EFFORTS IN IMPROVING STUDENTS MATHEMATICAL PROBLEM SOLVING ABILITY THROUGH REALISTIC MATHEMATICS
EDUCATION APPROACH ON SUBJECT QUADRILATERAL AT SMP NEGERI 6 MEDAN ACADEMIC YEAR 2012/2013
By
Iwan Prakasa
409312008
Bilingual Mathematics Education
THESIS
Submitted to the State University of Medan as Fulfillment as Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
PREFACE
Give thanks to Allah Subhanallahu Wata’ala give me more spirit to finish my thesis. The title of thesis is efforts in improving students mathematical problem-solving ability through realistic mathematics education approach on subject Quadrilateral at SMP Negeri 6 Medan Academic Year 2012/2013. This thesis wa arranged to satisfy the law to get the sarjana pendidikan of Mathematics and Science Faculty in State University of Medan.
For this chance I want to say thank you for the rector of State University of Medan, Mr. Prof. Dr. Ibnu Hajar, M.S and his staff, Mr. Prof. Drs. Motlan Sirait, M.Sc., Ph.D for dean of FMIPA UNIMED and his college assistant of Dean I, II, III in UNIMED, Mr. Drs. Syafari, M.Pd as a Leader of Mathematics Department, Mr. Drs. Zul Amry, M.Si as a Leader of Mathematics Education study program and then Mr. Drs. Yasifati Hia, M.Si as a secretary of Mathematics Department.
Big thanks for Mr. Dr. E. Elvis Napitupulu, MS as a supervisor who guide to prepare this thesis. And thanks a lot for Mr. Drs. Yasifati Hia, M.Si, Dr. Edi Syahputra, M.Pd, and Dr. Waminton Rajagukguk, M.Pd who’s the persons responsible for my thesis from the beginning until the end. Thanks to Mr. Dr. Waminton Rajagukguk, M.Pd as my academic supervisor and the thank you so much for all my lecturer and staff in FMIPA.
Special thanks to my lovely father Mr. Dasril Z and my lovely mother Yulastri for giving motivation, pray and all I need in finishing this thesis. And then thanks for love to my brother is Wahyu Andika Perdana and my sisters Irma Wulandari Am. Keb and Gita Yulanda.
Also thanks to big family in Bilingual Mathematics Education 2009 for sadness and happiness in class. Qori ‘qorche’, Enny ‘kocu’, Evy ‘vy ndut’, Joy ‘muncung I’, Iin ‘muncung II’, Siska ‘Jahe’, Rini, Rizki, Epril, Widia, Siti, Noyya ‘Cek Noy’,Nurhabibah ‘Bibeh’, Dilla, Dini, Retni, and very special thanks to you, Afrodita Munthe.
The writer should give a big effort to prepare this thesis, and the writer know that this thesis have so many weakness. So that, the writer needs some suggestions to make it this be better. And big wishes, it can be improve our knowledge.
Medan, August 2013 Writer
Efforts in Improving Students Mathematical Problem-Solving Ability Through Realistic Mathematics Education Approach on Subject Quadrilateral at SMP Negeri 6 Medan Academic Year 2012/2013
Iwan Prakasa (409312008) ABSTRACT
The aim of this research is to improve students mathematical problem-solving ability through realistic mathematics education approach on subject Quadrilateral at SMP Negeri 6 Medan. The type of this research is Classroom Action Research. The Research has done respect to students of VII-G in number of 37 students.
Instrument used to collect the data are problem-solving ability test and observation sheet. These research consist of two cycles and the end of every cycle given problem-solving ability test. Before given, at the first test must be validity. Validity test done is contents validity where expert as validator.
The result in this research has shown that learning by realistic mathematics education approach can improve problem-solving ability. From initial test given to student said that students has low ability level in prerequisite material. It indicate from the average value of 37 students is 20.7. This case shown from the result before treatment, in problem-solving ability test I of 37 students there are 24 students have achieved mastery learning with the average class 75.1.
