THE INCREASING OF PROBLEM SOLVING MATHEMATICAL ABILITY OF STUDENTS THROUGH REALISTIC MATHEMATICS EDUCATION APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM TERPADU OF MEDAN ACADEMIC YEAR 2012/2013.
THE INCREASING OF PROBLEM SOLVING MATHEMATICAL
ABILITY OF STUDENTS’ THROUGH REALISTIC MATHEMATICS
EDUCATION APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM
TERPADU
OF MEDAN ACADEMIC YEAR 2012/2013
By:
Selvi Septiani Harahap
ID. Number 408 611 007
Mathematics Education Study Program
A THESIS
Submitted to fulfill the requirement for the degree of
Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATIC AND SCIENCE
STATE UNIVERSITY OF MEDAN
MEDAN
2013
BIBLIOGRAPHY
Selvi Septiani Harahap was born in Medan, September 24th 1989. Writer’s
father name is (Alm) Drs. H. Haridan Harahap and mother’s name is Hotnaria
Daulay. She is the first child from three children. She has two brothers. In 1995,
writer studied in primary school SD Inpres number 105288 Sei Rotan and was
graduated in 2001. In 2001, the writer continued her study in junior high school
MTS Negeri 2 Medan and was graduated in 2004. In 2004, writer also continued
her study in senior high school MAN 1 Medan and was graduated in 2007.
In 2008, the writer was accepted in Mathematics Education of Bilingual
class, Faculty of Mathematic and Natural Science, State University of Medan.
During the study.
ACKNOWLEDGEMENT
Praise be to Allah SWT, most gracious, most merciful and master of the
judgment. Thanks are to Allah who gave the strength and ability to the writer, so
that this thesis can be finished. An innovation and greeting to Rasulullah SAW,
who brought people from the darkness into lightness. The title of this research was
“The Increasing of Problem Solving Mathematical Ability Through Realistic
Mathematics Education Approach in VIII Grade at SMP Islam Al-Ulum Terpadu
of Medan Academic Year 2012/2013.” as a partial fulfillment of the requirements
for the degree Sarjana Pendidikan of the mathematic department, Faculty of
Mathematic and Natural Science State University of Medan.
In this occasion, the writer would like to express thank you very much to
her supervisor Prof. Dr. Sahat Saragih, M.Pd for his advice, motivation,
suggestion and guidance to finish this thesis. To her lecturer examinator
Prof.Asmin Panjaitan, M.Pd, Dr.W.Rajagukguk,M.Pd, and Dra. Katrina Samosir,
M.Pd, for their correction with valuable comments to correct the manuscript of
scientific writing, to her academic lecturer Drs. Syafari, M.Pd for his advice
support to her.
The writer also would like to express thank you to Mr. Prof.Ibnu
Hajar,M.Si as ahead of university and staff in office of university head, to Mr.
Prof. Motlan, M.Sc,Ph.D as a dean of mathematic and natural science faculty and
staff in mathematic and natural science faculty, to Mr. Dr Mukhtar,M.Pd as a head
of mathematic department, Mr.Drs. Syafari, M.Pd as ahead of mathematic
education program, Mr. Prof.Dr.Herbert Sipahutar, M.S, M.Sc as a coordinator of
Bilingual program, Mr. Drs.Yasifati Hia,M.Pd as secretary of mathematic
department, Mrs. Dr. IIs Siti Jahro, M.Si as secretary of Bilingual program, and
all staff in mathematic department and Bilingual program to help the writer.
The writer also would like to express thank you to head master of SMP
Islam Al-Ulum Terpadu of Medan Mrs. Nur Rahima S, S.Pd who gave permission
to do the research, to math teacher Mrs. Herlina,S.Pd, Mr. Nurhadi, S.Pd and all
teacher and staff in SMP Islam Al-Ulum Terpadu of Medan that help the writer to
do the research.
