**APPLICATION REALISTIC MATHEMATICS EDUCATION TO IMPROVE**
**MATHEMATICS LEARNING OUTCOMES ON THE SUBJECT**

**QUADRILATERAL IN VII GRADE SMP NEGERI 11**
**MEDAN ACADEMIC YEAR 2014/ 2015**

**By:**

**SAPTA NOVITA NASUTION**
**4113312014**

**Mathematics Education Study Program**

**THESIS**

**Submitted to Fullfill the Requirement For Getting**
**the Degree of Sarjana Pendidikan**

**MATHEMATICS DEPARTMENT**

**FACULTY OF MATHEMATICS AND NATURAL SCIENCES**
**STATE UNIVERSITY OF MEDAN**

v

**PREFACE **

Give thanks to Allah Subhanahu Wata’ala give me more ssirit to finish my thesis. The title is of thesis is Assliccation of Realistic Mathematics Education on Quadrilateral in VII Grade SMP Negeri 11 Medan. Academic year 2014/2015. This thesis was 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. Syawal Gultom, M.Pd and his staffs, Mr.Prof. Drs. Motlan, M.Sc, Ph.D for Dean of FMIPA UNIMED and his college assistants of Dean I, II, III in Unimed, Mr. Dr. Edy Surya, M.Si as leader of mathematics desartment and as suservisor who guide to sresare this thesis.

Big thanks for Mr. Prof. Dr. B. Sinaga, M.Pd, Dr. Abil Mansyur, M.Si, Prof. Dr. Asmin, M.Pd who are sersons ressonsible for my thesis from the beginning until end. Thanks to Mr. Prof. Dr. Sahat Saragih, M.Pd as my academic suservisor and then thank you so much for all my lectures and staffs in FMIPA.

And then, thank you so much for helsing Mrs. Siti Khadijah, S.Pd, students in grade VII-4, all teachers and staffs in SMP Negeri 11 Medan for helsing and sussorting in doing research.

Ssecial thanks to my lovely father Mr. Miskuddin Nasution and my lovely mother Mrs. Syarifah .anum .asibuan for giving motivation, sray and all i need in finishing this thesis. And then thanks to my beloved sister, Nurina Nasution and her husband, Abdurrahman Pulungan for sussort me until the end of writer study. Also thanks to my brother, M.hafizh Nasution .

vi

The writer should give a big effort to sresare this thesis, and the writer knows that this thesis has so many weaknesses. So that, the writer needs some suggestions to make it this be better. And big wishes, it can be imsrove our knowledge.

Medan, 2015

Writer,

*iii*

**Application Realistic Mathematics Education (RME) to Improve Mathematics **
**Learning Outcomes on the Subject Quadrilateral in VII Grade SMP Negeri **

**11 Medan Academic Year 2014/ 2015 **

**Sapta Novita Nasution (4113312014) **

**ABSTRACT **

The purpose of this study was 1) know how the categories of realistic mathematics education process on the subject quadrilateral? 2) know the increase of mathematics learning outcomes by using realistic mathematics education on the subject quadrilateral in VII grade SMP Negeri 11 Medan academic year 2014/2015? 3) know how the learning activities of realistic mathematics education students when applied on the subject quadrilateral in VII grade of SMP Negeri 11 Medan academic year 2014/2015?

The subjects were students of class VII-4 school year 2014/ 2015, consist of 48 people consisting of 21 boys and 27 girls. The object of this research is the mathematics learning outcomes, student activities and realistic mathematics education (RME).

This study consisted of two cycles, the first cycle consists of two meetings and the second cycle consists of two meetings. Mathematics learning outcomes tested at the endingmeeting and the observation of students was observed in the learning process takes place.

In the action on the first cycle obtained that category realistic learning process on quadrilateral included either. It is seen from an average of 2.6 observations and the second cycle gained an average of observations is 2.9.

