THE IMPLEMENTATION OF PROBLEM BASED LEARNING

MODEL THROUGH GROUP INVESTIGATION IN

MATHEMATICS LEARNING VIEWED FROM STUDENT’S

ADAPTIVE REASONING IN SMP NEGERI 1 SURAKARTA

RESEARCH PAPER

Submitted as Partial Fulfillment of The Requirements

for Getting Bachelor Degree of Education

in Mathematics Department

by :

APRILIA ARISTIYANI

A 410 090 258

SHOOL OF TEACHER TRAINING AND EDUCATION

MUHAMMADIYAH UNIVERSITY OF SURAKARTA

2013

APPROVAL

THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL

THROUGH GROUP INVESTIGATION IN MATHEMATICS LEARNING

VIEWED FROM STUDENT'S ADAPTTVE REASONING IN SMP NEGERI

1 SURAKARTA

APRILIA ARISTTYANI

A 410 090 2s8

Approved to be Examined by the Consultant;

By:

ACCEPTANCE

THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL

THROUGH GROUP INVA,STIGATION IN MATHEMATICS LEARNING

VIEWED FROM STUDENT'S ADAPTryE REASONING IN SMP NEGARI

1 SURAKARTA

Written By :

APRILIA ARISTTYANI

A 410 090 2s8

Accepted and Approved by The Board of Examiners

On Date : March 2013

The Board of Examiners :

Dra. N. Setyaningsih, M.Si

Rita P. Khotimah, M.Sc.

Dr. H. Sumardi, M.Si

Surakarta.

Muhammadiyah University of Suraka rta

Training And Education

l.t

3.

iii

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TESTIMOIYY

Herewith, I testifu that in this research paper there are no plagiarisms of the

previous literacy works which have been raised to obtain bachelor degree of a

university, nor there are opinions or masterpieces which have been written or

published by others, except these in which the writing was referred in the

manuscript and mentioned in the bibliography.

Hence, if it is proven that there are some untrue statement in this research

paper, I will be fully responsible.

Surakarta,

A 41[ 0e0 2s8

iv

v  

MOTTO

Which then of the bounties of your Lord will you deny ?

(Q.S. Ar-Rahman : 13)

I swear by the time, most surely man is in loss, except those who believe and do good, and enjoin on each other truth, and enjoin on each other patience.

(Q.S. Al Ashr : 1-3)

Science is better than wealth. Science will keep you and you keep wealth. Science id punisher (judge), whereas the condemned wealth. If the wealth shall be reduced

when spent, but the science will increase when done.

(Sayyidina Ali bin Abi Thalib)

Science without religion is lame, religion without science are blind.

(Albert Einstein)

  

vi  

DEDICATION

Alhamdulillahi Robbil ‘Alamiin, praise to Allah SWT, He has all the soul, by

the mercy and the the gift of Him this research can be completed. I gratefully

dedicate this research paper to :

1. Her beloved mom, mom, mom, my inspiration, the soul still always give

love, passion, and the sweet memories which engraved in my heart

beautifully. Mom… your pleasure is God’s blessing to me. She leave you in

Allah ta’ala.

2. Her beloved father, who gives the researcher love, advice, support in her

study. Thank you for your hard work and prayers during this time.

Hopefully in the hereafter your daughter can give you a beautiful crown “my

father and my mom”.

3. Her lovely sister Wury Wulandhony, thanks for support, pray and laughter.

4. Her lovely nephew Verda Hafidhah Rahmadhony, thanks for jokes in times

of fatigue. May Allah make you little angel in paradise later.

5. All of the lecturers of Mathematics Laboratory, thanks for precious

knowledge given to the researcher.

6. Her collaborations friend of this research Ike Zetti, thanks for your

cooperation and spirit as a friend to exchange ideas in this research.

7. Her friends in Mathematics RSBI class, International Islamic Boarding

School KH. Mas Mansyur, Mathematics Laboratory Assistant, HMP of

Mathematics, ISO, thanks for coloring the day, love, support, friendship,

experience and kindness.

vii  

ACKNOWLEDGMENT

Assalamualaikum Wr.Wb.

Alhamdulillahirobbil’alamin, praise and gratitude for Allah SWT, the

Glorious, the Lord, and the All Mighty, who has given opportunity and bless for

the researcher to finish the research paper entitled “The Implementation of

Problem Based Learning Model through Group Investigation in Mathematics

Learning Viewed from Student’s Adaptive Reasoning in SMP Negeri 1 Surakarta”

as the requirement for getting bachelor degree of education in Mathematics

Department of Muhammadiyah University of Surakarta.

Peace is upon to Muhammadiyah SAW, the last messenger of Allah, who

be hero for all his followers in the life after. The researcher realizes that this

researcher paper would never been possible without other people’s help, so that

the writer would like to express her gratitude and appreciation to:

1. Drs. H. Sofyan Anif, M.Si., the Dean of the School of Teacher Training and

Education of Muhammadiyah University of Surakarta.

