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 MODEL TO INCREASE STUDENTS’ MATHEMATICAL PROBLEM
SOLVING ABILITY AT SMP NEGERI 1 TANJUNG MORAWA
By: Friska Simbolon IDN. 4123312010
Bilingual Mathematics Education
SKRIPSI
Submitted in Partial Fulfillmentof The Requirements for The Degree of Sarjana Pendidikan
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
MEDAN 2016
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BIOGRAPHY
Friska Simbolon was born in Tanjung Morawa on April 6th, 1994. Her father’s name is Eddy Simbolon and her mother name is Pinondang Silalahi. She is the fifth child of her family and she has 3 sisters are Melda Simbolon, Eva Simbolon and Winda Simbolon and a brother is Satrio Simbolon. She was Elementary School in SD Negeri 101877 on 2000 and then graduated in 2006. She was graduated from SMP Negeri I Tanjung morawa on 2009 and then she continued in SMA Negeri I Tanjung Morawa on 2009 and graduated on 2012. After graduated from SMA Negeri I Tanjung Morawa, she continued her study in State University of Medan (Unimed) in Bilingual Class of Mathematics Education 2012.
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THE IMPLEMENTATION OF PROBLEM-BASED LEARNING MODEL TO INCREASE STUDENTS’ MATHEMATICAL PROBLEM SOLVING
ABILITY AT SMP NEGERI I TANJUNG MORAWA Friska Simbolon (NIM 4123312010)
ABSTRACT
The purposes of this study was to know that Problem-based learning model could increase students’ mathematical problem solving ability in grade 8 at SMP Negeri 1 Tanjung Morawa. The type of this research was Classroom Action Research (CAR) which was implemented in SMP Negeri I Tanjung Morawa.The subject of this research were students’ of class VIII-5 of academic year 2015/2016 that consist of 38 students. The objects of this research is mathematical problem solving ability.
This study consisted of two cycles. Each cycle had two meetings. Every meeting was given student activity sheet. Students’ mathematical problem solving ability was tested in the end of cycle.
After giving a treatment to students, in the first cycle, the average score of their mathematical problem solving ability was 2.35 with classical completeness 20 of 38 students (52.63%) gained score 2.66. The average score of students’ activities’ observation sheet was 45.80% which classified as passive class category The average score of teacher activities’ observation sheet was 3.57 which classified as very good category. In the second cycle, students’ average score increased become 3.04 with classical completeness 33 of 38 students (86.84%) gained score 2.66. The average score of students’ activities’ observation sheet was 86.90% which is classified active class category in problem solving. The average score of teacher activities’ observation sheet was 3.81 which is classified as very good category.
From the result of research, it can be concluded that the implementation of problem-based learning model is effective to increase students’ problem solving ability. For teacher are encouraged to be able to implement problem-based learning model as an alternative in the learning process that can increase problem solving ability.
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PREFACE
Thanks and blessing for our Almighty God Tuhan Yesus Kristus for giving me spirit and health to complete my thesis. The tittle of thesis is “The Implementation of Problem-Based Learning Model to Increase Students’ Mathematical Problem Solving Ability At SMP Negeri I Tanjung Morawa”. This thesis was arranged to satisfy the law to get Sarjana Pendidikan of Mathematics and Science Faculty in State University of Medan.
For this opportunity, I want to say big thanks for the rector of State University of Medan, Mr. Prof. Dr. Syawal Gultom, M.Pd. and his staff, Mr. Dr. Asrin Lubis, M.Pd. for Dean of FMIPA Unimed and his college assistant of Dean I,II,III in Unimed. Thanks for Mr. Dr. Edy Surya, S.Si, M.Si. is as Leader of Mathematics Departement, Mr. Drs. Zul Amry, M.Si. is as Leader of Mathematics Education Study Program, Mr. Drs. Yasifati Hia, M.Si. is as secretary of Mathematics Departement and then for Coordinator of Bilingual Program Mrs. Dr. Iis Siti Jahro, M.Si.
I am so thankful for Mr. Dr. E. Elvis Napitupulu, M.S. as my Thesis Supervisor who guided me, teach me and give motivation to complete this thesis. Then thanks for my thesis advisor who responsible and guide me to repair my thesis become better for Prof. Dr. Bornok Sinaga, M.Pd., Denny Haris, S.Si, M.Pd., and Prof. Dr. Mukhtar, M.Pd. who is also as my Academic Supervisor. Then Thanks you so much for all my lectures and staffs in FMIPA Unimed.
Thankful for God to give me the best person in the world, my parents are my lovely father Mr. Eddy Simbolon and the most beautiful woman, My mother is Mrs. Pinondang Silalahi for love me, struggle for my life and pray for me to finish this obligation. Thanks also for my sisters, Melda, Eva, Winda and my handsome brother Satrio for all your spirit in my study. I present this for you all my family.
