THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL TO IMPROVE THE STUDENTS’ MATHEMATICAL PROBLEM SOLVING AND MATHEMATICAL COMMUNICATION ABILITY OF GRADE VIII SMP NEGERI 30 MEDAN.

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THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL TO IMPROVE THE STUDENTS’ MATHEMATICAL PROBLEM

SOLVING AND MATHEMATICAL COMMUNICATION ABILITY OF GRADE VIII SMP NEGERI 30 MEDAN

By :

Adi T.P Sinambela IDN 4123312001

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

2017

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BIOGRAPHY

Adi T.P Sinambela born in Rantau Prapat May, 27th 1993. His father’s name is Salon Sinambela and his mother’s name is Nurmaliana br. Hasibuan. He is the third child of his family. he was joined in SD swasta Methodist – 2 Rantau Prapat on 1999 and graduated in 2005. In 2005, He continued the study to SMP Negeri 2 Rantau Utara graduated in 2008. In 2008, he continued the study to SMA Swasta Sutomo 1 Medan, and 2010 he move to SMA Swasta Methodist – 1 Medan. graduated in 2012. After graduated from Senior High School, he continued his study in State University of Medan as student in bilingual class for Mathematics Education 2012.

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THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL TO IMPROVE THE STUDENTS’ MATHEMATICAL PROBLEM

SOLVING AND MATHEMATICAL COMMUNICATION ABILITY OF GRADE VIII SMP NEGERI 30 MEDAN

Adi T.P. Sinambela (4123312001) ABSTRACT

The purpose of this research was to know that Problem Based Learning model could improve the ability of mathematical problem solving and mathematical communication ability in grade eighth at SMP Negeri 30 Medan. The type of this research is classroom action research (CAR) which was implemented in SMP Negeri 30 Medan. The subject of this research were students’ of class VIII-6 of academic year 2016/2017 that consist of 30 students’. The objects of this research is mathematical problem solving and mathematical communication ability.

This study consisted of two cycles. Each cycle has two meetings. Every meeting was given student activity sheet. Students’ mathematical problem solving and mathematical communication ability was tested in the end of cycle.

After giving a treatment to students’ in the first cycle, the value of problem solving ability, with classical completeness 11 of 30 students (36.66%) has reached a level of mastery classical learning and 19 of 30 students (63.33%) have not yet reached the level of mastery learning problem solving ability, while the value of communication ability, with classical completness 11 of 30 students’ (36.67%) has reached a level of mastery classical learning, a percentage value ≥ 65%, while 19 of 30 students’ (63.33% ) has not reached the level of mastery learning communication ability.The average score of observation students’ activity is 24.167 and the average score of teacher activity is 3.3 After the revision from the first cycle to the second cycle. the value of problem solving ability, with classical completeness 30 of 27 students’ (90.00%) has reached a level of mastery classical learning and 3 students’ (10.00%) have not yet reached the level of mastery problem solving ability. While the value of communication ability mastery classical learning, 30 of 26 students’ (86.67%) has reached a level of mastery classical learning reached a value of ≥ 65% and 4 students’ (13.33%) have not yet reached the level of mastery learning communication ability, The average score of observation students’ activity is 28.133 and the average score of teacher activity is 3.85.

From the result of research, it can be concluded that implementation of problem based learning model is effective to improve students’ problem solving and mathematical ability. For teacher are encouraged to be able to implement problem based learning model as an alternative in the learning process that can improve problem solving and communication ability.

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PREFACE

Give thankfulness to God that gives the God’s mercy and spirit so that

writer can finish this thesis. The title of this thesis is “The Implementation of

Problem Based Learning Model to Improve The Students’ Mathematical Problem Solving and Mathematical Communication Ability of Grade VIII SMP Negeri 30 Medan”. This thesis was arranged to satisfy the requirement to obtain the Degree of Sarjana Pendidikan from Faculty of Mathematics and Natural Science in State University of Medan.

In the completion of this thesis, the writer received support from various parts, therefore it was appropriate writer big thanks to Mr. Pardomuan N.J.M Sinambela, S.Pd, M.Pd as my thesis supervisor who has provided guidance, direction, and advice to the perfection of this thesis. Thanks are also due to Mr. Dr. Edy Surya, M.Si, Mr. Dr. KMS. Amin Fauzi, M.Pd and Mr. Dr. Denny Haris, S.Si, M.Pd as my examiners who have provided input and suggestion from the planning to the completion of the preparation of the research of this thesis. Thanks are also extended to Prof. Dr. Asmin, M.Pd as academic supervisor and then thank you so much for all my lecturers in FMIPA.

My thanks are extended to Mr. Prof. Dr. Syawal Gultom, M.Pd, as rector of State University of Medan and employee staff in office of university head Mr. Dr. Asrin Lubis, M.Pd as Dean Faculty of Mathematics and Natural Sciences and to coordinator of bilingual Mrs. Dr. Iis Siti Jahro, M.Si and Mr. Dr. Edy Surya, M.Si. as Chief of Mathematics Department, Mr. Zul Amry, M.Si, Ph.D as Chief of Mathematics Education Study Program, Mr. Drs. Yasifati Hia, M.Si as Secretary of Mathematics Education, and all of employee staff who have helped the author.

Thanks to Mrs. Dra. Marta Ria Samosir, M.Si as principle of SMP Negeri 30 Medan who has given permission to writer do research, Mrs. Nursiah S.Pd as mathematics teacher and all teacher, staffs and also the students in grade VIII-6 SMP Negeri 30 Medan who have helped writer conducting the research.

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Especially the writer would like to express my gratitude to my dear father Salon Sinambela and my dear mother Nurmaliana br. Hasibuan that always be my hero and continues to provide motivation and prayers for the success of the writer completed this thesis. Special big thanks to my beloved brothers Pardomuan Sinambela, Dmitri Sinambela, my sisters in law Elvri Sembiring, Riana Putri and my nephews Orlando Sinambela, Orlyn Sinambela, Orlanneil Sinambela and Skye Sinambela that always give me support even moril or material and all my family for all pray, motivation, and support until the end of writer’s study.

Writer wants to say thanks to my best friends in Bilingual Mathematics Class 2012 especially for Aida, Aisyah, Desy, Erika, Febby, Friska E, Friska S, Mutiara, Padillah, Rahima, Rani, Bella, Windy and Bro Wibowo, Bro Rudi, Bro Satoto for the valuable support and motivation. And also my familiy in IKBKM and for my friends in PPL SMA Negeri 2 Lintong Nihuta for motivation and your support that have give me the best experience.

The writer should give a big effort to prepare this skripsi, and the writer know that this skripsi have so many weakness. So that, the writer needs some suggestions to make it be better. And big wishes, it can be improve our knowledge.

Medan, January 2017 Author,

Adi T.P. Sinambela ID. 4123312001

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PREFACE

Give thankfulness to God that gives the God’s mercy and spirit so that

writer can finish this thesis. The title of this thesis is “The Implementation of

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Medan, January 2017 Author,

Adi T.P. Sinambela ID. 4123312001

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TABLE OF CONTENTS

Page

Sheet of Agreement i

Biography ii

Abstract iii

Preface iv

Contents vi

List of Figure ix

List of Table xi

List of Appendix xiii

CHAPTER I INTRODUCTION 1

1.1. Background 1

1.2. Problem Identification 14

1.3. Problem Limitation 14

1.4. Problem Formulation 15

1.5. Research Objectives 15

1.6. Research Benefits 15

1.7. Operational Defenitions 16

CHAPTER II LITERATURE REVIEW 17

2.1. Theoretical Framework 17

2.1.1. Mathematical Problem Solving Ability 17 2.1.2. Mathematical Communication Ability 20

2.2. Problem Based Learning 28

2.2.1. Characteristics of Problem Based Learning 30 2.2.2. Principles of Problem Based Learning 31 2.2.3. Problem Based Learning Objectives 32 2.3. Learning Theory Support of Problem Based Learning 32 2.4. The Steps of Problem Based Learning Model 34 2.5. The Learning Model of Problem Based Learning 34 2.5.1. Application of Problem Based Learning Model 35