2. Dra. Sri Sutarni, M.Pd., the Chief of Mathematics Department who gave the

agreement for the writer’s research paper title.

3. Dra. Nining Setyaningsih, M.Si., as the consultant and counselor who has

given a valuable guidance and suggestion during the completion of this

research paper.

viii  

4. Mr. Syakuri, as the consultant, for being good consultant and giving the

researcher suggestion in correcting of grammar writing this research paper.

5. Dra. Hj. Sri Suwartinah, M.Pd and Pudjiastuti, S.Pd, as the principal and

mathematics teacher of SMP Negeri 1 Surakarta who have given permission

and the opportunities in the implementation of the study.

6. Students of class VIII A and VIII B in SMP Negeri 1 Surakarta who are

willing to be the subject of research, thank you for your cooperation.

7. All parties who may not enumerated which have helped in completing this

research.

Finally, the researcher realizes that this research paper is still far from

being perfect, so all suggestions and criticism for improving this research are

accepted widely and happily. Hopefully, this research paper useful for the readers

and prospective researchers.

Wassalammualaikum Wr. Wb.

Surakarta, March 2013

The Writer

xii

LIST OF FIGURE

Page

Figure 2.1 Experiment to Find the Formula of Area of Circle .................. 14

Figure 2.2 Circle ....................................................................................... 15

Figure 2.3 The Research Paradigm ........................................................... 17

Figure 4.1 Histogram of Student’s Achievement Mathematics

in Control Class ....................................................................... 46

Figure 4.2 Histogram of Student’s Achievement Mathematics

in Experiment Class ................................................................ 48

Figure 4.3 Histogram of Student’s Adaptive Reasoning

in Control Class ....................................................................... 49

Figure 4.4 Histogram of Student’s Adaptive Reasoning

In Experiment Class ................................................................ 51

Figure 4.5 The Average of Student’s Mathematics Achievement

in Experiment and Control Class viewed from

Adaptive Reasoning ................................................................. 58

xiii

LIST OF TABLE

Page

Table 2.1 Differences and Similarities Reasearch ....................................... 9

Table 2.2 The Stages of Problem Based Learning Model ........................... 11

Table 3.1 The Activities Researcher in 2012/2013 Academic Year ............ 19

Table 3.2 Criteria for Assessment Questionnaire ........................................ 25

Table 3.3 Layout Data .................................................................................. 34

Table 3.4 Summary of Analysis of Variance Two Ways............................. 38

Table 4.1 Balance Test ................................................................................. 42

Table 4.2 Frequency Distribution of Mathematics Achievement

in Control Class .......................................................................... 46

Table 4.3 Frequency Distribution of Mathematics Achievement

In Experiment Class .................................................................... 47

Table 4.4 Frequency Distribution of Student’s Adaptive Reasoning

in Control Class .......................................................................... 49

Table 4.5 Frequency Distribution of Student’s Adaptive Reasoning

in Experiment Class .................................................................... 50

Table 4.6 The Data of Student’s Adaptive Reasoning based on Criteria ..... 52

Table 4.7 The Analysis Result of Normality Test ........................................ 53

Table 4.8 The Analysis Result of Homogeneity Test .................................. 54

Table 4.9 The Summary of Analysis of Variance Two Ways with

Unequal Cell ............................................................................... 54

xiv

Table 4.10 The Summary of Analysis of Multiple Comparison Test

Between Columns ....................................................................... 56

Table 4.11 The Average of Mathematics Achievement in Experiment and Control

Class viewed from Adaptive Reasoning .................................... 57

xv

LIST OF APPENDIXS

Page

Appendix 1 The List of Students of Tryout Class ........................................ 68

Appendix 2 The List of Students of Control Class ....................................... 69

Appendix 3 The List of Students of Experiment Class ................................. 70

Appendix 4 The List of Score of Student’s Initial Ability ............................ 71

Appendix 5 The Balance Test ....................................................................... 73

Appendix 6 The Lattice of Questionnaire of Student’s Adaptive

Reasoning (Tryout) ................................................................... 75

Appendix 7 Questionnaire of Adaptive Reasoning ....................................... 77

Appendix 8 Answer Sheet ............................................................................. 82

Appendix 9 The Lattice of Achievement Test (Tryout)................................ 83

Appendix 10 Achievement Test (Tryout) ....................................................... 84

Appendix 11 Key Answers of Achievement Test (Tryout) ............................ 87

Appendix 12 Guidelines Scoring of Achievement Test .................................. 91

Appendix 13 Validity and Reliability of Adaptive Reasoning

Questionnaire (Tryout) .............................................................. 92

Appendix 14 Validity and Reliability of Achievement Test (Tryout) ............ 94

Appendix 15 Lesson Plan of Problem Based Learning Model through

Group Investigation ................................................................... 95

Appendix 16 Learning Material of First Meeting .......................................... 104

Appendix 17 Learning Material of Second Meeting ...................................... 105

xvi

Appendix 18 Group Assignment of First Meeting ......................................... 106