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Then, thanks you so much for Mrs. Arwidah Parinduri, S.Pd. is as headmaster of SMP Negeri I Tanjung Morawa and Mrs. Murti, S.Pd is as Mathematics teacher of SMP Negeri I Tanjung Morawa who guide, advise and help me in doing research.
I am also thanks for Bilingual Mathematics Members 2012 for our fourth year times and happiness in the class to face everything in Unimed. Thanks for Nondik Mathematics Class 2012 for our friendship, place for me share my experience, having fun together and place to share my difficulty in my study and also thanks to PPLT SMA Negeri I Sidikalang for our three month togetherness to face the first experience as real teacher in good or bad condition there. At last, especially thanks for my best friends from first semester, PPL mates and same thesis supervisor is Desy Agustina Situngkir where we always start together from title of thesis until ACC our thesis.
The writer does big effort to complete this thesis but the writer realize this thesis have weakness and need some suggestion to make it better. So that the writer needs some suggestion from the reader and I hope this thesis can increase our knowledge.
Medan, June 2016 Writer,
Friska Simbolon ID.4123312010
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CONTENTS
Page
Sheet of Agreement i
Biography ii
Abstract iii
Preface iv
Contents vi
List of Figure ix
List of Table x
List of Appendix xi
CHAPTER I INTRODUCTION 1
1.1. Background 1
1.2. Problem Identification 9
1.3. Problem Limitation 10
1.4. Problem Formulation 10
1.5. Research Objectives 10
1.6. Benefits of Research 11
1.7. Operational Definitions 11
CHAPTER II LITERATURE REVIEW 13
2.1. Mathematical Problems 13
2.2. Problem Solving Ability 14
2.3. Models of Teaching 19
2.3.1. Problem-Based Learning Model 20
2.3.2. The Syntax of Problem-Based Learning 23 2.3.3. The Advantages and Disadvantages of Problem-Based Learning 25 2.3.4. Learning Theory That Support Problem-Based Learning 25 2.3.4.1. Piaget’s Theory and Constructivism Opinion 26
2.3.4.2. Vigotsky’s Theory 26
2.3.4.3. Jerome Bruner’s Theory 26
2.3.4.4. David Ausubel’s Theory 27
2.3.5. Summary of Subject Matter 27
2.3.5.1. Definition of Proportion 27
2.3.5.2. Directly Proportion 28
2.3.5.3. Inversely Proportional 29
2.4. Relevant Research 30
2.5. Conceptual Framework 31
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CHAPTER III RESEARCH METHODOLOGY 33
3.1. Type of Research 33
3.2. Location and Time of Research 33
3.3. Subject and Object of Research 33
3.3.1. Subject of Research 33
3.3.2. Object of Research 33
3.4. Research Procedure 33
3.4.1. CYCLE I 34
3.4.1.1. Problem I 34
3.4.1.2. Action Plan I 35
3.4.1.3. Action Implementation I 35
3.4.1.4. Observation I 36
3.4.1.5. Data Analysis I 36
3.4.1.6. Reflection I 36
3.4.2. CYCLE II 37
3.4.2.1. Action Plan II 38
3.4.2.2. Action Implementation II 38
3.4.2.3. Observation II 38
3.4.2.4. Data Analysis II 38
3.4.2.5. Reflection II 39
3.5. Instruments of Research 40
3.5.1. Initial Capability Test 40
3.5.2. Mathematics Problem Solving Ability Test 41 3.5.2.1 Scoring Mathematics Problem Solving Ability Test 42 3.5.2.2 Validity Students’ Mathematics Problem Solving
Ability Test 43
3.5.3. Observation Sheet 44
3.6. Data Analysis Technique 44
3.6.1. Data Reduction 44
3.6.2. Data Analysis 45
3.6.2.1. Data Analysis of Mathematics Problem Solving
Ability 45
3.6.2.2. Data Analysis of Classical Learning Mastery 46 3.6.2.3. Increasing of Students’ Mathematical Problem
Solving Ability 47
3.6.2.4. Analysis Observation of Students’ Activity 48 3.6.2.5. Analysis Observation of Teacher’s Activity 48
3.6.3. Get conclusion 49
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CHAPTER IV RESULT AND DISCUSSION 51
4.1. Description of Research Result 51
4.1.1 Description of Research Result in Cycle I 51
4.1.1.1 Problem I 51
4.1.1.2 Action Plan I 53
4.1.1.3 Action Implementation I 54
4.1.1.4 Observation I 58
4.1.1.5 Data Analysis I 59
4.1.1.5.1 Data Analysis Problem Solving Ability Test 59 4.1.1.5.2 Data Analysis of Student’s Activity 60 4.1.1.5.3 Data Analysis of Teacher’s Activity 62
4.1.1.6 Reflection I 63
4.1.2 Description of Research Result in Cycle II 68
4.1.2.1 Problem II 68
4.1.2.2 Action Plan II 69
4.1.2.3 Action Implementation II 69
4.1.2.4 Observation II 74
4.1.2.5 Data Analysis II 75
4.1.2.5.1 Data Analysis Problem Solving Ability Test 75 4.1.2.5.2 Data Analysis of Student’s Activity 77 4.1.2.5.3 Data Analysis of Teacher’s Activity 78
4.1.2.6 Reflection II 79
4.1.3 The Increasing of Research Result 81 4.1.3.1Increasing of Problem Solving Ability Test 82 4.1.3.2Increasing Students’ Activity In Implementation of
Problem Based Learning Model 83 4.1.3.3Increasing Teacher’s Activity In Implementation of
Problem Based Learning Model 84
4.1.4 Research Findings 85
4.1.5 Discussion of Research Results 86
CHAPTER V CONLUSION AND SUGGESTION 88
5.1. Conclusion 88
5.2. Suggestion 88
REFERENCE 91
APPENDIX 95
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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
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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
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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 Score’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
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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
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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
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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 names … 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
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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.