The writer also would like to express her deepest love gratitude to her
father (Alm) Drs, H. M. Haridan Harahap, her mother Hj. Hotnaria Daulay, her
brother Imam Al-Rasyid Harahap and Sakti Rizki Fauzi Harahap affectionately
which gave birth and enlarge to writer, gave morale support, material and pray
and so all her family. To her friend Angelica Pardede and lovely all friends in
mathematic bilingual program 2008 thank you very much for your support,
helping to finish this thesis.
The writer has effort as maximal as she can in doing this thesis. But with
her humble heart, the writer hopes construct suggestion and critics from the reader
for perfection this thesis. The writer hopes this thesis can be useful and give many
function to the reader specifically about subject matter which was researched in
this thesis.
Medan,
February 2013
Writer
Selvi Septiani Harahap
THE INCREASING OF PROBLEM SOLVING MATHEMATICAL ABILITY OF
STUDENTS’ THROUGH REALISTIC MATHEMATICS EDUCATION
APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM TERPADU
OF MEDAN ACADEMIC YEAR 2012/2013
Selvi Septiani Harahap (ID. Number 408 611 007)
ABSTRACT
The purpose of this research to know increasing problem solving ability of
students that taught realistic mathematical education approach is better than the
mathematical problem-solving ability of students taught expository approach in VIII
grade at SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013. This type of
research is quasi-experimental research on first (odd) semester of VIII grade SMP Islam
Al-Ulum Terpadu Medan academic year 2012/2013. The population in this research is
all students of VIII grade SMP Islam Al-Ulum Terpadu School of Medan consisting of
118 students. Sample was taken by using random sampling; it means that each class had
the same chance to be sampled. The sample in this study consisted of two classes. The
experiment class in VIII-A was taught by applies Realistic Mathematics Education
(RME) approach and the control class in VIII-B was taught by applies Expository
approach. Research instrument in collecting data in this study were a test and an
observation sheet.
The kinds of test is essay test, contains four questions for pre-test and four
questions for post-test that related to the problem solving about Linear equation two
variables system. The instrument that arranged have legalized by expert validator
namely lecturer and mathematic teachers. Before hypothesis that will be test must be
done normality test and homogeneity test. For normality test used Liliefors normality
test and for homogeneity test is used F-test. From test can get the sample is distributes
normal and homogeneous. Data analysis technique that used T-test formula.
The average of pre test in experiment class is 26.0714 and the average of pre test
in control class is 26.0714. The average of posttest in experiment class is 85.1785 and
the average of post test in control class is 72.5. Analysis result of gain for problem
solving using t testing with significant level α=0.05 for the hypothesis is tcalculate =
3.9861 and ttable = 2.0048 so that -2.0048 < tcalculate < 2.0048, Because of that, the criteria
t-α/2 < tcal < tα/2 is rejected. It means H0 is rejected. So can be concluded, The increasing
problem solving ability that taught by using RME greater than solving math problems
that students taught with Expository approach in linear equation two variables system at
VIII SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013.
ii
TABLE OF CONTENTS
Page
Sheet agreement ........................................................................................ i
Table of contents ....................................................................................... ii
Table list .................................................................................................... iii
List of appendix......................................................................................... iv
Figure list ................................................................................................. v
CHAPTER 1: INTRODUCTION .......................................................... 1
1.1 Background ........................................................................................ 1
1.2 Problem Identification......................................................................... 7
1.3 Problem Limitation ............................................................................. 7
1.4 Problem Formulation .......................................................................... 8
1.5 Research Objectives ........................................................................... 8
1.6 Operational defenition......................................................................... 8
1.7 Benefit of Researh................................................................................ 9
CHAPTER 2: LITERATURE REVIEW .............................................. 10
2.1. Theoretical Background ..................................................................... 10