2.5.2. Learning Example 35

2.6. The Advantages and Diadvantages of Problem Based Learning 37

2.7. Relevant Research 37

2.8. Conceptual Framework 38

2.8.1. Application of Problem Based Learning can Improve 38 Mathematical Problem Solving

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vii

Mathematical Communication

2.9. Hypothesis Action 40

CHAPTER III RESEARCH METHODOLOGY 41

3.1. Type of Research 41

3.2. Location and Time of Research 41

3.2.1 Location of Research 41

3.2.2 Time of Research 41

3.3. Subject and Object of Research 41

3.3.1. Subject of Research 41

3.3.2. Object of Research 42

3.4. Research Procedure 42

3.5. The Procedure of Research 44

3.5.1.1st Cycle 45

3.5.1.1. Problem I 45

3.5.1.2. Planning Action I 46

3.5.1.3. Implementation of Action I 46

3.5.1.4. Observation I 47

3.5.1.5. Data Analysis I 48

3.5.1.6. Reflection I 48

3.5.2.2nd_Cycle ₄₉

3.5.2.1. Planning Action II 49

3.5.2.2. Implementation of Action II 49

3.5.2.3. Observation II 50

3.5.2.4. Data Analysis II 50

3.5.2.5. Reflection II 50

3.6. Data Collection Instruments 53

3.6.1. Observation 53

3.6.2. Mathematical Problem Solving and Mathematical 53 Communication Ability Test

3.7. Data Resources 53

3.8. Research Instruments 54

3.9. Observation 54

3.9.1. Mathematical Problem Solving and Mathematical 55 Communication Ability Test

3.10. Data Analysis Techniques 55

3.11. The Process of Students Answers 56

3.12. Indicator of Success 64

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CHAPTER IV RESULTS AND DISCUSSION 66

4.1. Description of Research Result 66

4.1.1.1st Cycle 66

4.1.1.1. Problem I 66

4.1.1.1.1. Mathematical Problem Solving 66 4.1.1.1.2. Mathematical Communication 68

4.1.1.2. Action Planning I 69

4.1.1.3. Implementation of Action I 70

4.1.1.4. Observation I 71

4.1.1.5. Data Analysis I 72

4.1.1.5.1. The Results of Mathematical Problem 72 Solving and Mathematical Communication Test 1 (1st Cycle)

4.1.1.5.2. Analysis of Teacher Ability to Manage 79 Learning Process (1st_Cycle)

4.1.1.5.3. Analysis of Students’ Sheet Activity 81 (1st Cycle)

4.1.1.6. Reflection (1st Cycle) 83

4.1.1.7. Conclusion (1st Cycle) 85

4.1.2. 2nd Cycle 85

4.1.2.1. Problem II 85

4.1.2.2. Action Planning II 86

4.1.2.3. Implementation of Action II 86

4.1.2.4. Observation II 87

4.1.2.5. Data Analysis II 88

4.1.2.5.1. The Results of Mathematical Problem 88 Solving and Mathematical Communication Test 2 (2nd Cycle)

4.1.2.5.2. Analysis of Teacher Ability to Manage 94 Learning Process (2nd Cycle)

4.1.2.5.3. Analysis of Students’ Sheet Activity 96 (2nd Cycle)

4.1.2.5.4. Reflection (2nd Cycle) 97 4.1.2.5.5. Conclusion (2nd Cycle) 98 4.2. Discussion of Research Result 103

CHAPTER V CONCLUSION AND SUGGESTION 106

5.1. Conclusion 106

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REFERENCE 108

APPENDIX 112

DOCUMENTATION OF RESEARCH 218

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TABLES

Page Table 2.1 Syntax of Problem Based Learning

Table 3.1 The Steps in 1st Cycle Table 3.2 The Steps in 2nd Cycle Table 3.3 Guidance Scoring of Mathematical Problem Solving

Ability

Table 3.4 Guidance Scoring of Mathematical Communication Ability

Table 3.5 Criteria of Avarage Assesment Observation

34 51 52 56 57 58 Table 3.6 List of Scores Predicate and Criteria

Table 3.7 Interval Score of Communication Ability

59 60 Table 3.8 List of Score Predicate and Criteria

Table 3.9 Level of Achievement and Teacher to Qualification the Classroom Manage

Table 3.10 Criteria of Assesment Students’ Activity

Table 4.1 Description of Diagnostics Test of Mathematical Problem Solving

Table 4.2 Description of The Level of Students’ Problem Solving Ability in Diagnostics Test

Table 4.3 Description of Diagnostics Test of Mathematical Communication 60 62 63 66 67 68

Table 4.4 Description of The Level of Students’ Communication Ability in Diagnostics Test

Table 4.5 Percentages of Mathematical Problem Solving Completeness I

Table 4.6 The Level of Students’ Ability to Understand The problem of Problem Solving Test I

Table 4.7 The Level of Students’ Ability to Plan The problem of Problem Solving Test I

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Table 4.8 The Level of Students’ Ability to Solve The problem of Problem Solving Test I

Table 4.9 The Level of Students’ Ability to Looking Back The Result of Problem Solving Test I

Table 4.10 Percentages of Mathematical Communication Completeness I

Table 4.11 Description of Observation Teacher Activity in 1st_Cycle

Table 4.12 Description of Observation Students Activity in 1st_Cycle Table 4.13 Percentages of Mathematical Problem Solving

Completeness II

Table 4.14 The Level of Students’ Ability to Understand The problem of Problem Solving Test II

Table 4.15 The Level of Students’ Ability to Plan The problem of Problem Solving Test II

Table 4.16 The Level of Students’ Ability to Solve The problem of Problem Solving Test II

Table 4.17 The Level of Students’ Ability to Looking Back The Result of Problem Solving Test II

Table 4.18 Percentages of Mathematical Communication Completeness II

Table 4.19 Description of Observation Teacher Activity in 2nd Cycle Table 4.20 Description of Observation Students’ Activity in

2nd_Cycle Table 4.21 The Results of Mathematical Problem Solving Ability

1st_{Cycle and 2}nd_Cycle

Table 4.22 The Results of Mathematical Communication Ability 1st Cycle and 2nd Cycle

79 82 88

94 97

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ILLUSTRATION

Page Figure 1.1 Sample of Students’ Answer Sheet Number 1

Figure 1.2 Sample of Students’ Answer Sheet Number 2 Figure 1.3 Sample of Students’ Answer Sheet Number 3

Figure 1.4 Sample of Students’ Answer Sheet Number 4 8 11 11 12 12 Figure 3.1 Classroom Action Research Process of Kemmis Model

Figure 4.1 The Ability of Problem Solving Students’ 1st_{Cycle and} 2nd Cycle

Figure 4.2 The Level of The Number of Students’ Complete The Study of Mathematical Problem Solving Ability Test 1st Cycle and 2nd Cycle

Figure 4.3 The Ability of Communication Students’ 1st_{Cycle and 2}nd Cycle

Figure 4.4 The Level of The Number of Students’ Complete The Study of Mathematical Communication Ability Test 1st Cycle and 2nd Cycle

Figure 4.5 The Level of The Teacher Ability to Manage The Learning Process 1st Cycle and 2nd Cycle

Figure 4.6 The Level of Percentages Students’ Activity 1st Cycle and 2nd Cycle

42 99

100

101

102

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APPENDICES LIST

Page

Appendix 1 Lesson Plan I 112

Appendix 2 Lesson Plan II 119

Appendix 3 Lesson Plan III 126

Appendix 4 Lesson Plan IV 133

Appendix 5 Students’ Activities Sheet I 140

Appendix 6 Students’ Activities Sheet II 142

Appendix 7 Students’ Activities Sheet III 144

Appendix 8 Students’ Activities Sheet IV 146

Appendix 9 The Alternative Solution of SAS I 148

Appendix 10 The Alternative Solution of SAS II 149 Appendix 11 The Alternative Solution of SAS III 150 Appendix 12 The Alternative Solution of SAS IV 152 Appendix 13 Blueprint of Initial Diagnostic Test 154 Appendix 14 Blueprint of Mathematical Problem Solving Ability Test I 155 Appendix 15 Blueprint of Mathematical Problem Solving Ability Test II 156 Appendix 16 Blueprint of Mathematical Communication Ability Test I 157 Appendix 17 Blueprint of Mathematical Communication Ability Test II 158