Appendix 19 Group Assignment of Second Meeting .................................... 108

Appendix 20 Discussion Material I ................................................................ 111

Appendix 21 Discussion Material II ............................................................... 112

Appendix 22 Key Answers of Discussion Material I...................................... 113

Appendix 23 Key Answers of Discussion Material II .................................... 116

Appendix 24 The Master Data of Research .................................................... 118

Appendix 25 Normality Test ........................................................................... 125

Appendix 26 Homogeneity Test ..................................................................... 133

Appendix 27 Hypothesis Test ......................................................................... 137

Appendix 28 Multiple Comparison Test ......................................................... 143

Appendix 29 Documentation .......................................................................... 146

Appendix 30. Surat Ijin Riset ........................................................................... 147

Appendix 31. Surat Keterangan Penelitian ...................................................... 148

Appendix 32. Jadwal Bimbingan Pembimbing ................................................ 149

xvii  

SUMMARY

APRILIA ARISTIYANI. A410090258. THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL THROUGH GROUP INVESTIGATION IN MATHEMATICS LEARNING VIEWED FROM STUDENT’S ADAPTIVE REASONING IN SMP NEGERI 1 SURAKARTA. RESEARCH PAPER. MUHAMMADIYAH UNIVERSITY OF SURAKARTA. 2013.

The purpose of this research is to analyze: (1) the influence of the use of problem based learning model through group investigation to student’s mathematics achievement, (2) the influence of adaptive reasoning ability to student’s mathematics achievement, (3) the interaction between the use of problem based learning model through group investigation and adaptive reasoning ability to student’s mathematics achievement. This research uses an experimental research. The populations are all students of grade VIII of 2012/2013 academic year in SMP Negeri 1 Surakarta. Samples taken in this research as many as two classes, consist of VIII B as experiment class with 27 students and VIII A as control class with 28 students. The sampling technique used in this research is cluster random sampling. Data collection methods used are questionnaire method, method of test and documentation method. Data analysis techniques use two ways analysis of variance with unequal cells, a prerequisite test used the Lilliefors method to normality test and the Barlett method to homogeneity test. From the analysis of data with 5% of significant level, it is satisfied that : (1) there is no influence of the use of problem based learning model through group investigation to student’s mathematics achievement with FA = 3,33, (2) there is the influence of adaptive reasoning ability to student’s mathematics achievement with FB = 6,54, and (3) there is no interaction between the use of problem based learning model through group investigation and adaptive reasoning ability to student’s mathematics achievement with FAB = 0,16.

Key Words: Problem based Learning, Group Investigation, adaptive reasoning.

 

 

ix

TABLE OF CONTENT

Page

TITLE ............................................................................................................... i

APPROVAL ..................................................................................................... ii

ACCEPTANCE ............................................................................................... iii

TESTIMONY ................................................................................................... iv

MOTTO ........................................................................................................... v

DEDICATION ................................................................................................. vi

ACKNOWLEDGMENT .................................................................................. vii

TABLE OF CONTENT ................................................................................... ix

LIST OF FIGURE ............................................................................................ xii

LIST OF TABLE ............................................................................................. xiii

LIST OF APPENDIXS .................................................................................... xv

SUMMARY ..................................................................................................... xvii

CHAPTER I: INTRODUCTION

A. Background of the Study ..................................................... 1

B. Identification of Problem ...................................................... 4

C. Limitation of Probelm ........................................................... 4

D. Problem Formulation ............................................................ 5

E. Objectives of the Study ........................................................ 5

F. Benefits of the Study ............................................................ 6

x

CHAPTER II: THEORY

A. Relevant Research ................................................................ 7

B. Literature Review .................................................................. 10

1. Mathematics achievement ................................................. 10

2. Learning model ................................................................. 10

3. The concept of adaptive reasoning ................................... 13

4. Material ............................................................................. 13

C. Thinking Framework ............................................................ 16

D. Hypothesis ............................................................................ 17

CHAPTER III: RESEARCH METHOD

A. The Type and Design of Research ....................................... 18

B. Object of Research ................................................................ 18

C. Population, Sample, and Sampling ....................................... 19

D. Variable of Research ............................................................. 22

E. Data Collection Techniques .................................................. 24

F. Instrument of Research .......................................................... 26

G. Data Analysis Techniques .................................................... 31

CHAPTER IV: RESEARCH FINDING AND DISCUSSION

A. The Implementation of Research .......................................... 42

B. Data Description ................................................................... 45

C. Prerequisites Analysis Test ................................................... 52

D. Hypothesis Test .................................................................... 54

E. Discussion of Data Analysis ................................................. 57

xi

CHAPTER V: CONCLUSIONS, IMPLICATIONS AND SUGGESTIONS

A. Conclusions ........................................................................... 62

B. Implications ........................................................................... 63

C. Suggestions ........................................................................... 64

BIBLIOGRAPHY ............................................................................................ 65

ATTACHMENT .............................................................................................. 68