2.1.1 Mathematical Problem Solving Ability.................................. 10
2.1.2 Understanding of Realistic Mathematics Education approach 17
2.1.3 Principles and Characteristics of RME ................................. 19
2.1.4 Steps of Realistic Mathematics Education ............................. 24
2.1.5 The Excess and Complexity of RME ..................................... 27
2.1.6 Expository Approach.............................................................. 29
2.1.7 The Difference of RME and Expository ................................ 33
2.1.8 The lesson material................................................................. 34
2.2 The Relevant Research ........................................................................ 40
2.3 Conceptual Framework ....................................................................... 41
2.4 Hypothesis ........................................................................................... 42
iii
CHAPTER 3: RESEARCH METHODS .............................................. 43
3.1 Type of research .................................................................................. 43
3.2 Place and Time of research ................................................................. 43
3.3 Population and Sample........................................................................ 43
3.3.1 Population of Research ............................................................. 43
3.3.2 Sample of Research................................................................... 43
3.4 Research Variables .............................................................................. 44
3.5 Research Design ................................................................................. 44
3.6 Research Procedure ............................................................................ 45
3.7 Instrument Analysis Technique .......................................................... 50
3.8. Data Analysis ..................................................................................... 52
1 Hypothesis test ................................................................................ 52
a. Mean score .............................................................................. 52
b. Standard deviation .................................................................. 52
c. Normality test .......................................................................... 53
d. Homogeneity test .................................................................... 54
e. Hypothesis test ........................................................................ 54
CHAPTER 4: RESULT AND DISCUSSION ...................................... 56
4.1 The Result of Problem Solving .......................................................... 56
4.1.1 Pre Test of Experiment and Control classes ................................... 56
4.1.2 Post Test of Experiment and Control Classes .................................. 57
4.1.3 Gain of Experiment and Control Classes ........................................ 59
4.1.4 Normality Testing of Data .............................................................. 61
4.1.5 Homogeniety Testing of Data ......................................................... 62
4.1.6. Hypotesis Testing ........................................................................... 62
4.2 Discussion ......................................................................................... 64
CHAPTER 5 : CONCLUTION AND SUGGESTION ....................... 68
5.1 Conclution .......................................................................................... 68
5.2 Suggestion .......................................................................................... 68
REFERENCES ........................................................................................ 68
Appendix .................................................................................................. 69
TABLE LIST
Page
Table 2.1 Cooperative Learning Phase
12
Table 2.2 Approaches to Cooperative Learning
14
Table 2.3 The Steps of Think Pair Share (TPS)
19
Table 2.4 Calculating of Gaining Score
21
Table 2.5 Example of Giving Gaining Score
22
Table 2.6 Technique of Giving Score For Each Step in Problem Solving
24
Table 3.1 Research Design
33
Table 3.2 Criteria of Student Mastering Level
44
Table 4.1 Pretest result of the first and second experiment classes
46
Table 4.2 Post test result of the first and second experiment classes
47
Table 4.3 Gain of the first and second experiment classes
48
Table 4.4 Result of Normality Testing
50
Table 4.5 Result of Homogeneity Testing
50
Table 4.6 The Result of Hypothesis Testing
52
Table 4.7 Description of Student Misatake for number 1using jigsaw
53
approach
Table 4.8 Description of Student Misatake for number 2 using jigsaw
54
approach
Table 4.9 Description of Student Misatake for number 3 using jigsaw
55
approach
Table 4.10 Description of Student Misatake for number 4 using jigsaw