Appendix 18 Diagnostic Test 159

Appendix 19 Mathematical Problem Solving and Communication Ability 160 Test I

Appendix 20 Mathematical Problem Solving and Communication Ability 163 Test II

Appendix 21 The Alternative Solution of Diagnostic Test 165 Appendix 22 The Alternative Solution of Mathematical Problem Solving 168

and Communication Ability Test I

Appendix 23 The Alternative Solution of Mathematical Problem Solving 174 and Communication Ability Test II

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Appendix 24 Validation Sheet of Mathematics Problem Solving Ability 178 Test I

Appendix 25 Validation Sheet of Mathematics Communication Ability 179 Test I

Appendix 26 validation Sheet of Mathematics Problem Solving Ability 180 Test II

Appendix 27 Validation Sheet of Mathematics Communication Ability 181 Test II

Appendix 28 Validation Sheet of Mathematics Problem Solving Ability 182 Test I

Appendix 29 Validation Sheet of Mathematics Communication Ability 183 Test I

Appendix 30 validation Sheet of Mathematics Problem Solving Ability 184 Test II

Appendix 31 Validation Sheet of Mathematics Communication Ability 185 Test II

Appendix 32 Validation Sheet of Mathematics Problem Solving Ability 186 Test I

Appendix 33 Validation Sheet of Mathematics Communication Ability 187 Test I

Appendix 34 validation Sheet of Mathematics Problem Solving Ability 188 Test II

Appendix 35 Validation Sheet of Mathematics Communication Ability 189 Test II

Appendix 36 Guidelines for Scoring of Diagnostics Test 190 Appendix 37 Guidelines for Scoring of Mathematical Problem Solving 192

and Mathematical Communication Ability Test I

Appendix 38 Guidelines for Scoring of Mathematical Problem Solving 194 and Mathematical Communication Ability Test I

Appendix 39 Observation Sheet of Students’ Activity (1st_Meeting) ₁₉₇ Appendix 40 Observation Sheet of Students’ Activity (2nd_Meeting) ₁₉₉

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Appendix 41 Observation Sheet of Students’ Activity (3rd Meeting) 201 Appendix 42 Observation Sheet of Students’ Activity (4th Meeting) 203 Appendix 43 Observation Sheet of Teacher Activity (1st Cycle) 205 Appendix 44 Observation Sheet of Teacher Activity (2nd Cycle) 207 Appendix 45 The Result of Diagnostic Test Mathematical Problem Solving 209 Appendix 46 The Result of Diagnostic Test Mathematical Communication 210 Appendix 47 The Result of Mathematical Problem Solving Test I 211 Appendix 48 The Result of Mathematical Problem Solving Test II 212 Appendix 49 The Result of Mathematical Communication Test I 214 Appendix 50 The Result of Mathematical Communication Test II 215 Appendix 51 The Result of Observation Students’ Activity (1st_Cycle) ₂₁₆ Appendix 52 The Result of Observation Students’ Activity (2nd_Cycle) ₂₁₇

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CHAPTER 1 INTRODUCTION

1.1.Background

Mathematics is one of the subjects studied at each school level both at the primary, secondary and higher education. Mathematical objects have an abstract and deductive thinking patterns and consistent (Depdikbud, 1996). In addition, functions of mathematics is to develop the ability of students’ to communicate using numbers and symbols as well as the sharpness of reasoning that can help clarify and resolve problems in daily life.

Mathematics in school is not just for the purposes of the calculation, but more than that, mathematics already being used to help the development of a variety of science and technology. The importance of mathematics to study because so many potential uses include the study of mathematics, we are able to do other calculations, the calculation becomes more simple and practical, and to learn mathematics is expected that students’ were able to become a man who thinks logically, critically, diligent, responsible and capable of resolving the problems (Ruseffendi, 1991: 70)

The world we live where change is accelerating and where the need for mathematics as way of representing, communicating and predicating events is improving. In the century the important requrement is what we learn must be utilized in daily life to cope with dynamic competition. To face the situation we (teachers) want to produce critical thingking capabilities among the learners. Through there are many methods to teach mathematics in the world the only method being adopted by mathematics teacher is lecture method (instruction). Poor learning outcome is due to pooe instructional strategy. This is an important problem in teaching mathematics among the learners. This way supported by Ogunbiyi (2004) in his study it has been quoted “in most part of the world it has been discovered that lecture method or traditional expository method is being used by mathematics teachers.

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Antonoplos (1985) and Stevenson (1987) in their studies showed the understanding the importance of mathematics, superiority of Japanese students’ in mathematics when compared with their counterparts from Sweden, Australia, England and the United states. Stevenson also explained that the Japanese teachers are enthusiastic in their classroom practices. They engage the attention of the pupils in discussion and debate on mathematics. The children were encouraged to make meanings and connections through discussion and giving various meanings on the same idea or cocept to be leant (Stigler, lee and Stevenson, 1987: Antomoplos 1985). The length of hour put into mathematics teaching and learning was highest when compared with those other countries. The commitment has also justified their cultural believe in hard work for success in mathematics rather than innate ability (Abimbade,2012)

To engage the attention of the learners our teachers must adopt some different method to teach mathematics which provide plaform to learners to think, active, brainstorm and learning have come to the fore in discussions of classroom or transferable learning and gives motivation. The only economical method which provides all the above said is problem based learning (PBL) method. This article first describes different philosophy and methods of teaching mathematics and problem based learning (PBL) and goal of PBL and the adcantages, secondly it provide evidence that PBL is effective for teaching mathematics by conducting experiment.

Problem solving is a basic human activity in life because in order to survive and develop human beings are always dealing with the problem. education is expected to help students’ have good problem solving abilities in order to resolve issues and questions relating to the subjects, especially mathematics. In fact, according to most students as mathematics is a science and a mere abstract formula. The students’ perceptions makes the subjects of mathematics instruction are not well liked by the students so the effect on students' ability to master and have an impact on the ability of mathematical problem solving. Mathematics is part of the science that has great contribution in the development of science and technology (Sopiah,S.,dkk, 2009). The rapid development of science and

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technology have a positive impact of improving the welfare of society but unconsciously also had a negative impact on the development of science and technology one of which is the pollution of the river were not immediately stopped eating will reduce water quality and increase the chances of flooding.

Improving the chances of flooding can not be separated from human actions. One cause is the lack of public awareness on the environment as a result of a lack of public understanding about it - whatever it can cause flooding. Therefore, the duty of a teacher to prepare young people to better understand the causes of flooding and other natural disasters, through the study of disaster (Rusilowati,A.,dkk,2012)

Alternative learning model that can condition students’ to be more active and can enhance the understanding of disaster is a model of Problem Based

Learning Visionary SETS (Envireontment Science Technology and Society). PBL

is a learning model centered on the learner that empower learners to experiment / lab work, integrate theory and practice and apply their knowledge and abilities to develop a viable solution to the problem as defined (Savery,J.R., 2006). In learning activities with a model PBL students’ will be faced with the problems that exist in their environment or problems in real life. As a result, students can improve solving abilities and allows the student to understand the concept (Trianto,2011: 67). PBL learning model provides a positive influence to improve problem solving abilities, critical and creative thinking (Selcuk, 2013)

SETS element integrated in the subjects of mathematics in the learning activities will facilitate students’ in understanding the events - natural disasters with mathematical concepts. SETS is the integration between science (Science), the environment (Environment), technology (Technology) and communities (Society) (RusilowatiA.,dkk, 2012). SETS element in mathematics learning activities will provide an overview or a real example of the relation of science (mathematics) with objects or events that occur in the life of an environmental day - day. Consequently SETS can enhance students’ understanding of disaster.

