DIFFERENCE OF STUDENTS MATHEMATICAL CONNECTION ABILITY USING REALISTIC MATHEMATICS EDUCATION APPROACH AND PROBLEM POSING APPROACH IN SMP SWASTA KATOLIK ASSISI MEDAN ACADEMIC YEAR 2014/2015.
DIFFERENCE OF STUDENTS′ MATHEMATICAL CONNECTION
ABILITY USING REALISTIC MATHEMATICS EDUCATION
APPROACH AND PROBLEM POSING APPROACH IN
SMP SWASTA K ATOLIK ASSISI MEDAN
ACADEMIC YEAR 2014/2015
by:
Petra Surya Daniel
IDN 4103312022
Mathematics Education Study Program
Thesis
Submitted in Fulfilment of The Requirements for Degree of Sarjana
Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND SCIENCE
UNIVERSITAS NEGERI MEDAN
MEDAN
2014
i
ii
DIFFERENCE OF STUDENTS′ MATHEMATICAL CONNECTION
ABILITY USING REALISTIC MATHEMATICS EDUCATION
APPROACH AND PROBLEM POSING APPROACH IN
SMP SWASTA KATOLIK ASSISI MEDAN
ACADEMIC YEAR 2014/2015
Petra Surya Daniel (IDN 4103312022)
ABSTRACT
This research is quasi-experiment. The purpose of this research was to know if
students’ mathematical connection ability in RME class is different with students’
mathematical connection ability in Problem Posing class at SMP Swasta Katolik
Assisi Medan Academic Year 2014/2015.
Population of this research was all students of SMP Swasta Katolik Assisi Medan.
As sample for this research choosen two class in eighth grade. Class VIII-4 as
experimental class I which taught with RME approach and class VIII-2 as
experimental class II which taught with Problem Posing approach. Each class
consist of 31 students. Collecting data technique of this research was
mathematical connection ability test that was given in the end of learning.
Based on normality test and homogenity test that already done, the data sample
was taken from normal distributed and homogeneous population. From the data
analysis by using t-test with significance level = 0.05, it was obtained that
tcalculated = -1.785 and ttable = 1.670. It means that t calculated < -ttable, then H0 is
rejected and Ha is accepted.
It can be concluded that there is significant difference of students’ mathematical
connection ability in RME approach class and students’ mathematical connection
ability in Problem Posing approach class at SMP Swasta Katolik Assisi Medan.
From the research that has been done, researcher suggest the use of RME
approach and problem posing approach as alternative approach in improving
students’ mathematical connection ability.
iv
PREFACE
Praise and gratitude to the God Almighty for all the blessings of His
grace so this thesis that entitled "Difference of Students’ Mathematical
Connection Ability Using Realistic Mathematics Education Approach and
Problem Posing Approach in SMP Swasta Katolik Assisi Medan Academic Year
2014/1015" can be completed. This thesis is submitted in partial fulfillment of the
requirements for the degree of Sarjana Pendidikan in Mathematics Department,
Mathematics and Natural Science Faculty in Universitas Negeri Medan.
Special gratitude especially from the author goes to the beloved family,
Papi, Dj. D. Matondang (+) and Mami, A. Marpaung, brother Brastian Matondang
and sister Eva Pardede and also for Evan and Cinta for everlasting support,
patience, love, and pray. This thesis dedicated for them.
The author is also grateful to Prof. Dr. Edi Syahputra, M.Pd. as thesis
supervisor which has a lot of spare time and thoughts to assist the author writing
in completing this thesis. Thank you also for Dr. E. Elvis Napitupulu, M.S., Dr.
Izwita Dewi, M.Pd., and Drs. Zul Amry, M.Si. as examiners who gave
constructive suggestion untill this thesis compilation was done. And also for Prof.
Dr. Asmin, M.Pd. as academic counselor that already guide and help the author
for lecture period.
The author would like to say thank you to Prof. Dr. Ibnu Hajar, M. Si. as
rector of Universitas Negeri Medan and employee staff in office of university
head, Prof. Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural
Sciences and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si.,
Drs. Syafari, M.Pd. as Chief of Mathematics Department, Drs. Zul Amry, M.Si. 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.
The author also want to thank Dra. Restia Situmorang as School
Principle in SMP Sw. Katolik Assisi Medan, Drs. R. V. Lingga. as Vice Principle,
v
and R. Sidauruk, S. Pd. as mathematics teacher in eighth grade and also for all
teachers and staff for helping and guidance as research.
Special thanks for great family of BilMath ’10, Abdul, Anggi, Dian, Dwi,
Elfan, Erlin, Kiki, Falni, Lia, Mila, Maria, Meiva, Martyanne, Melin, Nelly,
Surya, Riny Oktora Purba, Rully, Sartika, Sheila, Siti, Wulida, Kak Mimi for all
togetherness during college. And for Josua and Windy as best friends for author.
Special thanks also for friends of PPLT in Pandan, and all partner of SM POUK
Tj.Sari Medan, Kak Melda, Hendro, Sela, Moniq, Lady, Amon, and Deli and for
all friends and people that not mention for their support and pray throughout this
process.
The author realized that this thesis has its shortcomings either in
contents, grammar, or technical writing. Therefore, author hope for constructive
criticism and suggestion from the reader for perfection of this thesis. Hope this
thesis could be useful for further researcher and useful in enrichment the
knowledge.
Medan, September
The author,
Petra Surya Daniel
4103312022
, 2014
vi
CONTENTS
Page
Authentication Sheet
i
Biography
ii
Abstract
iii
Preface
iv
Contents
vi
List of Figure
viii
List of Table
ix
List of Appendices
x
CHAPTER I INTRODUCTION
1
1.1. Background
1
1.2. Problem Identification
8
1.3. Problem Limitation
8
1.4. Problem Formulation
8
1.5. Research Objectives
8
1.6. Research Significance
9
1.7. Operational Definition
9
CHAPTER II LITERATURE REVIEW
11
2.1.