56
approach
Table 4.11 Description of Student Misatake for number 1using TPS
58
approach
Table 4.12 Description of Student Misatake for number 2using TPS
59
approach
Table 4.13 Description of Student Misatake for number 3using TPS
61
approach
Table 4.14 Description of Student Misatake for number 4using TPS
62
approach
Table 4.15 Level of Problem solving Skills
63
Table 4.16 The average of observation result of learning process
66
FIGURE LIST
Page
Figure 2.1 Jigsaw Teams
15
Figure 2.2 Jigsaw Steps
17
Figure 2.3 Example of prism
26
Figure 2.4 Triangular Prism and its nets
27
Figure 2.5 Dividing Cuboids become Two Triangular Prisms
28
Figure 3.1 Research Procedures Scheme
36
Figure 4.1 Average of pre test, post test and gain
48
Figure 4.2 Level of Problem Solving
64
Figure 4.3 Students Mistake in Understanding Problem Number 2,3,1,and
69
4 using Jigsaw
Figure 4.4 Student Mistake for arranging Strategy using Jigsaw Approach
70
Figure 4.5 Mistake in calculating using Jigsaw
71
Figure 4.6 Mistake in Putting Some Values
71
Figure 4.7 Student’s Mistake for Understanding Problem using TPS
73
Approach
Figure 4.8 Student’s Mistake for Arranging Strategy to Solve Problem
74
Figure 4.9 Student’s Mistake in Implementing the Planning
74
APPENDIX LIST
Page
Appendix 1 First Lesson Plan for Experiment Class A
81
Appendix 2 Second Lesson Plan for Experiment Class A
88
Appendix 3 First Lesson Plan for Experiment Class B
95
Appendix 4 Second Lesson Plan for Experiment Class B
101
Appendix 5 Student Work Sheet I
107
Appendix 6 Student Work Sheet II
113
Appendix 7 Latticework of Pre-test
119
Appendix 8 Latticework of Post-test
120
Appendix 9 Pre-test Question
121
Appendix 10 Alternative Solution of Pre-test
123
Appendix 11 Post-test Question
126
Appendix 12 Alternative Solution of Post-test
128
Appendix 13 Observer Assessment Scale
131
Appendix 14 Validator Assessment Paper
133
Appendix 15 Validator Names
134
Appendix 16 Observation Paper of Learning Process Using Cooperative
135
Learning Jigsaw Approach
Appendix 17 Observation Paper of Teacher Activity for cooperative
137
learning Think Pair Share (TPS) Approach
Appendix 18 Technique of Giving Score For Mathematic Problem
139
Solving
Appendix 19 Validation Analysis of Validator Agreement for Pre Test
140
Appendix 20 Validation Analysis of Validator Agreement for Post Test
142
Appendix 21 Reliability Analysis of Pre Test
144
Appendix 22 Reliability Analysis of Post Test
146
Appendix 23 Pre Test for the First Experiment Class
148
Appendix 24 Pre Test for the Second Experiment Class
150
Appendix 25 Post Test for the First Experiment Class
152
Appendix 26 Post Test for the Second Experiment Class
154
Appendix 27 Pre Test and Post Test Mark for the First and Second
156
Experiment Classes
Appendix 28 Calculation of Normality Testing
157
Appendix 29 Calculation of HomogenietyTesting
161
Appendix 30 Calculation of Gain Score
164
Appendix 31 Calculation of Hypothesis Testing
165
Appendix 31 Documentation of Research
169
CHAPTER I
INTRODUCTION
1.1. Background
Education is one of very important aspects of life. Giving the role of
education is an effort to form a high quality human, then the problem of education
in the spotlight, especially in Indonesia. One of the goals of national development
in the field of education is the intellectual life of the nation and to improve the
quality of Indonesian human. Through improving the quality of education at all
levels of education, which enables its citizens to develop themselves as whole
human beings Indonesia. To realize the national development in the field of
education needed improvement and refinement of education in accordance with
the development of science and technology (Science and Technology).
Mathematics is one of the basic sciences in school curriculum and must be
learned in educational institutions. Based on the data above, Indonesia ranks are
located in 39th of the 41 states and this must be very worrying. This problem must
be improved immediately and be seriously handled because the usefulness of
mathematics and very important both in development thinking, mastery of science
and technology and its role in several other scientific subjects. It is also expressed
by the Daniel Muijs and David Reynolds (2008: 332) which states mathematics is
the main means for developing the ability of logical thinking and higher cognitive
skills in children and plays an important role in several other scientific fields such
as physics, engineering, statistics and others. Therefore, it is necessary teach
students to mastery the mathematics early on creating, face and master modern
technology for globalization era. Then, Cornelius in Abdurrahman (2003: 253)
show several reasons for studying mathematics, namely:
1.
2.
3.
4.
5.
Means of a distinct and logical thinking
Means to solve problems of daily life
Means to know the patterns, relationships and generalization of experience
Means to develop creativity
Means to increase awareness of cultural development.
