for my beloved father Mr. Wikanto and my mother Mrs. Marinem S.Pd also one and only brother Rial Rinaldi S.Kep. Ns, my both grandmothers, my aunties, my uncles, and all family who have supported, material, prayed, and gave the author encouragement and funding to complete the study in Mathematics Department.

The author also thanks to Girls’ Generation members Aisyah Tohar, Erika A. Simbolon, Febby Faudina Nestia, Mutiara Naibaho, Rahima Azzakiya, Shinta Bella G.S and Windy Erlisa who have made my life was happy, enjoyable and memorable and I hope we can always together until Jannah. For my best friend Nurhalimah Simbolon that has been with me since in Junior High School, thanks for moment that we spend together and sorry for the fault that I have ever done, because human nothing perfect, right? For my roommate Naimah Lubis, Yusrina Azizah, sister Masliana, sister Nita, sister Mayang, Endang and Vira thank you for your patience with me for the last few years. Also big thanks for second family of BilMath 2012: Adi, Desy, Friska Elvita, Friska Simbolon, Bowo, Rudi, Dillah, Rani, and Totok for all support, sadness, happiness and togetherness during first semester until eight semester. For all partner of PPLT Unimed 2015 of SMA Negeri 1 Tebing Tinggi, those are Mutiara, Nesya, Dwi, Syifa, Biuti, Rimbun, and Yudis thanks for the support during PPLT, for my senior BilMath 2008, 2009, 2010, 2011 thanks for the guidance during the lecture and my junior BilMath 2013, 2014, all my students when I was doing practice in SMAN 1 Tebing Tinggi thanks for the support and motivation to finish my study.

And the last, thanks for all the lecturers of State University of Medan in Mathematics Department that have taught us along four years. It’s a lot of knowledge and experience to try understanding, solving the problem every subject and matter that exist along the lecture. Thanks for the patience in teaching us, thanks for sharing the knowledge and experience to us. I hope we can apply all of

your knowledge that have been transferred to us in our daily life especially in teaching mathematics.

At last, the author has finished and maximally to complete this thesis. But certainly there are still some imperfection in this research. The author receive welcome any suggestions and constructive criticism from readers for this thesis perfectly. The author also hope the content of this research would be useful in enriching the reader’s knowledge. Thank you.

Medan, September 2016 Author,

Aida Syahfitri ID. 4123111004

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TABLE OF CONTENTS

Pages

Ratification Sheet i

Biography ii

Abstract iii

Preface iv

Table of Contents vii

List of Tables x

List of Figures xi

List of Appendices xii

CHAPTER I INTRODUCTION 1

1.1Background 1

1.2Problem Identification 9

1.3Problem Limitation 10

1.4Problem Formulation 10

1.5Research Objective 10

1.6Research Benefit 10

1.7Operational Definition 11

CHAPTER II RELATED LITERATURE 12

2.1 The Theoretical Framework 12

2.1.1 The Learning of Mathematics 12

2.1.2 Problem in Mathematics 14

2.1.3 The Problem Solving in Mathematics 15 2.1.4 Mathematical Problem Solving Ability 16

2.1.4.1 Understanding the Problem 17 2.1.4.2 Make a plan to resolve the problem 17 2.1.4.3 Implement problem solving 17 2.1.4.4 Check the answers which’s obtained 18

2.1.5 Contextual Teaching Learning 18

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2.1.6.1 Constructivism 19

2.1.6.2 Inquiry 20

2.1.6.3 Questioning 20

2.1.6.4 Learning Community 21

2.1.6.5 Modeling 22

2.1.6.6 Reflection 22

2.1.6.7 Authentic Assessment 23

2.1.7 The Implementation of CTL Approach in the Classroom 24 2.1.8 The Advantages and Disadvantages of CTL 25 2.1.9 Realistic Mathematics Education Learning 25 2.1.10 The Characteristics of Realistic Mathematics

Education Learning 26

2.1.11 The Advantages and Disadvantages of Realistic

Mathematics Education Implementation 31

2.1.12 The Summary of Material Summary 33

2.2 Relevant Research 37

2.3 Conceptual Framework 38

2.4 Hypothesis 40

CHAPTER III RESEARCH METHODOLOGY 41

3.1Time and Location of Research 41

3.2Population and Sample 41

3.2.1 Population of Research 41

3.2.2 Sample of Research 41

3.3 Variables and The Instrument of Research 41

3.3.1 Independent Variable 41

3.3.2 Dependent Variable 42

3.3.3 The Research Instruments 42

3.4 Validity 43

3.4.1 Internal Validity 43

3.4.2 External Validity 44

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3.5 Procedure of Research 45