Theoretical Framework
11
2.1.1. Mathematical Connection Ability
11
2.1.2. Realistic Mathematics Education Approach
13
2.1.3. Advantages and Drawbacks of Realistic
Mathematics Education
18
2.1.4. Learning Theory Which Underlies Realistic Mathematics
Education
20
2.1.5. Problem Posing Approach
20
2.1.6. Problem Posing Strategies
21
2.1.7. Advantages and Drawbacks of Problem Posing
22
vii
2.2. Conceptual Framework
23
2.3. Hypothesis
24
CHAPTER III RESEARCH METODOLOGY
25
3.1. Location and Time of Research
25
3.2. Population and Sample
25
3.3. Variable and Research Instrument
25
3.3.1 Research Variable
25
3.3.1.1
Independent Variable
25
3.3.1.2
Dependent Variable
26
3.3.2 Research Instrument
26
3.3.3 Instrument Trial
29
3.4. Design Research
30
3.5. Technique of Data Collection
31
3.6. Technique of Data Analysis
33
3.6.1 Normality Test
33
3.6.2 Homogenity Test
33
3.6.3 Hypothesis Test
33
CHAPTER IV RESULT AND DISCUSSION
35
4.1
Research Result Description
35
4.1.1 Mathematical Connection Ability Test
35
4.1.2 The Description of Mathematical Connection Ability Test
36
Analysis of Research Data
37
4.2.1 Normality Test
37
4.2.2 Homogenity Test
38
4.2.3 Hypothesis Test
39
Research Discussion
41
CHAPTER V CONCLUSION
45
5.1
Conclusion
45
5.2
Suggestion
45
REFERENCES
47
4.2
4.3
ix
LIST OF TABLES
Page
Table 2.1
Step of Realistic Mathematics Education Approach
17
Table 3.1
The Lattice Test of Mathematical Connection Ability
26
Table 3.2
The Scoring Guidelines Test of Mathematical Connection
Ability
26
Table 3.3
Instrument Validiy Result
29
Table 3.4
Criteria of Reliability
30
Table 3.3
Posttest Only Group Design
31
Table 4.1
Descriptive Statistic of Experimental Class I and II
35
Table 4.2
Mean of Mathematical Connection Ability Indicators
36
Table 4.3
Normality Test of Mathematical Connection Ability in
Both Experiment Class
Table 4.4
Table 4.5
38
Homogeneity Test of Mathematical Connection Ability
in Both Experiment Class
39
The Result of Hypothesis Test
41
viii
LIST OF FIGURE
Page
Figure 1.1
Ilustration of City A, B, and C
Figure 1.2
Variations in Students' Answers to the Connection
with Physics
Figure 1.3
4
Variations in Students' Answers to the Connection
with Real Life
Figure 1.4
4
5
Variation of Students' Answers to the Connections
Between Mathematical Topics
5
Figure 2.1
Horizontal Mathematization and Vertical Mathematization 15
Figure 3.1
Flow Chart of Research Procedure
Figure 4.1
Histogram of Minimum Score, Maximum Score, and
Mean in Result of Mathematical Connection Ability Test
32
36
x
LIST OF APPENDICES
Page
Appendix 1
Lesson Plan 1 Experiment Class I (RME)
50
Appendix 2
Lesson Plan 2 Experiment Class I (RME)
55
Appendix 3
Lesson Plan 1 Experiment Class II (PP)
60
Appendix 4
Lesson Plan 2 Experiment Class II (PP)
64
Appendix 5
Students Activity Sheet 1 Experiment Class I (RME)
68
Appendix 6
Students Activity Sheet 2 Experiment Class I (RME)
75
Appendix 7
Students Activity Sheet 1 Experiment Class II (PP)
79
Appendix 8
Students Activity Sheet 1 Experiment Class II (PP)
82
Appendix 9
Lattice of Mathematical Connection Ability Test
85
Appendix 10 Test of Mathematical Connection Ability
86
Appendix 11 Guidelines for Scoring of Mathematical Connection
Ability
88
Appendix 12 Posttest Score
91
Appendix 13 Instrument Validity
92
Appendix 14 Instrument Reliability
96
Appendix 15 Step Using SPSS in Normality Test
98
Appendix 16 Normality Test
100
Appendix 17 Step Using SPSS in Homogeneity Test
101
Appendix 18 Homogeneity Test
103
Appendix 19 Step Using SPSS in Compare Mean Test
104
Appendix 20 Compare Mean Test
106
Appendix 21 r-table Value of Product Moment
107
Appendix 22 t-table Value of t-distribution
108
Appendix 23 Documentation
109
CHAPTER I
INTRODUCTION
1.1. Background
Mathematics is one of the science that has many important roles and
close to human life. Therefore, mathematics became one of the principal subjects
taught in formal education since elementary school level. By learning
mathematics from an early age, students are trained to think critically, systematic,
logical, and creative.
In the book Standar Isi untuk Sekolah Menengah Pertama (BSNP,
2006:140) stated that the aim of mathematical subjects so that students have the
ability to: (1) understanding math concepts, explains the relationship between
concepts and apply the concepts and algorithms, flexibly, accurately, efficiently,
and appropriately, in solving the problem, (2) using the pattern and nature of
reasoning, mathematical manipulation in making generalizations, compile
evidence, or explain mathematical ideas and statements; (3) solving problems that
include the ability to understand the problem, devised a mathematical model,
solve the model and interpret the obtained solution; (4) communicate ideas with
symbols, tables, diagrams, or other media to clarify the situation or problem; (5)
has the respect usefulness of mathematics in life, namely to have curiosity,
concern, and interest in studying mathematics, as well as a tenacious attitude and
confidence in solving problems.
In line with the above, Fauzan and Yerizon (2013) stated:
“Tujuan utama pembelajran matematika di sekolah adalah agar siswa
memiliki kemampuan matematis yang memadai untuk melanjutkan
pendidikan ke jenjang yang lebih tinggi dan untuk menyelesaikan
masalah dalam kehidupan sehari-hari. Kemampuan matematis yang
dimaksud meliputi pemecahan maslah, penalaran, komunikasi, koneksi,
dan representasi matematis, sera kemampuan berpikir tingkat tinggi,
seperti berpikir kritis dan kreatif”.
1
2
Sumarmo (2006) classifies basic math skills in five standards, there are
the ability: (1) to know, understand and apply the concepts, procedures, principles,
and mathematical ideas, (2) mathematical problem solving, (3) mathematical
reasoning; (4) mathematical connection, and (5) mathematical communication.
Mathematical connection ability is one of the basic skills that are
important for students. Widarti (2013) revealed that the mathematical connection
is a skill that must be developed and studied, contextual problem solving activities
are activities that help students to be able to determine the relationship of various
concepts in mathematics and applied mathematics in everyday life.
Most of students usually forget their previous mathematics learning
material. They think that any mathematics material has no connection each other.
In fact, every topic in mathematics has connections and some of them as a
prerequisite for studying other topics. Students are still having trouble connecting
knowledge they have learned previously with their newly learned knowledge. In
other cases, students are lazy to learn math because they assume some
mathematical topics that they studied only a theory and has no use in daily life. In
fact, every subject taught in school mathematics has its benefits and immediate
application in daily life that they may not realize. With connection ability,
students are able to view mathematics as a unified whole. Students will realize
that every mathematical ideas do not stand alone and isolated. NCTM (2000: 64)
argues "when students can connect mathematical ideas, their understanding is
deeper and more lasting". So the connection ability can increase students'
understanding and make that understanding last longer.
Mathematical ideas are not only connected in the mathematics itself, but
also connected to the outside of mathematics. Without realizing it, many human
activities are carried out based on mathematical ideas. Many people who do the
math without realizing that they are working on math. With connection ability,
students will be able to understand and appreciate the useful of mathematics in
their daily life.
In addition there is term known as mahtematics as queen of science and
mathematics as servant of science. From both of the term can be seen that
3
mathematics has an important role in the development and progress of science.
Mathematics is used as a tool or as a way of thinking in science to another. With
connection ability, students will be able to see and understand the connection
between the mathematical ideas with other sciences.
From the above explanation can be seen that with mathematical
connection ability, students can build his understanding of mathematics itself. In
addition they can also find patterns and relationships between mathematics well
with others and with the science or daily life. Upon learning of these relationships,
students can learn math more meaningful. In fact on the field, there are many
students who have the low ability to connect. In a study conducted Yunita (2013)
as well as Nainggolan (2013) showed that the ability of junior high school
students the connection is still low. Nainggolan (2013) stated that students still
have difficulty formulating the connection between math with other subjects.
Initial tests of the eighth grade students of SMP Assisi Medan show
unsatisfactory results. Many students are still having trouble connecting
mathematics in dailly life. In addition they are also still difficulties in making
connections with other subjects, especially physics.
Here are the questions and answers of students to the questions given by
researchers in order to find out the mathematical connection ability students in the
school items, namely:
1.
