THE DIFFERENCE OF STUDENTS MATHEMATICAL REPRESENTATION ABILITY BY USING PROJECT BASED LEARNING AND PROBLEM BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE X SMA NEGERI 1 PERCUT SEI TUAN.

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THE DIFFERENCE OF STUDENTS' MATHEMATICAL REPRESENTATION ABILITY BY USING PROJECT BASED LEARNING AND PROBLEM

BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE X SMA NEGERI 1 PERCUT SEI TUAN

By:

Widi AuliaWidakdo ID 4113111080

Mathematics Education Study Program

THESIS

Submitted to Qualify for Academic Title of Sarjana Pendidikan

MATHEMATICS DEPARTMENT

FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN

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PREFACE

Praise and great thanks to Allah SWT that gives the amazing grace, love, strength and health so that writer can finish this thesis. The title of this thesis is “The Difference Of Students' Mathematical Representation Ability By Using Project Based Learning And Problem Based Learning On The Topic Of Statistics In Grade X Sma Negeri 1 Percut Sei Tuan”. This thesis was arranged to satisfy the requirement to obtain the Degree of Sarjana Pendidikan from Faculty Mathematics and Natural Science in State University of Medan

In the completion of this thesis, the writer received support from various parties, therefore it was appropriate writer big thanks to Mr. Prof. Dr. Asmin, M.Pd as my thesis supervisor who has provided guidance, direction, and advice to the perfection of this thesis. Thanks are also due to Prof. Dr. Mukhtar, M.Pd, Dr. Asrin Lubis, M.Pd and Faiz Ahyaningsih, M.Si as author’s examiners who have provided input and suggestion from the planning to the completion of the preparation of the research of this thesis. Thanks are also extended to Dr. W. Rajagukguk, M.Pd as academic supervisor and then thank you so much for all author’s lecturer in FMIPA Unimed.

My thanks are extended to Prof. Dr. Syawal Gultom, M. Si. as rector of Unimed, Prof. Drs. Motlan, M.Sc, Ph.D as Dean of Mathematics and Natural Sciences Faculty and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si, Dr. Edy Surya, M.Si. as Chief of Mathematics Department, Drs. Zul Amry, M.Si, Ph.D as Chief of Mathematics Education Study Program, Drs. Yasifati Hia, M. Si as Secretary of Mathematics Education, and all of employee staff who have helped the author.

Thanks to Mr. Muliadi, S.Pd. M.Si as principle of SMA N 1 Percut Sei Tuan, Mrs. Dra. Libes Doloksaribu, S.Pd as mathematics teacher and all teacher, staffs and also the students in grade X IIS 1 and X IIS 3 SMA N 1 Percut Sei Tuan who have helped writer conducting the research.

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motivation and prayers for the success of me completed this thesis. Special big thanks to my beloved sister Firda Saufika, Nabila Nadra and Also my brother M. Khair Arrayyan for giving support even moril or material and all my family for all pray, motivation, and support until the end of my study.

I also thanks to my lovely second family of Himpunan Mahasiswa Islam (HMI) which always help me and support in every condition without any exception. Especially for Vivi, Taufik, Sapwan, Juli, Ilmi, Maryam, Widya, for all of your crazy thing, Bang Elfan, Bang Dedi, Bang Imam, Bang Badzlan, Kak Imel and Kak Mora for all of the suggestion and incredible advice. Thank you very much for Rizki Ramadhana, Satoto, Hakim, Fatkhu, Zaki, also Anggun, Nadia, and Putri Rizki for every helping you’ve given as my sisters and brothers in this university. I love you and thanks for every spirit my freak friends Debby, Nelly and Yohannes also my classmate in Bilingual Mathematics Education 2011.

At last, the author has finished this thesis in maximum level but author realized there are some imperfections. For that, the author asks for building comments and suggestions in order to reach the perfection of this thesis. The author wishes that this thesis would be useful to improve the knowledge should give a big effort to prepare this thesis, and the writer know that this thesis have so many weakness. So that, the author needs some suggestions to make it this be better. And big wishes, it can be improve our knowledge, understanding and enrich the science education.

