THEDIFFERENCE OF STUDENTS’ MATHEMATICAL REPRESENTATION ABILITY BY USING PROBLEMBASED LEARNING AND INQUIRY BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE VIII SMP NEGERI 1TANJUNG MORAWA ACADEMIC YEAR 20 1 6 /2 01 7.

THE DIFFERENCE OF STUDENTS’ MATHEMATICAL REPRESENTATION ABILITY BY USING PROBLEMBASED LEARNING AND INQUIRY

BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE VIII SMP NEGERI 1TANJUNG MORAWA

A C A D E M I C Y E A R 2 0 1 6 / 2 0 1 7

By:

Erika Agustina Simbolon ID. 4123312007

Mathematics Education Study Program

SKRIPSI

Submittedto Fulfill The Requirement for Getting The Degree of SarjanaPendidikan

MATHEMATICS DEPARTMENT

FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN

MEDAN 2017

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BIOGRAPHY

Erika Agustina Simbolon was born on August 29th, 1994 in Medan, North Sumatera. She is the second child of Mr.Togar PandapotanSimbolon and Mrs.Megawati br.Situmorang. She attended elementary school, SDN 101880Tanjung Morawa in2000. After Graduated from elementary school in 2006, she continued her study to SMP Negeri 1 Tanjung Morawa and graduated in 2009. Later, She continued her study to SMA Negeri 1 Tanjung Morawa. In 2012, she finished her study in SMA Negeri 1 Tanjung Morawa and accepted as a student in Mathematics Education Bilingual, Mathematics Department, Faculty of Mathematics and Natural Sciences, State University of Medan and graduated in January 2017.

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THE DIFFERENCE OF STUDENTS’ MATHEMATICAL REPRESENTATION ABILITY BY USING PROBLEM BASED LEARNING AND INQUIRY

BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE VIII SMP NEGERI 1 TANJUNG MORAWA

A C A D E M I C Y E A R 2 0 1 6 / 2 0 1 7

Abstract

The type of this research is quasi – experiment.The aim of this research was to determine whether student’s Mathematical Representation Ability taught by using Problem Based Learning is higher than Inquiry Based Learning for Grade VIII in SMP Negeri 1 Tanjung Morawa. The population is all students of grade VIII in SMP Negeri 1 Tanjung Morawa A.Y. 2016/2017. Sampling Techniques that is used in this research is Purposeful sampling. There are two samples in this research namely, Experimental class A isVIII-1 taught by Problem Based Learning and Experimental class B is VIII-2 taught by Inquiry Based Learning. This research using posttest only group control, Technique of analzying data is consisted of normality, homogeneity, and hypothesis test. Based on normality and homogeneity test, the data was taken from normal distribution and homogeneous population. The result of the research shows that the mean score are 83.08 in experiment class A and 78.58 in experiment class B and results of hypothesis test of data from both experimental class in post test was found that . It indicates that H₀ is rejected. So, we can conclude that the students’ mathematical representation ability in the classroom taught using Problem-Based Learning model is higher than in the class taught using Inquiry Based Learning model.

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PREFACE

Praise to God Almighty who I believed in Jesus Christ, who accompany every step in life, including in education so that writer can finish this skripsi. The title of this skripsi is “The Difference Of Students' Mathematical Representation Ability By Using Problem Based Learning And Inquiry Based Learning On The Topic Of Statistics In Grade VIII SMP Negeri 1 Tanjung Morawa”. This skripsi was arranged to satisfy the requirement to obtain the Degree of Sarjana Pendidikan from Faculty Mathematics and Natural Science in State University of Medan.

During the process of the writing of this skripsi, the writer received support from various parties. Special thanks go to Mr. Dr. Edy Surya, M.Si as my skripsi supervisor who has provided guidance, direction, and advice to the perfection of this skripsi. Thanks are also due to Prof. Dr. Asmin, M.Pd, Dr. Mulyono, M.Si and Pardomuan N.J.M Sinambela, S.Pd, M.Pd as author’s examiners who have provided input and suggestion from the planning to the completion of the preparation of the research of this skripsi. Thanks are also extended to Prof.Dr.Hasratuddin, M.Pd as academic supervisor and then thank you so much for all author’s lecturer in FMIPA Unimed.