A rectangular field with a length of 25m and has an area of 200m2. One
afternoon Steven and Joni exercise running around the field.
a. When Steven ran at a constant speed of 1m / s, how many minutes the time
it takes Steven to circumnavigate the field twice?
b. Joni rest after circling the field one time. After checking his watch Johnny
realizes that he may take a minute to circumnavigate the field. What is the
average speed of Joni when running?
c. From the information above, if Joni and Steven collided run the same
distance, who do you think will be the winner? Mention the reason!
4
2.
B
C
A
Figure 1.1 Ilustration of City A, B, and C
In the figure 1.1, city A and city C is 130 km, while the city A and city B is
50 km. Andy plans toward the city C from city A to drive a car. Because the
bridge that connects the city A and 'city C' was broken, Andi rotate past the
'city' B '. Because in all the way to the 'city C' there is no gas station Andi had
to refuel from 'A town'. If Andi’s car spent 1 liter of premium to travel as far
as 15 km, at least how many liters of premium to be charged to his car Andi?
Variance of student’ answer:
1.
Figure 1.2 Variations In Students' Answers To The Connection
With Physics
From the results of the figure 1.2 it can be seen that the students
have difficulty in connecting mathematics with physics in determining
the relationship of distance, speed, and time. Total percentage of
students in the class that have difficulty to connect mathematics with
physics is 66.67%.
5
2.
Figure 1.3 Variations In Students' Answers To The Connection
With Real Life
From the results of the figure 1.3 it can be seen that the students
have difficulty in connecting math to the daily life, that is determining
the race winner based on information about the runner's speed. Total
percentage of students in the class that have difficulty to connect
mathematics with daily life is 40%.
3.
Figure 1.4 Variation Of Students' Answers To The Connections
Between Mathematics Topics
From the results of the figure 1.4 it can be seen that students are
have difficulty connecting Pythagorean theorem to calculate length of
path. Total percentage of students in the class that have difficulty to
6
connect mathematics with daily lifebetween mathematics topics is
46.67%.
Based on the results of interviews with one of the teachers of
mathematics in eighth grade, it is known that most students are able to write down
the information that is known from contextual problem into mathematical form.
But in the settlement, they have difficulty. They did not complete the
mathematical models they have made, but rather to answer questions based on
their daily experiences. It can be said the students have difficulties to connect
math to everyday life.
According to constructivist learning theory, knowledge can not simply
transferred from teacher to the students. Students need to build their own
knowledge. Learning approach that could make active learning and develop
students’ mathematical connection ability are Realistic Mathematics Education
approach and Problem Posing approach. Both of these learning approach use real
context which could help students build their own knowledge.
To develop students’ mathematical connection ability, Realistic
mathematics education have an unique characteristics that is intertwinement.
Realistic mathematics education puts intertwinement between mathematical
concepts as things to be considered in the learning process (Wijaya, 2010: 23).
Further Wijaya (2010) said "through this connection, the study of mathematics is
expected to introduce and build more than one at the same mathematical concepts
(although there is a dominant concept)”. With intertwinement as the main
characteristic of realistic mathematics education, then the mathematical
connection ability of students could be better.
Characteristics of realistic mathematics education, namely: (1) the use of
context, (2) the use of a model for progressive mathematization, (3) utilization of
students' construction, (4) interactivity, and (5) intertwinement. The use of context
means the learning process comes from contextual problems. The use of models in
realistic mathematics education means the use of models and models for. Model
of used in horizontal mathematization, ie to connect to the real problems in the
form of informal mathematical While model for use in vertical mathematization,
7
ie to change the form of the mathematical form of formal or informal to formal
form to the form of formal higher.
Furthermore, in realistic mathematics education students are required to
construct their own knowledge of the problems faced. Because the students
construct their own ideas, then they have the various answers. It can be used to
compare the response of teachers and draw conclusions. The results of the
research Yunita (2013) showed that students’ mathematical connection ability in
realistic mathematics class is better than students’ mathematical connection ability
in conventional class. It means that realistic mathematics education could increase
students’ mathematical connection ability.
Problem posing is learning approach which is the development of
problem solving. In this learning approach, students require to pose problem and
also the solution based on the given situation. The problem that can pose by the
students could be problem from daily life, new problem from given problem, or
problem that similar to given problem. The problem may be worded or re-worded
either before its solution or during the solving process or after it. Problem posing
affects both students’ learning and teachers’ teaching of mathematics (Barlow &
Cates, 2006). Problem posing enable students to reflect their mathematical
perceptions. Problem solving also allows students to connect their mathematical
knowledge and abilities to each other, which helps them develop reasoning and
communicating skills (Kilic, 2013). The result of research by Ramdhani (2012)
showed that problem posing approach could increase mathematical connection
ability of students. This means that problem posing approach has positive impact
to students’ mathematical connection ability.
Based on the above researchers interested in conducting research on
realistic mathematics education and problem posing with the title: “Difference of
Students′ Mathematical Connection Ability Using Realistic Mathematics
Education Approach and Problem Posing Approach In SMP Swasta Katolik
Assisi Medan Academic Year 2014/2015”
8
1.2. Problem Identification
Based on the background of the problems described above, we can
identify issues that are relevant to the study include:
1. Students are still difficulties in connecting between concepts in
mathematics.
2. Students are still difficulties in connecting mathematical concepts
with other subjects.
3. Students are still difficulties in connecting concept mathematics in
daily life.
1.3. Problem Limitation
Seeing the wide scope of the problems identified than the time and ability
to research, the investigator felt the need to limit the issues to be studied in order
to analyze the results of this research can be conducted more in-depth and
focused. Issues that will be examined in this study is limited to mathematical
connection ability of eight grade junior high school students academic year
2014/2015 who are taught with Realistic Mathematics Education approach and
Problem Posing approach.
1.4. Problem Formulation
Based on the background that has been disclosed, the formulation of the
problem in this research are:
Is there any difference of students’ mathematical connection ability
taught using Realistic Mathematics Education approach and Problem Posing
Approach?
1.5. Research Objectives
As for the objectives of this research were: To know any differnce of
students’ mathematical connection ability taught using Realistic Mathematics
Education approach and Problem Posing approach.
9
1.6. Research Significance
After doing this research study is expected to provide significant benefits,
namely:
1.
As an input for teachers and prospective teachers of mathematics concerning
the application of realistic mathematics instruction to increase student
capacity of the mathematical connections.
2.
As hint and enthusiasm for students to increase mathematical connection
ability in mathematics learning.
3.
For information and comparisons to other writers or readers who are
interested in doing similar research.
1.7. Operational Definition
1.
The indicators of students’ mathematical connection ability which will be
measured are:
a. To use connection between mathematical topics
b. To use connection of mathematics to other subject (Physics)
c. To use connection of mathematics to daily life
2.
The syntax of Realistic Mathematics Education approach as follows:
a. Understanding contextual problem
Teacher giving SAS that contain contextual problem and ask the student
to understand the problem
b. Solving contextual problem
Students discuss in their own group to solve the contextual problem.
c. Comparing or discussing answer
Students present their group answer and the other group giving opinion
and choose the best solution.
d. Concluding
Students make summary and conclusion from their activities.
3.
The syntax of Realistic Mathematics Education approach as follows:
a. Giving facts (situation)
Teacher giving situation in SAS.
10
b. Discover problem
Students discover problem that they can met based on given situation in
SAS.
c. Understanding problem
Students doing management of information got from situation and pose
question.
d. Meditate solution
Students discuss alternative solution of their own question.
e. Solving problem
Students discuss their group question and solution with another group.
CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion
Based on the analysis and discussion of research results, then it can be
concluded that there is significant difference of student’s mathematical connection
ability which taught by Realistic Mathematics Education approach (experimental
class I) with Problem Posing approach (experimental class II) at SMP Swasta
Katolik Assisi Medan Academic Year 2014/2015.
For indicator to use connection between mathematical topics and to use
connection of mathematics to other subject, students’ mathematical connection
ability taught using problem posing approach is higher than using realistic
mathematics education approach. For indicator to use connection of mathematics
to daily life, students’ mathematical connection ability taught using realistic
mathematics education approach is higher than using problem posing approach.
5.2 Suggestion
Based on the results of research, then researcher submits some
suggestions, as follows:
1.
Based on mathematical connection indicator that will be achieved, problem
posing approach is more effective than realistic mathematics education
approach with requirement that teacher should be able to manage time
effectively.
2.
Contextual problem that used in realistic mathematics education class should
ask students to do real activity and situation that given in problem posing
class should contain many information that could used by students.
3.
Learning process of mathematics by using Realistic Mathematics Education
approach and Problem Posing approach needs longer time since in its
learning, students receive information from teacher indirectly, so that is
needed preparation and used time effectively in its implementation.
45
46
4.
For further researcher, result and instrument of this research can be used as
consideration to implement Realistic Mathematics Education approach and
Problem Posing approach in different class level and topic.
47
REFERENCES
Alam, B. I., 2012, Peningkatan Kemampuan Pemahaman dan Komunikasi
Matematika Siswa SD Melalui Pendekatan Realistic Mathematics
Education (RME), Seminar Nasional Matematika dan Pendidikan
Matematika FMIPA UNY
Best, J W. And James V. Kahn, 2007, Research In Education: Ninth Edition, New
Delhi: Prentice-Hall of India
BSNP, 2006, Standar Isi Untuk Satuan Pendidikan Dasar dan Menengah, Jakarta
Cai, J, 1995, A Cognitive Analysis of U.S and Chinese Students’ Mathematical
Performance On Tasks Involving Computation, Simple Problem Solving,
and Complex Problem Solving, Journal for Research in Mathematics
Education Monograph series 7, Reston, VA: NCTM
, 2005, U.S and Chinese Teachers’ Knowing, Evaluating, and Constructing
Representation in Mathematics Instruction, Mathematical thinking and
Learning 7(2): 135-169
Daryanto, 2013, Inovasi Pembelajaran Efektif, Bandung: Yrama Widya
Fauzan, A. dan Yerizon, 2013, Pengaruh Pendekatan RME dan Kemandirian
Belajar Terhadap Kemampuan Matematis Siswa, Semirata FMIPA
Universitas Lampung, 7-14
FMIPA UNIMED, 2012, Pedoman Penulisan Proposal dan Skripsi Mahasiswa
Program Studi Kependididkan, FMIPA, Medan
Ghasempour, et.al., 2013, Innovation In Teaching and Learning through Problem
Posing Tasks and Metacognitive Strategies, International Journal of
Pedagogical Innovations 1(1): 53-62
Jaelani, A., 2012, Standar Isi dan Standar Proses Dalam Pembelajaran
Matematika, Seminar Nasional Pendidikan Matematika
Lavy, I and Atara Shriki, 2007, Problem Posing As A Means For Developing
Mathematical Knowledge of Prospective Teachers, Proceedings of the
31st Conference of the International Group for the Psychology of
Mathematics Education (3): 129-136
48
Nainggolan, A.C., 2013, Peningkatan Kemampuan Pemecahan Masalah dan
Koneksi Matematis Siswa Kelas VIII SMP Rayon VII Kotamadya Medan
Melalui P-Pendekatan Matematika Realistik, Thesis, Pascasarjana,
Unimed, Medan
Nainggolan, P., 2009, Pengaruh Pendekatan Matematika Realistik Dan Motivasi
Belajar Siswa Terhadap Kemampuan Pemodelan Matematika Siswa
SMP di Lubuk Pakam TP.2008/2009, Thesis, Pascasarjana, Unimed,
Medan
Nalole, M., 2008, Pembelajaran Pengurangan Pecahan Melalui Pendekatan
Realistik Di Kelas V Sekolah Dasar, INOVASI 5(3): 136-147
Nasution, A.V., 2013, Pengaruh Pendekatan Matematika Realistik Terhadap
Kemampuan Penalaran dan Kemampuan Koneksi Matematis Siswa SD
Negeri Medan, Thesis, Pascasarjana, Unimed, Medan
Nasution, W., 2012, Peningkatan Kemampuan Pemecahan Masalah Matematika
Siswa Sekolah Menengah Pertama Melalui Pendekatan Matematika
Realistik, Thesis, Pascasarjana, Unimed, Medan
NCTM, 2010, Principles and Standards for School Mathematics, Reston, VA:
NCTM
Ramdhani, S, 2012, Pembelajaran Matematika Dengan Pendekatan Problem
Posing Untuk Meningkatkan Kemampuan Pemecahan Masalah dan
Koneksi Matematis Siswa, Thesis, Pascasarjana, UPI, Bandung
Saragih, R. M. B., 2011, Peningkatan Kemampuan Pemecahan Masalah
Matematika Siswa Melalui PendekatanMatematika Realistik, Thesis,
Pascasarjana, Unimed, Medan
Sfard, A., 2012, Why Mathematics? What Mathematics?, The Mathematics
Educator 22(1): 3-16
Silver, E. A, 1995, On mathematical problem posing, For the Learning of
Mathematics 14(1): 19-28
Singer, et.al., 2011, Problem Posing In Mathematics Learning and Teaching: A
Research Agenda, Proceedings of the 35th Conference of the
International Group for the Psychology of Mathematics Education (1):
137-166
Siregar, E and Hartini Nara, 2010, Teori Belajar dan Pembelajaran, Bogor:
Ghalia Indonesia
49
Stoyanova, E, 2003, Extending students understanding of mathematics via
problem posing, Mathematics Teacher 59(2): 32-40
Supardi U., 2013, Aplikasi Statistika Dalam Penelitian: Konsep Statistika yang
Lebih Komprehensif, Jakarta: Smart
Sumarmo, U., 2006, Pembelajaran Keterampilan Membaca Matematika Pada
Siswa Sekolah Menengah, FPMIPA UPI
Sumarmo, U, 2010, Berpikir dan Disposisi Matematik: Apa, Mengapa, dan
Bagaimana Dikembangkan Pada Peserta Didik, FPMIPA UPI
Suryadi, D. dan Turmudi, 2011, Kesetaraan Didactical Design Research (DDR)
Dengan Matematika Realistik Dalam Pengembangan Pembelajaran
Matematika, Seminar Nasional Matematika dan Pendidikan Matematika
UNS 2011, 1-12
Suryanto, et.al, 2010, Sejarah PMRI, Departemen Pendidikan Nasional, Jakarta
Trianto, 2011, Mendesain Model Pembelajaran Inovatif-Progresif, Jakarta:
Kencana
Warwick, J., 2007, Some Reflections on the Teaching of Mathematical Modeling,
The Mathematics Educator 17(1): 32-41
Widarti, A., 2012, Kemampuan Koneksi Matematis Dalam Menyelesaikan
Masalah Kontekstual Ditinjau dari Kemampuan Matematis Siswa,
[Online], Available: http://ejurnal.stkipjb.ac.id/index.php/AS/article/view
File/205/141
Wijaya, A., 2010, Pendidikan Matematika Realistik: Suatu Alternatif Pendekatan
Pembelajaran Matematika, Yogyakarta: Graha Ilmu
Yunita, H. S., 2013, Perbedaan Kemampuan Komunikasi dan Koneksi Matematis
Siswa dengan Pendekatan Matematika Realistik dan Konvensional,
Thesis, Pascasarjana, Unimed, Medan
ABILITY USING REALISTIC MATHEMATICS EDUCATION
APPROACH AND PROBLEM POSING APPROACH IN
SMP SWASTA K ATOLIK ASSISI MEDAN
ACADEMIC YEAR 2014/2015
by:
Petra Surya Daniel
IDN 4103312022
Mathematics Education Study Program
Thesis
Submitted in Fulfilment of The Requirements for Degree of Sarjana
Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND SCIENCE
UNIVERSITAS NEGERI MEDAN
MEDAN
2014
i
ii
DIFFERENCE OF STUDENTS′ MATHEMATICAL CONNECTION
ABILITY USING REALISTIC MATHEMATICS EDUCATION
APPROACH AND PROBLEM POSING APPROACH IN
SMP SWASTA KATOLIK ASSISI MEDAN
ACADEMIC YEAR 2014/2015
Petra Surya Daniel (IDN 4103312022)
ABSTRACT
This research is quasi-experiment. The purpose of this research was to know if
students’ mathematical connection ability in RME class is different with students’
mathematical connection ability in Problem Posing class at SMP Swasta Katolik
Assisi Medan Academic Year 2014/2015.