*iv*

63.6875%, aspects of student activity number 2 and 3 are achieved while other aspects are not achieved. Once given the action on the second cycle of data obtained an average percentage 75.01125% into aspects of student activity number 1, 2, 3, and 4 are also achieved. An increase in the percentage of achievement active activity ideal time for 11.32375% of the first cycle based criteria ideal time to learn the lesson of this activity has reached the target and increased.

Of action I, through the provision of a test result of learning I gained 37 students (77,083%) of the 48 students have achieved mastery learning (value ≥ 65), while 11 students (21.875%) was not finished. After the second action, by providing test results of the second study obtained 45 students (93.75%) of the 48 students who have completed. increase in the percentage of 16,667% classical completeness. Based on the criteria, then the percentage of completeness classical completeness is compliant.

vii

1.7. Operational Definitions 9

**CHAPTER II LITERATURE REVIEW ** **10 **

2.1. Theoretical Framework 10

2.1.1. The Essence of Learning 10

2.1.2. The Essence of Learning Mathematics 11

2.1.3. Learning Outcomes 12

2.1.4. Learning gctivities 14

2.1.5. Realistic Mathematics Education (RME) 16

2.1.5.1. The Characteristic of RME on gpproach 18

2.1.5.2. The Principle of RME 21

2.1.5.3. The Step of RME 22

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2.1.5.5. Design of RME Lesson 25

2.1.6. Content Materials 29

2.1.6.1. Rectangle 29

2.1.6.2. Square 32

2.2. Review of Relevant Research 35

2.3. Conceptual Framework 36

2.4. Hypothesis Research 36

**CHAPTER III RESEARCH METHODOLOGY ** **37 **

3.1. Location and Research Time 37

3.2. Research Subject 37

3.3. Research Object 37

3.4. Operational Definitions 37

3.5. Type of Research 38

3.6. Research Procedure 38

3.7. Instrument of Data Collection 42

3.8. Data gnalysis Technique and Interpretation of Data 44

3.8.1. Data gnalysis 44

3.8.1.1. Completeness of Learning Outcomes 44

3.8.1.2. gnalyze the Result of Observation 46

3.8.2. Interpretation of Data 47

3.8.2.1. Interpretation of Test Result to Learn 47

3.8.2.2. Interpretation of the Results of Observation 48

3.9. Performance Indicators 51

**CHAPTER IV RESULT AND DISCUSSION ** **53 **

4.1. Research Result 53

4.1.1. Implementation and Research in Cycle I 53

4.1.1.1. Problem I 53

4.1.1.2. gction Planning Phase I 54

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4.1.1.4. Observation I 57

4.1.1.5. Data gnalysis I 58

4.1.1.6. Reflection I 66

4.1.2. Implementation and Research in Cycle II 67

4.1.2.1. Problems II 67

4.1.2.2. gction Planning Phase II (Issues and Problems II) 68

4.1.2.3. Implementation of gction II 69

4.1.2.4. Observations II 71

4.1.2.5. Data gnalysis II 72

4.1.2.6. Reflection II 78

4.2. Research Findings 79

4.3. Discussion of Results 79

**CHAPTER V INTRODUCTION ** **83 **

5.1 Conclusion 82

5.2 Suggestion 83

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Appendix 5 Student Activity Sheet I 122

Appendix 6 Student Activity Sheet II 126

Appendix 7 Student Activity Sheet III 130

Appendix 8 Student Activity Sheet IV 134

Appendix 9 Validation of Initial Test (Capability Test) 138 Appendix 10 Validation Test I of Mathematics Learning outcome 141 Appendix 11 Validation Test II of Mathematics Learning outcome 144 Appendix 12 Initial Test (Capability Test) 147 Appendix 13 Test I of Mathematics Learning outcome 148 Appendix 14 Test II of Mathematics Learning outcome 149 Appendix 15 Alternative Solution of Initial Test 150 Appendix 16 Alternative Solution Test II of Mathematics Learning outcome 152 Appendix 17 Alternative Solution Test II of Mathematics Learning outcome 156 Appendix 18 Observation Sheet of Implementation RME on Teacher Side 160 Appendix 19 Observation Sheet of Implementation RME on Student Side 172 Appendix 20 List of the Serial Numbers of Students in Class VII-4 184