Curriculum of mathematics has been approved to change the system of mathematics education with the development of Indonesian society. Mathematical

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knowledge will be obtained by students through the learning process. Learning will be more successful if it had known the objectives to be achieved. On curriculum Education Unit (KTSP) described awarded mathematics learning objectives are:

(1) Understanding the mathematical concept, explain the link between concepts and apply concepts or algorithms in a flexible, accurate, efficient, and precise in problem solving,

(2) Using the reasoning in the patterns and nature, perform mathematical manipulation in making generalizations, compile evidence or explain mathematical ideas and questions,

(3) Solve problems that include the ability to understand the problem, devised a mathematical model, complete the mathematical model and interpret the obtained solution,

(4) Communicate ideas with symbols, tables, diagrams or other media to clarify the situation or problem,

(5) Having respect for the usefulness of mathematics in life is curiosity, concern and interest in studying mathematics, as well as the resilient nature and confidence in problem solving (BSNP, 2006).

In accordance with the common goal of learning mathematics formulated NCTM (National Countil of Teachers of Mathematics) is a problem solving ability, communication abilities, ability to teconnect, reasoning ability, and representation. The purpose of learning mathematics not only divert the mathematical knowledge to students, but also develop the potential of the students’ and has the knowledge allowing the occurrence of a change in the mindset of the students’.

The mathematical problem solving and mathematical communication is ability of students’ in mathematics to be possessed by students Junior High School in the achievement of the curriculum, (BSNP 2006) suggested that mathematics learning objectives, among others:

(1) Solve problems that include the ability to understand the problem, devised a mathematical model, finish models and interpret the obtained solution,

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(2) To communicate ideas with symbols, tables, diagrams, or other media to clarify the circumstances or problem.

Both of these are very necessary for a students’ to develop the abilities of mathematical, as disclosed Sumarmo (in Somakin; 2007) problem solving ability, and mathematical communication is referred to as the power of mathematics (mathematical power) or the abilities of mathematical (doing the math), so that mathematics can be classified into thinking low level and higher level thinking.

NCTM (2000) argued that solving the problem is the process of applying the knowledge that has been acquired earlier in new and different situations. In addition NCTM also express purpose of teaching problem solving in general is to (1) Build knowledge of new mathematics,

(2) Solve problems that arise in mathematics and in the context of other contexts,

(3) Implement and customize a variety of appropriate strategies to solve the problem

(4) Monitor and reflect on the process of mathematical problem solving.

In addition to the ability of mathematical problem solving, mathematical communication ability also need to be developed, as disclosed Baroody (in Ansari; 2009) that there are at least two important reasons why communication in mathematics learning need to be nurtured in school, the first is not just a mathematical thinking tools, tools to find patterns, solve problems or take decisions but mathematics as well as a tool to communicate their ideas clearly, precisely and concisely, the second is as a social activity in learning school mathematics, mathematics as well as a vehicle for interaction between students’ and also as a means of communication teachers and students’.

Suherman, (2003: 92) argues that "an issue usually contains a situation that encourages a person to solve it will but do not know firsthand what is to be done to resolve it ". Therefore, if a problem is given to a students’, and the students’ can know immediately answer correctly to the question is given, then the issue is not said to be a problem.

Problem solving is a process involving a task that the solution method is not known before, to find solution students’ should map out their knowledge, and

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through this process they often develop new knowledge about mathematics, thus solving the problem is an integral part in all parts of mathematics, and also should not be taught in isolation from mathematics (Turmudi, 2008).

Branca (Krulik and Reys, 1980) suggests that solving the problem of having three interpretations, that is: problem solving (1) as the main purpose; (2) as a process, and (3) as a basic skill. Thirdly it has implications in mathematics.

First, if problem solving is an objective he regardless of the issues or a specific procedure, also regardless of the material of mathematics, the most important is how to solve the problem until it succeeds. In this case the problem solving as the main reason for learning mathematics. Second, if problem solving as a process point of view, the emphasis is not solely on the results, but rather how the methods, procedures, strategies and measures were developed through reasoning and communication to solve the problem. Third, problem solving as basic abilities or life abilities (life skills), because every human being should be able to solve its own problems. So problem solving is the basic abilitiess should be owned by every students’.

Mathematics teachers must teach students not only to solve problem but also to learn about mathematics through problem solving. While “many students’ may develop procedural fluency...”. they often lack the deep conceptual understanding necessary to solve new problems or make connections between mathematical ideas. This presents a challenge for teachers: problem based learning (PBL) provides oppurtunities for teachers to meet this challenge.

PBL exists a teaching method grounded in the ideals of constructivism and students’ centered learning. When using PBL, teachers help students’ to focus on solving problems within a real life context, encouraging them to consder the situation in which the problem exists whrn trying to find solutions. The majority of research examining PBL focuses on its use in medical schools, wih the key features being (a) the use of collaborative small group work, (b) a student centered approach, (c) the teacher as facilitator and (d) the use of real – life problems as the organizing focus.

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In the medical arena, groups of students’ are given a set of realistic patient symptoms and expected to research possible diagnoses and courses of treatment; groups work independently, developing and answering their own questions. If, during this diagnostic phase, a group is unsuccesful in adressing key issues, the instructor notes this on their assestment but does not provide the solution. In the classroom setting, it is this aspect of PBL which presents the most significant challenge, requiring teachers to shift from direct instruction to supporting students’ organize their own learning

To measure the ability of solving mathematical problems required several indicators. The indicator according Sumarmo (2012) as the following:

(1) identify the elements that are known, asked, and the adequacy of the elements,(2) create a mathematical model, (3) implement a strategy to solve the problem within / outside of mathematics, (4) to explain / interpret the results, (5) complete the mathematical model and real problems, (6) use math significantly. According to George Polya explained in How to Solve It outlines put forward four main steps in solving the problem, namely: Understanding the problem, Devising a Plan, Carrying out the Plan, and Looking Back (Motter, 2010).

In this research, problem solving capabilities will be measured through students ability to solve a problem by using the steps in solving problems by Polya, namely: (1) understand the problem, (2) plan the solution, (3) execute a plan settlement issues, and (4) lookings back, arguing that strategy commonly used.

Mathematical communication abilities and problem solving is important to be mastered by students’. This is because people need intellectuals who are able to solve the problem in a systematic and able to interpret into spoken or written language that is easy dipaham. College as a place of formal education is expected to facilitate the development of mathematical communication abilities and problem solving students’.

Problem Based Learning (PBL) as one of the learning model has a characteristic that always begins and focused on the issue. In the PBL students can work in groups - small groups and have to identify what they know and what they

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do not know and have to learn fatherly solve a problem. The main role of the faculty to facilitate the group process and learn, not to provide a direct answer.

Several studies of PBL in mathematics / statistics obtained positive results (Warigan 2007; Dina, 2008). But research at the same time see the mathematical communication abilities and problem solving through PBL on statistics has not been done. Hand, the research related to communication abilities are mathematically still unsatisfactory results (Firdaus, 2005).

Based on initial observation are PGRI Sumbar STKIP student who took the course, Elementary Statistics is found that underprivileged students in solving mathematical problems related to the real world and are not accustomed to pour thoughts orally or in writing. Their difficulty in determining the problem, steps that must be selected to find a solution and to determine patterns that can be used. Students’ prefer that the matter be given in the form of symbols and numbers that instantly know what to search without having to interpret the matter beforehand. Questions about the "why" the most difficult to answer. Students’ are groundless, "know the answer but hard for phrased".

Besides the ability to problem solving, mathematical communication ability are also required in the learning of mathematics. According to The Intended Learning Outcomes (Armiati 2009), mathematical communication is a essential abilities in mathematics, namely the ability to express mathematical ideas coherently to friends, teachers and others through the spoken and written language. Through this mathematical communication abilities students’ can develop an understanding of mathematics when using correct mathematical language to write about mathematics, clarify ideas and learn to make the argument and represents the mathematical ideas verbally, images and symbols.