3.5.1 Stage Preparation 46

3.5.2 Stage Implementation 46

3.5.3 Stage Final 46

3.6 Techniques of Analysis Data 48

3.6.1 Normality Test 48

3.6.2 Homogeneity Test 49

3.6.3 Hypothesis Test 49

CHAPTER IV RESULT AND DISCUSSION 51

4.1. The Result of Students’ Mathematics Problem Solving Ability 51

4.1.1 Post-test of Experiment Class A and Experiment Class B 51 4.1.2 Normality Test of Student’s Mathematics Problem

Solving Ability 52

4.1.3 Homogeneity Test of Student’s Mathematics

Problem Solving Ability 52

4.1.4 Hypotheses Test of Student’s Mathematics Problem

Solving Ability 54

4.2. Discussion of Result 55

4.2.1 Mathematics Problem Solving Ability 55

4.2.2 Contextual Teaching Learning 55

4.2.3 Realistic Mathematics Education 55

4.2.4 The Weakness of The Research 56

CHAPTER V CONCLUSION AND SUGGESTION 57

5.1. Conclusion 57

5.2. Suggestion 57

REFFERENCES 58

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LIST OF TABLES

Pages Table 2.1 The Syntax of Contextual Teaching Learning 23 Table 2.2 The Syntax of Realistic Mathematics Education 30 Table 2.3 The Differences between RME and CTL 32 Table 3.1 Scoring Capabilities of Problem Solving 42 Table 3.2 Research Design of Randomized Control Group Only 45 Table 4.1 Data Post-test of Student’s Mathematics Problem Solving

Ability of Class A and Class B 51 Table 4.2 The Statistic of Data Post-test of Student’s Mathematics

Problem Solving Ability of Class A and Class B 52 Table 4.3 Result of Normality Data Post - Test in Class A and Class 53 Table 4.4 Result of Homogeneity Test of Data Post-Test

in Class A and Class B 53

Table 4.5 Hypotheses Test of Student’s Mathematical Problem

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LIST OF FIGURES

Pages Figure 1.1 The Students’ Answer Sheets in Diagnostic Test 4 Figure 2.1 Horizontal and Vertical Mathematization 28

Figure 3.1 Procedure of Research 47

Figure 4.1 Graph of Hypothesis Result 54

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APPENDICES LIST

Pages

Appendix 1 Lesson Plan I (CTL) 60

Appendix 2 Lesson Plan II (CTL) 66

Appendix 3 Lesson Plan I (RME) 71

Appendix 4 Lesson Plan II (RME) 76

Appendix 5 Student Activity Sheet I (CTL) 81

Appendix 6 Student Activity Sheet II (CTL) 91

Appendix 7 Student Activity Sheet I (RME) 96

Appendix 8 Student Activity Sheet I (RME) 105 Appendix 9 Alternative Solution of Student Activity Sheet I (CTL) 110 Appendix 10 Alternative Solution of Student Activity Sheet II (CTL) 118 Appendix 11 Alternative Solution of Student Activity Sheet I (RME) 123 Appendix 12 Alternative Solution of Student Activity Sheet II (RME) 131

Appendix 13 Post Test 136

Appendix 14 Alternative Solution of Post Test 138

Appendix 15 Blueprint of Post Test 153

Appendix 16 Validity Sheet of Post Test 155

Appendix 17 Validity Sheet of Post Test 156

Appendix 18 Validity Sheet of Post Test 157

Appendix 19 Rubric of Scoring 158

Appendix 20 Procedure to Calculate the Normality 159 Appendix 21 Procedure to Calculate the Homogeneity 162 Appendix 22 Procedure to Calculate the Hypotheses Test 163 Appendix 23 List of Critical Value for Liliefors 165

Appendix 24 Table t Distribution 166

Appendix 25 List of Area Under Normal Curve 0 to x 168

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LIST OF TABLES

Pages Table 2.1 The Syntax of Contextual Teaching Learning 23 Table 2.2 The Syntax of Realistic Mathematics Education 30 Table 2.3 The Differences between RME and CTL 32 Table 3.1 Scoring Capabilities of Problem Solving 42 Table 3.2 Research Design of Randomized Control Group Only 45 Table 4.1 Data Post-test of Student’s Mathematics Problem Solving

Ability of Class A and Class B 51 Table 4.2 The Statistic of Data Post-test of Student’s Mathematics

Problem Solving Ability of Class A and Class B 52 Table 4.3 Result of Normality Data Post - Test in Class A and Class 53 Table 4.4 Result of Homogeneity Test of Data Post-Test

in Class A and Class B 53

Table 4.5 Hypotheses Test of Student’s Mathematical Problem

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LIST OF FIGURES

Pages Figure 1.1 The Students’ Answer Sheets in Diagnostic Test 4 Figure 2.1 Horizontal and Vertical Mathematization 28