Based on the above quotation through the learning of mathematics is
expected that students can develop the ability to think, reason, develop creativity,
communicate and present ideas and information and solve problems in daily
activities. According to the National Council of Teacher Mathematics (NCTM)
and its agenda for action in Alfred S. Posamentier Jay Stepelman (1990: 109) state
that problem solving as primary goals for mathematics education and teacher are
urged to:
1.
2.
3.
4.
Create a classroom environment and develop appropriate curricular
materials in which problem solving can flourish
Give priority to identification and analysis of specific problem solving
strategies
Develop examples of good problem
Encourage students to question , experiment, estimate, explore and
suggest explanations
KEMDIKNAS 2006 in http://pmat.uad.ac.id/perkembangan-pembelajaranmatematika-di-indonesia.html then stated:
"The goal of learning mathematics, namely: (1) understand math concepts,
explain the relationship among concepts and apply the concepts or
algorithms in widely, accurate, efficient, and appropriately in problem
solving, (2) using the pattern and characteristics of reasoning, mathematical
manipulations in making generalization, arrange evidence, or explain
mathematical ideas and statements, (3) solve problems that include the
ability to understand the problem, design mathematical model, complete
model and interpreting solution obtained, (4) communicate ideas with
symbols, table, diagrams, or other media to explain the situation and
problem, (5) respect of the usefulness of mathematics in life, which has the
curiosity, attention, and interest in studying mathematics and a competent
attitude and confidence in problem solving.”
From the above statement, one of the aspects emphasized in the goal of
learning mathematics is problem solving ability. It is very important because in
solving the problem usually involves some of the concepts and skills in new
situations or different that in the process possible the students’ learning gain
experience in using knowledge and skills to be applied in problem solving.
Learning of mathematics and its evaluation system have been less provides
an opportunity for students to come up with ideas for students to learn
mathematics. This is because learning is more focused on the teacher (teacher
centered) are generally directly transferring his knowledge to students so that
students become passive. More emphasis on learning outcomes (product) in which
students live using formula rather than emphasizing the process. Thus some
actives to learn mathematic is to be trained in order to solve the problems.
This is also reinforced one of them by the results of The Third International
Mathematics and Science Study (TIMSS) that the junior high school students in
Indonesia are very weak, but pretty good problem solving in procedural
skills. (Al-jupri & kartika). In addition Hudojo (2003: 152) states that teaching
students to solve problems allow students to become more analytical in taking
decisions for life. In other words if a student is trained to resolve problems, the
students were able to make decisions for the students to have skills on how to
gather relevant information, analyze information and realize the need to reexamine the results already obtained. But most of mathematics educators are
concerned about the narrow focus of many schools programs, the limited
treatment of content that they view as important for students, and the lack of
attention given to developing in reasoning and problem solving (Lindquist, 1980:
9).
Furthermore, Tarwiyah (2011) explains that solving problems in
mathematics learning is an approach and goals to be achieved. As an approach,
problem solving is used to discover and understand the material and mathematical
concepts. Meanwhile, as the goal, it is expected that students can identify the
unknown elements, and asked the necessary elements of adequacy, formulating
the problem of everyday situations in mathematics, implement strategies to solve
problems (similar and new problems) within or outside of mathematics, describes
the results as origin of the problem, develop a meaningful mathematical
model. As the implications of the problem-solving skills should be possessed by
all the children who learn mathematics. In learning process, students are passive,
fearful, some are bored and some even feel that mathematics is a terrible
lesson. In other words the students have not responded well to the challenges that
exist in math. As a result, students are not able to be independent and do not know
what to do. It can be concluded that the increase in students ability in solving
mathematical problems have a considerable role for students. However, the
problem-solving is an activity in the learning process has not become a major
activity so that there are many students who find it difficult when faced with
problem solving.
Mathematical problem solving ability has get attention because it is a
necessary capability in learning. Mathematical problem solving ability to
encourage students in meaningful learning and togetherness, but it can help
students in dealing with mathematical problems and issues of everyday life in
general. Weak student math problem-solving ability is not out of lack of
opportunity and not frequently students do problem solving. Mathematical
problems presented in the classroom tend to routine problems. So that the students
are not accustomed to solving problems in determining what is known and what is
asked on the matter and to what to use.
