THE EFFORT TO INCREASE THE PROBLEM SOLVING ABILITY OF STUDENT BY IMPLEMENTING PROBLEM BASED LEARNING
(PBL) IN THE TOPIC OF TRIGONOMETRY IN GRADE X OF SMA NEGERI 1 PERBAUNGAN
IN THE YEAR OF 2012/2013
By:
Joy Juli Great Simanjuntak Reg. Number 409312020
Bilingual Mathematics Education Program
THESIS
Submitted to Fulfill Requirement for Sarjana Pendidikan Degree
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
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ACKNOWLEDGMENTS
Firstly, writer would like to thanks be to Almighty God for His mercy and blessing to writer thus because of His love to writer thus this research can be finished well appropriate with time that has been planned.
Thesis entitled “The Effort to Increase the Problem Solving Ability of Student by Implementing Problem Based Learning (PBL) in the Topic of Trigonometry in Grade X of SMA Negeri 1 Perbaungan in the Year of 2012/2013” is compiled to fulfill requirement for Sarjana Pendidikan degree.
In this chance, writer wants to extend gratitude to Mr. Dr. Hasratuddin, M.Pd as thesis advisor who has made his time for giving brief and guidance from beginning until the end of writing process of this thesis. Gratitution also writer delivers to Mr. Drs. H. Banjarnahor, M.Pd, Mr. Dr. E. Elvis Napitupulu, MS and Mr. Dr. Edy Surya, M.Si as thesis examiner who have given advices and suggestions from beginning of research planning until the compiling of this thesis finished.
Thanks a lot also to Mr. Prof. Dr. Mukhtar, M.Pd as academic advisor and as head of mathematics department who has given guidance, suggestion and even facilitation along the study in State University of Medan. Thanks a lot also to Mr. Prof. Dr. Ibnu Hajar, M.Si as head of State University of Medan, Mr. Prof. Drs. Motlan, M.Sc, Ph.D as dean of mathematics and natural sciences faculty, Mr. Drs. Yasifati Hia, M.Si as secretary of mathematics department, Mr. Drs. Syafari, M.Pd as head of mathematics education program, Mr. Dr. rer. net. Binari Manurung, M.Si as coordinator of bilingual program and also for all lecturer and staff of mathematics department who has helped and facilitation during compiling process of this thesis.
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The special gratitude, writer wants deliver to dear loving father Alm. Todung Simanjuntak and the dearest mother Lesman br Sihotang who have given a lot of love, pray, motivation and spirit who help writer to finish the study until now. Special thanks to my beloved sister Vickytri Afriani br Simanjuntak and all family for all pray, motivation and support up to now.
Thanks to every member of IKBKM for all spirit, support and experience that has been shared to writer. Thanks also for Adi, Ardianto, Reinojum, Suprianto and Wes that united in Touring Team 2013 for all sprit, support and time to have relax time together. Writer is indebted to bilingual mathematics education 2009 big family for helping along the study in State University of Medan, they are Dini, Enny, Evy, Epril, Faradilla, Iin, Iwan, Noya, Nurhabibah, Qori, Retni, Rini, Rizki, Siska, Siti, and Widia. Big and special thanks to Siska Nopa Tambunan that is one of writer best friend for helping and giving big motivation, praying and even giving spirit in every activity that done by writer. Moreover, thanks to all colleagues in PPLT Unimed 2012 in SMA Negeri 1 Perbaungan who always support and share their experience to writer.
Writer realized that there are still weaknesses in contents and grammar of this thesis, so writer receives critics and advices from the reader to make this thesis be better. Hopefully, this thesis can be useful for education world.
Medan, June , 2013 Writer,
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THE EFFORT TO INCREASE THE PROBLEM SOLVING ABILITY OF STUDENT BYIMPLEMENTING PROBLEM BASED LEARNING
(PBL) IN THE TOPIC OF TRIGONOMETRY IN GRADE X OF SMA NEGERI 1 PERBAUNGAN
IN THE YEAR OF 2012/2013
Joy Juli Great Simanjuntak (Reg. Number 409312020)
ABSTRACT
This research aims to increase the problem solving ability of student in grade X of SMA Negeri 1 Perbaungan by implementing problem based learning (PBL) model in trigonometry topic.
Type of this research is Classroom Action Research (CAR). Subject in this research is student in class XU-1 of SMA Negeri 1 Perbaungan that consists of 26 students. This research is conducted in two cycles. Data in this research is obtained from learning implementation and student activity observation, problem solving ability test, student response questionnaire and documentation.