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From the explanation above it is meant that mathematical problem solving ability is a component of the process standard that trains high order of students’ thinking ability. Mathematical problem solving ability is an effort made by an individual or group to find the solution of a problem with the knowledge, understanding and skills that people possess. In students’ mathematical problems solving, it is trained to determine what is known, what is asked in the problem and how to use what are wore. Because in completing math problems do not just want to get the answer or outcome measures but rather on how students solve the mathematical problem.
Oon-Tan Seng (2009) said that problem can trigger curiosity, inquiry, and thinking in meaningful and powerful ways. Education needs a new perspective of searching for problem and looking at problems that will achieve the aim of helping students construct their own knowledge.
Mathematics experts stated that problem is the question that must be answered or responded. However, not all questions is a problem. As said by Hudojo (2005) that a question would be a problem only if a person has no certain rule or law can be used to find answers to these questions as soon as possible.
To solve the problems is needed some strategies are named problem solving. National Council of Teachers of Mathematics (NCTM, 2000) mentioned that problem solving was not only as a mathematics learning target, but also was as main tools to do the learning. Because of that, problem solving ability is as mathematics learning focus in all level, from elementary school until university. By learning problem solving in mathematics, the students will get thinking ability, accustomed to be diligent, and curiosity, and also self confident in unusual situation, as situation that will them face out of mathematics class. In daily life and the work world, become a good problem solver can give big benefit.
Mathematical problem solving is a process which involves the method solution is unknown in advance, to find the solution students should mapping their knowledge, and through this process they often develop new knowledge about mathematics. Based on Downey (in Joyce, 2000) said that the core of good
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thinking is the ability to problem solving. The essence of problem solving is the ability to learn in puzzling situation. Indicator which can show what a student has problem solving ability based on National Council of Teacher of Mathematics (NCTM, 2003) was: (1) Applying and adapting some approach and strategy to problem solving, (2) Solving the problem that occur in mathematics or in other context related mathematics, (3) Creating new mathematics knowledge toward problem solving, and (4) Monitoring and reflection in mathematics problem solving process. There are four important phase to solve mathematics problem. In this research problem solving ability will be measured through students' ability to complete a problem by using problem solving steps as follows:
1. Understanding the problem
In this step, students should be able to point out the principal parts of the problem include the unknown and the data.
2. Devising a plan
In second steps, there are some alternatives to do include students can find the connection between the data and the unknown.
3. Carrying out the plan
Students be able to implementing problem solving strategies based on plan and operate of integers correct.
4. Looking back
Student be able to derive the result differently and use method for some other problem (Polya, 2004).
Based on survey data of Trends in International Mathematics and Sciences Study (TIMSS) (in La Arul, 2009) under the International Association for the Evaluation of Educational Achievement (IEA) is the average score of students below the international average score. Indonesia is in the position 34 for field of mathematics and in position 36 for field of science of 45 countries surveyed. This suggests that Indonesian students are included in low category, which means students in Indonesia have a little basic knowledge. Students have not able to formulate and solve non-routine problems. So the goal of learning
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mathematics for solving problems is not achieved in Indonesia. It is not achieved the goal of learning mathematics, especially mathematical problem solving. The problem also occurs in SMP Negeri 1 Tanjung Morawa. Low mathematical problem solving ability is found in the eighth grade through interview and diagnostic tests.