After given treatment so the students do the problem-solving ability test II of 37 students there are 31 students have achieved mastery learning with the average class 80.5. The observation sheet get average score 2.75 in cycle I, its in good category. In cycle II get average score 3.5, it indicate teacher is very good category in implement realistic mathematics education in classroom.
TABLE LIST
Table 2.1. Implementation of Realistic Mathematics Learning Approach
Syntax 20
Table 3.1. Scoring Techniques 42
Table 4.1. Description of Student Problem-Solving Ability Levels in
Initial Tests 47
Table 4.2. Description of Student Ability Level in Understanding the Problem on Problem-Solving Ability Test I 49 Table 4.3. Description of Student Ability Level in Planning the
Problem on Problem-Solving Ability Test I 50 Table 4.4. Description of Student Ability Level in Solving the
Problem on Problem-Solving Ability Test I 51 Table 4.5. Description of Student Ability Level in Looking Back
Solution Obtained on Problem-Solving Ability Test I 51 Table 4.6. Description of Student Ability Level in Solving
Problem on Problem-Solving Ability Test I 53 Table 4.7. Descriptions of Teacher Observation Result in Doing
the Lesson on Cycle I 54
Table 4.8. The difficulty lies Students In Solving Problems
Ability Test I 61
Table 4.9. The Level of Students Understanding Problem Ability in Problem-Solving Ability Test II 64
Table 4.10. The Level of Students Planning Problem Ability in Problem-
Solving Ability Test II 65
Table 4.11. The Level of Students Solve Problem Ability in
Problem-Solving Ability Test II 66 Table 4.12. The Level of Students Looking Back Solution Obtained
Ability in Problem-Solving Ability Test II 66 Table 4.13. Description of Solve Problems Level Ability on
GRAPH LIST
Graph 3.1. Implementation Procedures of Action Research Based on
the Plot 41
Graph 4.1. Students Problem-Solving Ability Level on Initial Test 47 Graph 4.2. Student Ability Level in Doing Problem-Solving
Ability Test I 52
Graph 4.3. Students Mathematical Problem-Solving Ability Level on Problem Solving Ability Test I 53
Graph 4.4. The Level of Students Conducting Solving Problem in
Problem-Solving Ability Test II 67 Graph 4.5. Students Problem-Solving Ability Level on
Problem-Solving Ability Test II 68
APPENDIX LIST
Appendix 1. Lesson Plan I (Cycle I) 88 Appendix 2. Lesson Plan II (Cycle I) 92 Appendix 3. Lesson Plan III (Cycle II) 96 Appendix 4. Student Activity Sheet I (LAS-I) 100 Appendix 5. Student Activity Sheet II (LAS-II) 103 Appendix 6. Student Activity Sheet III (LAS-III) 106 Appendix 7. Validity of Research Instrument Calculation 108 Appendix 8. Validity Test Calculations 111 Appendix 9. Validation Sheet of Problem-Solving Ability Test 112 Appendix 10. Calculation of Reliability Test 118 Appendix 11. Initial Test of Observation 119 Appendix 12. Problem-Solving Ability Test Blue Print 120 Appendix 13. Problem-Solving Ability Test I 121 Appendix 14. Problem-Solving Ability Test II 122 Appendix 15. Alternative Solve Problem of Initial Test 123 Appendix 16. Alternative Solution of Student Activity Sheet I (Las-I) 126 Appendix 17. Alternative Solution of Student Activity Sheet II (Las-II) 130 Appendix 18. Alternative Solution of Student Activity Sheet III (Las-III) 135 Appendix 19. Alternative Solution of Problem-Solving Ability Test I 137 Appendix 20. Alternative Solution of Problem-Solving Ability Test II 141 Appendix 21. Guidelines of Scoring For Initial Test and
Problem-Solving Ability Test 144 Appendix 22. List of Initial Test Scores 146 Appendix 23. Percentage Determination Table of Students
Problem-Solving Ability for Every Step in Initial Test 148 Appendix 24. Scores List of Problem-Solving Ability Test I 150 Appendix 25. Scores List of Problem-Solving Ability Test II 153 Appendix 26. Observation Sheet in Meeting I 156 Appendix 27. Observation Sheet in Meeting II 160 Appendix 28. Observation Sheet in Meeting III 164
Appendix 29. Observation Sheet 168
CHAPTER I INTRODUCTION 1.1. Background
Words of education, counseling, teaching, learning, and training are technical terms concerning to activities united in educational activity. Education is one of the basic needs for human life, because through education human can change a person's attitude and ethics code in daily life. According to Sumber Referensi Online (2012), ”education is the process of changing attitudes and ethic code of a person or a group of people in effort to human mature through the efforts of teaching and training; process, ways, manufacture.”