Results of this research show that PBL can increase problem solving ability of student. The increasing can be seen in three things such as, (1) average of class score in cycle I is 71.04 becomes 78.35 in cycle II or increases 5.38 (10.29%), (2) total of student who completed in understanding problem step in cycle I is 21 becomes 24 in cycle II or increases 3 students (14.29%), total of student who completed in making a plan step in cycle I is 21 becomes 26 in cycle II or increases 5 students (23.51%), total of student who completed in doing the plan step in cycle I is 16 becomes 23 in cycle II or increases 7 students (43.75%), total of student who completed in checking solution step in cycle I is 15 becomes 23 in cycle II or increases 8 students (53.33%) and (3) total of student who completed to solve problem in cycle I is 13 becomes 23 in cycle II or increases 10 students (76.92%). Based on gain score criteria, the increasing of students’ problem solving ability is classified into low category.
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1.2. Problem Identification 5
1.3. Problem Limitation 5
1.4. Problem Formula 6
1.5. Research Objective 6
1.6. Research Benefit 6
CHAPTER II LITERATURE REVIEW 8
2.1. Theoretical Background 8
2.1.1. Definition of Learning Mathematics 8 2.1.2. Learning Mathematics in School 9
2.1.3. Problem in Mathematics 11
2.1.4. Mathematics Problem Solving 12 2.1.5. Mathematics Problem Solving Ability 17
2.1.6. PBL Model 18
2.1.7. Summary of Subject Matter 22 2.1.7.1. Trigonometry Ratios that Formed by Angle of Right Triangle 22 2.1.7.2. Trigonometry Ratios Value of Specific Angles 23
2.2. Relevant Research 25
2.3. Theoretical Frame 26
2.4. Action Hypothesis 29
CHAPTER III RESEARCH METHODOLOGY 30
3.1. Type of Research 30
3.2. Place and Time of Research 30
3.3. Subject and Object of Research 30
3.3.1. Subject of Research 30
3.3.2. Object of Research 30
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3.5.1. Observation 34
3.5.2. PSA Test 34
3.5.3. Questionnaire of Student Response 34
3.5.4. Documentation 34
3.6. Instrument in Collecting Data 34
3.6.1. Observation Guidance 35
3.6.2. PSA Test 35
3.6.2.1. Validity of Test 35
3.6.2.2. Reliability of Test 36
3.6.3. Questionnaire of Student Response Sheet 37
3.7. Data Analysis Techniques 37
3.7.1. Data analysis of Learning Implementation and Student Activity
in Learning by Using PBL 37
3.7.2. Analysis of Mathematics PSA 38 3.7.3. Questionnaire of Student Response Sheet 41
3.7.4. Documentation Result 42
3.8. Increasing Criteria of Mathematics PSA 43
3.9. Effectiveness of PBL 43
3.9.1. Calculating Level of Student Mastery 43 3.9.2. Calculating Completeness of Student Learning 44 3.9.3. Calculating Completeness Attainment of Basic Competence 44
Indicator 44
3.10. Data Explanation 45
3.11. Conclusion Drawing 45
CHAPTER IV RESULT AND EXPLANATION OF RESEARCH 46
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4.1.3.5.1. Analysis of Observation Result Data 73 4.1.3.5.2. Analysis of PSA Test II Data 77 4.1.3.6. Description of Reflection II 79 4.1.4. Effectiveness of PBL in Cycle I 82 4.1.4.1. Level of Student Mastery in Cycle I 82 4.1.4.2. Completeness of Student Learning in Cycle I 82 4.1.4.3. Completeness Attainment of Basic Competence Indicator in
Cycle I 83
4.1.5. Effectiveness of PBL in Cycle II 84 4.1.5.1. Level of Student Mastery in Cycle II 84 4.1.5.2. Completeness of Student Learning in Cycle II 84 4.1.5.3. Completeness Attainment of Basic Competence Indicator in
Cycle II 85
4.1.6. Result of Response Questionnaire 86
4.1.7. Research Result 88
4.1.8. Research Result Discussion 89
CHAPTER V CONCLUSION AND SUGGESTION 95
5.1. Conclusion 95
5.2. Suggestion 95
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LIST OF TABLE
Page Table 1.1. Total of Students who Complete in Problem Solving Steps 4 Table 2.1. Value of Trigonometry Ratios 23 Table 2.2. Signs of Trigonometry Ratios 24 Table 3.1. Guideline of Class Score Average 38 Table 3.2. Scoring Guideline of Test 38 Table 3.3. Scoring for Each Category of Student Answer in
Questionnaire 41
Table 3.4. Criteria of Student Response Percentage 42
Table 3.5. Increasing Criteria 42
Table 3.6. Criteria of Percentage of Study Result Attainment 43 Table 4.1. Average of Class Score 46 Table 4.2. Total of Students who Complete in Problem Solving Steps 47 Table 4.3. Total of Student who Completes to Solve Problem 47 Table 4.4. Description of Observation Result of Teacher Ability in
Implementing the Learning in Cycle I 52 Table 4.5. Description of Observation Result of Student Activity in
Learning in Cycle I 54
Table 4.6. Average of Class Score 56 Table 4.7. Total of Students who Complete in Problem Solving Steps 56 Table 4.8. Total of Students who Complete to Solve Problem 57 Table 4.9. Investigation of Reflection I Result in Cycle I 63 Table 4.10. Description of Observation Result of Teacher Ability in
Implementing the Learning in Cycle II 74 Table 4.11. Description of Observation Result of Student Activity in
Learning in Cycle II 76