Based on the interview (December 11th, 2015) of researcher with mathematics teacher grade VIII of SMP Negeri 1 Tanjung Morawa, Mrs. Murti, S.pd said that students’ mathematical problem solving was low. Students are difficult to make the step of mathematics problem solving. They can understand the concept and the formula but they were difficult to use the concepts if find problem in real life which relate with concept have. Teacher also use conventional model in learning activity where the teacher is as the center of learning process.
Then from the result of survey that was conducted by researcher (December 14th, 2015) by giving problem solving diagnostic test to students of grade VIII - 5 at SMP Negeri 1 Tanjung Morawa in the topic of Pythagorean. The problem was tested by the student was: “Known is cube of ABCD.EFGH with the length AB = 15 cm. Determine space diagonal length of AG?
The answers were as following: 1. Understanding the problem
Students can’t understand the problem. It can be seen in Figure 1.1.
Figure 1.1. Student’s sheet in understanding the problem step The Sketch of Problem
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From the answer above, students can’t understand the problem solving step well. Students were less able to identify what asked was and identify what known was. It should be the students must clearly explain that known was length AB of cube ABCD.EFGH = 15 cm and for asked was not too defined well because the question asked was length of space diagonal of AG. Then some students can draw the sketch but it did not complete and some students don’t draw the figure at all. The students should draw the cube ABCD.EFGH and draw outline based on known length AB = 15 cm and determine space diagonal of AG but in fact some students didn’t make it at all. They couldn’t determine the question was needed. This indicates that students have not been able understand the problems. There were only 9 of 38 or 23.68% of students understand about the problem well.
2. Devising the Planning
Figure 1.2. Student’s sheet in planning the problem step
From the Figure 1.2 above, we can see that students’ devising a plan were
still bad. The students’ can’t find formula that could be useful for the problem The
students’ can’t introduce some auxiliary element to help solving the problem. For
planning the problem there were 6 of 38 students or 15.78 % can make good planning.
3. Carrying Out The Plan
The students can’t implement problem solving strategies well. Students can not find an appropriate strategy to solve the problem. The students can’t determine the suitable formula to solving the problem. Students’can’t check each step clearly was correct. There were 2 or 5.26% of students can implement problem solving strategy. Student’s ability in carrying out the plan was shown in Figure 1.3.
The Formula of Problem Solving
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Figure 1.3. Student’s sheet in carrying out the plan
4. Looking Back
Student’s answer in looking back step is shown in Figure 1.4.
Figure 1.4. Student’s sheet in looking back step
Based on Figure 1.4 above, there was no or 0 % of students can derive the result differently and use other formula or step solving to determine the diagonal length of AG. Students’ problem solving ability result above can be shown in Table 1.1.
Table 1.1. Students’ Problem Solving Ability Result of Diagnostic Test Problem Solving Step Total of Students Percentage
1. Understanding the problem 9 23.68 %
2. Devising a plan 6 15.78%
3. Carrying out the plan 2 5.26 %
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From students’ answer, it was indicated that students didn’t know what they solved. Students can’t implement problem solving strategies. Students can not find an appropriate strategy to solve the problem. From all figure above, we can see that the student can’t do the completion based on the plan has been made.
Almost all students can’t implement problem solving strategies well.
Diagnostic test result is also shown that there were not students who completed to solve problem. From some of description above, it can be seen that many of students just remind the concepts and not able to use the concepts if find problem in real life which relate with concept had. For further, students were not able to determine the problem and formulate it. Almost all students were not able to relate between what they learned with how the knowledge will be used or applied in the new situation.
According to Arends (1997) that it is strange that we expect students to learn yet seldom teach then about learning, we expect student to solve problems yet seldom teach then about problem solving. That means that in learning, teacher always demand students to study and solve the problem but seldom teach how should the students solve the problem. It makes learning process is meaningless to
students that cause low ability of students’ mathematics problem solving ability.
To achieve objectives learning election methods, strategies and approaches in a classroom situation is concerned very important. Therefore, learning in the classroom should be converted into student-centered. One model of learning that makes students active and interested in learning mathematics is problem-based learning model. Problem based learning (PBL) process essentially consists of the following stages: (1) meeting the problem; (2) problem analysis and generation of learning issues; (3) discovery and reporting; (4) solution presentation and reflection; and (5) overview, integration, and evaluation, with self directed learning bridging one stage and the next (Tan, 2003).
In PBL, the problem is cast in realistic context that the students might encounter in future. Although creative individuals tends to work alone, students in
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PBL classes work in groups brainstorming issues pertaining to understanding of the problem and defining it by group consensus. They then work independently on their own to search for more information related to the problem before generating hypotheses and possible explanation to the problem. While this stage may be similar to some of stage involved in creative problem solving.
