RESULT AND DISCUSSION 51 CONLUSION AND SUGGESTION 88

ix LIST OF FIGURE Page Figure 1.1. Student’s Sheet in Understanding the Problem Step 5 Figure 1.2. Student’s Sheet In Devising a Planning Problem 6 Figure 1.3. Student’s Sheet In Carrying Out The Plan 7 Figure 1.4. Student’s Sheet in Looking Back Step 7 Figure 2.1. Problem Solving Step 17 Figure 2.2. Learner Outcomes for Problem Based Learning 22 Figure 2.3. The Role of Students and Teacher in Problem-Based learning 23 Figure 2.4. The Implementation of Problem Based Learning 25 Figure 3.1. Procedure of Classroom Action Research 34 Figure 4.1. The Result of Initial Capability Test 52 Figure 4.2. Student’s Presented Problem Solving in Apperception 55 Figure 4.3. Teacher Guided The Students to Do Problem Solving 57 Figure 4.4. The Result of Problem Solving Ability Test I 60 Figure 4.5. The Result of Students’ Activity 61 Figure 4.6. The Result of Teacher’s Activity 63 Figure 4.7. Student’s Understanding the Problem 64 Figure 4.8. Student’s Divising a Plan of Problem Solving 65 Figure 4.9. Student’s Carrying Out the Problem Solving 65 Figure 4.10. Student’s Looking Back the Problem Solving Solution 65 Figure 4.11. Researcher Asked Students’ about Difficulty in Cycle I 70 Figure 4.12. The Result of Problem Solving Ability Test II 76 Figure 4.13. The Result of Students’ Activity 77 Figure 4.14. The Result of Teacher’s Activity 78 Figure 4.15. Student’s Understanding Problem Solving Ability Test II 79 Figure 4.16. Student’s Devising a Plan in Problem Solving Test II 80 Figure 4.17. Student’s Carrying Out the Plan in Problem Solving Test II 80 Figure 4.18. Student’s Looking Back in Problem Solving Test II 80 Figure 4.19. The Result of Cycle I and Cycle II 82 Figure 4.20. The Increasing of Observation Students’ Activity 84 Figure 4.21. The Increasing of Observation Teacher’s Activity 85 ix LIST OF FIGURE Page Figure 1.1. Student’s Sheet in Understanding the Problem Step 5 Figure 1.2. Student’s Sheet In Devising a Planning Problem 6 Figure 1.3. Student’s Sheet In Carrying Out The Plan 7 Figure 1.4. Student’s Sheet in Looking Back Step 7 Figure 2.1. Problem Solving Step 17 Figure 2.2. Learner Outcomes for Problem Based Learning 22 Figure 2.3. The Role of Students and Teacher in Problem-Based learning 23 Figure 2.4. The Implementation of Problem Based Learning 25 Figure 3.1. Procedure of Classroom Action Research 34 Figure 4.1. The Result of Initial Capability Test 52 Figure 4.2. Student’s Presented Problem Solving in Apperception 55 Figure 4.3. Teacher Guided The Students to Do Problem Solving 57 Figure 4.4. The Result of Problem Solving Ability Test I 60 Figure 4.5. The Result of Students’ Activity 61 Figure 4.6. The Result of Teacher’s Activity 63 Figure 4.7. Student’s Understanding the Problem 64 Figure 4.8. Student’s Divising a Plan of Problem Solving 65 Figure 4.9. Student’s Carrying Out the Problem Solving 65 Figure 4.10. Student’s Looking Back the Problem Solving Solution 65 Figure 4.11. Researcher Asked Students’ about Difficulty in Cycle I 70 Figure 4.12. The Result of Problem Solving Ability Test II 76 Figure 4.13. The Result of Students’ Activity 77 Figure 4.14. The Result of Teacher’s Activity 78 Figure 4.15. Student’s Understanding Problem Solving Ability Test II 79 Figure 4.16. Student’s Devising a Plan in Problem Solving Test II 80 Figure 4.17. Student’s Carrying Out the Plan in Problem Solving Test II 80 Figure 4.18. Student’s Looking Back in Problem Solving Test II 80 Figure 4.19. The Result of Cycle I and Cycle II 82 Figure 4.20. The Increasing of Observation Students’ Activity 84 Figure 4.21. The Increasing of Observation Teacher’s Activity 85 x LIST OF TABLE Page Table 1.1. Students’ Result of Diagnostic Test Table 2.1. The Syntax of Problem-Based Learning Table 3.1. Descriptive about Cycle I Table 3.2. Descriptive about Cycle II Table 3.3. Blueprint of Initial Test of Problem Solving Ability Table 3.4. Blueprint of Problem Solving Test I Table 3.5. Blueprint of Problem Solving Test II Table 3.6. Scoring Guidelines Mathematics Problem Solving Ability Table 3.7. List of S core’s Predicate and The Criteria Table 3.8. Interpretation of Gain Normalization Table 3.9. Criteria of Average Teacher Observation Table 4.1. Initial capability Test Result Table 4.2. Schedule of Cycle I Table 4.3 The Result of Problem Solving Ability Test I Table 4.4 . The Result of Students’ Activity Cycle I Table 4.5 . The Result of Teacher’s Activity Cycle I Table 4.6. Schedule of Cycle II Table 4.7. The Result of Problem Solving Ability Test II Table 4.8 . The Result of Students’ Activity Cycle II Table 4.9 . The Result of Teacher’s Activity Cycle II Table 4.10. Increasing Criteria of Students’ Problem Solving Ability Table 4.11. Observation Result of Students’ Activity Table 4.12 . Observation Result of Teacher’s Activity 7 24 37 39 40 41 42 42 44 47 49 52 54 59 61 62 70 75 77 78 82 83 84 xi LIST OF APPENDIX Page Appendix 1 Lesson Plan I 95 Appendix 2 Lesson Plan II 102 Appendix 3 Lesson Plan III 109 Appendix 4 Lesson Plan IV 116 Appendix 5 Student Activity Sheet I 123 Appendix 6 Student Activity Sheet II 127 Appendix 7 Student Activity Sheet III 130 Appendix 8 Student Activity Sheet IV 133 Appendix 9 Alternative Solution of Student Activity Sheet I 136 Appendix 10 Alternative Solution of Student Activity Sheet II 139 Appendix 11 Alternative Solution of Student Activity Sheet III 141 Appendix 12 Alternative Solution of Student Activity Sheet IV 144 Appendix 13 Blueprint of Initial Test 146 Appendix 14 Blueprint of Mathematical Problem Solving Ability Test I 147 Appendix 15 Blueprint of Mathematical Problem Solving Ability Test II 148 Appendix 16 Initial Capability Test 149 Appendix 17 Mathematical Problem Solving Ability Test I 150 Appendix 18 Mathematical Problem Solving Ability Test II 154 Appendix 19 Alternative Initial Capability Test 158 Appendix 20 Alternative Solution of Mathematical Problem Solving Ability Test I 161 Appendix 21 Alternative Solution of Mathematical Problem Solving Ability Test II 165 Appendix 22 Scoring Guidelines of Mathematical Problem Solving Ability Test 169 Appendix 23 Validation Sheet of Initial Capability Test 171 Appendix 24 Validation Sheet of Problem Solving Ability Test I 174 Appendix 25 Validation Sheet of Problem Solving Ability Test II 177 Appendix 26 Result Description of Diagnostic Test 180 Appendix 27 Result Description of Problem Solving Ability Test I 182 xii Appendix 28 Result Description of Problem Solving Ability Test II 184 Appendix 29 Result Description of Gain Score 186 Appendix 30 Observation Sheet of Students’ Activity 188 Appendix 31 Observation Sheet of Teacher ’s Activity 200 Appendix 32 Attendance List of Students 212 Appendix 33 Name of Group Cycle I 213 Appendix 34 Name of Group Cycle II 214