Baroody (Chap Sam and Cheng Meng, 2007) suggests that there is two reasons to focus on the first mathematical communication, mathematics is a language which is essential for mathematics itself. Mathematics is not just as thinking tools that help students’ to develop a pattern, solve problems and provide conclusions, but also as a means to communicate thoughts, varying ideas in a clear, precise and concise. Second, learning and teaching mathematics is a social

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activity that involves at least two parties, namely the teachers and students’. Communicating with friends is an important activity to develop abilities communication, so that students can learn as a mathematician and able to solve the problem successfully.

To measure the students mathematical communication abilities required some of the indicators proposed by Sumarmo (2012), among others is

(1) Connect real objects, pictures and diagrams into mathematical ideas,

(2) Explain ideas, situations and relationships math orally or in writing with real objects, pictures, graphics or algebraic form,

(3) States the events of everyday language or math symbol, (4) Listening, discussing and writing about the mathematics,

(5) Reading and writing mathematics presentation prepare questions that are relevant,

(6) To make a conjecture, make the argument, formulate definitions and generalizations.

Meanwhile, according to NCTM (2000) indicators mathematical communication can seen from:

(1) The ability to express mathematical ideas through word of mouth, writing, and demonstrate and describe it visually,

(2) The ability to understand and evaluate mathematical ideas, either orally, in writing, or in other visual forms,

(3) The ability to use terms, notations of mathematics and structure of the structure to present ideas, describe relationships with models of the situation.

Indicators of mathematical communication ability that will be used in this study were

(1) Explain the idea and the situation in writing,

(2) Certify the picture or diagram into mathematical ideas, (3) Certify the situation into mathematical models / drawings.

The above description shows that a high level of ability in mathematics such as problem solving and mathematical communication is still much to be desired in the curriculum of KTSP 2006. Based on observations of researchers in

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SMP Negeri 30 Medan obtained information that mathematics learning in school do not fully develop High level capabilities such as the ability of students’ mathematical problem solving and mathematical communication. Learning mathematics is generally still traditionally takes place with the characteristics centered on the teacher, using an approach that is expository so the teacher to dominate the process of learning activities in the classroom while students passively, in addition to training provided more questions that are routine, so less trained power of reason in problem solving and thinking abilities students’ only at low levels.

Conditions in schools, math teacher pay less attention to the improved activity of students’ in learning. This was disclosed Wahyuddin (in Rahman, 2012) that most students’ looked closely following any explanation or information from the teacher. Students’ very rarely ask questions to the teacher so the teacher engrossed himself explained what he had prepared, and the students’ receives course delivered by teachers. Learning so inclined in one direction, learning activities more teachers than the interaction between students’. That is, learning tends to be centered on the teacher (teacher centered).

Low ability mathematical problem solving and communication students’ also happened in SMP Negeri 30 Medan. Based on observations and interviews with teachers of mathematics courses on Wednesday, February 10th 2016 at the school, there was information that the students often have difficulty expressing problem situation into a mathematical model, especially if the matter is done in need of an image in its completion. This suggests that the ability of the students’ described the situation problem and stated solution to the problem using pictures, charts, tables, or algebraically still low.

Low ability mathematical problem solving and communication students’ can be seen from one of the examples of the tested sample questions to the students of SMP Negeri 30 Medan in class VIII-6.

Problems example 1 :

1. Budi buy 20 candies in the shop which is near his home. When he was at home, his brothers and sister (Iwan, Wayan, and Wati) asking for candy and

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then, Budi candies remaining 11 seeds. How much candy requested by the third brother Budi?

Figure 1.1 Sample of Students’ Answer Sheet Number 1

Based on Figure 1.1 students do not write what is known on the matter, in which communication and problem solving abilities are indispensable in writing what is known and what is asked in the question to resolve the problem.

Problem example 2 :

2. Every day Fitri set aside allowance for savings at home. After a 11days Fitry money get to Rp 154,000.00. How much money, Fitri aside her money every day?

Figure 1.2 Sample of Students’ Answer Sheet Number 2

Based on Figure 1.2 students also did not write what is known and what is asked the question, where this is necessary in solving problems and also students do not write completely the formula used in solving the problem. Problem example 3 :

3. Knowing, the price pairs of shoes twice the price of a pair of slippers. A trader bought four pairs of shoes and three pairs of slippers. The traders must paying Rp 275,000.00.

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a. Make a mathematical model of the description above.

b. Solve the mathematical model. Then, specify the price of 3 pairs of shoes and 5 pairs of slippers.

Figure 1.3 Sample of Students’ Answer Sheet Number 3

Problem example 4

4. A farmer has a rectangular shaped piece of land. The land width of 6 m shorter than the length. If the ground around 60 m, determine the land area farmers.

Figure 1.4 Sample of Students Answer Sheet Number 4

Based on the students work on the Figure 1.1, Figure 1.2, Figure 1.3 and Figure 1.4 we can see that the wrong occurred because the students’ have not been able to outline what is known and what is asked in the problem so that the students’ answers yet precise and students tend to solve problems quickly regardless of the question on the matter properly and carefully, based on the results of diagnostics tests given to students’ obtained results that the students’ ability in planning to solving the problem, solve the problem, looking back the problems were resolved and communicate what is gained from the issue is still

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very low it can be seen from the results of diagnostics tests of students who have been granted before this research begin.

Based on case that have been mentioned above the problem solving and mathematical communication is important to be known by students. Therefore, it should be considered an attempt to enhance the problem solving and mathematical communication, One strategy to enhance the mathematical problem solving and mathematical communication is to provide a guides that can steer students toward problem solving and mathematical communication, which it found in Problem based learning (PBL).

Problem based learning is an approach to learning that involves students’ actively optimally, allowing students to explore, observation, experimentation, investigation, problem solving abilities and concepts that integrate the basic concepts of the various content areas. These lessons include deduce information about the problem, synthesize and present what has been obtained by the students’ to be presented to the other students. Problem based learning (PBL) means that students’ make sense of the situation and seek to build and understand the concept of a material in a way involved in solving the problem. In problem based learning teachers are expected to be able to create learning activities that allow students’ and mathematical processes and investigate, compile conjecture, explore, plan your moves and then complete the steps to resolve the problem. In this case the teacher acts as a guide, facilitator and motivator, based on Teaching experience program in school (PPL), I discovered that the problem solving and communication abilities students are very low so I was interested to do this research using the Problem based learning model and the first step I did was to measure the level of problem solving abilities and communication abilities of students’ in diagnostics tests improved testing diagnostics student must achieve a minimum of 85% of the total students, so it can be said that the problem solving and communication students succeed to improved.

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Based on this background, the researchers are interested to do research with title : The Implementation of Problem Based Learning Model to Improve The Students’ Mathematical Problem Solving and Mathematical Communication ability of Grade VIII SMP Negeri 30 Medan.

1.2. Problem Identification

Based on the background of the problems that have been mentioned above then becomes identifying the causes of the low ability of mathematical problem solving and communication students’ are:

1. Students’ mathematical problem solving and communication ability is low.

2. Students’ has difficulty to solve mathematical problem solving and mathematical communication.

3. Learning process is dominated by the teacher so the students’ only receive without have learning experience.

4. Implementation of Problem Based Learning is an effort to improve students’ mathematical problem solving and mathematical communication ability.

1.3 Problem Limitation

Because the extent of the problem and limited ability, time and cost so the researchers need to make a limitation problem in this research. As for the Limitation Problem in this research are:

1. Research subject is the eighth grade students of SMP Negeri 30 Medan in academic year 2016/2017.

2. Model of learning used is Problem Based Learning (PBL).

3. Problem solving and communication ability the eighth grade students’ of SMP Negeri 30 Medan in academic year 2016/2017.

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1.4. Problem Formulation

Problem Formulation od this research is:

1. Does the implementation of Problem Based Learning model improve students’ mathematical problem solving and communication ability in grade VIII at SMP Negeri 30 Medan ?