Appendix 21 Result of Test I 185

Appendix 22 Result of Test II 188

1

**CHAPTER I**
**INTRODECTION **

**1.1 Problem Background**

Education is investment in human resources who have a long-term strategic value for the survival of human civilization in the world. As well as the presentation (Kunandar, 2011: 8)

Assessing the quality of a nation's human resources in general can be seen from the quality of the nation's education. History has proven that the progress and prosperity of a nation in the world is determined by the development in the field of education.

Therefore, almost all countries put education variable as something important and major in the context of nation building. Likewise, Indonesia put education as an important and major. It can be seen from the contents of the fourth paragraph of the Preamble of the 1945 Constitution which asserts that one of the national goals of Indonesia is the intellectual life of the nation.

The quality of education in Indonesia is considered by many people is still low. As shown by data from TIMSS (Trends in International Mathematics and Science Study) 2011 (inhttp://timss.bc.edu/timss2011/downloads/ T11_IR_ Mathematics_FullBook.pdf) that the achievement of mathematics education in Indonesia was ranked 38 out of 41 countries with score of 386 and far behind by other ASEAN countries such as Italy (score 498), Malaysia (score 440) and

Thailand (score 427). This fact clearly shows that mathematics education in

Indonesia is still disappointing. Thought, mathematics is a basic of all discipline science and very importing in daily life.

As proposed by Cockroft (in Abdurrahman, 2009: 253) that “Mathematics

should be taught to students because of (1) is always used in life; (2) all fields of

2

communication; (4) can be used to present information in a variety of ways; (5)

improve the ability to think logically, accuracy, and awareness spatial; (6) provide satisfaction to solve business challenging problem.”

According Johnson and Myklebust in (Abdurrahman, 2009: 253) "Mathematics is a symbolic language to express the practical function relations of quantitative and spatial. And, the theoretical function is to facilitate thinking".

The evidence suggests, not least school students who still think math is a subject that create stress, making the mind confused, spend time and tend to just messing about with a formula that is not useful in life. Consequently, mathematics is seen as a science that does not need to be learned and can be ignored. In addition, it is also supported by the learning process in schools that still only oriented work practice questions only. Rare mathematics learning process directly linked to real life.

Meanwhile, according to the Palling (Abdurrahman, 2003: 252) the human ideas about mathematics vary, depending on experience and knowledge of each. Some say that the mathematical calculations only include add, minus, multiply, for; but others involve topics such as algebra, geometry, and trigonometry. Many also believe that mathematics includes everything associated with logical thinking.

This contradiction will certainly make the learning of mathematics be without meaning, so that students assume mathematics is unimportant. This of course will affect the result of the students' mathematics learning.

Furthermore Palling in (Abdurrahman, 2003: 252) argues that mathematics is a way to find answers to the problems facing humanity; a way to use the information, using knowledge of the count, and the most important is the thought in man itself in seeing and using relationships.

quality of teaching, each teacher of mathematics should be given training and the introduction of models, methods and approach to learning is good and right in order to achieve good results also learn mathematics.

From interviews conducted by researchers to Mrs. mathematics teacher SMP Negeri 11 Medan,

outcomes are still very low in math as a whole. students were enthusiastic about math.

process. They only hear the teacher lectures and do the problems without much criticism, comments or questions to the teacher.

teacher's explanations, they are reluctant to ask the teacher.

every mathematical material including flat wake quadrilateral when students are given a problem, they have

quality of teaching, each teacher of mathematics should be given training and the , methods and approach to learning is good and right in order to achieve good results also learn mathematics.