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LIST OF FIGURE
Page Figure 2.1. Problem Solving Process by Polya 15
Figure 2.2. Right Triangle 22
Figure 2.3. Scheme of Problem Solving with PBL 28
Figure 3.1. CAR Design 33
CHAPTER I
INTRODUCTION
1.1. Background
Education is one form of human culture manifestation that dynamic and full of development. Therefore, a change or a development of education is indeed should be in line with the change of life culture. Education that can support future development is education that able to develop potential of learners, so the concerned is able to face and to solve the life problems that he/she is faced. Education should touch the inner potential and the competence potential of learners (Trianto, 2011:1).
Mathematics is a subject that very important in every level of education, from primary to high education. This is because mathematics can train students to think logically, to be responsible and to have a good personality and skill in solving problems in real life.
As one of basic sciences, mathematics has an essential value that can be applied in various fields of life. Mathematics learning is qualified or not, it cannot be separated from role of teachers and students. Teachers are required to create an active learning situation, innovative, creative, effective and fun in the learning process that the result will be reflected in student achievement that high.
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attack which is the most optimal from a launcher weapon, to be able to throw the projectile as far as possible; determine how the highest gradient of a hill on a public road in the mountains, so that all vehicles can pass it safely; and the simplest example of the daily events, when we walk in the stairs, we do not want to make the gradient of the stair to be too big or the angle is too small because its range is low (Bawazir, 2012).
However, what happened today is contrary to the expectations; it was indicated by low of students' mathematics achievement. Generally, the learning of mathematics in Indonesia, including learning trigonometry in high school is still far from satisfactory and sometimes can be said still disappointing. (Setiawan, 2004:1).
Based on survey data of Trends in International Mathematics and Sciences Study (TIMSS) 2003 under the International Association for the Evaluation of Educational Achievement (IEA) that: "Indonesia in the position 34 for field of mathematics and in position 36 for field of science of 45 countries surveyed" (Karwono, 2009).
The success of mathematics learning can be measured by the success of students who follow learning activity. That success can be seen from student’s activity in participating in classroom activities and learning mathematics achievement. The better activity and mathematics learning achievement, then level of success of learning mathematics process is higher.
Many things affect the low mathematics learning achievement of students. One of them is the use of approaching or the learning model which is irrelevant to topic that taught by teacher. Generally, learning model that implemented is conventional learning model that often called with teacher center. Suherman (2012) expresses the same thing:
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material to be studied, students come without sufficient knowledge as bringing an empty container.
According to Arends (in Trianto, 2011:90): “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”.
Teachers are required to make the students learn actively. This is an important factor in the outcome of teaching and learning activities. Learning mathematics still does not reach the substance of problem solving. Students are more likely to memorize concept than to understand the meaning thus students' ability in solving mathematical problems is low. Prayudi (2008) states that:
One of KTSP advantages is declared that problem solving, reasoning, communication as a goal of learning mathematics in elementary school, junior high school, senior high school, and vocational school beside goals which are related to concept of understanding which has been known by teacher.
Problem solving can be considered as a method of learning in which students are trained to solve problems. The problem may come from the teacher, a phenomenon or real problems that encountered by students. Problem solving refers to child's brain function, develops creative thinking to recognize problem and seek alternative solutions. Mathematics problem solving includes "problem solving" as cognitive behavior and "mathematics" as the object of being studied. Process thinking in mathematical problem solving requires a certain intellectual skills that will organize strategy that pursued in accordance with data and problem that encountered. Therefore, it can be understood that before mastering mathematical problem solving, it is required to mastery lower cognitive aspects firstly, namely memory, understanding and application.