In problem-based learning, teacher provide to students mathematics problem until students interested to solve the problem. Problem cannot be solved using procedure routine so students perceive the problem as a challenge. Mathematics teachers have a duty to help students to improve student’s problem solving ability. Teachers should strive to enable students to solve problems was given of problem based learning model. Problem-based learning model believed can enhance students’ problem solving ability that require students to seek their own solution problem independently that will give a concrete experience, the experience can be used also to solve the similar problem will give meaning itself for the learners. Students solve mathematics problem until students’ mathematical problem solving ability increased. So, problem-based learning provides the opportunity for students to solve mathematics problem and increase students’ mathematics problem solving.
Based on above background, the researcher interested in conducting research entitled : "The Implementation of Problem-Based Learning Model to Increase Students’ Mathematical Problem Solving Ability At SMP Negeri I Tanjung Morawa.’
1.2. Problem Identification
Based on the background of the issues that have been mentioned above, some problems can be identified as follows:
1. Students’ mathematical problem solving ability is low.
2. Student has difficulty to solve mathematical problems.
3. Learning process is dominated by the teacher so the students only receive without have learning experience
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4. Implementation of PBL is an effort to increase students’ mathematical problem solving ability
1.3. Problem Limitation
Because the extent of the problem and limited ability, time and costs 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 1 Tanjung Morawa in academic year 2015/2016.
2. Model of learning used is Problem Based Learning Model.
3. Problem solving ability the eighth grade students of SMP Negeri 1 Tanjung Morawa in academic year 2015/2016.
1.4. Problem Formulation
In accordance with the extent of the problem described above, the research question in this study:
1. Does the implementation of Problem Based Learning Model increase students’
mathematical problem solving ability in grade VIII at SMP Negeri 1 Tanjung Morawa?
2. How does Problem Based Learning Model increase students’ mathematical problem solving ability in grade VIII at SMP Negeri 1 Tanjung Morawa?
3. Do students’ activities increase after the implementation of Problem Based
Learning Model in grade VIII at SMP Negeri 1 Tanjung Morawa? 1.5. Research Objectives
Based on the problem formulation, then objectives of this research is: 1. Knowing whether students’ problem solving ability increase after the
implementation of problem-based learning model.
2. Improving students’ Mathematical Problem Solving ability through problem based learning in grade VIII at SMP Negeri 1 Tanjung Morawa .
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3. Knowing the increasing of students’ activities after the implementation of Problem Based Learning Model in grade VIII at SMP Negeri 1 Tanjung Morawa.
1.6. Benefits of Research
After conducting this research study is expected to provide significant benefits, namely:
1. For student, instil a high order thinking skills in problem solving, formulating problems, and ability to cooperate to solve the problem.
2. For teachers, it can use problem based learning model for improving students' mathematical problem solving ability in learning activities.
3. For researchers, as information for students who are conducting research using Problem Based Learning to improve students' mathematical problem solving ability in learning activities.
1.7. Operational Definition
To avoid the occurrence differences in interpretation of the terms contained in the formulation of the problem in this research, the operational definition be stated as follows:
a. Problem-Based Learning
Problem-based learning is a learning model that applies to the process stages: Orient student to the problem,
Organize students for study,
Assist individual and group investigation, Develop and present artifacts and exhibits,
Analyze and evaluate the problem solving process. b. Problem Solving Ability
Problem solving is the students' ability in solving mathematical problems based on the stages of problem solving, namely:
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Understanding the problem
Planning problem solving strategies Implementing problem solving strategies Checking the results of solving the problem
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CHAPTER V
CONCLUSION AND SUGGESTION
5.1. Conclusion
Based on the results and the discussion in chapter IV, for the implementation of learning through problem-based learning model, obtained some conclusions which are the answers to the questions posed in the formulation of the problem. Conclusions are:
1. The implementation of Problem-based learning model can increase students’ mathematical problem solving ability in SMP Negeri I Tanjung Morawa class VIII-5 Academic Year 2015/2016.
2. There are increasing 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 is 2.35 with classical completeness 52.63% and average score of cycle II is 3.04 with classical completeness 86.84%. By using gain score, the increasing of average score is 0.41 is classified into medium category (enough achieved).
3. Students’ activity increase after implementation of Problem-based learning model, it is seen that in cycle I, all groups are passive group with average score 45.80% so that the class is said passive class in learning activity in implementation PBL learning cycle I but in Cycle II, there are improvement in learning activity with average score 86.90%. All the group reach score , it means that all the group in cycle II are active in learning activity. 5.2. Suggestion
Based on these result, the authors propose some suggestion for learning mathematics in problem solving ability that can be given as follow:
1. Learning mathematics by implementation PBL model can be used as an alternative effective learning to increase students’ mathematical problem solving ability and students’ activity. But for the first implementation teacher fell difficult in preparing learning and condition the class. Because
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PBL is firstly giving real problem to the students without explain far explanation of the topic, 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, they can face the trouble by sharing with their group to solve the problem.
