THE IMPLEMENTATION OF PROBLEM BASED LEARNING MODEL THROUGH GROUP INVESTIGATION IN The Implementation Of Problem Based Learning Model Through Group Investigation In Mathematics Learning Viewed From Student’s Adaptive Reasoning In SMP Negeri 1 Surakarta.

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

By:

APRILIA ARISTTYANI
A 410 090 2s8

Approved to be Examined by the Consultant;

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 :

l.

Dra. N. Setyaningsih, M.Si

t Rita P. Khotimah,

M.Sc.

3. Dr. H. Sumardi, M.Si

Surakarta.
Muhammadiyah University of Suraka rta

Training And Education

#ffis

*'/ r "*"Efr\v
t
iii

sii*l

NIK.547

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

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)

v 
 

 
 

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.
vi 

 

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.

vii 
 

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

viii 
 

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

xii

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

xiii

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

xiv

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

xv

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

xvi

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.
 
 

xvii 
 

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

ix

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

x

CHAPTER V: CONCLUSIONS, IMPLICATIONS AND SUGGESTIONS
A. Conclusions........................................................................... 62
B. Implications........................................................................... 63
C. Suggestions ........................................................................... 64
BIBLIOGRAPHY ............................................................................................ 65
ATTACHMENT .............................................................................................. 68

xi