Thanks to Mrs.Arwidah Parinduri, S.Pd. as principle of SMP Negeri 1 Tanjung Morawa, Mrs. Duena Maritha Sihotang, S.Pd as mathematics teacher and all teachers, staffs and also the students in grade VIII-1 and VIII-2 SMP Negeri 1 Tanjung Morawa who have helped writer conducting the research.

Most special thanks to my beloved parents, Togar Pandapotan Simbolon and Megawati br. Situmorang, who take care of me from since I was born, who always be there for me, who pray days and nights and giving me motivation and all i need in finishing this skripsi. Big thanks to my beloved sister Rame Novayanti Simbolon and my brother in law Fernando Cay Hasibuan, my brother Andreas Maraden Simbolon, my nephew Kevin and my niece Revita for giving

support even moril or material and all my family for all pray, motivation, and support until the end of my study.

This Skripsi was compiled from the strength, spirit, and endless friendship ever given by author’s best partner Febby, Bella, Aisyah, Mutiara, Aida, Windy, Rahima, Ariyanto, Bowo, Adi, and Rudi. Thanks to my big family in Bilingual Mathematics Education 2012, Dessy, Friska Simbolon, Friska Elvita, Rani, Satoto, and Dilla for sadness and happiness in the class.For all partner of PPLT Unimed Bilingual 2016 of SMA Negeri 2 Balige, for my senior and junior in mathematics department, my students SPECTRO 24th generation when author was doing practice in SMA Negeri 2 Balige, thanks for the support and motivation to finish my study. Thanks for every one who cannot be mentioned one by one who support and motivate the author.

This skripsi, of course, has its own advantages and limitations. Building critics and suggestions are needed to improve the quality for this skripsi. The best wish is that this skripsi is useful for those who use this skripsi now and future.

Medan, April 2017 Author,

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CONTENT

Ratification Sheet i

Biography ii

Abstract iii

Preface iv

Contents vi

List of Figure ix

List of Table x

List of Appendix xi

CHAPTER I INTRODUCTION

1.1 Background 1

1.2 Problem Identification 9

1.3 Problem Limitation 9

1.4 Problem Formulation 9

1.5 Research Purpose 10

1.6 Benefit of Research 10

1.7 Operational Definitions 10

CHAPTER II LITERATURE REVIEW

2.1 Theoretical Framework 12

2.1.1 Representation in Mathematics 12

2.1.2 Mathematical Representation Ability 13

2.1.3 Problem Based Learning 19

2.1.3.1 The Characteristic of PBL 21

2.1.3.2 Syntax of Problem Based Learning 23 2.1.3.3 Advantages and Disadvantages of PBL 23

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2.1.4.1The process of Learning by using Inquiry Methods 27 2.1.4.2Syntax of Inquiry Based Learning 28 2.1.4.3Advantages and Disadvantages of IBL 29 2.1.5 Summary of Subject Matter (Statistics) 30

2.2 Relevant Research 32

2.3 Conceptual Framework 34

2.4 Hypothesis 35

CHAPTER III RESEARCH METHOD

3.1 Time and Location of Research 36

3.2 Population and Sample 36

3.2.1 Population of Research 36

3.2.2 Sample Of Research 36

3.3 Variable of Research 36

3.3.1 Independent Variable 36

3.3.2 Dependent Variable 37

3.4 Instrument of Research 37

3.4.1 Initial Test 37

3.4.2 Test of Students’ Mathematical Representation Ability 37

3.5 Type and Design of Research 43

3.6 Procedure of Research 44

3.7 Techniques of Data Analyzing 46

3.7.1 Normality Test 46

3.7.2 Homogeneity test 46

3.7.3 Hypothesis Test 47

CHAPTER IV RESULT AND DISCUSSION

4.1. Research Results 49

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4.1.1.1. Students’ Mathematical Representation Ability in the Problem Based Learning Classroom 50 4.1.1.2. Students’ Mathematical Representation Ability in the