2. Problem-Based Learning Model can develop critical thinking ability of students because it needs high thinking ability of students to understand the problem and for lazy students, it is difficult 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 increase students' mathematical problem solving ability, then the teacher must :
a. Able to make problem question which can be used to exercise the students to do problem solving step.
b. Management of time as good as possible when learning is done. c. Understanding the phases that must be applied in problem-based
learning model.
d. Doing small learning groups designed which are heterogeneous. e. Guide and help students to open mind to solve problem.
f. Facilitating learning activities as a facilitator by promoting patient, tenacity and always innovative attitudes.
4. To increse research result of the research, the fourth step of Polya (looking back) must get extra attention.
5. Before enter cycle I, it is needed more accurate data beside teacher data to spread the group.
6. To school, by due process of learning by using problem-based learning requires infrastructure to provide the facilities needed to support
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90
improvement of learning in order to improve the quality of learning, in this case an effort to improve students' mathematical problem solving ability. 7. For the next researcher, it is expected to use research result as comparison
matter and implement PBL model in other topic, using attractive book and nteresting SAS to make students are more interesting to do learning actively.
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91
REFERENCES
Abdurrahman, M., (2012), Anak Berkesulitan Belajar, Rineka Cipta, Jakarta.
Amustofa, (2009), Strategi Pemecahan Masalah dalam Matematika,
http://amustofa70.wordpress.com. Accessed on (December, 10th 2015) Aunurrahman, (2012), Belajar dan Pembelajaran, Alfabeta, Bandung. Arends, R.I., (2012), Learning to Teach 9th Edition, McGraw-Hill, New York.
Arikunto, S., (2010), Prosedur Penelitian Suatu Pendekatan Praktik, Rineka Cipta, Jakarta.
Badan Standar Nasional Pendidikan, (2006), Standar Kompetensi dan Kompetensi Dasar Tingkat, Balitbang, Jakarta.
Chapman, O. (2005), Constructing, pedagogical knowledge of problem solving: pre-service mathematics teachers. In H. L. Chick, & S.L. Vincent (Eds.), Proceeding of the 29thConference of the International Group for the Psychology of Mathematics Education. (Vol.2, pp. 225-232). Melbourne: International Group for the psychology of mathematics Education.
Chi, M.T.H., (1985), Problem solving ability, Human abilities: An information processing approach, Freeman, New York.
Fatade, A.O., (2012), Investigating The Effectiveness of Problem Based Learning in the Further Mathematics Classroom, Dissertation, Mathematics, Science and Technology Education, University of South Africa, Africa.
Joyce, Bruce & Weil, Marsha., (1980), Models of Teaching, Printice Hall, Inc, United States of America .
(31)
92
Judith Lioyd Yero, (2002), The Meaning of Education, http://www.TeachersMind.com. (Accessed on December 31, 2015).
Kementerian Pendidikan dan Kebudayaan, (2014), Matematika Studi dan Pengajaran Kurikulum 2013, Kementerian Pendidikan dan Kebudayaan, Jakarta.
La Arul, (2009), International Results in Mathematics, TIMSS & PIRLS International Study Center United States.
Linda, (2002), Problem As Possibilities Problem Based Learning For K16 education 2nd Edition, ASCD, Alexandria Virginia USA.
Mayer, R.E. (1983). Thinking, problem solving and cognition. New York, Freeman. National Council of Teacher of Mathematics, (2000), Principles and Standards for
School Mathematics, NCTM, Reston, Virginia.
National Council of Teachers of Mathematics. (2003). NCTM Program Standards. Programs for Initial Preparation of Mathematics Teachers. Standards for
Secondary Mathematics Teachers, http://www.nctm.org/ uploadedFiles/Math_Standards/ (Accessed on Feb 18th, 2016)
National Research Council (1999). How people learn: Bridging research and practice, National Academy Press, Washington, DC.
Nuralam, (2009), Pemecahan Masalah sebagai Pendekatan dalam Belajar Matematika, Jurnal Edukasi, Vol. V, No.1,142-154.
Nuharini D., (2008), Matematika Konsep dan Aplikasinya, CV.Usaha Makmur, Surakarta.
Oon S.T., (2003), Problem Based Learning Innovation, GALE Cengage Learning, Singapore.
(32)
93
Polya, G., (2004), How to Solve It A New Aspect of Mathematical Method, Princeton Science Library, USA.