Medan, July 2015 Author,

Widi Aulia Widakdo

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CHAPTER III RESEARCH METHODOLOGY

3.1. Type of Research 34

3.2. Place and Time of Research 34

3.3. Population and Sample 34

3.4. Variable of Research 35

3.4.1. Independent Variable 35

3.4.2. Dependent Variable 36

3.5. Instrument of Research 36

3.5.1. Initial Test 36

3.5.2. Test of Students’ Mathematical Representation Ability 36

3.5.3. Test Validity 41

3.5.4. Test Reliability 42

3.5.5. Difficulty Level Index 43

3.5.6. Discrimination Power of the Test 43

3.6. Design of Research 45

3.7. Procedure of Research 45

3.8. Technique of Data Analyzing 48

3.8.1. Normality Test 48

3.8.2. Homogeneity Test 49

3.8.3. Hypothesis Test 50

CHAPTER IV RESULTS AND DISCUSSIONS

4.1 Research Results Description 52

4.1.1 The Description of Students’ Mathematical 52 Representation Ability

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4.2. Analysis of Research Data 54

4.2.1 Normality Test 54

4.2.2 Homogeneity Test 55

4.2.3. Compare Means Test (One-tailed) 56

4.2.4 Analysis of Observation Sheet 58

4.3. Research Discussion 58

CHAPTER V CONCLUSION AND SUGGESTION 5.1 Conclusion 61

5.2 Suggestion 61

REFFERENCE 62

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LIST OF FIGURE

Figure 1.1. The Question of Observation Question Number 2 4 Figure 1.2. The Student’s Answer of Observation Question Figure 1.3. The Student’s Answer of Questionnaire 5 Figure 2.1. The Relationship Between Internal and External

Representation Developing Child’s Understanding

Of The Concept Of Numeracy 13

Figure 2.2. The Problem-Based Learning Cycle 22 Figure 2.3. Learner knowledge and Zone of Proximal Development 27

Figure 2.4. Bar Graphs 30

Figure 2.5. Pie Charts 31

Figure 2.6. Line Chart 31

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LIST OF APPENDIX

Appendix 1. The Blueprint of Mathematical Representation Ability

Initial Test 68

Appendix 2. Initial Test Of Mathematical Representation Ability 69

Appendix 3. Alternative Solution of Mathematical Representation

Ability Initial Test 70

Appendix 4. Questionnaire of Student’s Opinion 71

Appendix 5. Lesson Plan of problem based learnimg model 72

Appendix 6. Lesson Plan of Project Based Learning 95

Appendix 7. Worksheet 104

Appendix 8. The Blueprint of Students’ Mathematical Representation

Ability Test 113

Appendix 9. Test of Mathematical Representation Ability (Post Test) 115

Appendix10. Alternative Solution of Mathematical Representation

Ability 118

Appendix11. Validation Sheet of Mathematics Problem

Solving Ability Test II 122

Appendix12. Observation Sheet Of Teacher’s Activities in

Experimental Class A: Project Based Learning 132

Appendix 13. Sheet Of Teacher’s Activities in Experimental

Class B: Prblem Based Learning 141

Appendix 14. Validity Of Post Test - Test In Trial Class 152

Appendix 15. Reliability Of Post Test - Test In Trial Class 155

Appendix 16. Discrimination Power Analysis And

Difficulty Level Index Of Pre – Test 157

Appendix 17. Attendance Of Students In Experimental 160

Appendix 18. Attendance Of Students In Experimental

Class I (Prblem Based Learning) 161

Appendix 19. Group Division Both Experiment Class 163

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Appendix 21. Normality Test 167

Appendix 22. Homogeneity Test 168

Appendix 23. Independent Sample t-test 169

Appendix 24. Documentation 170

Appendix 25. T-table Value of t-distribution 176

Appendix 26. T-table Value of t-distribution 177

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CHAPTER 1 INTRODUCTION

1.1. Background

The National Education which based on Pancasila and the 1945 Constitution of the Republic of Indonesia was explained in Law Number 20 year 2003 about National Education System. The National Education functions is to develop the capability, character, and civilization of the nation for enhancing its

intellectual capacity, and is aimed at developing learners' potentials so that they

become persons imbued with human values who are faithful and pious to one and only God; who process morals and noble character; who are healthy, knowledgeable, competent, creative, independent; and as citizens, are democratic and responsible (Seameo, 2015).