Figure 3.1 Procedure of Research 47

Figure 4.1 Graph of Hypothesis Result 54

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APPENDICES LIST

Pages

Appendix 1 Lesson Plan I (CTL) 60

Appendix 2 Lesson Plan II (CTL) 66

Appendix 3 Lesson Plan I (RME) 71

Appendix 4 Lesson Plan II (RME) 76

Appendix 5 Student Activity Sheet I (CTL) 81

Appendix 6 Student Activity Sheet II (CTL) 91

Appendix 7 Student Activity Sheet I (RME) 96

Appendix 8 Student Activity Sheet I (RME) 105 Appendix 9 Alternative Solution of Student Activity Sheet I (CTL) 110 Appendix 10 Alternative Solution of Student Activity Sheet II (CTL) 118 Appendix 11 Alternative Solution of Student Activity Sheet I (RME) 123 Appendix 12 Alternative Solution of Student Activity Sheet II (RME) 131

Appendix 13 Post Test 136

Appendix 14 Alternative Solution of Post Test 138

Appendix 15 Blueprint of Post Test 153

Appendix 16 Validity Sheet of Post Test 155

Appendix 17 Validity Sheet of Post Test 156

Appendix 18 Validity Sheet of Post Test 157

Appendix 19 Rubric of Scoring 158

Appendix 20 Procedure to Calculate the Normality 159 Appendix 21 Procedure to Calculate the Homogeneity 162 Appendix 22 Procedure to Calculate the Hypotheses Test 163 Appendix 23 List of Critical Value for Liliefors 165

Appendix 24 Table t Distribution 166

Appendix 25 List of Area Under Normal Curve 0 to x 168

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CHAPTER I INTRODUCTION

1.1Background

Words of education, counseling, teaching, learning, and training are technical terms concerning to activities united in educational activity. Education is one of the basic needs for human life, because through education human can change a person’s attitude and ethics code in daily life. Furthermore, education is investment in human resources who have a long-term strategic value for the survival of human civilization in the world. As well as the presentation, the quality of nation’s human resources in general can be seen from the quality of the nation’s education. History has proven that the progress and prosperity of a nation in the world is determined by the development in the filed of education.

Therefore, almost all countries put education variable as something important and major in the context of nation building. Likewise, Indonesia put education as an important and major. It can be seen from the contents of the fourth paragraph of the Preamble of the 1945 Constitution which asserts that one of the national goals of Indonesia is the intellectual life of the nation.

Mathematics as one of the fundamental science education develop in people’s life and very needed in the development of science and technology. Therefore, mathematics can be said as the mother of all science, so mathematics is very important to be taught. As proposed by Cockroft (1982: 1-5) that “Mathematics should be taught to students because of (1) is always used in life; (2) all fields of study require skills appropriate mathematics; (3) is a powerful means of communication; (4) can be used to present information in a variety of ways; (5) improve the ability to think logically, accuracy, and awareness spatial; (6) provide satisfaction to solve business challenging problem.

Because mathematics is very important to learn, so mathematics is considered as the main lesson in education, so time lesson for mathematics is much than the other lesson. Even though mathematics lesson is very important to be taught in school but many students have many problems in study mathematics

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in school. This problem is because of students assumed that mathematics is a lesson that very difficult to be studied and mathematics is not interested to be studied.

There some factors that caused the students have assume that mathematics is difficult and not interested to be studied, one of the problem is students have less problem solving ability in mathematics. There some competences that hoped be able to reach by students in study mathematics in every level of education such as SD, SMP until SMA. Depdiknas (in Shadiq, 2014 : 11 ), he said that the competence that be hoped can be reached by students are:

1. Showed the understanding mathematical concept that be studied, explained the relation between concept widely, accurately, efficiency, and right in problem solving.

2. Have the ability to communicate the idea using symbols, tables, graphs, or diagrams in explaining the problem.

3. Using reasoning in pattern, characteristic or do manipulate mathematics in make generalization, arranging the fact or explaining idea and mathematics statement.

4. Showing the strategy ability in making (formulating) the model of mathematics in problem solving.

5. Having the respect in used mathematics in daily life.

Based on the competences that be hoped by Depdiknas, problem solving ability must be have by students in study mathematics in school. Because of problem solving ability was very important to have by students, the problem solving ability must be one of the factors that students have in mastering and understanding of mathematics especially in solving the problem.

Problem solving is considered central to school mathematics as being states from NCTM (in Chapman, 2005):

Instructional programs should enable all students to build new mathematical knowledge through problem solving; solve problem that arise in mathematics and in other contexts; apply and adapt a variety of

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appropriate strategies to solve problems; and monitor and reflect on the process of mathematical problem solving.

Similarly, Kilpatrick et al (2001: 420) explained,

Studies in almost every domain of mathematics have demonstrated that problem solving provides an important context in which students can learn about number and other mathematical topics. Problem solving ability is enhanced when students have opportunities to solve problems themselves and to see problems being solved. Further, problem solving can provide the site for learning new concepts and for practicing learned skills.