Indonesia as a country gives much attention toward education in the development of the nation. Education is considered to be a main tool to build the next generation of the nation. As written in UU RI No.20 in 2003 on National Education System Chapter I Article I:
Education is defined as a conscious effort and deliberate to create an atmosphere of learning and the learning process so that learners are actively developing the potential for him to have the spiritual strength of religious, self-control, personality, intelligence, noble character, and the necessary skills themselves, society, nation and country.
Mathematics as one of the fundamental science education develop in people's life’s and very needed in the development of science and technology. As stated by Cornelius (in Abdurrahman 2003: 253), that five reasons for studying mathematics : (1) a means to think clearly and logically, (2) a means to solve the problems of everyday life, (3) the means to know the patterns of relationships and generalization of experience, (4) the means to develop creativity, and (5) means to raise awareness of cultural development.
ways, (5) To increase the ability to think logical, accurate and spatial awareness, and (6) Give satisfaction toward effort to solve a challenging problem."
According to Satria (2012), quality of mathematics in Indonesia is still unsatisfied. Based on data from UNESCO, mathematics education quality in Indonesia was ranked 34 of 38 countries surveyed. Other data showing that "From 1997 to 2007 education in Indonesia is in the following order in 1997 from 49 countries studied rank of Indonesia is 39. In 1999, of the 47 countries surveyed Indonesia was ranked 46. In 2002 of the 49 countries surveyed Indonesia was ranked 47 and in 2007 of the 55 countries surveyed, Indonesia got ranks 53, stated by Asri (2009). Then based on the TIMMS, "junior high school students' mathematics abilities in Indonesia was ranked 35th of 46 countries. In science, Indonesia ranked 37th of 46 countries", stated by Sea (2004). So far, Indonesia has not been able to escape from under the board row.
The object of mathematics is abstract. So, often students always have difficulties to learn concepts, principles and existing operations in mathematics. Students difficulties in learning mathematical concepts is one of the important factors of student learning. Students get difficulties in learning mathematics concepts can effects to students’ mathematical low scored.
Researchers also conducted an initial test to the students of grade VII in SMP Negeri 6 Medan. The test is given in the form of initial ability test in the form of essay to see the students' ability to solve mathematics problems. Here is it problem/question in problem solving ability that given to students.
Mr. Budi's build a house shaped like trapezoidal. Known trapezoid PQRS problem, so from this conclude that students problem solving ability still low.
Based on the test results can be known difficulties experienced by students in solving problems initial ability test between a lot of students that have difficulty in determining the mathematical concepts that will be used in solving a problem, students have difficulties in relating the known with asked of problem and many students have difficulties in letting convert sentences problem into sentences about mathematics (modeling). In each step problem-solving activities in the ability of students categorized as very low, therefore the overall take conclusions, students in problem solving is low.
From the survey results obtained by World Competitiveness Year Book, we can conclude that learning outcomes of student in Indonesia still disappointed especially in mathematics. This is possible because students are less able to understand the concepts and principles that effects to students not able to solve mathematical problems. Cause of student's difficulties in understanding of various concepts and principles of mathematics is a strategy or approach used by teachers that less variation, in teaching process just focus on text book, only provide information formula followed by giving questions, so that students feel satisfied, and effects to achievement of learning outcomes of students is not optimal. As expressed by Djamarah (2011:239):
subjects were held; relationship of teacher with student is less harmonious; teacher give lesson standard above of the ability of student; teachers do not have the skills in an effort to diagnose the learning difficulties of students, and the way of teacher teach is less good.