2. How does Problem Based Learning model improve students’ mathematical problem solving and communication ability in grade VIII at SMP Negeri 30 Medan ?

3. Do students’ activities improve afer the implementation of Problem Based Learning in grade VIII at SMP Negeri 30 Medan ?

1.5. Research Objectives

This research was conducted with the following objectives:

1. Knowing whether students’ problem solving and communication ability improve after the implementation of problem based learning model. 2. Improving students’ mathematical problem solving and mathematical

communication ability through problem based learning in grade VIII at SMP Negeri 30 Medan.

3. Knowing the improving of students’ activities after the implementation of Problem Based Learning in grade VIII at SMP Negeri 30 Medan.

1.6. Research Benefits

The results of this study are expected to provide information and to provide the following benefits:

1. For students’, in still high order thingking abilities in problem solving and communication.

2. For teachers, it can use problem based learning model for improving students’ mathematical problem solving and communication ability in learning activities.

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3. For researchers, as information for students’ who are conducting research using Problem Based Learning (PBL) to improve students’ mathematical problem solving and communication ability in learning activities.

1.7 Operational Definitions

Here are some terms that need to be defined operationally with the intent to avoid the mistakes of interpretation:

1. Problem based learning model: a model of learning which refers to five learning basic steps: (1) orentation students’ on issues (2) organize the students’ to learn (3) guiding the investigation of individual and group (4) develop and presents the results of work (5) analyze and evaluate the problem solving process.

2. The ability of problem solving is the students' ability in solving mathematical problems by paying attention to the process of finding answers by step troubleshooting steps: (1) understand the problem, (2) planning processes, (3) execute processes, (4) to re examine the truth of the answers.

3. The ability mathematics communication is written communication ability as measured by students' ability to answer the questions test the communication ability shaped mathematical description consisting of (1) states the problem of daily life the day into a symbol or a mathematical language, (2) interpret images into a mathematical model, (3) write down the information on the statement into the language of mathematics.

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CHAPTER V

CONCLUSION AND SUGGESTION

5.1. Conclusion

Based on the results of research and discussion obtained the following conclusions:

1. The implementation of problem based learning model can improve students mathematical problem solving ability in SMP Negeri 30 Medan class VIII-6 Academic Year 2016/2017

2. There are improving of students mathematical problem solving ability after implementation of Problem Based Learning Model. It is determined based on test result in cycle I and cycle II, average score of cycle I average value of 58,92 and improved in the second cycle into 76.75.

3. There are improving of students mathematical communication ability after implementation of Problem Based Learning Model. It is determined based on test result in cycle I and cycle II, average score of cycle I average value of 56,38 and improved in the second cycle into 75.69 and In the cycle I the number of students who complete the mathematical problem solving ability is 36.67% (11 students) and the cycle II improved to 90.00% (27 students). and in cycle I the number of students who complete the mathematical communication ability is 36,67% (11 students) and cycle II is 86,67% (26 students)

5.2. Suggestion

The suggestion can be taken from the results of this research, such as: 1. Learning mathematics by impelementation Problem Based Learning

model can be used as an alternative effective learning to improve students mathematical problem solving ability and students activity. But for the first implementation teacher fell defficult in preparing learning and condition the class. Because Problem Based Learning is firsly giving real problem to the students without explain far explanation of the topic,

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107

students are not accostumed in solve problem will fell boring and lazy to learn. It is therefore recommended for the teacher before do learning process, teacher asks students to prepare learning material at home such as reading the topic which will be learned. So in learning students find difficulty, the can face the trouble by sharing with their group to solve the problem.

2. Problem based learning model can develop critical thingking ability of students because it needs high thingking ability of students to understand the problem and for lazy students, it is difficukt to do it so the teacher must be more guide and observe each group working so that all group member demand to be active in the group.

3. For teacher that the application of problem based learning model to improve students mathematical problem solving and mathematical communication should be applied in learning process, then the teacher must:

 Able to make problem question whicah can be used to exercise the students to do problem solving step.

 Management of time as goog as possible when learning is done.

 Understanding the phases that must be applied in problem based learning model.

 Doing small learning groups designed which are heterogenous.

 Guide and help students to open mind to solve problem.

4. To school, by due process of learning by using problem based learning requires infrastructure to provide the facalities needed to support improvement of learning in order to improve the quality, in this case an effort to improve students mathematical problem solving and mathematical communication ability.

5. For the next researcher, it is expected to use research result as comparison matter and implement problem based learning model in other topics, using attractive book and interesting SAS to make students are more interesting to do learning actively.

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108

BIBLIOGRAPHY

Abimbade, A and Afolabi, S.S.(2012), A Study of Pedagogical Approach of Mathematics Teaching In Southwestern States Of Nigeria. International Journal of Asian Social Science vol 2,no 8,pp 1182-1192. (Johann Heinrich Pestalozzi and Vitterine De Feltre)

Amir, M.T. (2009). Inovasi Pendidikan Melalui Problem Based Learning. Jakarta : Kencana Prenada Media Group

Ansari, B.I. (2009). Komunikasi Matematika: Konsep dan Aplikasi. Banda Aceh: Yayasan PeNA Banda Aceh.

Antonoplos, D.P.(1985), Students characteristics learning and curriculum in

Japan. Washington DC, Office of Educational Research and

Improvement (ed.)

Arends, Richard I. (2008). Learning To Teach (Belajar untuk Mengajar) Buku Satu. Yogyakarta: Pustaka Pelajar.

, (2011), Learning to Teach, McGraw Hill, New York.

Arikunto, Suharsimi (1991). Prosedur Penelitian : Suatu Pendekatan Praktik. Jakarta : Rineka Cipta.

Armiati. 2009. Komunikasi Matematis dan kecerdasan emosional. Seminar nasional matematika dan pendidikan matematika. FMIPA UNY. Badan Standar Nasional Pendidikan (BSNP). (2006). Panduan Penyusun KTSP

Jenjang Pendidikan Dasar dan Menengah. Jakarta: Depdiknas.

Ben – Zeev, T, & Sterberg, R.J. (1996). The Nature Of Mathematical Thingking.

Mahwah. NJ: Lawrence Erlbaum Assosiates. Inc.

Chap sam, LIM, Cheng Meng, CHEW. 2007. Mathematical Communication in Malaysian Billingual Classrooms. Paper to be presented at the 3__ APEC-Tsukuba International Conference 9-14 2007 at Tokyo and Kanazawa: Japan.

Cangara, H. (1998). Pengantar Ilmu Komunikasi. Jakarta: Raja Grafind Persada. Dahlan, J.A. (2011). Analisis Kurikulum Matematika. Jakarta: Universitas

Terbuka.

Departemen Pendidikan Nasional. 2003, Kurikulum berbasis kompetensi. Jakarta: Depdiknas.

Depdikbud. (1996). Kurikulum Sekolah Dasar, Buku IIIA, Pedoman Khusus. Jakarta: Balai Pustaka

Dina Mellita. 2008, Metode pembelajaran peer teaching dan problem based

learning untuk memotivasi sosialiasasi dalam kelas (pada

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109

Firdaus. 2005. Melalui pembelajaran dalam kelompok kecil tipe team assited indidualization (TAI) dengan pendekatan berbasis masalah (eksperimen pada salah satu SMA di Bandung). Tesis tidak dipublikasikan. Bandung: UPI

Hake, R. R., (1999).Analyzing Change/Gain Score, American Educational, Amerika.

Hari Suderajat, 2003. Implementasi kurikulum berbasis kompetensi (KBK). Jakarta: Depdiknas.

Hudojo. H. (1990). Pengembangan Kurukulum Matematika dan Pelaksanaannya di Depan Kelas. Surabaya: Usaha nasional.

Hudojo. H. (2001). Common Textbook: Pengembangan Kurikulum dan Pembelajaran Matematika. Edisi Revisi. Malang: JICA – Universitas Negeri Malang.