From some explanation above, we know that problem-solving ability is a process of applying the knowledge that has been acquired prior to the new situation that has not been known. Problem solving method is a way of learning to exposes students to a problem to be solved or resolved. Problem solving in mathematics learning is an approach and goals are achieved. Used as a problem-solving approach to discover and understand the material or mathematical concepts. While solving the problem as the expected destination for students to identify elements that are known, were asked and the adequacy of the required elements, to formulate the problem and explain the results according to the origin of the problem. In solving the problem students are encouraged and given the widest possible opportunity to take the initiative and systematic thinking in the face of a problem with applying the knowledge gained previously. Polya illustrates the problem solving ability of students is constructed include the ability of students to understand the problems, plan solutions, resolve the issue according the plan and to re-examine the results of the settlement procedure.

Problem solving has the main function in the activity of teach and learn mathematics. By mathematical problem solving, students can try to interpret the concepts, theorems and skills that be studied. (Hudojo, 2005)

From the description above can be concluded that problem solving plays an important role and needs to be improved in learning. But the facts on the field show that the problem solving ability of students is still low. For example, as seen from the students' answers on questions that measuring students' mathematical

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problem solving on the subject probability in class X SMA Negeri 1 Lubukpakam T / A 2015/2016 as follows:

Ani menerima kembalian uang Rp 300 berupa tiga buah uang logam. Ia melemparkan ketiga uang tersebut secara bersamaan. Jika sisi uang logam tersebut berupa gambar (G) dan angka (A) maka tentukanlah ruang sampel dan banyak ruang sampel dari kejadian tersebut!

The question story above is an example of matter for problem solving, to solve the problem students often do not know how to make a mathematical model so that the matter is considered difficult to do. To resolve the problem with the necessary steps students must understand the problems, develop mathematical models and finishes with the basic knowledge then they draw conclusions from the settlement. Here are the answers to the students of one of the problems that exist

(a)

(b)

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From the students’ answer above it can be seen that the answer is incomplete yet. The answers are from two students in different class. At figure a) the answer didn’t use the steps of problem solving. The students was directly answer without trying to understand the problem first. So we did not know how to solve or how to determine the sample space and the point space of the problem.

And for the students’ answer in figure b), the student had been known how to understand the problem by classifying the solution into known, asked, and answer. It means that the student understand what are being known from the problem, what are being asked from the problem and the last try to solve the problem. But in process to answer, it can be looked that the student did not know how to solve it. The student can not relate one item to another item and the student can’t to give conclusion or another way that may be can be used to solve the problem in the last solution of that worked.

From the answers which’s shown, it can be seen that the students do not fully understand the problems that exist while these materials are basic probability subject that already exist in their current ninth grade material, but they are not yet fully understood in the problem of solving the problem.

In solving the mathematics problem, it can be denied that we must understanding what the problems are, what the questions are, what is plan to solve it, how to solve it and is there any another way to solve the problem or not? All of that contents are so important to be applied in solving mathematics problem. The step below can be applied in solving the given problem.

a. Understanding the problem

Known : three coins are thrown simultaneously Picture side as G and number side as A

Asked : Determine the sample space and the number of sample space!

b. Devising a Plan

For knowing the sample space of this event, we have to draw the tree line as follow:

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c. Carrying Out the Plan

We have devise to solve this problem, we have to make the tree line.

d. Looking Back

From the tree line above it can be seen that the sample space of the event are (AAA), (AAG), (AGA), (AGG), (GAA), (GAG), (GGA), (GGG). And if we count that the sample space so the total is 8. So the number of sample space n(S) is 8.

To solve the that problem we can not jus using the tree line but we can using the table of probability .

The explanation above are the way to solve the given problem by focusing in students’ understanding in solving the problem by steps. If we compare the solution above with the students’ solution are very different. So we can know that the students’ problem solving ability in mathematics subject is still low.

Furthermore, it’s very needed to increase the students mathematical problem solving ability. To increasing this ability, the teacher have to create the learning system which will make the students’ desire of learning, understanding, and solve the problem of mathematics are increasing. Some lectures have

A G A G A G AAA AAG AGA AGG

Coin 1 Coin 2

A G Coin 3 A G A G A G GAA GAG GGA GGG

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researched that there are some learning model which able in increasing the students’ mathematical problem solving ability. Some of them are problem based learning, contextual teaching learning, cooperative learning, realistic mathematic education, etc.

There are some learning model that looked like very similarity. Some of them is Contextual teaching Learningand Realistic Mathematics Education. Both of them are applying the mathematics learning model that focus in problem of mathematics which relate with daily life context. And there are some of researchers have researched that both learning model able to increasing the student’s mathematical problem solving ability. This is reinforced by the relevant research conducted by Yeni Septiani Rambe 2013 states that Contextual Teaching Learning can improve students’ mathematical problem solving ability. It means that, Realistic Mathematics Education and Contextual Teaching Learning can improve students’ mathematical problem solving ability. As well as research conducted by Iwan Prakasa in 2013, the results showed that the implementation of Realistic Mathematics Education can improve students’ mathematical problem solving ability.

Another research by Julham Sahmulia state that there are significant differences in both learning model. From his research, he got that the students’ outcomes which’s taught by the Contextual Teaching Learning is better than the students’ outcomes which’s taught by the Realistic Mathematics Education those were taught in VIII grade. These make the researcher would like to do the research between that two model learning in difference school level and difference problem.