Based on the initial observation (February 18, 2013) implemented at SMP Negeri 6 Medan, curriculum that used in schools is Kurikulum Tingkat Satuan Pendidikan (KTSP), but the lesson is still using the old pattern (direct instruction in the classical style that is giving examples, one-way interaction, and the sometimes teacher asked students to answer, giving the task at home). Researchers did not find students learn in groups. Activities of students during learning activities are listening to the teacher's explanation, noting the things that are important. Students are afraid to ask the teacher although given the encouragement and motivation. Clever students prefer to work alone. Teachers train students working on routine problems (using formulas and rules that exist in the material being taught). Teachers less attention to the development of student learning, and often do not relate to students' prior knowledge with new material that is being taught. Learning tends not meaningful for students, indicated less active of students in learning process.
The researchers also conducted interviews with mathematics teacher’s (Mrs. Ermas Napitupulu S.Pd) said: "In the process of mathematics learning most students are not active, rare among them want to ask, or give feedback. If given problem solving related with word problem in daily life, the values obtained by the students tend to be lower than about objective ". From the answers given student can be seen that most of the students find it difficult to interpret the given problem into mathematical form. In addition, students also have difficulties in determining the mathematical concepts that can be used to solve a given problem. They tend to conclude to perform arithmetic operations on numbers that exist in terms of word problem without understanding and thinking about what is required in the problem.
the learning material but the students still have difficulty to use knowledge to solve mathematical problems related to daily life.
There are some problems experienced by students in VII class in learning mathematics, especially rectangles based on the observation, students' understanding of concepts that are still low, and the difficulty of the students in the use of concepts learned in solving mathematical problems in the subject quadrilaterals. Realizing it required an effort to increase students 'understanding of mathematical concepts in daily life. To overcome these problems is appropriate to use realistic mathematics learning approach. According to Hans Freudenthal (in Wijaya 2012: 20) realistic mathematics learning approach is “mathematics is a human activity.” Statement "mathematics is a human activity" shows that Freudenthal not put mathematics as a ready product, but rather as a form of activity or process. According to Freudenthal mathematics should not be given to students as a ready product that is ready to use, but rather as a form of activity in constructing mathematical concepts. Freudenthal familiar with the term "guided reinvention" as the students are actively committed to rediscover a mathematical concept with teacher guidance. Furthermore, do not put mathematics as a closed system (closed system) but rather as an activity called mathematize.
mathematics education starts from a realistic problem is expected that students will be able to construct their own understanding and will make learning more meaningful so that students' understanding of the material more depth that would be beneficial to enhance the ability in problem solving.
The relevant research toward research conducted by Laily Rahmi. From the research conducted there are significant differences problem solving abilities of students who are taught using realistic mathematics education taught by the ordinary model.
She concluded that after the study is done, it turns out to obtain more effective results for students. In other words, that makes the learning of students as subjects and their own initiative in learning activities and students' skills in solving problems experienced increase after the act. In general, students are learning to apply the learning process has a realistic mathematical problem-solving ability is better than before given the learning process. Overall, realistic mathematics education can be an alternative to improve students' problem-solving abilities.
Based on the description above that the problem-solving ability is the goal of learning mathematics is very important, and one of the lessons that can increasing students' problem-solving abilities is realistic mathematics learning approach. Therefore, researchers are interested in doing research with taking the title: Efforts In Improving Students Mathematical Problem-Solving Ability Through Realistic Mathematics Education Approach On Subject Quadrilateral At Smp Negeri 6 Medan Academic Year 2012/2013.
1.2. Problem Identification
Based on background above, can be identified some problems as follows: 1. Quality of mathematics education in Indonesia still low.