Restructuring Associates, (2008), Step of Problem Solving, http://www.yale.edu/bestpractices/resources/docs/problemsolvingmodel.pdf. (accessed on December 31, 2015)
Richard R.H., (1999), Analyzing Change/Gain Score, http:www.Physic.Indiana.edu/sdiAnalyzingChange-gain.pdf. (Accessed on januari 31st, 2016)
Rideout, (2001), Transforming Nursing Education Through Problem based Learning, Jones & Barlett Learning, USA.
Rusman., M.Pd., Dr., (2012), Model-Model Pembelajaran Mengembangkan Profesionalisme Guru Edisi Kedua, PT. Raja Grafindo Persada, Jakarta. Ruseffendi, E.T., (2006), Pengantar kepada membantu Guru Mengembangkan
Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA, Tarsito, Bandung.
Schoenfeld, A. H., (1985), Mathematical Problem Solving, Academic Press, Florida. Schoen, H.L., (1980), A New Approach to the Measurement of Problem solving
Skills, National Council of Teachers of Mathematics, Reston VA.
Sembiring, Suwah., (2010), Pelajaran Matematika Bilingual, Yrama Widya, Bandung.
Sudjana, (2005), Metoda Statistika, Tarsito, Bandung.
Suherman, E., (2001), Strategi Pembelajaran Matematika Kontemporer, UPI, Bandung.
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94
Sukayati, (2008), Penelitian Tindakan Kelas, PPPPTK Matematika, Yogyakarta. Suyanto, (1997), Pedoman Pelaksanaan Penelitian Tindakan Kelas (PTK)
Pengenalan Penelitian Tindakan Kelas, Dirjen Dikti, Yogyakarta.
Syawal G., dkk, (2010), Matematika Kompeten Berhitung, Citapustaka Media Perintis, Medan.
Tan O.S., (2003), Problem-Based Learning Innovation: Using problems to power learning in the 21st century, Singapore, Thomson Learning.
Torp, (1998), Illnots Mathematics and Science Academy, Certer for Problem Based Learning, Aurora IL, Virginia.
Trianto, (2009), Mendesain Model Pembelajaran Inovatif-Progresif, Prenada Media Group, Jakarta.
Wardhani, S., (2010), Pembelajaran Kemampuan Masalah Matematika di SMP, PPPPTK Matematika, Yogjakarta.
Widjajanti, D.B., (2009), Kemampuan Pemecahan Masalah Matematis Mahasiswa Calon Guru Matematika: Apa dan Bagaimana Mengembangkannya, Seminar Nasional Matematika dan Pendidikan Matematika Page 25
(1)
PBL is firstly giving real problem to the students without explain far explanation of the topic, 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, they can face the trouble by sharing with their group to solve the problem.
2. Problem-Based Learning Model can develop critical thinking ability of students because it needs high thinking ability of students to understand the problem and for lazy students, it is difficult 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 increase students' mathematical problem solving ability, then the teacher must :
a. Able to make problem question which can be used to exercise the students to do problem solving step.
b. Management of time as good as possible when learning is done. c. Understanding the phases that must be applied in problem-based
learning model.
d. Doing small learning groups designed which are heterogeneous. e. Guide and help students to open mind to solve problem.
f. Facilitating learning activities as a facilitator by promoting patient, tenacity and always innovative attitudes.
4. To increse research result of the research, the fourth step of Polya (looking back) must get extra attention.
5. Before enter cycle I, it is needed more accurate data beside teacher data to spread the group.
6. To school, by due process of learning by using problem-based learning requires infrastructure to provide the facilities needed to support
(2)
improvement of learning in order to improve the quality of learning, in this case an effort to improve students' mathematical problem solving ability. 7. For the next researcher, it is expected to use research result as comparison
matter and implement PBL model in other topic, using attractive book and nteresting SAS to make students are more interesting to do learning actively.
(3)
REFERENCES
Abdurrahman, M., (2012), Anak Berkesulitan Belajar, Rineka Cipta, Jakarta.
Amustofa, (2009), Strategi Pemecahan Masalah dalam Matematika, http://amustofa70.wordpress.com. Accessed on (December, 10th 2015)
Aunurrahman, (2012), Belajar dan Pembelajaran, Alfabeta, Bandung.
Arends, R.I., (2012), Learning to Teach 9th Edition, McGraw-Hill, New York.
Arikunto, S., (2010), Prosedur Penelitian Suatu Pendekatan Praktik, Rineka Cipta, Jakarta.
Badan Standar Nasional Pendidikan, (2006), Standar Kompetensi dan Kompetensi Dasar Tingkat, Balitbang, Jakarta.
Chapman, O. (2005), Constructing, pedagogical knowledge of problem solving: pre-service mathematics teachers. In H. L. Chick, & S.L. Vincent (Eds.), Proceeding of the 29thConference of the International Group for the Psychology of Mathematics Education. (Vol.2, pp. 225-232). Melbourne: International Group for the psychology of mathematics Education.