Contextual Teaching and Learning (CTL) is a concept that helps teachers link the content of subjects to real world situations and motivate students to make connections between knowledge and application in their lives as family members, citizens, and workers

Elaine B. Johnson (in Trianto, 2009) said contextual learning is a system that stimulates the brain to compose patterns that embody meaning. Furthermore, Elaine says that contextual learning is a learning system that matches the brain

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that produce meaning by linking academic content to the context of the daily life of students. Thus, contextual learning is an attempt to make students active in pumping ability without losing ourselves in terms of benefits, because the students are trying to give the concept of simultaneously apply and relate it to the real world.

Contextual Teaching is a teaching that allows students kindergarten till high school to strengthen, expand, and apply their academic knowledge and skills in a variety of arrangements in and outside the school in order to solve the problems of the real world or simulated problems. (Trianto,2009: 104 – 105)

Meanwhile, according to Hans Freudenthal (in Wijaya, 2012: 20) realistic mathematics learning approach is “mathematics is a human activity”. Statement “mathematics is a human activity” shows that Freudenthal not put mathematics as a ready product, but rather as a form of activity or process. According to Freudenthal mathematics should not be given to students as a ready product that is ready to use, but rather as a form of activity in constructing mathematical concepts. Freudenthal familiar with the term “guided reinvention” as the students are actively committed to rediscover a mathematical concept with teacher guidance. Furthermore, do not put mathematics as a closed system but rather as an activity called mathematize.

A realistic problem is not necessarily a real-world problem and usually found in daily life of students. A problem called “realistic” if the problem can be imagined or real in the student’s mind (Wijaya, 2012: 20-21). Realistic problem presented by teacher at the beginning of the learning process so that the idea or mathematical knowledge can appear from the realistic problems. During the process of solving realistic problems, students will learn problem solving and reasoning, in the discussion the students will learn to communicate. The results obtained during the learning process will be easy to remember because mathematical ideas students find themselves with the help of the teacher. In the end, the students will have respect for mathematics because with realistic problem related to real life day-to-day learning process of mathematics not directly to the abstract from so that students are motivated to learn mathematics and develop

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their ideas and solve problems in mathematics. Using realistic mathematics education starts from a realistic problem is expected that students will be able to construct their own understanding and will make learning more meaningful so that students’ understanding of the material more depth that would be beneficial to enhance the ability in problem solving.

Because Contextual Teaching Learning and Realistic Mathematics Education have some similarity especially that both of learning model start from the contextual problem that related to the human daily life, so the researcher want to know whether between of both models is better in helping the students to understanding the mathematics especially in solving the problems that always exist in mathematics.

Based on the description above, the researcher has interested in conducting research entitled “The Comparison of Students’ Mathematical Problem Solving Ability on Contextual Teaching Learning and Realistic Mathematics Education Implementation on Grade XI in SMAN 1 Lubukpakam Academic Year 2016 / 2017”

1.2Problem Identification

Based on the background above, some problems can be identified as follows:

1. The students ability to solve the mathematics problem are still low. 2. Mathematics students outcome are still low because the problem

solving ability of students are still low.

3. For some students, mathematics is still as a difficult subject.

4. Students still dominant passive and tend to only receive information from the teacher.

5. Many of students still argue that mathematics can’t be applied in their daily life.

6. There are some learning model that can be applied to increase the students’ mathematical problem solving ability.

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7. The contextual teaching learning and realistic mathematics education are two models that looked similar.

1.3Problem Limitation

Based on the problem identification and the relevant research that have been described before, the research is limited on students’ mathematical problem solving ability in SMAN 1 Lubukpakam using Contextual Teaching Learning and Realistic Mathematics Education for Probability subject.

1.4Problem Formulation

Based on the problem limitation above, then the problem can be formulated as follows:

“Is the students’ mathematical problem solving ability in the classroom taught using Contextual Teaching Learning is higher than students’ mathematical problem solving ability in the classroom that using Realistic Mathematics Education?”

1.5Research Objective

Specifically, the objectives of the research is to know whether the students’ mathematical problem solving ability in the classroom taught using Contextual Teaching Learning is higher that students’ mathematical problem solving ability in the classroom that taught using Realistic Mathematics Education.

1.6Research Benefits

1. For teachers mathematics:

To be an alternatives sources for teacher in selecting the appropriate instructional model in the classroom to enhancing students’ mathematical problem solving.

2. For school:

To be as reference that can be used by the other teacher. 3. For students:

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4. For other researchers:

To be inspiration or comparison to do or develop the similar research. 1.7Operational Definition

1. Students’ mathematical problem solving ability is the ability of students in solving problem in mathematics, starting from understanding the problem, devising the plan, carrying out the plan till looking back to the problem. 2. Contextual Teaching and Learning is a kind of instructional that helps

students to understand the significance of the subject matter learned by relating the material to the context of their daily lives and help teachers relates instructional activities to subjects matter.