From interviews conducted by researchers to Mrs. Siti Khadijah as a mathematics teacher SMP Negeri 11 Medan, obtained that student learning es are still very low in math as a whole. In everyday students, only a few students were enthusiastic about math. Students are still less active in the learning They only hear the teacher lectures and do the problems without much ts or questions to the teacher. If they do not understand the teacher's explanations, they are reluctant to ask the teacher. This happens

every mathematical material including flat wake quadrilateral when students are given a problem, they have trouble writing it into the language of mathematics.

3

quality of teaching, each teacher of mathematics should be given training and the , methods and approach to learning is good and right in order

Figure 1.1.the student's answer from

Figure 1.1.the student's answer from initial test

5

This is in line with the test given to the student researcher VIII-7 at the school. Tests are given about quadrilateral they've learned in class VII. Many students still make mistakes such as not being able to apply their knowledge to solve problems. Following the conclusion of initial tests of students of class VIII-7:

**Table 1.1 Classical Completeness in Class VIII-7**

≥ 65 <65 Classical Criteria

VIII-7 68.75% 31.25% Incomplete

The class not meet the criteria of classical completeness in accordance with the said (Trianto, 2009: 241), a class is said to be completed in the classical if ≥ 85% which has absorption ≥ 65. Researchers also made observations when the teacher teaches, the researchers saw that the student activity is still far from ideal.

the role of the teacher in the learning of mathematics in general is as follows.

First, how the subject matter was given to students in accordance with the

standard curriculum.

Second, how p roses learning takes place by involving learners in full and active,

in terms of the learning process that takes place fun.

Regarding the teaching methods used in schools, from the observation that be obtained mathematics learning activities during this is teacher-oriented. The use of this method resulted in students being passive and positioned students as listeners and receiver. As a result, students are not trained to think independently and creatively to solve problems.

6

accustomed to accept and memorize what is delivered by teachers without motivated to understand the mathematical concepts, students can only complete the exact same problem with sample questions given by the teacher.

From the descriptions above, it was concluded that in order to retain knowledge longer remain in the memory of the student, there should be a maximum of learning that involves student activities. It should teachers provide learning experiences that engage students in the subject matter accompanied landing guidance of a teacher.

One alternative to this problem is the Realistic Mathematics Education. Because this accordance with the character of Realistic Mathematics Education, namely mathematics learning of the problems that exist in everyday life, which comes from the experience of each student. This lesson also requires that students actively involved in learning. Actually, so many factors can to increase mathematics learning outcomes. There are internal and external factors. But in this case, writer only discuss about external factor that can to increase mathematics learning outcomes, namely is model realistic mathematics education

As Zainurie in (Soviawati, 2011: 81) "Mathematics is the realistic school

math applied by placing realities and experiences of students as a starting point the point of learning. Problems realistically used as a source of the emergence of mathematical concepts or formal mathematical knowledge. "

Based on the description of the background, then writer interest to do a

research with title **"Application Realistic Mathematics Education to Improve **

7

**1.2 Problem Identification**

From the description of the background obtained by the identification of

problemsitems, namely:

1. Mathematics learning outcomes is low

2. Learning methods are Often used is still centered on the teacher

3. Mathematic knowledge is not built from meaningful life context and relevant to

student

4. Realistic Mathematics Education approach is not yet implied

**1.g Problem Limitation**

As described above, there are many problems that are identified, there needs to be more focus on the problem of restrictions. In this study the problems that Arise bounded on "Application Realistic Mathematics Education (RME) to Improve Mathematics Learning Outcomes on the Subject Quadrilateral in Grade VII SMP Negeri 11 Medan Academic Year 2014/2015".

**1.4.Problem formulation**

mathematics education on the subject quadrilateral in VII grade SMP Negeri 11 Medan academic year 2014/2015?

3. How the student learning activities of realistic mathematics education when

8

**1.5.Research Objective**

Based on the problem formulation above, the purpose of this research are:

1. To know how the categories of realistic mathematics education process on the

subject quadrilateral?