The Causes of low mathematical problem-solving ability is due to intake of
students who have previously not met the standards. Knowledge and experience
of the material previously learned material will affect the learning process
further. This is reinforced by Herman Hudojo statement that: "Studying the
concept B is based on the concept of A, that person may not understand the
concept of B. This means, learning mathematics should be gradual and sequential,
and then based on their learning experience."
From the observation of the junior high school Al-Ulum Islamic Terpadu
Academic Year 2012/2013, students tend not to like math because of lack of
delivery of material related to everyday life so that academic concepts are difficult
to understand. The teachers still teach and learn conventional learning models as a
center of learning where the teacher (teacher cantered). Conventional learning
gives effect to the inactivity of learning actors. Thus resulting to a total mastery of
Mathematics and ultimately affect the competences and learning outcomes of
students in mathematics.
One of the subjects of mathematics involved in this problem is Linear
Equation of Variables system. Students have difficulty in learning the subject
matter of linear equation of variables system, the majority of students are difficult
to understand the concept of the linear equation of variables system. Students are
less able to translate the linear equation of variables system itself in everyday life.
As the initial observations by the author on Islam Al-Ulum Terpadu in VIII class
academic year 2012/2013 that most of the students were unable to resolve the
problem concerning the complete linear equation of variables system. One
problem, the ratio of rika and rido’s money is 3:2, if the amount of their money is
Rp.20.000, their money is the difference? Of course the problem can be regarded
as a social arithmetic. But it would be better if we look as a problem in linear
Equation of variables system. In linear equation of variables system, the problem
above can be seen as a problem with two equations and two unknown
variables. But in fact most students are not able to solve algebra problems
thoroughly.
Based on these observations it can be identified that many mistakes which
made by students at SMP VIII Al-Ulum Islam Terpadu Medan for solving
problem of linear equation two variables system. caused by the weakness of
students in aspects of pouring, declaring, disclosing, or making a model of ideas,
mathematical concepts, and relationships among them into a new mathematical
form variety in the form of words (written text), graphics, tables, diagrams,
drawings, equations (mathematical expression), or a form of concrete (props) and
use them in solving problems with the sort of things are known, asked, then
answered.
In an effort to improve students' problem-solving skills, teachers should
strive to train and familiarize students to the form of problem solving in learning
activities, such as giving students the chance to hold a conversation in order to use
the scientific opinions, conclusions or develop alternative solutions to a
problem. Therefore, teachers need to select appropriate learning approaches to
encourage students to learn to do math problem solving. Make learning math is
boring and students do not think that mathematics is an abstract lesson in class,
the teacher needs to choose a learning approach that requires an active
involvement of students and also develop thinking skills by using the real thing
around them, so that the learning objectives can be achieved. Learning math will
head in the right direction and managed to find out if the characteristics of
mathematics. Mathematics has its own characteristics in terms of both aspects of
competency to be achieved, as well as from the aspect of the material being
studied to support the achievement of competence.
Realistic Mathematics Education (RME) is a learning system based on the
philosophy that one will be able to absorb the subject matter if they can grasp the
meaning of learning. RME is a comprehensive system that consists of five
components, namely the contextual issues, modeling, production and contribution
of students, interactions, linkages. If any parts of the RME intertwined with each
other it will produce effects that exceed the results given in the parts separately
and involve different processes as well, when it is used together to enable the
students to make connections with each other produce. Learning mathematics
using Realistic Mathematics Education approach (RME), which concerned local
conditions (culture or environment or context) shows that students are not afraid
to express their ideas, has begun to dare to give a different problem solving with
their
peers,
grow
their
creativity
in
doing
problem
solving(problem
solving) together.