3. Realistic Mathematics Education is a procedure used in discussing mathematics materials that have characteristics using context, model, students contribution, interactive activities, has related material between guided reinvention and progressive mathematization principles, learning phenomenon (didactical phenomenology) and self-developed model.

57 CHAPTER V

CONCLUSION AND SUGGESTION

5.1 Conclusion

Based on the result and discussion of research in the previous chapters, can be concluded that In Hypothesis test, the data are processed based on difference of pre-test and post-test shows _{� �} = 2.878 and _� = 1.672 then _{� �} > _� that it’s mean H₀ rejected. So, can be concluded that students’ mathematics problem solving ability taught using CTL is higher than taught using RME.

5.2 Suggestion

Based on the conclusion and relevant study of this research, there are some suggestions as follows:

1. For mathematics teacher, to implement the contextual teaching learning in the learning activity such that students’ problem solving ability can be increased the students’ problem solving ability.

2. For students, to cooperate with teachers by following the steps of learning process and don’t ignore the steps of problem solving ability.

3. For next researcher, to observe another students’ ability of mathematics which can be affected by using contextual teaching learning and another choices of learning model.

4. From the research that was held, Contextual Teaching learning should be implemented as the one of the learning model in class and Realistic Mathematics Education can be implemented too in class as the other source of learning model.

5. Because in this research the learning models are implemented to subject Program Linear, it is suggested to try another topic of mathematics and relate it to others factor which may influent students’ learning outcomes.

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Abdurrahman, M. 2012. Anak Berkesulitan Belajar: Teori, Diagnosis, dan Remediasasinya. Rineka Cipta: Jakarta.

Alam, B.I. 2012. Peningkatan Kemampuan Pemahaman dan Komunikasi Matematika Siswa SD Melalui Pendekatan Realistic Mathematics Education (RME). Seminar Nasional Matematika dan Pendidikan Matematika FMIPA UNY.

Chapman, O. 2005. Constructing Pedagogical knowledge of Problem Solving: Preservice Mathematics Teachers. University of Calgary : . Cockroft, W.H. 1982. Mathematics Counts. HMSO: London.

Daryanto. 2013. Inovasi Pembelajaran Efektif. Yrama Widya: Bandung.

De Lange, Jan. 2006. Mathematical Literacy for Living from OECD-PISA Perspective. Freudenthal Institute: Netherlands.

Freudenthal, Hans. 2002. Revisiting Mathematics Education. Kluwer Academic Publishers: London.

Hudojo, Herman. 2005. Pengembangan Kurikulum dan Pembelajaran Matematika. UM Press: Malang.

Kilpatrick, J., Swafford, J., and Findell, B. (Eds.). 2001. Adding it up: Helping children learn mathematics. National Academy Press: Washington DC. Muslich. M. 2008. KTSP Pembelajaran Berbasis Kompetensi dan Kontekstual.

Bumi Aksara: Jakarta.

Ohlund, Barbara and Chong-ho Yu. .Threats to validity of Reasearch Design. : .

(available accessed at : http://web.pdx.edu/~stipakb/d ownload/PA555/ResearchDesign.html

Prakasa, Iwan. 2013. Efforts in Improving Students Mathematical Problem-Solving Ability Through Realistic Mathematics Education Approach on Subject Quadrilateral at SMP Negeri 6 Medan Academic Year 2012/2013. Skripsi. FMIPA. Unimed: Medan.

Polya, G. 1957. How To Solve It. Princeton University Press: New Jersey.

Putri, Maharani. 2012. Perbedaan Kemampuan Pemecahan Masalah Matematika Siswa yang Diajar Menggunakan Pembelajaran Matematika Realistik dengan Pembelajaran Konvensional di Kelas IX SMPN 3 Lubukpakam T.A 2012/2013. Skripsi. FMIPA. Unimed: Medan.

59

Rao, Dr. Digumarti Bhaskara. 2005. Issues in School Education.New Delhi: Discovery Publishing House.

Rambe, Yeni Septiani. 2013. Upaya meningkatkan kemampuan pemecahan masalah siswa melalui pendekatan contextual teaching and learning (ctl) pada materi sistem persamaan linear dua variabel di kelas viii MTs. Cerdas Murni T.A. 2012/2013. Skripsi. FMIPA. Unimed: Medan.

Rusman. 2012. Model-model Pembelajaran Edisi Kedua. RajaGrafindo Persada : Jakarta.

Sahmulia, J. 2014. Perbedaan Peningkatan Hasil Belajar Yang Diajar Pada Materi Sistem Persamaan Linear Dua Variabel Melalui Pendekatan Realistik dan Pendekatan Kontekstual Di Kelas VIII Mts Al-Jamiyatul Washliyah Tembung Tahun Ajaran 2013/2014. Skripsi. FMIPA. Unimed: Medan.