Inquiry Based Learning Classroom 51

4.1.2 Result of Normality Test 52

4.1.3. Result of Homogeneity Test 52

4.1.4. Result of Hypothesis Test 53

4.2. Research Discussion 54

CHAPTER V CONCLUSION AND SUGGESTION

5.1. Conclusion 55

5.2. Suggestion 55

REFERENCES 58

APPENDICES 61

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LIST OF FIGURE

Figure 1.1 Observation Result of Student’s Answer Number 1 4 Figure 1.2 Observation Result of Student’s Answer Number 2 5 Figure 1.3 The Question of Observation Question Number 3 6 Figure 1.4 Observation Result of Student’s Answer Number 3 6

Figure 2.2 Bar Graphs 31

Figure 2.3 Pie Charts 31

Figure 2.4 Line Charts 32

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LIST OF TABLE

Table 2.1 Operational Form of Mathematical Representation Ability 16 Table 2.2 Indicator of Mathematical Representation Ability 18

Table 2.3 Syntax Problem-Based Learning 23

Table 2.4 Syntax Inquiry Based Learning 28

Table 3.1 The Blueprint of Mathematical Representation Ability 36 Table 3.2 The Rubric of Mathematical Representation Ability 37 Table 3.3 Research design of randomized control group only 41 Table 3.3 The Statistical Validity Confirmation of Mathematical

Representation Ability Test 34

Table 3.4 The Reliability Confirmation of Mathematical

Representation Ability Test 35

Table 4.1 Descriptive Statistics Summary 49

Table 4.2 Descriptive Statistics for PBL Score 50

Table 4.3 Descriptive Statistics for iBL Score 51

Table 4.4 Kolmogorov – Smirnov Test of Normality 52

Table 4.5 Test of Homogeneity of Variances 52

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LIST OF APPENDICES Appendix 1. The Blueprint of Mathematical Representation

Ability Initial Test 61

Appendix 2. Initial Test of Mathematical Representation Ability 62 Appendix 3. Alternative Solution of Mathematical Representation

Ability Initial Test 64

Appendix 4. Lesson Plan of Experimental Class I 66

Appendix 5. Lesson Plan of Experimental Class II 76

Appendix 6. Worksheet of Experimental Class I 85

Appendix 7. Worksheet of Experimental Class II 90

Appendix 8. The Blueprint of Students’ Mathematical Representation

Ability 96

Appendix 9. Test of Mathematical Representation Ability (Post Test) 97 Appendix 10. Alternative Solution Of Mathematical Representation

Ability (Post Test) 101

Appendix 11. Validity Of Students Mathematical Representation

Ability Sheet 104

Appendix 12. Statistical Validity of The Test 110

Appendix 13. Reliability of The Test 113

Appendix 14. The Scores of PBL and IBL Classroom 115

Appendix 15. Normality Test 116

Appendix 16. Homogeneity Test 119

Appendix 17. Hypothesis Test 121

Appendix 18. Critical r –table 124

Appendix 19. t – table

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CHAPTER I INTRODUCTION 1.1Background

Mathematics is a branch of science that has an important role in the development of science and technology, either as a toolin applications for other scientific fields as well as in the development of mathematics. Various applications of mathematics can be used to solve the daily life problems. As disclosed Cornelius (in Abdurrahman 2009:204) that:

Lima alasan perlunya belajar matematika karena matematika merupakan (1) sarana bepikir yang jelas dan logis, (2) sarana utuk memecahkan masalah kehidupan sehari-hari, (3)sarana mengenal pola-pola hubungan dan generalisasi pengalaman, (4) sarana untuk mengembangkan kreativitas, dan (5) sarana untuk meningkatkan kesadaran terhadap perkembangan budaya.