3. Mathematics teacher in SMP Negeri 6 Medan not uses realistic mathematics education approach in learning mathematics.
4. Students still low to apply concepts in solving mathematical problem. 5. Mathematical problem-solving ability of students still low.
1.3. Problem Limitation
Seeing many aspects of problems that identified over time and ability of researcher, so researcher need to give limitation toward the problem that will be analyzed, it’s can be conducted more depth. Appropriate to problem identification above, so researcher just gives problem limitation about: efforts in improving mathematical problem-solving ability through realistic mathematics education approach on subject of quadrilateral.
1.4. Problem Formulation
Based on background, problem identification and problem limitation mentioned above, so the problem that will be analyzed in this research formulated as follows:
1. How level of students' mathematical problem-solving ability to solve problem after taught by realistic mathematics education approach on subject of quadrilateral seventh grade students of SMP Negeri 6 Medan Academic Year 2012/2013?
1.5. Research Objectives
The objectives of this research are:
1. To know the level of students' mathematical problem solving ability to solve problem after taught by realistic mathematics education approach on subject of quadrilateral class VII SMP Negeri 6 Medan in Academic Year 2012/2013.
2. To know whether implementation of realistic mathematics education approach can improve students' problem-solving ability on subject of quadrilateral class VII SMP Negeri 6 Medan in Academic Year 2012/2013.
1.6. Research Benefits
After conducting research expected the result of this research can gives good benefits are:
1. For teachers, it can broaden the knowledge of realistic mathematics education approach in helping students solve mathematics problems. 2. For students, through realistic mathematics education approach
expected gives positive learning attitude and creative in solving problems.
3. For researchers, it can increase knowledge for my selves, especially about development and needs of students, before entering the real learning process.
4. For schools, have benefit to take right decision in improving quality of teaching, as well as consideration or reference materials to improve student achievement especially in mathematics.
1.7. Operational Definition
To be able to perform quantitative research variables so variables are defined as follows:
1. Mathematical Problem solving ability in this research is the study result of students in solving problems based on quadrilateral material toward problem solving stages as follows:
• Understanding the problem
• Making a plan of completion
• Implementing of a plan
• Checking answer obtained
2. Realistic Mathematics Education Approach
CHAPTER V
CONCLUSION AND SUGGESTION 5.1. Conclusions
The conclusions that can be drawn from the results of this study are: 1. The level of students' problem-solving abilities on initial tests obtained is
very low. After the action in the cycle I with realistic mathematics learning approach taught by the students obtained the level of problem-solving ability is medium. Furthermore, after the implementation of the action in the cycle II, known level of student ability to solve problems is high. 2. Based on the analysis of research data, indicated that the implementation
of realistic mathematics learning approach can improve students mathematical problem-solving ability in VII grade of SMP Negeri 6 Medan on the subject of the quadrilateral, where an increase was obtained after the cycle II conducted.
5.2. Suggestions
The advice is taken from the results of this study, namely:
1. To mathematics teacher especially mathematics teachers of SMP Negeri 6 Medan to involve students in the learning process and use realistic mathematics as an alternative learning approach to improve students' ability in solving mathematical problems.
3. To Head of SMP Negeri 6 Medan, in order to coordinate the teachers to implement realistic mathematics approach to improve students' mathematical problem-solving ability.
REFERENCES
Abdurrahman, M., (2003), Pendidikan Bagi Anak Berkesulitan Belajar, Rineka Cipta, Jakarta.
Aedi, N., (2008), Pelaporan Supervisi, http://file.upi.edu/Direktori/FIP/JUR._
ADMINISTRASI_PENDIDIKAN/197205282005011-NUR_AEDI/4-25/BAB_7_Pelaporan_Supervisi_%5BNur_ Aedi%5D.pdf ( Accessed April 14, 2013)
Arikunto, friends., (2010), Penelitian Tindakan Kelas, Bumi Aksara, Jakarta. Armanto, D., (2002), Teaching Multiplication and Division Realistically in
Indonesian Primary Schools: A Prototype of Local Instructional Theory,
Journal of Mathematics Education.