Education gives knowledge, good thinking patterns, and a more systematic framework. Education need logical thinking to connect the abstract part in the mind to applied in solving problem of reality life. To construct this logical thinking, it needs mathematics.

Mathematics subject is one of the principal subjects taught begin during elementary school until to the university. Mathematics subject is also one of the subjects tested in the national examination both at the elementary school, junior high schools, as well as in senior high school.

Mathematics is a foundation and framework of the development of science and technology. In everyday life we use and need mathematical concepts and principles, as a tool in applications other disciplines as well as in the development of mathematics itself. Seeing the importance of the role of mathematics in everyday life, mastery of the subject areas of mathematics is a must.

Mathematics is one of the most important subjects that provide several vital skills to the learners. The characteristics of math abilities also as principle and process standards in mathematics that will be developed in the National Council of Teachers of Mathematics (NCTM, 2000) are problem

solving, reasoning, communication, connection, and representation. The five of

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mathematics is a learning that has final result more than a score in the final report, but Cockroft (1982) said that ―Mathematics can improve the ability of logical thinking, accuracy, and spatial awareness, also gives effort the ability to solve

challenging problems‖.

Hudojo (2005: 64) said in his book that ―hakekat matematika berkenaan

dengan ide-ide, struktur-struktur dan hubungan-hubungannya yang diatur menurut urutan yang logis. Jadi matematika berkenaan dengan konsep-konsep

abstrak”. So it can be conclude that mathematics is a lesson that can improve the

way to think in life.

―A representation is a configuration that can represent something else in

some manner‖ (Goldin, 2002: 208).

People develop representations in order to interpret and remember their experiences in an effort to understand the world. Bruner (1966) found three distinct ways in which people represent the world: (a) through action, (b) through visual images, and (c) through words and language. He called these kinds of representations enactive, iconic, and symbolic, respectively. Most researchers agree that these three types of representations are important in human understanding. (Salkind, 2007: 3)

Based on the explanation above, can be concluded that representation is a term to make connection between abstract idea with logical thinking to understanding mathematics, it needs representation.

Goldin and Shteingold (2001) wrote of two systems of representation.

―External systems of representation include conventional representations that are usually symbolic in nature. Internal systems of representation are created within a

person’s mind and used to assign mathematical meaning‖. Our numeration

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Based on explanation above, can be concluded that representation is one of the important thing in understanding mathematics. Mathematics can be understood if the students have good representation. So they able to describe, interpret, express, symbolize or even modeling ideas, mathematical concepts and the coherence among them and contained in a configuration, construction or certain situations that appear in various forms in order to obtain clarity of meaning, show understanding or looking for a solution of the problems.

In fact, our students in Indonesia has low quality in understanding mathematics. It shows from the result of the survey of Program for International Study Assessment (PISA) in 2012 showed that from 65 survey countries for

mathematics, reading and science skills, Indonesia was in 64th _{level with the mean}

score of mathematics skill was 375 while the average of OECD (Organization for

Economic Co-Operation and Development) was 494

( http://www.theguardian.com/news/datablog/2013/dec/03/pisa-results-country-best-reading-maths-science accessed on 7th_{of April, 2015).}

Based on the observation of researcher did on January, 25th_{2015 by doing}

interview to the vice principle and giving questions and questionnaire to the students, this problem also happened in SMA Negeri 1 Percut Sei Tuan. there are many students who failed the examinations. Their grade is lower than KKM that required by the school, it is about 65%, while the KKM in this school is 2.88 in scale of 4,00 or 72 in scale of 100. By giving the questions about statistics to the 37 students of grade X at SMA Negeri 1 Percut Sei Tuan as follows:

1. The scores of 35 students on a mathematical quiz are as follows:

75 60 41 77 89 90 65 70 100 55 60 76 80 60 75 90 55 90 100 95 91 50 60 75 80 100 90 55 85 89 70 75 70 100 60

a. Prepare a frequency table for the grouped data.

b. How many students passed the science quiz if the standard score > 70?

c. Determine the value of mean

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Figure 1.1 The Question of Observation Question no.2

Describe in brief, the overall pattern the number of students based on their ethnic background ?