Based on the interview (January 22, 2013) of researcher with mathematics teacher of grade X of SMA Negeri 1 Perbaungan, Mr. Ishak Saragih, said that:
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learning process is not maximal. This might be due to methods which are used do not appropriate or methods do not make students be motivated to learn, so problem solving ability of students in trigonometry topic is low.
From result of survey that conducted by researcher (February 4, 2013) by giving the problem solving diagnostic test to students of grade XU-1 of SMA Negeri 1 Perbaungan, in topic of Angle Size and Angle Triangle as a prerequisites matter of trigonometry topic. From 26 students who took the test, the average of class score that obtained is 54.23 (score scale 0 – 100). Based on the test result is also obtained that total of student who complete in understanding the problem step is 10 students (38.46%), in making a plan step is 13 students (50%), in doing the plan step is 4 students (15.39%) and in checking solution step is 0 student (0%). The complete result can be seen in the following table:
Table 1.1. Total of Students who Complete in Problem Solving Steps
No. Problem Solving Step Diagnostic Test
Total of Student Percentage 1. Understanding problem 10 38.46%
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students to solve problems because one focus of learning mathematics is problem solving, so that basic competencies that should be owned by every student is a minimum standard of knowledge, skills, attitudes and values which is reflected in
learning of mathematics with habits of thought and action to solve problem. Powerful learning model that believed can enhance students' problem solving abilities are learning models 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 because experience will give meaning itself for the learners. Learning model that has the characteristics above is problem based learning (PBL). PBL model is a learning model that based on a number of issues that require authentic investigation that is an investigation that require a real solution from the real issues (Trianto, 2011: 90).
Based on the explanations above, researcher is interested to conduct a research which entitled: The Effort to Increase the Problem Solving Ability of Student by Implementing Problem Based Learning (PBL) in the Topic of Trigonometry in Grade X of SMA Negeri 1 Perbaungan in the Year of 2012/2013
1.2. Problem Identification
Based on background, some issues that can be identified as follows: 1. Learning approaches which is used by teachers is irrelevant.
2. Learning activities are still centered on teacher.
3. Student ability in solving mathematics problem is low.
4. Implementation of PBL is an effort to increase mathematics problem solving ability of students.
1.3. Problem Limitation
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mathematics problem solving ability of student and to know difficulties which is faced by students in doing trigonometry problem.
1.4. Problem Formula
Based on problem limitation above, then problems formula of this research are
1. How increasing of students’ problem solving ability by implementing PBL in trigonometry topic?
2. Is PBL effective in learning of trigonometry topic?
3. How do students response to implementation of PBL in learning of trigonometry topic?
1.5. Research Objective
The objective of this research such as
1. To find out the increasing of students' problem solving ability with implementation of trigonometry topic.
2. To know effectiveness of PBL in trigonometry topic learning.
3. To know the response of student to implementation of PBL in learning of trigonometry topic.
1.6. Research Benefit
After this research is done, it is expected to be beneficial to all people, including:
1. For teacher/teacher candidate that is as information about student achievement in solving problems by implementing PBL in trigonometry topic.
2. For principal that can be considered matter for teacher to implement PBL in teaching and learning activities in school.
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CHAPTER V
solving ability test II in cycle II, there exist increasing of average of class score. Average of class score increases 10.29%. By using gain score formula, it is obtained that the gain score is 0.25. Based on gain score criteria, increasing of mathematics problem solving ability of student is classified into low category.2. Based on problem solving ability test II in cycle II and observation II, got that level of student mastery is 88.46% that means that completeness of student learning is complete classically, attainment of basic competence indicator at whole achieves 75% that means that completeness attainment of basic competence indicator is achieved and observation II shown that teacher ability is very good and student activity is good. So, problem based learning model is effective in learning of trigonometry topic in grade X.
3. Based on response questionnaire result, students are interested, happy and love learns mathematics by implementing problem based learning model especially in trigonometry topic.
5.2. Suggestion
Based on the conclusion above, researcher proposes some suggestions such as:
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2. To teacher and all school party of SMA Negeri 1 Perbaungan, in order to keep trying to develop and to find creative innovation of mathematics learning especially that relates to PBL model such as combine PBL model with cooperative learning such that mathematics learning in class be more interesting and please.
