RESULTS AND DISCUSSION 66 CONCLUSION AND SUGGESTION 106

ix REFERENCE 108 APPENDIX 112 DOCUMENTATION OF RESEARCH 218 xi TABLES Page Table 2.1 Syntax of Problem Based Learning Table 3.1 The Steps in 1 st Cycle Table 3.2 The Steps in 2 nd 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 69 73 74 75 xii 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 76 76 Table 4.10 Percentages of Mathematical Communication Completeness I Table 4.11 Description of Observation Teacher Activity in 1 st Cycle Table 4.12 Description of Observation Students Activity in 1 st 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 2 nd Cycle Table 4.20 Description of Observation Students ’ Activity in 2 nd Cycle Table 4.21 The Results of Mathematical Problem Solving Ability 1 st Cycle and 2 nd Cycle Table 4.22 The Results of Mathematical Communication Ability 1 st Cycle and 2 nd Cycle 77 79 82 88 90 91 91 92 93 94 97 98 100 ix 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 ’ 1 st Cycle and 2 nd Cycle Figure 4.2 The Level of The Number of Students ’ Complete The Study of Mathematical Problem Solving Ability Test 1 st Cycle and 2 nd Cycle Figure 4.3 The Ability of Communication Students ’ 1 st Cycle and 2 nd Cycle Figure 4.4 The Level of The Number of Students ’ Complete The Study of Mathematical Communication Ability Test 1 st Cycle and 2 nd Cycle Figure 4.5 The Level of The Teacher Ability to Manage The Learning Process 1 st Cycle and 2 nd Cycle Figure 4.6 The Level of Percentages Students ’ Activity 1 st Cycle and 2 nd Cycle 42 99 100 101 102 102 103 xiii 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 Student s’ Activities Sheet I 140 Appendix 6 Student s’ Activities Sheet II 142 Appendix 7 Student s’ Activities Sheet III 144 Appendix 8 Student s’ 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 xiv 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 1 st Meeting 197 Appendix 40 Observation Sheet of Students ’ Activity 2 nd Meeting 199 xv Appendix 41 Observation Sheet of Students ’ Activity 3 rd Meeting 201 Appendix 42 Observation Sheet of Students’ Activity 4 th Meeting 203 Appendix 43 Observation Sheet of Teacher Activity 1 st Cycle 205 Appendix 44 Observation Sheet of Teacher Activity 2 nd 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 1 st Cycle 216 Appendix 52 The Result of Observation Students ’ Activity 2 nd Cycle 217 Appendix 53 Documentation of Research 218

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. 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