CHAPTER I INTRODUCTION

1.1. Background

Education is as process of educating or teaching. Education is further defined as to develop the knowledge, skill and character of students. Ayn Rand in Judith Lioyd Yero, 2002 stated that the only purpose of education is to teach students how to life his live by developing his mind and equipping him to deal the reality. He has to be taught to think, to understand, to integrate, to prove and to solve the problem for daily life. According to Professor Shulman in Oon-Seng- Tan, 2003 of Stanford: Education is a process of helping people develop capacities to learn how to connect their troubles with useful puzzle to form problems. Educator fail most miserably when they fail; to see that the only justification for learning to do puzzle is when they relate to troubles. When the puzzles take on a life of their own problem sets employing mindless algorithms, lists of n ames … definitions – they cease to represent education. The puzzles become disconnected from troubles and remain mere puzzles. We may refer to them as problems, but that is a form of word magic, for they are not real problem. One of the subjects that reflect the goal is mathematics. Mathematics is one of the most important subject in education which we must learn since we were child although we haven’t been in school. Mathematics have important role to development knowledge and technology because the knowledge of mathematics are applied in development of technology to produce the newest invention such as HP, computer and other technology which make our life easier. Certainly we have asked why we must learn mathematics since we were elementary, junior high school and senior high school. More over when we are in university, mathematics is also learned and it becomes obligation subject. Many students asked what the purpose of learning mathematics is, what the relationship of learning mathematics for daily life is, why we must learn about integral, differential, function, counting volume, exponent etc and what mathematics influence for our life is. Mathematics is not only about calculation but from learning mathematics we can change our mindset systematically and arranged. By learning mathematics our brain is accustomed to solve problem systematically so that if we have problem in our daily life, we can solve our problem easily. Mathematics teach us to become careful people and accurate for doing something. It is proven when we do mathematics problem where we must careful to count the result, how many nol digit behind the comma and the measure of thing such as geometry. If we are not careful, it will cause our answer is wrong. Learning mathematic also learn us become patient people facing everything which we face. It is proven when we must solve the most difficult mathematics problem which it needs long and difficult calculation. It needs much patient and we must struggle to solve it but when it is solved and the answer is right, how happy it is. For daily life mathematics have important role, for example to counting bank interest, profit or lose out, determining sound, the magnitude of earthquake etc. In addition the learning objectives of mathematics according to Abdurrahman 2012 suggested that: Lima alasan perlunya belajar matematika karena matematika merupakan 1 sarana berpikir yang jelas dan logis, 2 sarana untuk memecahkan masalah kehidupan sehari-hari, 3 sarana mengenal pola-pola hubungan dan generalisasi pengalaman, 4 sarana untuk mengembangkan kreativitas, dan 5 sarana untuk meningkatkan kesadaran terhadap perkembangan budaya. One of important aspect in mathematics is mathematics problem solving. There is a competence that can be developed during and after the learning process of mathematics, as revealed by National Council Teacher of Mathematics 2000 in Principles and Standards for School Mathematics that there are five standard that describes the relationship mathematical understanding and mathematical competencies that teachers and students should know and can be done. Understanding, knowledge and skills that students need to be held covered in the standard process which includes: problem solving, reasoning, communication, connection and representation.