Figure 1.2 The Student’s Answer of Observation Question From 37 students who answer the question, can be seen that 66.67% of them have not been able yet to build their visual representations in making table exactly, while 70.27% of students also have not been able yet to build their mathematical representations ability in equation or mathematical expression aspects especially in making the equation. Mathematical model from initial representation is also given and 65,49% of students have not been able yet to represent their ideas or knowledge in writing the text form.

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Based on the observation that did on January 22th_{, 2015 through}

questionnaires were distributed randomly to 100 foreign students of SMA Negeri 1 Percut Sei Tuan, only 39% of students learn mathematics more than equal to 3 hours every week outside the school activity, For the example at house or course place. 38% of students learn mathematics less than 3 hours every week, and 33% never learn mathematics outside the school activity.

Figure 1.3 The Student’s Answer of questionnaire

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It can be concluded that mathematical representation in SMA Negeri 1 Percut Sei Tuan is still low. There are many factors can lead to low mathematics student learning achievements. Prasad (2008) said:

There are three dimensions – school environment, teacher-student relations and value orientation among teachers’ influence the whole educational process in the classroom situation. School environment is an external factor and teacher-student relation is an internal factor. We know that values among teacher decide and control both the factors.

It means, not only the students it self that can influence the student’s ability in understanding mathematics, but also teacher and its environment. Teacher can reduce this problem by giving innovative learning strategies that are considered the development of students’ cognitive abilities and independence. One of them is

by giving ―learning by doing‖ in teaching and learning process. Stalheim and

Smith (1998) said:

People have known for hundreds of years that they remember what they see and do. A 2000 year old proverb states: ―I hear and I forget. I see and I

remember. I do and I understand.‖ Experience has taught me the wisdom of

this proverb. Data given by Stice (1987) also supports this proverb. He indicates that learners remember 10% of what they read, 26% of what they hear, 30% of what they see, 50% of what they see and hear, 70% of what they say and 90% of what they say as they do something.

One model that provides learning by doing is Project based Learning. Project Based Learning is a teaching that is designed for complex problems in which students conduct an investigation to understand, emphasizing long learning activities, assignments given to students multidisciplinary, oriented products (artifacts). According Mahanal (2009) PBL learning in general have guidelines steps: planning, creating and processing.

In fact, a growing body of research suggests that students learn more deeply and perform better on complex tasks if they have the opportunity to engage

in more ―authentic‖ learning—projects and activities that require them to

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A project-based learning lesson provides students with the opportunity to learn in an authentic, challenging, multidisciplinary environment, to learn how to design, carry out, and evaluate a project that requires sustained effort over a significant period of time, to learn to work with minimal external guidance, both individually and in groups, to gain in self-reliance and personal accountability. (Özdemir in Bas 2011: 10)

In this study, student will be guided to make project as data processing and will be and these data will be presented in the form of a report in the form of board and packaged as attractive as possible which will then be exhibited in a mini exhibition to be presented to the visitors. This activity is expected to improve the mathematical representation of students through activities that stimulate the representation ability by presentation to the visitors. Giving their opinion about their project orally, in writing in the form of words, symbols, or expressions of mathematical notation, making graph, diagrams, tables or physical objects such as report board.

In this observation, the observer will compare the learning model of project-based learning with problem based learning model. PBL is one of model that make active learning is occurred. Arends (2012: 396) said ―the essence of problem-based learning consists of presenting students with authentic and meaningful problem situations that can serve as springboards for investigations

and inquiry‖.