2. To know the increase of mathematics learning outcomes by using realistic

mathematics education on the subject quadrilateral in VII grade SMP Negeri 11 Medan academic year 2014/2015?

3. To know how the learning activities of realistic mathematics education students

when applied on the subject quadrilateral in VII grade of SMP Negeri 11 Medan academic year 2014/2015?

**1.6.Benefits of Research**

1. For Students

a. It is expected students by the implement realistic mathematics learning can

improve student's mathematics learning outcome.

b. It can raise motivation and interest of students in mathematics.

2. For teachers, it is expected to be input in the use of the approach varied in

the pursuit of learning in the class room and can appeal relevant study for society in the next day.

3. For schools, it is expected to be used as input in policy innovations related

Reviews their learning in schools to improve the quality of teaching mathematics.

4. For the authors, this study is expected to be a positive feedback in preparing

themselves as prospective educators.

5. For other researchers, the study is expected be a medium for applying the

9

**1.7.** **Operational Definition of Variables**

In this study, there are two variables, namely:

1. The independent variables is realistic mathematics education which is

treated in the classroom

2. The dependent variable is the learning outcomes achieved after treated. The

84

**REFFERENCES **

*Abdurrahman, M. (2009). Pendidikan Bagi Anak Kesulitan Belajar. Medan: *

Larispa Indonesia

*Daryanto, (2007), Evaluasi Pendidikan, Jakarta: Rineka Cipta *

*Djamarah, Syaiful, Bahri., (2002), Psikologi Belajar, Jakarta: Rineka Cipta *

*Djamarah, Syaiful, Bahri., (2011), Psikologi Belajar, Jakarta: Rineka Cipta *

Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Medan,

*(2010), Buku Pedoman Penulisan Skripsi dan Proposal Penelitian *

*Pendidikan, FMIPA Unimed, Medan. *

*Hough, Sue and Gough, Steve., (2007), Realistic Mathematic Education, *

Mathematics Teaching 203 : 34 – 38 Available in

http://search.ebscohost.com/login.aspx?direct=true&db=sch&AN=266583

17&site=src-live(Accessed February 24th_{2014) }

*Husna, R., Improving of Problem Solving and Mathematical Communication *

*Ability in * *VII Grade SMP Langsa by Applying Realistic Mathematics *

*Education (RME) on the Subject Quadrilateral, Thesis, Pasca Sarjana, *

Unimed, Medan.

Kementerian Pendidikan dan Kebudayaan Republik Indonesia., (2013),

*Matematika Kurikulum 2013 Kelas VII SMP. Jakarta : Politeknik Negeri *

Media Kreatif

*Kunandar. (2011). Guru Profesional: Implementasi Kurikulum Tingkat Satuan *

*Pendidikan (KTSP) dan Sukses dalam Sertifikat Guru. Jakarta: Raja *

85

*Mantik, Iqbal Yudhistira., (2013). Pengembangan Perangkat Pembelajaran *

*Gerak Lurus SMA Dengan Metode Eksperimen Bervisi Karakter, *

Yoyakarta : Innovative Journal of Curriculum and Educational

Technology.

Mayer, R. E, (1992), Cognition and instruction:O n their historic meeting within

educational psychology. Journal of Educational Psychology, 84, 405-41

available in *en.wikipedia.org/wiki/Instructional_theory * *(Accessed *

*February 14th _{ 2015) }*

*National Council of Teacher of Mathematics.,(2003),NCTM Program Standards, *

Available in

http://timssandpirls.bc.edu/timss2011/international-results-mathematics.html (Accessed February 25th 2015)

*Panhuizen-Heuvel, Den Van Marja, (2003), The Didactical Use Of Models In *

*Realistic Mathematics Education: An Example From A Longitudinal *

*Trajectory On Percentage1, Kluwer Academic Publishers 54 : 9-35 *

Sa’adah, W *. 2010. Peningkatan Kemampuan Penalaran Matematis Siswa *
*Kelas VIII SMP Negeri 3 Banguntapan dalam Pembelajaran Matematika *