Ibrahim, dkk., (2000), Pembelajaran Berdasarkan Masalah, UNESA, Surabaya. Isjoni, (2009), Pembelajaran Kooperatif Meningkatkan Kecerdasan Komunikasi

Antar Peserta Didik., Pustaka Pelajar, Yogyakarta

Kadir. (2008). Pendekatan Pemecahan Masalah Dalam Pembelajaran Matematika di SMP. (online).

(http://kadirrea.blogspot.com/2008/06/pendekatan-pemecahan-masalah.

Kemendikbud. (2013). Matematika SMP/MTs Kelas VIII Semester 1, Kemendikbud, Jakarta.

Kemendikbud. (2014). Matematika SMP/MTs Kelas VIII Semester 1, Kemendikbud, Jakarta.

Motter, A. 2010. George Polya, “How To Solve It?”.

(online): http://www.math.twsu.edu/history/men/polya.html.

Marzuki, A. (2006). Implementasi Pembelajaran Kooperatif (Cooperative

Learning) Dalam Upaya Meningkatkan Kemampuan Koneksi dan

Pemecahan Masalah Matematik Siswa.

Mulyana, D. (2005). Ilmu Komunikasi Suatu Pengantar. Bandung: Remaja Rosdakarya.

Mayer, R. E., &Wittrock, R. C., (2006), Problem solving, In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd Ed), Erlbaum, Mahwah, NJ.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and

(39)

110

NCTM. (1989). Curriculum and Evaluation Standards For School Mathematics. Reston, VA: Authur.

Oemar Hamalik, 1995. Kurikulum dan pembelajaran. Jakarta: Bumi Aksara Ogunbiyi, O. (2—4), New Challeges in the methodologies of teaching:A case for

inservice programme for school teachers mandate on education and social development in Negeria,D.F.Elaturoti and A.Babarinde Eds., Nigeria.Stirling-Horden Publishers,pp 152-157

Ontario Ministry of Education (2006). Teaching and Learning mathematics: The report of the expert panel on mathematics in grades 4 to 6 in Ontario. Toronto, ON: Author

Paulina Pannen, 2001, Konstruktivisme dalam pembelajaran. Jakarta: PAU-PPAI, Universitas Terbuka.

Posamentier, A. S., and Krulik, S., (1998), Problem solving strategies for efficient and elegant solutions, Corwin Press, USA.

Polya, G. (1985). On Solving Mathematical Problem In High School, dalam kulik Stephan & Ray’s, Robert E (eds) Problem Solving In School mathematics. Reston – Virginia. NCTM

Ronnis, Diane, 2000. Problem Based Learning for math and science: integrating inquiry and the internet. Illnois: Skylight Professional Development. Ruseffendi, (1998). Pengantar Kepada Membantu Guru Mengembangkan

Kompetensinya Dalam Mengajar Matematika Untuk Meningkatkan CBSA. Bandung: Tarsito.

, (1991). Pengajaran Matematika Modern Untuk Orang Tua, Murid, Guru, dan SPG Seri Kelima. Bandung: Tarsito.

,(1998). Statistika Dasar Untuk Penelitian. Bandung: IKIP Bandung Press.

,(1991). Pengantar Kepada Membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA. Bandung: Tarsito

,(2006). Pengantar kepada membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA, Tarsito, Bandung.

Saragih, S. (2007). Mengembangkan Kemampuan Berpikir Logis dan Komunikasi

Matematika Siswa Sekolah Menhengah PertamaMelalui Pendekatan

Matematika Realistik. Disertasi tidak diterbitkan, Bandung: PPS UPI Bandung.

Savery, G.S> 2013. A Comparason of Achievement In Problem Based, Strategic and Traditional Learning Classes In Math. International Journal on New Trends in Education and Ther Implications, Volume 4 (1).

(40)

111

Shadiq, F. 2004. Pemecahan Masalah, Penalaran dan Komunikasi dalam

Pembelajaran Matematika. Depdiknas Dirjen Dikdasmen PPPG

Matematika. Yogyakarta

Sinaga, B. (1999). Efektivitas Model Pembelajaran Berdasarkan Masalah (Problem Based Instruction) Pada Kelas 1 SMU Dengan Bahan kajian Fungsi Kuadrat. Tesis tidak diterbitkan. Surabaya: PPS IKIP Surabaya.

Stevenson,MC.(1987), The Asian Advantage: The case of mathematics, American educator. Vol 11,No 4,pp 26-31.

Sopiah, S., Wiyanto, Sugianto. 2009. Pembiasaan Bekerja Ilmiah Pada Pembelajaran Matematika Untuk Siswa SMP. Jurnal Pendidikan Matematika Indonesia, Volume 9 (5).

Sukayati, (2008), Penelitian Tindakan Kelas, PPPPTK Matematika, Yogyakarta.j Suherman, E. dkk., (2003), StrategiPembelajaranMatematikaKontemporer, JICA

UPI, Bandung

Sumarno, U. (1994). Suatu Alternatif Pengajaran Untuk Meningkatkan

Kemampuan Pemecahan Masalah Matematika Siswa SMA di kodya

Bandung. Laporan Penelitian IKIP bandung:

Sumarmo, U. 2012. Pendidikan Karakter serta pengembangan berpikir dan

disposisi Matematika dalam Pembelajaran Matematika. Makalah

disajikan pada seminar pendidikan Matematika di NTT tanggal 25 Februari 2012

Suyanto, (1997), Pedoman Pelaksanaan Penelitian Tindakan Kelas (PTK) Pengenalan Penelitian Tindakan Kelas, Dirjen Dikti, Yogyakarta. Trianto, 2009, Mendesain Model Pembelajaran Inovatif-Progesif, Prenada

Media Group, Jakarta.

, 2011. Model – model Pembelajaran Inovatif Berorientasi Konstruktivistik. Jakarta: Tim Prestasi Pustaka.

Turmudi. 2008. Pemecahan Masalah Matematika (online) (http://file.upi.edu/browse.php?dir=Direktori/FPMIPA/JUR_PEND_ MATEMATIKA/196101121987031-TURMUDI/

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CHAPTER V

CONCLUSION AND SUGGESTION

5.1. Conclusion

Based on the results of research and discussion obtained the following conclusions:

1. The implementation of problem based learning model can improve students mathematical problem solving ability in SMP Negeri 30 Medan class VIII-6 Academic Year 2016/2017

5.2. Suggestion

The suggestion can be taken from the results of this research, such as: 1. Learning mathematics by impelementation Problem Based Learning

(2)

 Able to make problem question whicah can be used to exercise the students to do problem solving step.

 Management of time as goog as possible when learning is done.  Understanding the phases that must be applied in problem based

learning model.

 Doing small learning groups designed which are heterogenous.  Guide and help students to open mind to solve problem.

(3)

BIBLIOGRAPHY

Abimbade, A and Afolabi, S.S.(2012), A Study of Pedagogical Approach of Mathematics Teaching In Southwestern States Of Nigeria. International Journal of Asian Social Science vol 2,no 8,pp 1182-1192. (Johann Heinrich Pestalozzi and Vitterine De Feltre)

Amir, M.T. (2009). Inovasi Pendidikan Melalui Problem Based Learning. Jakarta : Kencana Prenada Media Group

Ansari, B.I. (2009). Komunikasi Matematika: Konsep dan Aplikasi. Banda Aceh: Yayasan PeNA Banda Aceh.

Antonoplos, D.P.(1985), Students characteristics learning and curriculum in Japan. Washington DC, Office of Educational Research and Improvement (ed.)

Arends, Richard I. (2008). Learning To Teach (Belajar untuk Mengajar) Buku Satu. Yogyakarta: Pustaka Pelajar.

, (2011), Learning to Teach, McGraw Hill, New York.

Arikunto, Suharsimi (1991). Prosedur Penelitian : Suatu Pendekatan Praktik. Jakarta : Rineka Cipta.

Jenjang Pendidikan Dasar dan Menengah. Jakarta: Depdiknas. Ben – Zeev, T, & Sterberg, R.J. (1996). The Nature Of Mathematical Thingking.