Chi, M.T.H., (1985), Problem solving ability, Human abilities: An information processing approach, Freeman, New York.
Fatade, A.O., (2012), Investigating The Effectiveness of Problem Based Learning in the Further Mathematics Classroom, Dissertation, Mathematics, Science and Technology Education, University of South Africa, Africa.
Joyce, Bruce & Weil, Marsha., (1980), Models of Teaching, Printice Hall, Inc, United States of America .
(4)
Judith Lioyd Yero, (2002), The Meaning of Education, http://www.TeachersMind.com. (Accessed on December 31, 2015).
Kementerian Pendidikan dan Kebudayaan, (2014), Matematika Studi dan Pengajaran Kurikulum 2013, Kementerian Pendidikan dan Kebudayaan, Jakarta.
La Arul, (2009), International Results in Mathematics, TIMSS & PIRLS International Study Center United States.
Linda, (2002), Problem As Possibilities Problem Based Learning For K16 education 2nd Edition, ASCD, Alexandria Virginia USA.
Mayer, R.E. (1983). Thinking, problem solving and cognition. New York, Freeman. National Council of Teacher of Mathematics, (2000), Principles and Standards for
School Mathematics, NCTM, Reston, Virginia.
National Council of Teachers of Mathematics. (2003). NCTM Program Standards. Programs for Initial Preparation of Mathematics Teachers. Standards for
Secondary Mathematics Teachers, http://www.nctm.org/ uploadedFiles/Math_Standards/ (Accessed on Feb 18th, 2016)
National Research Council (1999). How people learn: Bridging research and practice, National Academy Press, Washington, DC.
Nuralam, (2009), Pemecahan Masalah sebagai Pendekatan dalam Belajar Matematika, Jurnal Edukasi, Vol. V, No.1,142-154.
Nuharini D., (2008), Matematika Konsep dan Aplikasinya, CV.Usaha Makmur, Surakarta.
Oon S.T., (2003), Problem Based Learning Innovation, GALE Cengage Learning, Singapore.
(5)
Polya, G., (2004), How to Solve It A New Aspect of Mathematical Method, Princeton Science Library, USA.
Restructuring Associates, (2008), Step of Problem Solving, http://www.yale.edu/bestpractices/resources/docs/problemsolvingmodel.pdf. (accessed on December 31, 2015)
Richard R.H., (1999), Analyzing Change/Gain Score, http:www.Physic.Indiana.edu/sdiAnalyzingChange-gain.pdf. (Accessed on januari 31st, 2016)
Rideout, (2001), Transforming Nursing Education Through Problem based Learning, Jones & Barlett Learning, USA.
Rusman., M.Pd., Dr., (2012), Model-Model Pembelajaran Mengembangkan Profesionalisme Guru Edisi Kedua, PT. Raja Grafindo Persada, Jakarta. Ruseffendi, E.T., (2006), Pengantar kepada membantu Guru Mengembangkan
Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA, Tarsito, Bandung.
Schoenfeld, A. H., (1985), Mathematical Problem Solving, Academic Press, Florida. Schoen, H.L., (1980), A New Approach to the Measurement of Problem solving
Skills, National Council of Teachers of Mathematics, Reston VA.
Sembiring, Suwah., (2010), Pelajaran Matematika Bilingual, Yrama Widya, Bandung.
Sudjana, (2005), Metoda Statistika, Tarsito, Bandung.
Suherman, E., (2001), Strategi Pembelajaran Matematika Kontemporer, UPI, Bandung.
(6)
Sukayati, (2008), Penelitian Tindakan Kelas, PPPPTK Matematika, Yogyakarta. Suyanto, (1997), Pedoman Pelaksanaan Penelitian Tindakan Kelas (PTK)
Pengenalan Penelitian Tindakan Kelas, Dirjen Dikti, Yogyakarta.
Syawal G., dkk, (2010), Matematika Kompeten Berhitung, Citapustaka Media Perintis, Medan.
Tan O.S., (2003), Problem-Based Learning Innovation: Using problems to power learning in the 21st century, Singapore, Thomson Learning.
Torp, (1998), Illnots Mathematics and Science Academy, Certer for Problem Based Learning, Aurora IL, Virginia.
Trianto, (2009), Mendesain Model Pembelajaran Inovatif-Progresif, Prenada Media Group, Jakarta.
Wardhani, S., (2010), Pembelajaran Kemampuan Masalah Matematika di SMP, PPPPTK Matematika, Yogjakarta.
Widjajanti, D.B., (2009), Kemampuan Pemecahan Masalah Matematis Mahasiswa Calon Guru Matematika: Apa dan Bagaimana Mengembangkannya, Seminar Nasional Matematika dan Pendidikan Matematika Page 25