*melalui Pendekatan Pendekatan Matematika Realistik Indonesia (PMRI).*

Skripsi. FMIPA. UNY. Yogyakarta.

http://eprints.uny.ac.id/2273/1/SKRIPSI_WIDAYANTI__NURMA_SA%

27ADAH.pdf (Accessed January 18th_{ 2015) }

*Sagala, S.,(2005),Konsep dan Makna Pembelajaran, Bandung: Alfabeta *

*Sagor, Richard., (2005), The Action Research Guidebook, Thousand Oaks, CA: *

86

*Saleh., (2007) Jurnal Mathedu, Vol. 2, Suplemen, Journal of realistic *

*mathematics education in Topik rectangle and square topic in class VII *

*SMP Negeri 9 Kendari *

*Sardiman, (2011). Interaksi dan Motivasi Belajar Mengajar, Jakarta: Wali Pers *

*Saragih, R., (2011), Improvement of Problem solving Ability by Applying *

*Realistic Mathematics * *Education * *(RME) * *on * *the * *Subject *

*Quadrilateral, Thesis, Pasca Sarjana, Unimed, Medan. *

*Scott, Jenna., (2012), Understanding the Basics of Measuring Student *

*Achievment, CECR : United States *

Soviawati, E.(2011). *Pendekatan * *Matematika * *Realistik * *(PMR * *Untuk *

*Meningkatkan Kemampuan Berfikir Siswa di Tingkat Sekolah Dasar *

*Spring, Summer., (2011),Online mathematics module: A Century Of Leadership *

*In *

*Mathematics and Its Teaching, Journal of Mathematics Education at Teachers *

*College *

*Stiff, V. Lee, (1999),Developing Mathematical Reasoning in Grades K-12, Reston *

Va : National Council of Teacher of Mathematics.

*Sudjana, N.(2009). Penilaian Hasil Proses Belajar Mengajar. Bandung: Remaja *

Rosdakarya

Suprijono, Agus, (2009) cooperative Learning Teori dan Aplikasi paikem.

87

*Tandililing,Edy, (2012), Implementasi Realistic Mathematics Education (RME) *

*DI Sekolah, Jurnal Guru Membangun : 2 *

*Trianto, (2009), Mendesain Model Pembelajaran Inovatif-Progresif, Surabaya: *

Prenada Media

*Trianto, (2011), Mendesain Model Pembelajaran Inovatif-Progresif, Surabaya: *

Prenada Media

*Van den Heuvel-Panhuizen, M.(1996). Assesment and Realistic Mathematics *

*Education. Den Haag: Koninklijke Bibliotheek. *

*Wardhani, Sri., (2008), Analisis SI dan SKL Mata Pelajaran Matematika *

*SMP/MTs untuk Optimalisasi Tujuan Mata Pelajaran Matematika, Pusat *

Pengembangan Dan Pemberdayaan Pendidik Dan Tenaga Kependidikan

Matematika Tahun 2008, Yogyakarta.

*Widjaja, B. Yenni and Heck Andre, (2003), How a Realistic Mathematics *

*Education Approach and Microcomputer-Based Laboratory Worked in *

*Lessons on Graphing at an Indonesian Junior High School, AMSTEL *

Institute, University of Amsterdam, The Netherlands. Available in

*:www.science.uva.nl/~heck/.../art/JSMESA.pdf (Accessed December 15*th

2014)

*Wijaya, A., (2012), Pendidikan Matematika Realistik; Suatu Alternatif *

*Pendekatan Pembelajaran Matematika, Yogyakarta: Graha Ilmu *

*Zulkardi., (2010), How to Design Mathematics Lesson Based On The Realistic *

*Approach? Available in : http://reocities.com/ratuilma/rme.html(Accessed *