Asri, M., (2009). Ranking Pendidikan Indonesia http://t4belajar.wordpress. com/tag/ranking-pendidikan-indonesia/ (Accessed December 22, 2012). Astrini (2010), Bakat dan Intelegensi, http://edukasi.kompasiana.com/2010/12/09/
bakat-dan-intelegensi-325057.html (Accessed January 29, 2013). Cockcroft, W.H., (1981), Mathematics Counts. London: HMSO. Djamarah, S.B. (2011), Psikologi Belajar, Rineka Cipta, Jakarta.
Djamarah, S, B., and Zain, A., (2006), Strategi Belajar Mengajar, Rineka Cipta, Jakarta.
FMIPA, (2011), Pedoman Penulisan Proposal dan Skripsi Mahasiswa Program Studi Pendidikan, FMIPA UNIMED, Medan.
Gulo, W,. (2002), Strategi Belajar-Mengajar, PT.Grasindo, Jakarta.
Hadi, S., (2010), Pendidikan Matematika PMR: Menjadikan Pelajaran Matematika Lebih Bermakna Bagi Siswa, FKIP, Universitas Lambung
Istarani, (2010), Penelitian Tindakan Kelas, MEDIAPERSADA, Medan. Istarani., (2011), 58 Model Pembelajaran Inovatif, Media Persada, Medan.
Kesumawati, N,. (2011), Development Mathematical Problem Solving Problems At Junior High School, Proceeding July 2011.
Muslich, M., (2008), KTSP Pembelajaran Berbasis Kompetensi dan Kontekstual, Bumi Aksara, Jakarta.
Nasution, H., (2006), Pembelajaran Matematika Realistik Topik Pembagian di Sekolah Dasar, Jurnal Pendidikan Matematika dan Sains ISSN : 1907-7157.
Nisaajnukmi, (2012), http://nisaajnukmi.blog.uns.ac.id/2012/11/21/ (Accessed April 8, 2013)
Notoatmojo, S., (2005), Metodologi Penelitian Kesehatan, Edisi Ketiga,Rineka Cipta, Jakarta.
Polya, G., (…), Polya’s Problem Solving Techniques : http://math.berkeley. edu/~gmelvin/polya.pdf (Accessed February 20, 2013)
Rosnawati, S, and friends., (2009), Pelatihan Pembelajaran Matematika dengan Pendekatan Pendidikan Matematika Realistik Indonesia (PMRI) Bagi Guru-Guru Sekolah Dasar Selain Mitra Tim PMRI UNY, http://staff.uny.ac.id /sites/default/files/tmp/Laporan%20ppm2009.pdf (Accessed February 1, 2013)
Sea. (2004). Kemampuan Matematika dan Sains Siswa Indonesia Masih Berada di Papan Bawah. www.groups.yahoo.com. (Accessed December 23, 2012). Satria, AN, (2012), http://www.ugm.ac.id/index.php?page=rilis&artikel=4467
(Accessed April 7, 2013).
Sukanadi and friends, (2011), Peningkatan Kemampuan Memahami Cerita Dongeng Melalui Metode Diskusi Pada Siswa Kelas V SD Negeri 10 Sanur,
Jurnal Santiaji Pendidikan, 1(2): 146-157.
Suryanto and friends, (2010), Sejarah Pendidikan Matematika Realistik Indonesia PMRI, Jakarta: Depdiknas.
Undang-Undang Nomor 20 Tahun 2003 tentang Sistem pendidikan nasional Pasal 1, ayat 1.
Warli (…), Pembelajaran Matematika Realistik Materi Geometri Kelas IV MI, Jurnal Pendidikan Matematika.
Wijaya, A., (2012), Pendidikan Matematika Realistik Suatu Alternatif Pendekatan Pembelajaran Matematika, Graha Ilmu, Yogyakarta.
Winda, (2012), Penerapan Pembelajaran Matematika Realistik Sebagai Upaya Meningkatkan Kemampuan Pemecahan Masalah Siswa Pada Pokok
i
CURRICULUM VITAE