Mastery of mathematics by students become a necessity that can not be bargained in structuring reasoning and decision-making in an increasingly competitive era of competition at this time.Mathematics learning activities is expected to be able makes students ability to resolve the problems it faces, both in mathematics and outside of mathematics, and makes students developing their reasoning, so that students able to think critically, logically, systematically and finally expected that students able to be objective, honest and discipline.

Mathematics as a very important science should have been the lesson that favored by students that being learned mathematics. However, in reality the math including lessons that disliked a lot of students.Fears of students are not only caused by the students themselves, but rather the lack of ability of teachers in creating a situation that could bring students interested inmathematics.The main cause of the failure of a teacher in teaching in front of the class is superficiality of knowledge of teachers against whom students and how their learning ways. So every action learning that programmed even more mistakes than a policy taken.Due to fears of the students, the purpose of mathematical education is not achieved.

2

According to National (NCTM, 2000: 206) that learning mathematics with understanding is the main thing. Conceptual understanding and procedural isan inseparable part of mathematicsproblemssolving.In NCTM (2000) also described there are five standardsmathematical ability should be owned by students, namely:

problem solving, communication, connection, reasoning, and

repreprsentation.Based on the description, NCTM contains representations as one of the standards that must be owned by students so that mathematical representation of student really need to developed.

The mathematical representation ability is one of the general objectives of learning mathematics in school. This ability is particularly important for students and closely related to communication skills and problem-solving. To communicate something, someone needs a good representation in the form of pictures, graphs, charts, and other forms of representation. With representation, problems that initially seem difficult and complicated can be seen more easily and simply, so that the issues presented can be solved more easily.Goldin (2002: 208) state that:

Representasiadalahelemen yang

sangatpentinguntukteoribelajarmengajarmatematika,

tidakhanyakarenapemakaian system simbolis yang

jugapentingdalammatematikadan kaya akankalimatdan kata, beragamdan

universal, tetapijugauntuk 2 alasanpentingyaitu (1)

matematikamempunyaiperananpentingdalammengkonseptualisasiduniany

ata; (2) matematikamembuathomomorphis yang

merupakanpenurunandaristrukturhal-hal lain dari yang pokok.

Hudiono (2005:19) state that the representation ability can support students to understand mathematical concepts that learned and the relationship; to communicate mathematical ideas of students, to know more about the relationship (connection) between mathematical concepts; or apply mathematics in realistic mathematical problems through modeling.The role of representations is alsodescribed by NCTM (2000: 280)

Representation is central to the study of mathematics. Student can develop and deepen their understanding of mathematical concepts and relationships as they create, compare, and use various representations. Representations also help students communicate their thinking.

3

Representations should be treated as essential elements in supporting

students’ understanding of mathematical concepts and relationships; in

communicating mathematical approaches, arguments, and understandings to one’s self and to others; in recognizing connections among related mathematical concepts; and in applying mathematics to realistic problem situations through modeling. New forms of representation associated with electronic technology create a need for even greater instructional attention to representation. So, representations underpinconceptual understanding, communications, connections, and problem solving. All of these processes are assisted by an effective representation. Students should engage with each of these in all of their mathematics courses, so that effective presentations.

 Create and use representations to organize, record, and communicate mathematical ideas;

 Select, apply, and translate among mathematical representations to solve problems;

 Use representations to model and interpret physical, social, and mathematical phenomena

Based on explanation above can be concluded that representationis 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.But on last situation Mathematical representation ability of students is in school less attention since many studentsdon’t comprehend about their mathematical representation ability. Though mathematical representation ability is very important in learning mathematics since facilitating the students to represent problem in form of mathematical visual object which is more interesting.

4

From the initial test which has been conducted by researchers to students, it is known that the ability of students' mathematical representation is still low. It can be seen from the answers that they make. Some of them are notable to create a table of story problems correctly, notable to solve problems of the images presented, and less able to write the conclusion of the diagram presented. The following are some of the documentation of student test results.