Saragih, Eva M. (2014). Perbedaan kemampuan pemecahan masalah dan penalaran matematika siswa menggunakan strategi pembelajaran kontekstual dengan pembelajaran konvensional. Skripsi. FMIPA. Unimed: Medan.

Shadiq, Fadjar. 2014. Pembelajaran Matematika: Cara Meningkatkan Kemampuan Berpikir Siswa. Graha Ilmu: Yogyakarta.

Sirait, B. (2013). Peningkatan kemampuan pemecahan masalah dan komunikasi matematis siswa SMK melalui pembelajaran kontekstual. Skripsi. FMIPA. Unimed: Medan.

Sudjana. 2005. Metode Statistika. Tarsito : Bandung.

Suryanto, et al. 2010. Sejarah PMRI. Departemen Pendidikan Nasional: Jakarta. Trianto. 2009. Mendesain Model Pembelajaran Inovatif-Progresif. Kencana :

Jakarta.

Wijaya, A. 2010. Pendidikan Matematika Realistik: Suatu Alternatif Pendekatan Pembelajaran Matematika. Yogyakarta : Graha Ilmu.

9

their ideas and solve problems in mathematics. Using realistic mathematics education starts from a realistic problem is expected that students will be able to construct their own understanding and will make learning more meaningful so that students’ understanding of the material more depth that would be beneficial to enhance the ability in problem solving.

Because Contextual Teaching Learning and Realistic Mathematics Education have some similarity especially that both of learning model start from the contextual problem that related to the human daily life, so the researcher want to know whether between of both models is better in helping the students to understanding the mathematics especially in solving the problems that always exist in mathematics.

Based on the description above, the researcher has interested in conducting research entitled “The Comparison of Students’ Mathematical Problem Solving Ability on Contextual Teaching Learning and Realistic Mathematics Education Implementation on Grade XI in SMAN 1 Lubukpakam Academic Year 2016 / 2017”

1.2Problem Identification

Based on the background above, some problems can be identified as follows:

1. The students ability to solve the mathematics problem are still low. 2. Mathematics students outcome are still low because the problem

solving ability of students are still low.

3. For some students, mathematics is still as a difficult subject.

4. Students still dominant passive and tend to only receive information from the teacher.

5. Many of students still argue that mathematics can’t be applied in their daily life.

6. There are some learning model that can be applied to increase the students’ mathematical problem solving ability.

10

7. The contextual teaching learning and realistic mathematics education are two models that looked similar.

1.3Problem Limitation

Based on the problem identification and the relevant research that have been described before, the research is limited on students’ mathematical problem solving ability in SMAN 1 Lubukpakam using Contextual Teaching Learning and Realistic Mathematics Education for Probability subject.

1.4Problem Formulation

Based on the problem limitation above, then the problem can be formulated as follows:

“Is the students’ mathematical problem solving ability in the classroom taught using Contextual Teaching Learning is higher than students’ mathematical problem solving ability in the classroom that using Realistic Mathematics Education?”

1.5Research Objective

Specifically, the objectives of the research is to know whether the students’ mathematical problem solving ability in the classroom taught using Contextual Teaching Learning is higher that students’ mathematical problem solving ability in the classroom that taught using Realistic Mathematics Education.

1.6Research Benefits

1. For teachers mathematics:

To be an alternatives sources for teacher in selecting the appropriate instructional model in the classroom to enhancing students’ mathematical problem solving.

2. For school:

To be as reference that can be used by the other teacher. 3. For students:

11

4. For other researchers:

To be inspiration or comparison to do or develop the similar research. 1.7Operational Definition

1. Students’ mathematical problem solving ability is the ability of students in solving problem in mathematics, starting from understanding the problem, devising the plan, carrying out the plan till looking back to the problem. 2. Contextual Teaching and Learning is a kind of instructional that helps

students to understand the significance of the subject matter learned by relating the material to the context of their daily lives and help teachers relates instructional activities to subjects matter.

3. Realistic Mathematics Education is a procedure used in discussing mathematics materials that have characteristics using context, model, students contribution, interactive activities, has related material between guided reinvention and progressive mathematization principles, learning phenomenon (didactical phenomenology) and self-developed model.

57 CHAPTER V

CONCLUSION AND SUGGESTION

5.1 Conclusion

Based on the result and discussion of research in the previous chapters, can be concluded that In Hypothesis test, the data are processed based on difference of pre-test and post-test shows _{� �} = 2.878 and _� = 1.672 then _{� �} > _� that it’s mean H₀ rejected. So, can be concluded that

students’ mathematics problem solving ability taught using CTL is higher than taught using RME.

5.2 Suggestion

Based on the conclusion and relevant study of this research, there are some suggestions as follows:

1. For mathematics teacher, to implement the contextual teaching learning in the

learning activity such that students’ problem solving ability can be increased

the students’ problem solving ability.

2. For students, to cooperate with teachers by following the steps of learning

process and don’t ignore the steps of problem solving ability.