Population of this research was all students of SMP Swasta Katolik Assisi Medan.
As sample for this research choosen two class in eighth grade. Class VIII-4 as
experimental class I which taught with RME approach and class VIII-2 as
experimental class II which taught with Problem Posing approach. Each class
consist of 31 students. Collecting data technique of this research was
mathematical connection ability test that was given in the end of learning.
Based on normality test and homogenity test that already done, the data sample
was taken from normal distributed and homogeneous population. From the data
analysis by using t-test with significance level = 0.05, it was obtained that
tcalculated = -1.785 and ttable = 1.670. It means that t calculated < -ttable, then H0 is
rejected and Ha is accepted.
It can be concluded that there is significant difference of students’ mathematical
connection ability in RME approach class and students’ mathematical connection
ability in Problem Posing approach class at SMP Swasta Katolik Assisi Medan.
From the research that has been done, researcher suggest the use of RME
approach and problem posing approach as alternative approach in improving
students’ mathematical connection ability.
iv
PREFACE
Praise and gratitude to the God Almighty for all the blessings of His
grace so this thesis that entitled "Difference of Students’ Mathematical
Connection Ability Using Realistic Mathematics Education Approach and
Problem Posing Approach in SMP Swasta Katolik Assisi Medan Academic Year
2014/1015" can be completed. This thesis is submitted in partial fulfillment of the
requirements for the degree of Sarjana Pendidikan in Mathematics Department,
Mathematics and Natural Science Faculty in Universitas Negeri Medan.
Special gratitude especially from the author goes to the beloved family,
Papi, Dj. D. Matondang (+) and Mami, A. Marpaung, brother Brastian Matondang
and sister Eva Pardede and also for Evan and Cinta for everlasting support,
patience, love, and pray. This thesis dedicated for them.
The author is also grateful to Prof. Dr. Edi Syahputra, M.Pd. as thesis
supervisor which has a lot of spare time and thoughts to assist the author writing
in completing this thesis. Thank you also for Dr. E. Elvis Napitupulu, M.S., Dr.
Izwita Dewi, M.Pd., and Drs. Zul Amry, M.Si. as examiners who gave
constructive suggestion untill this thesis compilation was done. And also for Prof.
Dr. Asmin, M.Pd. as academic counselor that already guide and help the author
for lecture period.
The author would like to say thank you to Prof. Dr. Ibnu Hajar, M. Si. as
rector of Universitas Negeri Medan and employee staff in office of university
head, Prof. Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural
Sciences and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si.,
Drs. Syafari, M.Pd. as Chief of Mathematics Department, Drs. Zul Amry, M.Si. 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.
The author also want to thank Dra. Restia Situmorang as School
Principle in SMP Sw. Katolik Assisi Medan, Drs. R. V. Lingga. as Vice Principle,
v
and R. Sidauruk, S. Pd. as mathematics teacher in eighth grade and also for all
teachers and staff for helping and guidance as research.
Special thanks for great family of BilMath ’10, Abdul, Anggi, Dian, Dwi,
Elfan, Erlin, Kiki, Falni, Lia, Mila, Maria, Meiva, Martyanne, Melin, Nelly,
Surya, Riny Oktora Purba, Rully, Sartika, Sheila, Siti, Wulida, Kak Mimi for all
togetherness during college. And for Josua and Windy as best friends for author.
Special thanks also for friends of PPLT in Pandan, and all partner of SM POUK
Tj.Sari Medan, Kak Melda, Hendro, Sela, Moniq, Lady, Amon, and Deli and for
all friends and people that not mention for their support and pray throughout this
process.
The author realized that this thesis has its shortcomings either in
contents, grammar, or technical writing. Therefore, author hope for constructive
criticism and suggestion from the reader for perfection of this thesis. Hope this
thesis could be useful for further researcher and useful in enrichment the
knowledge.
Medan, September
The author,
Petra Surya Daniel
4103312022
, 2014
vi
CONTENTS
Page
Authentication Sheet
i
Biography
ii
Abstract
iii
Preface
iv
Contents
vi
List of Figure
viii
List of Table
ix
List of Appendices
x
CHAPTER I INTRODUCTION
1
1.1. Background
1
1.2. Problem Identification
8
1.3. Problem Limitation
8
1.4. Problem Formulation
8
1.5. Research Objectives
8
1.6. Research Significance
9
1.7. Operational Definition
9
CHAPTER II LITERATURE REVIEW
11
2.1.