Question 1

Given a following data

7, 9, 3, 6, 6, 8, 4, 5, 8, 7, 4, 5, 6, 9, 3 a. Calculate the mean values b. Median and mode of data Answer:

Figure 1.1Observation Result of Student’s Answer Number 1

From the answers above, we can conclude that the students have not been able to represent the data into the form of mathematical expressions. Theydon’t understandhow to calculate the mean of data and also don’t understand how to find mode and median.

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Sinchan body temperature for 10 days is shown by the following table. Table 1.1The Question of Observation Question Number 2

Harike 1 2 3 4 5 6 7 8 9 10

Suhu (o C) 35 36 37 36 37.5 38 37 38 38.5 37

a.Draw a line diagram of the above data

b. How many days sinchan’s body temperature is above normal(36.5o C)?? Answer :

Figure 1.2Observation Result of Student’s Answer Number 2

From the answers above, we can conclude that the students have not been able to represent the data into the form of graph. Students are not able to enter the data correctly into the graph, data which he wrotedifferent from the data in question

and also don’t understand how to put the datafrom tables that given, so the student

feel so difficult to answer the question.

Question 3

The bar chart below shows the acquisition value math test grade VII-A. Minimal completeness criteria (KKM) = 75.

6

Figure 1.3The Question of Observation Question Number 3 a. Calculate how much students that must follow the remedy

b. Make a conclusion from the above bar chart math scores Answer :

Figure 1.4 Observation Result of Student’s Answer Number 3 From theanswersabove, wecanconcludethat thestudentshave not beenable to representimagesinto written text correctlybecausestudents areless ableto appreciatethe diagram basedfactscontaineddata. Hejustunderstand thegraphbasedpersonal opinion.

Based onthese problems, researcherscansurmisethat thestudentswillhave difficultyin the futureto managethe problemso thatitwillalsoaffect

0 2 4 6 8 10

55 65 70 75 80 85 90 95 100

Fr

e

q

u

e

n

cy

Score

7

Student’smasteryand understanding inmathematics.Student’s Mathematical

Representation ability still low because thelearning modelused bymathematics teacherspoorlayin developing student’s ability.They still using conventional learning. It requires studentstostrivethemselvesin learning. Itis not suitableto be applied tothe studentinthismodernera.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.

Students should been courage to play an active role in learning, teachers must also be able to involve in technological sophistication in learning so that students feel more passion and learning are more interesting. So, Student’s Mathematical Representation ability will be improving well when teachers use the right teaching methods.Therefore, while efforts should be made to improve the ability of the student representation is to increase the competence of teachers in selecting a learning model.Preferably learning model chosen is to increase student engagement in the learning process because until now there are still many students which complain even make mathematics as a frightening specter.So that they become lazy to further explore more math.This tends to make students less active that cause actions or behavior of the students are less skilled in communicating ideas or their ideas.

Relating with the above description it is necessary to think about ways and strategies to overcome the above problems. One model of learning which applied in learning mathematics is the Problem-based learning.ProblemBased Learning is effective to improve students' mathematical representation based on multi-level and overall student achievement. According Tall (1995) in mathematical thinking, someone will be faced with an object (a problem in the form of numbers, symbols, statements, or other) in a learning environment, and it will have a perception of this object and perform an internal process to an action. This action in the form of a visuo-spatial representations (images or graphics, which will be the

verbal-8

deductive) through an object, or in the process of-concept with a conceptual link between them. Problem-based learning that begins with the real concept enables students to more easily understood better when working in groups as well as classical. Each student is required to undertake the completion of a variety of practice questions that had been prepared in the work sheet. PBL models can facilitate the conceptual change on students because of cognitive conflict through the exposed concrete problems.