3. For next researcher, to observe another students’ ability of mathematics which can be affected by using contextual teaching learning and another choices of learning model.

4. From the research that was held, Contextual Teaching learning should be implemented as the one of the learning model in class and Realistic Mathematics Education can be implemented too in class as the other source of learning model.

5. Because in this research the learning models are implemented to subject Program Linear, it is suggested to try another topic of mathematics and relate it to others factor which may influent students’ learning outcomes.

58

REFERENCES

Abdurrahman, M. 2012. Anak Berkesulitan Belajar: Teori, Diagnosis, dan Remediasasinya. Rineka Cipta: Jakarta.

Alam, B.I. 2012. Peningkatan Kemampuan Pemahaman dan Komunikasi Matematika Siswa SD Melalui Pendekatan Realistic Mathematics Education (RME). Seminar Nasional Matematika dan Pendidikan Matematika FMIPA UNY.

Chapman, O. 2005. Constructing Pedagogical knowledge of Problem Solving: Preservice Mathematics Teachers. University of Calgary : . Cockroft, W.H. 1982. Mathematics Counts. HMSO: London.

Daryanto. 2013. Inovasi Pembelajaran Efektif. Yrama Widya: Bandung.

De Lange, Jan. 2006. Mathematical Literacy for Living from OECD-PISA Perspective. Freudenthal Institute: Netherlands.

Freudenthal, Hans. 2002. Revisiting Mathematics Education. Kluwer Academic Publishers: London.

Hudojo, Herman. 2005. Pengembangan Kurikulum dan Pembelajaran Matematika. UM Press: Malang.

Kilpatrick, J., Swafford, J., and Findell, B. (Eds.). 2001. Adding it up: Helping children learn mathematics. National Academy Press: Washington DC. Muslich. M. 2008. KTSP Pembelajaran Berbasis Kompetensi dan Kontekstual.

Bumi Aksara: Jakarta.

Ohlund, Barbara and Chong-ho Yu. .Threats to validity of Reasearch Design. : .

(available accessed at : http://web.pdx.edu/~stipakb/d ownload/PA555/ResearchDesign.html

Prakasa, Iwan. 2013. Efforts in Improving Students Mathematical Problem-Solving Ability Through Realistic Mathematics Education Approach on Subject Quadrilateral at SMP Negeri 6 Medan Academic Year 2012/2013. Skripsi. FMIPA. Unimed: Medan.

Polya, G. 1957. How To Solve It. Princeton University Press: New Jersey.

Putri, Maharani. 2012. Perbedaan Kemampuan Pemecahan Masalah Matematika Siswa yang Diajar Menggunakan Pembelajaran Matematika Realistik dengan Pembelajaran Konvensional di Kelas IX SMPN 3 Lubukpakam T.A 2012/2013. Skripsi. FMIPA. Unimed: Medan.

59

Rao, Dr. Digumarti Bhaskara. 2005. Issues in School Education.New Delhi: Discovery Publishing House.

Rambe, Yeni Septiani. 2013. Upaya meningkatkan kemampuan pemecahan masalah siswa melalui pendekatan contextual teaching and learning (ctl) pada materi sistem persamaan linear dua variabel di kelas viii MTs. Cerdas Murni T.A. 2012/2013. Skripsi. FMIPA. Unimed: Medan.

Rusman. 2012. Model-model Pembelajaran Edisi Kedua. RajaGrafindo Persada : Jakarta.

Sahmulia, J. 2014. Perbedaan Peningkatan Hasil Belajar Yang Diajar Pada Materi Sistem Persamaan Linear Dua Variabel Melalui Pendekatan Realistik dan Pendekatan Kontekstual Di Kelas VIII Mts Al-Jamiyatul Washliyah Tembung Tahun Ajaran 2013/2014. Skripsi. FMIPA. Unimed: Medan.

Saragih, Eva M. (2014). Perbedaan kemampuan pemecahan masalah dan penalaran matematika siswa menggunakan strategi pembelajaran kontekstual dengan pembelajaran konvensional. Skripsi. FMIPA. Unimed: Medan.

Shadiq, Fadjar. 2014. Pembelajaran Matematika: Cara Meningkatkan Kemampuan Berpikir Siswa. Graha Ilmu: Yogyakarta.

Sirait, B. (2013). Peningkatan kemampuan pemecahan masalah dan komunikasi matematis siswa SMK melalui pembelajaran kontekstual. Skripsi. FMIPA. Unimed: Medan.

Sudjana. 2005. Metode Statistika. Tarsito : Bandung.

Suryanto, et al. 2010. Sejarah PMRI. Departemen Pendidikan Nasional: Jakarta. Trianto. 2009. Mendesain Model Pembelajaran Inovatif-Progresif. Kencana :

Jakarta.

Wijaya, A. 2010. Pendidikan Matematika Realistik: Suatu Alternatif Pendekatan Pembelajaran Matematika. Yogyakarta : Graha Ilmu.