Theoretical Framework
11
2.1.1. Mathematical Connection Ability
11
2.1.2. Realistic Mathematics Education Approach
13
2.1.3. Advantages and Drawbacks of Realistic
Mathematics Education
18
2.1.4. Learning Theory Which Underlies Realistic Mathematics
Education
20
2.1.5. Problem Posing Approach
20
2.1.6. Problem Posing Strategies
21
2.1.7. Advantages and Drawbacks of Problem Posing
22
vii
2.2. Conceptual Framework
23
2.3. Hypothesis
24
CHAPTER III RESEARCH METODOLOGY
25
3.1. Location and Time of Research
25
3.2. Population and Sample
25
3.3. Variable and Research Instrument
25
3.3.1 Research Variable
25
3.3.1.1
Independent Variable
25
3.3.1.2
Dependent Variable
26
3.3.2 Research Instrument
26
3.3.3 Instrument Trial
29
3.4. Design Research
30
3.5. Technique of Data Collection
31
3.6. Technique of Data Analysis
33
3.6.1 Normality Test
33
3.6.2 Homogenity Test
33
3.6.3 Hypothesis Test
33
CHAPTER IV RESULT AND DISCUSSION
35
4.1
Research Result Description
35
4.1.1 Mathematical Connection Ability Test
35
4.1.2 The Description of Mathematical Connection Ability Test
36
Analysis of Research Data
37
4.2.1 Normality Test
37
4.2.2 Homogenity Test
38
4.2.3 Hypothesis Test
39
Research Discussion
41
CHAPTER V CONCLUSION
45
5.1
Conclusion
45
5.2
Suggestion
45
REFERENCES
47
4.2
4.3
ix
LIST OF TABLES
Page
Table 2.1
Step of Realistic Mathematics Education Approach
17
Table 3.1
The Lattice Test of Mathematical Connection Ability
26
Table 3.2
The Scoring Guidelines Test of Mathematical Connection
Ability
26
Table 3.3
Instrument Validiy Result
29
Table 3.4
Criteria of Reliability
30
Table 3.3
Posttest Only Group Design
31
Table 4.1
Descriptive Statistic of Experimental Class I and II
35
Table 4.2
Mean of Mathematical Connection Ability Indicators
36
Table 4.3
Normality Test of Mathematical Connection Ability in
Both Experiment Class
Table 4.4
Table 4.5
38
Homogeneity Test of Mathematical Connection Ability
in Both Experiment Class
39
The Result of Hypothesis Test
41
viii
LIST OF FIGURE
Page
Figure 1.1
Ilustration of City A, B, and C
Figure 1.2
Variations in Students' Answers to the Connection
with Physics
Figure 1.3
4
Variations in Students' Answers to the Connection
with Real Life
Figure 1.4
4
5
Variation of Students' Answers to the Connections
Between Mathematical Topics
5
Figure 2.1
Horizontal Mathematization and Vertical Mathematization 15
Figure 3.1
Flow Chart of Research Procedure
Figure 4.1
Histogram of Minimum Score, Maximum Score, and
Mean in Result of Mathematical Connection Ability Test
32
36
x
LIST OF APPENDICES
Page
Appendix 1
Lesson Plan 1 Experiment Class I (RME)
50
Appendix 2
Lesson Plan 2 Experiment Class I (RME)
55
Appendix 3
Lesson Plan 1 Experiment Class II (PP)
60
Appendix 4
Lesson Plan 2 Experiment Class II (PP)
64
Appendix 5
Students Activity Sheet 1 Experiment Class I (RME)
68
Appendix 6
Students Activity Sheet 2 Experiment Class I (RME)
75
Appendix 7
Students Activity Sheet 1 Experiment Class II (PP)
79
Appendix 8
Students Activity Sheet 1 Experiment Class II (PP)
82
Appendix 9
Lattice of Mathematical Connection Ability Test
85
Appendix 10 Test of Mathematical Connection Ability
86
Appendix 11 Guidelines for Scoring of Mathematical Connection
Ability
88
Appendix 12 Posttest Score
91
Appendix 13 Instrument Validity
92
Appendix 14 Instrument Reliability
96
Appendix 15 Step Using SPSS in Normality Test
98
Appendix 16 Normality Test
100
Appendix 17 Step Using SPSS in Homogeneity Test
101
Appendix 18 Homogeneity Test
103
Appendix 19 Step Using SPSS in Compare Mean Test
104
Appendix 20 Compare Mean Test
106
Appendix 21 r-table Value of Product Moment
107
Appendix 22 t-table Value of t-distribution
108
Appendix 23 Documentation
109
CHAPTER I
INTRODUCTION
1.1. Background
Mathematics is one of the science that has many important roles and
close to human life. Therefore, mathematics became one of the principal subjects
taught in formal education since elementary school level. By learning
mathematics from an early age, students are trained to think critically, systematic,
logical, and creative.
In the book Standar Isi untuk Sekolah Menengah Pertama (BSNP,
2006:140) stated that the aim of mathematical subjects so that students have the
ability to: (1) understanding math concepts, explains the relationship between
concepts and apply the concepts and algorithms, flexibly, accurately, efficiently,
and appropriately, in solving the problem, (2) using the pattern and nature of
reasoning, mathematical manipulation in making generalizations, compile
evidence, or explain mathematical ideas and statements; (3) solving problems that
include the ability to understand the problem, devised a mathematical model,
solve the model and interpret the obtained solution; (4) communicate ideas with
symbols, tables, diagrams, or other media to clarify the situation or problem; (5)
has the respect usefulness of mathematics in life, namely to have curiosity,
concern, and interest in studying mathematics, as well as a tenacious attitude and
confidence in solving problems.
In line with the above, Fauzan and Yerizon (2013) stated:
“Tujuan utama pembelajran matematika di sekolah adalah agar siswa
memiliki kemampuan matematis yang memadai untuk melanjutkan
pendidikan ke jenjang yang lebih tinggi dan untuk menyelesaikan
masalah dalam kehidupan sehari-hari. Kemampuan matematis yang
dimaksud meliputi pemecahan maslah, penalaran, komunikasi, koneksi,
dan representasi matematis, sera kemampuan berpikir tingkat tinggi,
seperti berpikir kritis dan kreatif”.
1
2
Sumarmo (2006) classifies basic math skills in five standards, there are
the ability: (1) to know, understand and apply the concepts, procedures, principles,
and mathematical ideas, (2) mathematical problem solving, (3) mathematical
reasoning; (4) mathematical connection, and (5) mathematical communication.
Mathematical connection ability is one of the basic skills that are
important for students. Widarti (2013) revealed that the mathematical connection
is a skill that must be developed and studied, contextual problem solving activities
are activities that help students to be able to determine the relationship of various
concepts in mathematics and applied mathematics in everyday life.
Most of students usually forget their previous mathematics learning
material. They think that any mathematics material has no connection each other.
In fact, every topic in mathematics has connections and some of them as a
prerequisite for studying other topics. Students are still having trouble connecting
knowledge they have learned previously with their newly learned knowledge. In
other cases, students are lazy to learn math because they assume some
mathematical topics that they studied only a theory and has no use in daily life. In
fact, every subject taught in school mathematics has its benefits and immediate
application in daily life that they may not realize. With connection ability,
students are able to view mathematics as a unified whole. Students will realize
that every mathematical ideas do not stand alone and isolated. NCTM (2000: 64)
argues "when students can connect mathematical ideas, their understanding is
deeper and more lasting". So the connection ability can increase students'
understanding and make that understanding last longer.
Mathematical ideas are not only connected in the mathematics itself, but
also connected to the outside of mathematics. Without realizing it, many human
activities are carried out based on mathematical ideas. Many people who do the
math without realizing that they are working on math. With connection ability,
students will be able to understand and appreciate the useful of mathematics in
their daily life.
In addition there is term known as mahtematics as queen of science and
mathematics as servant of science. From both of the term can be seen that
3
mathematics has an important role in the development and progress of science.
Mathematics is used as a tool or as a way of thinking in science to another. With
connection ability, students will be able to see and understand the connection
between the mathematical ideas with other sciences.
From the above explanation can be seen that with mathematical
connection ability, students can build his understanding of mathematics itself. In
addition they can also find patterns and relationships between mathematics well
with others and with the science or daily life. Upon learning of these relationships,
students can learn math more meaningful. In fact on the field, there are many
students who have the low ability to connect. In a study conducted Yunita (2013)
as well as Nainggolan (2013) showed that the ability of junior high school
students the connection is still low. Nainggolan (2013) stated that students still
have difficulty formulating the connection between math with other subjects.
Initial tests of the eighth grade students of SMP Assisi Medan show
unsatisfactory results. Many students are still having trouble connecting
mathematics in dailly life. In addition they are also still difficulties in making
connections with other subjects, especially physics.
Here are the questions and answers of students to the questions given by
researchers in order to find out the mathematical connection ability students in the
school items, namely:
1.
A rectangular field with a length of 25m and has an area of 200m2. One
afternoon Steven and Joni exercise running around the field.
a. When Steven ran at a constant speed of 1m / s, how many minutes the time
it takes Steven to circumnavigate the field twice?
b. Joni rest after circling the field one time. After checking his watch Johnny
realizes that he may take a minute to circumnavigate the field. What is the
average speed of Joni when running?
c. From the information above, if Joni and Steven collided run the same
distance, who do you think will be the winner? Mention the reason!