The findings show that there is a change in the students’ misconceptions in

understanding mathematical representation. Problem Based Learning can facilitate students' conceptual change because this model gives students opportunity to syntesize the concept. Problem-based learning can facilitate changes of student misconceptions about multi mathematical representation for problem-based learning poses a challenge for students to develop a strategy to prove his hypothesis. Once the strategy is used, the teacher role is to support students in syntesizing of new concepts through questions support (scaffolding).

The learning model that can be applied in learning mathematics is Inquiry-Based Learning.Inquiry-Inquiry-Based Learning is well suited to helping students become active learners because it situates learning in real-world problems and makes students responsible for their learning. It has the dual emphasis of helping learners develop strategies and construct knowledge. Allowing students to interact with materials, models, manipulate variables, explore phenomena, and attempt to apply principle affords them with opportunities to notice patterns, discover underlying causalities, and learn in ways that are seemingly more robust. Learning by using Problem Based Learning (PBL) and Inquiry Based Learning (IBL) gives greater opportunities for students to develop students' mathematical representation ability. PBL and IBL learning model is expected to improve the ability of students' mathematical representation is low, especially in the statistics.Statistics not onlylearn the ability to find the truth and the absolute final answer, but also to obtain a conceptual understanding and application of learning in life. But,between both of models are definitely one better model applied to the topic statisticsand can and improve the ability of students' mathematical representation higher than

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the other models. Based on the general description above, then the researcher has

interested to do research entitled “The Difference of Students' Mathematical

Representation Ability By Using Problem Based Learning And Inquiry Based Learning on The Topic of Statistics in Grade VIII SMP Negeri 1 TanjungMorawa A.Y2016/2017.”

1.2 Problem Identification

Based on the explanation in the background, the problem identification: a. Students of in SMP Negeri 1 TanjungMorawa still have difficulties in

solving mathematical represetation tests, especially on the topic of statistics.

b. Students are not actively involved in the learning process.

c. Teacher in SMP Negeri 1 Tanjung Morawa never using a variety of learning models (PBL or IBL) on the topic of statistics so that are not visible differences better model used in topic of statistics because the learning is still teacher centered.

d. The learning process in the classroom rarely train and develop the skills of communication and interaction among students.

1.3 Problem Limitation

The problem limitation in this research are as follows:

1. The author sofocus with The Difference Of Student’s Mathematical Representation Ability Taught By Using Problem based learning With Inquiry based learning For Grade VIII in SMP Negeri 1 TanjungMorawa. 2. Learning in this Research topic is Statistics.

1.4 Problem Formulation

Based on the problem limitation and background above, the problem is formulated: Whether Student’s Mathematical Representation Ability taught by using Problem Based learning is higher than Inquiry Based Learning for Grade VIII SMP Negeri 1 TanjungMorawa?

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1.5 Research Purpose

The purpose of this research: to know whether student’s Mathematical Representation Ability taught by using Problem Based Learning is higher thanInquiry Based Learning for grade VIII SMPNegeri 1 TanjungMorawa.

1.6 Benefit of Research

The benefits of this research are:

1. For students: Helping students of SMP Negeri 1 TanjungMorawa for increasing their conceptual understanding in mathematics.

2. For teachers and prospective teachers: This study could be a reference in planning learning of statistics subject.

3. For school: Expectto 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.

4. For researcher: The result of research can be used as reference in developing the appropriate learning approach in learning process.

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. Problem-based learning that begins with the real concept enables students to more easily understood better when working in groups as well as classical. Each student is required to undertake the completion of a variety

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of practice questions that had been prepared in the work sheet. PBL models can facilitate the conceptual change on students because of cognitive conflict through the exposed concrete problems.The findings show that there is a change in the students’ misconceptions in understanding mathematical representation. Problem Based Learning can facilitate students' conceptual change because this model gives students opportunity to syntesize the concept. Problem-based learning can facilitate changes of student misconceptions about multi mathematical representation for problem-based learning poses a challenge for students to develop a strategy to prove his hypothesis.