PBL makes students work with classmates to solve complex and authentic problems that help develop content knowledge as well as problem – solving, reasoning, communication, and self-assessment skills. These problems also help to maintain student interest in course material because students realize that they are learning the skills needed to be successful in the field (White, 2011: 1).

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indicates that the problem solver has perceived the problem and serves to guide the student toward the solution plan.

Based on the general description above, then the researcher has interested

to do research entitled ―The Difference of Students' Mathematical

Representation Ability By Using Project Based Learning And Direct Instructional Learning Model on the Topic of Statistics in Grade X SMA Negeri 1 Percut Sei Tuan‖.

1.2. Problem Identification

Based on the explanation in the background, the problem identification:

a. Student’s mathematical learning in SMA Negeri 1 Percut Sei Tuan outcomes is

still low.

b. Mathematical representation ability of students in SMA Negeri 1 Percut Sei

Tuan is still low.

c. Students of in SMA Negeri 1 Percut Sei Tuan still have difficulties in solving

mathematical represetation tests.

d. Teacher learning model used is still less variation and the learning process is

still conventional.

1.3. Problem limitation

For more directing this research so focused and specific to the problem in this study in limited to the students’ mathematical representation ability on the topic of statistics grade X in SMA Negeri 1 Percut Sei Tuan A. Y. 2014/2015 as well as the learning model is applied in the model limit by Project Based Learning and Problem Based Learning.

1.4. Problem Formulation

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1.5. Research Objective

The purpose of this research: to know any difference students’ mathematical representation ability taught by Project Based Learning with Problem Based Learning on the topic of statistics in grade X SMA Negeri 1 Percut Sei Tuan A. Y. 2014/2015?

1.6. Research Benefits

The benefits of this research are:

1. Being incoming material for researchers as mathematics teacher candidates to

apply Project Based Learning as mathematics’ alternative learning model in school.

2. For teachers and prospective teachers, this study could be a reference in

planning learning of statistics subject.

3. For students, is expected to use Project Based Learning and can be used to

improve the students' mathematical representation ability.

4. For school, is expected to be a source of information or contribute ideas for

improvement of mathematics teaching, especially in school where the researcher conducted and the school in general.

1.7. Operational Definitions

In order to avoid the differences of clarity meaning about important terms contained in this research, the operational definitions will be noted as following :

1. Mathematical representation ability is students’ ability to express

mathematical ideas (problem, statement, definition, and so on) into form: (1) Picture, diagram, graph, or table; (2) Mathematical notation, numerical/algebra symbol; (3) Written texts/words the interpretation of their mind.

2. Project Based Learning is Project based learning is a model that organizes

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3. Projects are complex tasks, based on challenging questions or problems, that

involve students in design, problem-solving, decision making, or investigative activities; give students the opportunity to work relatively autonomously over extended periods of time; and culminate in realistic products or presentations.

4. PBL is one of model that make active learning is occurred. Arends (2010)

said that PBL is a student centered approach that organizes curriculum and

instruction around carefully crafted ―ill-structured‖ and real-world problems

situations. Learning is active rather than passive, integrated rather than fragmented, and connected rather than disjointed.

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CHAPTER V

CONCLUSION AND SUGGESTION 5.1 Conclusion

Based on the result of research and discussion can be conclude that: The students’ representation ability that taught by using Problem Based Learning Model is different with Project Based Learning Model on topic Statistics at grade X SMA Negeri 1 Percut Sei Tuan A.Y. 2014/2015.

5.2 Suggestion

Based on the result of research and the above conclusion, then researcher submits some suggestions, as follow:

1. For teacher, both of project based and problem based learning can be used to improve representation mathematical ability.

2. For next researcher should use another model of learning to improve mathematical representation ability or choose another topic of mathematics. 3. For students, give more attention and follow the instruction that teacher has

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THE DIFFERENCE OF STUDENTS MATHEMATICAL REPRESENTATION ABILITY BY USING PROJECT BASED LEARNING AND PROBLEM BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE X SMA NEGERI 1 PERCUT SEI TUAN.