4
2.
B
C
A
Figure 1.1 Ilustration of City A, B, and C
In the figure 1.1, city A and city C is 130 km, while the city A and city B is
50 km. Andy plans toward the city C from city A to drive a car. Because the
bridge that connects the city A and 'city C' was broken, Andi rotate past the
'city' B '. Because in all the way to the 'city C' there is no gas station Andi had
to refuel from 'A town'. If Andi’s car spent 1 liter of premium to travel as far
as 15 km, at least how many liters of premium to be charged to his car Andi?
Variance of student’ answer:
1.
Figure 1.2 Variations In Students' Answers To The Connection
With Physics
From the results of the figure 1.2 it can be seen that the students
have difficulty in connecting mathematics with physics in determining
the relationship of distance, speed, and time. Total percentage of
students in the class that have difficulty to connect mathematics with
physics is 66.67%.
5
2.
Figure 1.3 Variations In Students' Answers To The Connection
With Real Life
From the results of the figure 1.3 it can be seen that the students
have difficulty in connecting math to the daily life, that is determining
the race winner based on information about the runner's speed. Total
percentage of students in the class that have difficulty to connect
mathematics with daily life is 40%.
3.
Figure 1.4 Variation Of Students' Answers To The Connections
Between Mathematics Topics
From the results of the figure 1.4 it can be seen that students are
have difficulty connecting Pythagorean theorem to calculate length of
path. Total percentage of students in the class that have difficulty to
6
connect mathematics with daily lifebetween mathematics topics is
46.67%.
Based on the results of interviews with one of the teachers of
mathematics in eighth grade, it is known that most students are able to write down
the information that is known from contextual problem into mathematical form.
But in the settlement, they have difficulty. They did not complete the
mathematical models they have made, but rather to answer questions based on
their daily experiences. It can be said the students have difficulties to connect
math to everyday life.
According to constructivist learning theory, knowledge can not simply
transferred from teacher to the students. Students need to build their own
knowledge. Learning approach that could make active learning and develop
students’ mathematical connection ability are Realistic Mathematics Education
approach and Problem Posing approach. Both of these learning approach use real
context which could help students build their own knowledge.
To develop students’ mathematical connection ability, Realistic
mathematics education have an unique characteristics that is intertwinement.
Realistic mathematics education puts intertwinement between mathematical
concepts as things to be considered in the learning process (Wijaya, 2010: 23).
Further Wijaya (2010) said "through this connection, the study of mathematics is
expected to introduce and build more than one at the same mathematical concepts
(although there is a dominant concept)”. With intertwinement as the main
characteristic of realistic mathematics education, then the mathematical
connection ability of students could be better.
Characteristics of realistic mathematics education, namely: (1) the use of
context, (2) the use of a model for progressive mathematization, (3) utilization of
students' construction, (4) interactivity, and (5) intertwinement. The use of context
means the learning process comes from contextual problems. The use of models in
realistic mathematics education means the use of models and models for. Model
of used in horizontal mathematization, ie to connect to the real problems in the
form of informal mathematical While model for use in vertical mathematization,
7
ie to change the form of the mathematical form of formal or informal to formal
form to the form of formal higher.
Furthermore, in realistic mathematics education students are required to
construct their own knowledge of the problems faced. Because the students
construct their own ideas, then they have the various answers. It can be used to
compare the response of teachers and draw conclusions. The results of the
research Yunita (2013) showed that students’ mathematical connection ability in
realistic mathematics class is better than students’ mathematical connection ability
in conventional class. It means that realistic mathematics education could increase
students’ mathematical connection ability.
Problem posing is learning approach which is the development of
problem solving. In this learning approach, students require to pose problem and
also the solution based on the given situation. The problem that can pose by the
students could be problem from daily life, new problem from given problem, or
problem that similar to given problem. The problem may be worded or re-worded
either before its solution or during the solving process or after it. Problem posing
affects both students’ learning and teachers’ teaching of mathematics (Barlow &
Cates, 2006). Problem posing enable students to reflect their mathematical
perceptions. Problem solving also allows students to connect their mathematical
knowledge and abilities to each other, which helps them develop reasoning and
communicating skills (Kilic, 2013). The result of research by Ramdhani (2012)
showed that problem posing approach could increase mathematical connection
ability of students. This means that problem posing approach has positive impact
to students’ mathematical connection ability.
Based on the above researchers interested in conducting research on
realistic mathematics education and problem posing with the title: “Difference of
Students′ Mathematical Connection Ability Using Realistic Mathematics
Education Approach and Problem Posing Approach In SMP Swasta Katolik
Assisi Medan Academic Year 2014/2015”
8
1.2. Problem Identification
Based on the background of the problems described above, we can
identify issues that are relevant to the study include:
1. Students are still difficulties in connecting between concepts in
mathematics.
2. Students are still difficulties in connecting mathematical concepts
with other subjects.
3. Students are still difficulties in connecting concept mathematics in
daily life.
1.3. Problem Limitation
Seeing the wide scope of the problems identified than the time and ability
to research, the investigator felt the need to limit the issues to be studied in order
to analyze the results of this research can be conducted more in-depth and
focused. Issues that will be examined in this study is limited to mathematical
connection ability of eight grade junior high school students academic year
2014/2015 who are taught with Realistic Mathematics Education approach and
Problem Posing approach.
1.4. Problem Formulation
Based on the background that has been disclosed, the formulation of the
problem in this research are:
Is there any difference of students’ mathematical connection ability
taught using Realistic Mathematics Education approach and Problem Posing
Approach?
1.5. Research Objectives
As for the objectives of this research were: To know any differnce of
students’ mathematical connection ability taught using Realistic Mathematics
Education approach and Problem Posing approach.
9
1.6. Research Significance
After doing this research study is expected to provide significant benefits,
namely:
1.
As an input for teachers and prospective teachers of mathematics concerning
the application of realistic mathematics instruction to increase student
capacity of the mathematical connections.
2.
As hint and enthusiasm for students to increase mathematical connection
ability in mathematics learning.
3.
For information and comparisons to other writers or readers who are
interested in doing similar research.
1.7. Operational Definition
1.
The indicators of students’ mathematical connection ability which will be
measured are:
a. To use connection between mathematical topics
b. To use connection of mathematics to other subject (Physics)
c. To use connection of mathematics to daily life
2.
The syntax of Realistic Mathematics Education approach as follows:
a. Understanding contextual problem
Teacher giving SAS that contain contextual problem and ask the student
to understand the problem
b. Solving contextual problem
Students discuss in their own group to solve the contextual problem.
c. Comparing or discussing answer
Students present their group answer and the other group giving opinion
and choose the best solution.
d. Concluding
Students make summary and conclusion from their activities.
3.
The syntax of Realistic Mathematics Education approach as follows:
a. Giving facts (situation)
Teacher giving situation in SAS.
10
b. Discover problem
Students discover problem that they can met based on given situation in
SAS.
c. Understanding problem
Students doing management of information got from situation and pose
question.
d. Meditate solution
Students discuss alternative solution of their own question.
e. Solving problem
Students discuss their group question and solution with another group.
CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion
Based on the analysis and discussion of research results, then it can be
concluded that there is significant difference of student’s mathematical connection
ability which taught by Realistic Mathematics Education approach (experimental
class I) with Problem Posing approach (experimental class II) at SMP Swasta
Katolik Assisi Medan Academic Year 2014/2015.