3. Inquiry-based learning (IBL) is a pedagogy which best enables students to experience the processes of knowledge creation and the key attributes are learning stimulated by inquiry, a student-centred approach, a move to self-directed learning, and an active.

CHAPTER V

CONCLUSION AND SUGGESTIONS 5.1 Conclusion

In Hypothesis test, the data are processed based on post test shows that

(2.284) > (1.671) that it’s mean H₀ rejected. So, can be

concluded that Students’ mathematical representation ability taught by using Problem Based Learning is higher than Inquiry Based Learning.

5.2 Suggestions

Related to the writer’s research, some suggestions are pointed out as follows:

a. For Teachers, can be used as a references to choose a Problem Based Learning not only in Statistics but also in another topics, Teachers are expected to be active in guiding students in learning process so that weak student can be helped to improving their mathematical representation ability, and teachers should be able to guide and provide more detail to the students about how to present the random data into the correct distribution table groups

b. For prospective teachers, during the learning process takes place, the teacher must be able to control the class so no student is making noise in the classroom that can interfere with other students' concentration.

c. For School, is expected to be source of information or contribute ideas for improvement of mathematics teaching and learning.

d. Researcher expecting of this research can be enhanced by next researcher.

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Trianto, (2011), mendesain model pembelajaran inovatif progresif, Penerbit kencana, Jakarta.

Widakdo, Widi, (2014), The Difference of Students’ Mathematical Representation Ability by Using Project Based Learning and Problem Based Learning in Grade X SMA N 1 Percut Sei Tuan, Skripsi, FMIPA, Unimed, Medan.

1.5 Research Purpose

The purpose of this research: to know whether student’s Mathematical Representation Ability taught by using Problem Based Learning is higher thanInquiry Based Learning for grade VIII SMPNegeri 1 TanjungMorawa.

1.6 Benefit of Research

The benefits of this research are:

1. For students: Helping students of SMP Negeri 1 TanjungMorawa for increasing their conceptual understanding in mathematics.

2. For teachers and prospective teachers: This study could be a reference in planning learning of statistics subject.

3. For school: Expectto 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.

4. For researcher: The result of research can be used as reference in developing the appropriate learning approach in learning process.

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. Problem-based learning that begins with the real concept enables students to more easily understood better when working in groups as well as classical. Each student is required to undertake the completion of a variety

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of practice questions that had been prepared in the work sheet. PBL models can facilitate the conceptual change on students because of cognitive conflict through the exposed concrete problems.The findings show that there is a change in the students’ misconceptions in understanding mathematical representation. Problem Based Learning can facilitate students' conceptual change because this model gives students opportunity to syntesize the concept. Problem-based learning can facilitate changes of student misconceptions about multi mathematical representation for problem-based learning poses a challenge for students to develop a strategy to prove his hypothesis.

3. Inquiry-based learning (IBL) is a pedagogy which best enables students to experience the processes of knowledge creation and the key attributes are learning stimulated by inquiry, a student-centred approach, a move to self-directed learning, and an active.

In Hypothesis test, the data are processed based on post test shows that

(2.284) > (1.671) that it’s mean H₀ rejected. So, can be

concluded that Students’ mathematical representation ability taught by using Problem Based Learning is higher than Inquiry Based Learning.

5.2 Suggestions

Related to the writer’s research, some suggestions are pointed out as follows:

a. For Teachers, can be used as a references to choose a Problem Based Learning not only in Statistics but also in another topics, Teachers are expected to be active in guiding students in learning process so that weak student can be helped to improving their mathematical representation ability, and teachers should be able to guide and provide more detail to the students about how to present the random data into the correct distribution table groups

b. For prospective teachers, during the learning process takes place, the teacher must be able to control the class so no student is making noise in the classroom that can interfere with other students' concentration.

c. For School, is expected to be source of information or contribute ideas for improvement of mathematics teaching and learning.

d. Researcher expecting of this research can be enhanced by next researcher.

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