Mahwah. NJ: Lawrence Erlbaum Assosiates. Inc.

Cangara, H. (1998). Pengantar Ilmu Komunikasi. Jakarta: Raja Grafind Persada. Dahlan, J.A. (2011). Analisis Kurikulum Matematika. Jakarta: Universitas

Terbuka.

Departemen Pendidikan Nasional. 2003, Kurikulum berbasis kompetensi. Jakarta: Depdiknas.

Depdikbud. (1996). Kurikulum Sekolah Dasar, Buku IIIA, Pedoman Khusus. Jakarta: Balai Pustaka

Dina Mellita. 2008, Metode pembelajaran peer teaching dan problem based learning untuk memotivasi sosialiasasi dalam kelas (pada pembelajaran statistika). Jurnal Ilmiah Bina Edukasi, 1(2), 87-98.

(4)

Hake, R. R., (1999).Analyzing Change/Gain Score, American Educational, Amerika.

Hari Suderajat, 2003. Implementasi kurikulum berbasis kompetensi (KBK). Jakarta: Depdiknas.

Hudojo. H. (1990). Pengembangan Kurukulum Matematika dan Pelaksanaannya di Depan Kelas. Surabaya: Usaha nasional.

Hudojo. H. (2001). Common Textbook: Pengembangan Kurikulum dan Pembelajaran Matematika. Edisi Revisi. Malang: JICA – Universitas Negeri Malang.

Ibrahim, dkk., (2000), Pembelajaran Berdasarkan Masalah, UNESA, Surabaya. Isjoni, (2009), Pembelajaran Kooperatif Meningkatkan Kecerdasan Komunikasi

Antar Peserta Didik., Pustaka Pelajar, Yogyakarta

Kadir. (2008). Pendekatan Pemecahan Masalah Dalam Pembelajaran Matematika di SMP. (online).

(http://kadirrea.blogspot.com/2008/06/pendekatan-pemecahan-masalah.

Kemendikbud. (2013). Matematika SMP/MTs Kelas VIII Semester 1, Kemendikbud, Jakarta.

Kemendikbud. (2014). Matematika SMP/MTs Kelas VIII Semester 1, Kemendikbud, Jakarta.

Motter, A. 2010. George Polya, “How To Solve It?”.

(online): http://www.math.twsu.edu/history/men/polya.html.

Marzuki, A. (2006). Implementasi Pembelajaran Kooperatif (Cooperative Learning) Dalam Upaya Meningkatkan Kemampuan Koneksi dan Pemecahan Masalah Matematik Siswa.

Mulyana, D. (2005). Ilmu Komunikasi Suatu Pengantar. Bandung: Remaja Rosdakarya.

Mayer, R. E., &Wittrock, R. C., (2006), Problem solving, In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd Ed), Erlbaum, Mahwah, NJ.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston. VA: NCTM.

(5)

NCTM. (1989). Curriculum and Evaluation Standards For School Mathematics. Reston, VA: Authur.

Oemar Hamalik, 1995. Kurikulum dan pembelajaran. Jakarta: Bumi Aksara Ogunbiyi, O. (2—4), New Challeges in the methodologies of teaching:A case for

inservice programme for school teachers mandate on education and social development in Negeria,D.F.Elaturoti and A.Babarinde Eds., Nigeria.Stirling-Horden Publishers,pp 152-157

Ontario Ministry of Education (2006). Teaching and Learning mathematics: The report of the expert panel on mathematics in grades 4 to 6 in Ontario. Toronto, ON: Author

Paulina Pannen, 2001, Konstruktivisme dalam pembelajaran. Jakarta: PAU-PPAI, Universitas Terbuka.

Posamentier, A. S., and Krulik, S., (1998), Problem solving strategies for efficient and elegant solutions, Corwin Press, USA.

Polya, G. (1985). On Solving Mathematical Problem In High School, dalam kulik Stephan & Ray’s, Robert E (eds) Problem Solving In School mathematics. Reston – Virginia. NCTM

Ronnis, Diane, 2000. Problem Based Learning for math and science: integrating inquiry and the internet. Illnois: Skylight Professional Development. Ruseffendi, (1998). Pengantar Kepada Membantu Guru Mengembangkan

Kompetensinya Dalam Mengajar Matematika Untuk Meningkatkan CBSA. Bandung: Tarsito.

, (1991). Pengajaran Matematika Modern Untuk Orang Tua, Murid, Guru, dan SPG Seri Kelima. Bandung: Tarsito.

,(1998). Statistika Dasar Untuk Penelitian. Bandung: IKIP Bandung Press.

,(1991). Pengantar Kepada Membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA. Bandung: Tarsito

,(2006). Pengantar kepada membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA, Tarsito, Bandung.

Saragih, S. (2007). Mengembangkan Kemampuan Berpikir Logis dan Komunikasi Matematika Siswa Sekolah Menhengah Pertama Melalui Pendekatan Matematika Realistik. Disertasi tidak diterbitkan, Bandung: PPS UPI Bandung.

(6)

Shadiq, F. 2004. Pemecahan Masalah, Penalaran dan Komunikasi dalam

Pembelajaran Matematika. Depdiknas Dirjen Dikdasmen PPPG

Matematika. Yogyakarta

Sinaga, B. (1999). Efektivitas Model Pembelajaran Berdasarkan Masalah (Problem Based Instruction) Pada Kelas 1 SMU Dengan Bahan kajian Fungsi Kuadrat. Tesis tidak diterbitkan. Surabaya: PPS IKIP Surabaya.

Stevenson,MC.(1987), The Asian Advantage: The case of mathematics, American educator. Vol 11,No 4,pp 26-31.

Sopiah, S., Wiyanto, Sugianto. 2009. Pembiasaan Bekerja Ilmiah Pada Pembelajaran Matematika Untuk Siswa SMP. Jurnal Pendidikan Matematika Indonesia, Volume 9 (5).

Sukayati, (2008), Penelitian Tindakan Kelas, PPPPTK Matematika, Yogyakarta.j Suherman, E. dkk., (2003), StrategiPembelajaranMatematikaKontemporer, JICA

UPI, Bandung

Sumarno, U. (1994). Suatu Alternatif Pengajaran Untuk Meningkatkan Kemampuan Pemecahan Masalah Matematika Siswa SMA di kodya Bandung. Laporan Penelitian IKIP bandung:

Sumarmo, U. 2012. Pendidikan Karakter serta pengembangan berpikir dan disposisi Matematika dalam Pembelajaran Matematika. Makalah disajikan pada seminar pendidikan Matematika di NTT tanggal 25 Februari 2012

Suyanto, (1997), Pedoman Pelaksanaan Penelitian Tindakan Kelas (PTK) Pengenalan Penelitian Tindakan Kelas, Dirjen Dikti, Yogyakarta. Trianto, 2009, Mendesain Model Pembelajaran Inovatif-Progesif, Prenada

Media Group, Jakarta.

, 2011. Model – model Pembelajaran Inovatif Berorientasi Konstruktivistik. Jakarta: Tim Prestasi Pustaka.

Turmudi. 2008. Pemecahan Masalah Matematika (online) (http://file.upi.edu/browse.php?dir=Direktori/FPMIPA/JUR_PEND_ MATEMATIKA/196101121987031-TURMUDI/

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THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL TO IMPROVE THE STUDENTS’ MATHEMATICAL PROBLEM SOLVING AND MATHEMATICAL COMMUNICATION ABILITY OF GRADE VIII SMP NEGERI 30 MEDAN.

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

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MEDAN

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THE IMPLEMENTATION OF PROBLEM-BASED LEARNING MODEL TO INCREASE STUDENTS’ MATHEMATICAL PROBLEM SOLVING ABILITY AT SMP NEGERI I TANJUNG MORAWA.

THE IMPLEMENTATION OF PROBLEM BASED LEARNING WITH SCIENTIFIC APPROACH TO INCREASE THE STUDENTS’ MATHEMATICAL CREATIVE THINKING ABILITY IN SMPN 37 MEDAN.

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