For indicator to use connection between mathematical topics and to use
connection of mathematics to other subject, students’ mathematical connection
ability taught using problem posing approach is higher than using realistic
mathematics education approach. For indicator to use connection of mathematics
to daily life, students’ mathematical connection ability taught using realistic
mathematics education approach is higher than using problem posing approach.
5.2 Suggestion
Based on the results of research, then researcher submits some
suggestions, as follows:
1.
Based on mathematical connection indicator that will be achieved, problem
posing approach is more effective than realistic mathematics education
approach with requirement that teacher should be able to manage time
effectively.
2.
Contextual problem that used in realistic mathematics education class should
ask students to do real activity and situation that given in problem posing
class should contain many information that could used by students.
3.
Learning process of mathematics by using Realistic Mathematics Education
approach and Problem Posing approach needs longer time since in its
learning, students receive information from teacher indirectly, so that is
needed preparation and used time effectively in its implementation.
45
46
4.
For further researcher, result and instrument of this research can be used as
consideration to implement Realistic Mathematics Education approach and
Problem Posing approach in different class level and topic.
47
REFERENCES
Alam, B. I., 2012, Peningkatan Kemampuan Pemahaman dan Komunikasi
Matematika Siswa SD Melalui Pendekatan Realistic Mathematics
Education (RME), Seminar Nasional Matematika dan Pendidikan
Matematika FMIPA UNY
Best, J W. And James V. Kahn, 2007, Research In Education: Ninth Edition, New
Delhi: Prentice-Hall of India
BSNP, 2006, Standar Isi Untuk Satuan Pendidikan Dasar dan Menengah, Jakarta
Cai, J, 1995, A Cognitive Analysis of U.S and Chinese Students’ Mathematical
Performance On Tasks Involving Computation, Simple Problem Solving,
and Complex Problem Solving, Journal for Research in Mathematics
Education Monograph series 7, Reston, VA: NCTM
, 2005, U.S and Chinese Teachers’ Knowing, Evaluating, and Constructing
Representation in Mathematics Instruction, Mathematical thinking and
Learning 7(2): 135-169
Daryanto, 2013, Inovasi Pembelajaran Efektif, Bandung: Yrama Widya
Fauzan, A. dan Yerizon, 2013, Pengaruh Pendekatan RME dan Kemandirian
Belajar Terhadap Kemampuan Matematis Siswa, Semirata FMIPA
Universitas Lampung, 7-14
FMIPA UNIMED, 2012, Pedoman Penulisan Proposal dan Skripsi Mahasiswa
Program Studi Kependididkan, FMIPA, Medan
Ghasempour, et.al., 2013, Innovation In Teaching and Learning through Problem
Posing Tasks and Metacognitive Strategies, International Journal of
Pedagogical Innovations 1(1): 53-62
Jaelani, A., 2012, Standar Isi dan Standar Proses Dalam Pembelajaran
Matematika, Seminar Nasional Pendidikan Matematika
Lavy, I and Atara Shriki, 2007, Problem Posing As A Means For Developing
Mathematical Knowledge of Prospective Teachers, Proceedings of the
31st Conference of the International Group for the Psychology of
Mathematics Education (3): 129-136
48
Nainggolan, A.C., 2013, Peningkatan Kemampuan Pemecahan Masalah dan
Koneksi Matematis Siswa Kelas VIII SMP Rayon VII Kotamadya Medan
Melalui P-Pendekatan Matematika Realistik, Thesis, Pascasarjana,
Unimed, Medan
Nainggolan, P., 2009, Pengaruh Pendekatan Matematika Realistik Dan Motivasi
Belajar Siswa Terhadap Kemampuan Pemodelan Matematika Siswa
SMP di Lubuk Pakam TP.2008/2009, Thesis, Pascasarjana, Unimed,
Medan
Nalole, M., 2008, Pembelajaran Pengurangan Pecahan Melalui Pendekatan
Realistik Di Kelas V Sekolah Dasar, INOVASI 5(3): 136-147
Nasution, A.V., 2013, Pengaruh Pendekatan Matematika Realistik Terhadap
Kemampuan Penalaran dan Kemampuan Koneksi Matematis Siswa SD
Negeri Medan, Thesis, Pascasarjana, Unimed, Medan
Nasution, W., 2012, Peningkatan Kemampuan Pemecahan Masalah Matematika
Siswa Sekolah Menengah Pertama Melalui Pendekatan Matematika
Realistik, Thesis, Pascasarjana, Unimed, Medan
NCTM, 2010, Principles and Standards for School Mathematics, Reston, VA:
NCTM
Ramdhani, S, 2012, Pembelajaran Matematika Dengan Pendekatan Problem
Posing Untuk Meningkatkan Kemampuan Pemecahan Masalah dan
Koneksi Matematis Siswa, Thesis, Pascasarjana, UPI, Bandung
Saragih, R. M. B., 2011, Peningkatan Kemampuan Pemecahan Masalah
Matematika Siswa Melalui PendekatanMatematika Realistik, Thesis,
Pascasarjana, Unimed, Medan
Sfard, A., 2012, Why Mathematics? What Mathematics?, The Mathematics
Educator 22(1): 3-16
Silver, E. A, 1995, On mathematical problem posing, For the Learning of
Mathematics 14(1): 19-28
Singer, et.al., 2011, Problem Posing In Mathematics Learning and Teaching: A
Research Agenda, Proceedings of the 35th Conference of the
International Group for the Psychology of Mathematics Education (1):
137-166
Siregar, E and Hartini Nara, 2010, Teori Belajar dan Pembelajaran, Bogor:
Ghalia Indonesia
49
Stoyanova, E, 2003, Extending students understanding of mathematics via
problem posing, Mathematics Teacher 59(2): 32-40
Supardi U., 2013, Aplikasi Statistika Dalam Penelitian: Konsep Statistika yang
Lebih Komprehensif, Jakarta: Smart
Sumarmo, U., 2006, Pembelajaran Keterampilan Membaca Matematika Pada
Siswa Sekolah Menengah, FPMIPA UPI
Sumarmo, U, 2010, Berpikir dan Disposisi Matematik: Apa, Mengapa, dan
Bagaimana Dikembangkan Pada Peserta Didik, FPMIPA UPI
Suryadi, D. dan Turmudi, 2011, Kesetaraan Didactical Design Research (DDR)
Dengan Matematika Realistik Dalam Pengembangan Pembelajaran
Matematika, Seminar Nasional Matematika dan Pendidikan Matematika
UNS 2011, 1-12
Suryanto, et.al, 2010, Sejarah PMRI, Departemen Pendidikan Nasional, Jakarta
Trianto, 2011, Mendesain Model Pembelajaran Inovatif-Progresif, Jakarta:
Kencana
Warwick, J., 2007, Some Reflections on the Teaching of Mathematical Modeling,
The Mathematics Educator 17(1): 32-41
Widarti, A., 2012, Kemampuan Koneksi Matematis Dalam Menyelesaikan
Masalah Kontekstual Ditinjau dari Kemampuan Matematis Siswa,
[Online], Available: http://ejurnal.stkipjb.ac.id/index.php/AS/article/view
File/205/141
Wijaya, A., 2010, Pendidikan Matematika Realistik: Suatu Alternatif Pendekatan
Pembelajaran Matematika, Yogyakarta: Graha Ilmu
Yunita, H. S., 2013, Perbedaan Kemampuan Komunikasi dan Koneksi Matematis
Siswa dengan Pendekatan Matematika Realistik dan Konvensional,
Thesis, Pascasarjana, Unimed, Medan