The purpose of Realistic Mathematics Education is to solve the problems
facing students by linking the material to the real world so that students can solve
problems. This method is cooperative so to enhance cooperation among of
student, all students are guided and directed to an active and creative condition so
that the learning becomes more effective and efficient. Realistic Mathematics
approach is expected to make the students know the importance of mathematics in
everyday life. Learning innovations with Realistic Mathematics approach is
expected to foster a new spirit to be more enterprising students to learn
mathematics so that mathematical problem solving ability of students can be
increased. Based on the above background, the writer is interested in doing
research on "The Increasing of Problem Solving Mathematical Ability That
Taught Realistic Mathematics Education Approach in VIII grade at SMP Islam
Al-Ulum Terpadu of Medan Academic Year 2012/2013"
1.2.Problems Identification
Based on the background of problems it can be identified some problems, as
follows
1. Teachers who taught using teacher centered make students as passive
objects in the study.
2. Many mistakes which made by students in VIII grade at SMP Islam AlUlum
Terpadu Medan for solving problem of linear equation two
variables system.
3. The students are not yet accustomed to solve problems in mathematics
learning in the classroom.
4. Realistic mathematical approach has not been implemented in the school,
in general, teachers tend to prefer the conventional approach in teaching
mathematics.
1.3.Problem Limitation
Seeing the wide scope of issues identified and comparing the ability of the
researcher, the writer feels the need to limits the problems that are examined for
the results in this study that can be performed and directed.
In this study the problem under study is limited to the influence of Realistic
Mathematics Education for mathematical problem solving ability of students the
subject of linear equation of variables system in VIII grade at SMP Islam AlUlum Terpadu Medan Academic Year 2012/2013
1.4.Problem formulation
Dictated by the above problems, the formulation of the problem in the study
is "Is the increasing problem-solving mathematical ability of students that taught
realistic mathematical education approach is better than the mathematical
problem-solving ability of students taught by expository approach in VIII grade at
SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013.”
1.5.Research Objectives
Based on the above problem formulation, the objective of this study is "To
know the increased problem solving abilities of students that taught realistic
mathematical education approach is better than the mathematical problem-solving
ability of students taught by expository approach in VIII grade at SMP Islam AlUlum Terpadu Medan Academic Year 2012/2013.”
1.6.Operational definition
So that the terminology in this study is more clearly so that the objectives
and research directions to be is specific, then the variables are defined as follows:
a. Realistic Mathematics Education is an approach to learning mathematics
that has five characteristics: (1) using contextual problems as a first step,
(2) using a mathematical model developed by students, (3) consider the
contribution of students, (4) optimize the interaction with his students,
students with teachers and other supporting facilities, and (5) consider the
relationship between the topics.
b. Expository approach is a procedure commonly used by teachers in
teaching. The steps are the teachers prepare teaching materials in a
systematic and organized, explaining the subject matter, students are given
the opportunity to ask questions, students are given exercises that work on
the problems of teachers, students and teachers discuss the exercise, then
the teacher give homework.
c. Problem-solving ability is the ability of students in solving mathematical
problems by considering the process of finding answers based on problemsolving steps, namely: (1) understanding the problem, (2) making a plan
strategy, (3) Carrying out the plan (4) Looking back or checking the
answer.
1.7. Benefits of research
This study is expected to be useful:
1. As input material for teachers, especially SMP Islam Al-Ulum Terpadu
Medan is a way to improve students' mathematical problem solving
ability.
2. As input and consideration for prospective teachers in implementing the
teaching and learning activities
3. As input for other researchers to conduct further research. RME learning
implementation is expected to increase student learning outcomes for
mathematics courses
68
CHAPTER V
CONCLUSSION AND SUGGESTION
5.1.
Conclusion
Based on the result research from data analysis, can be obtained some conclusion,
those are
1.
By testing hypothesis using t-test of the gain average in the control and
experiment classes, then can be concluded the increasing of problem solving
mathematical ability students that taught realistic mathematics education
approach is better than the mathematical problem solving ability of students
taught with expository approach on subtopic system of linear equations two
variables in VIII grade at SMP Islam Al-Ulum Terpadu Medan Academic
Year 2012/2013.
2.
Based on the observation of the application of realistic mathematics approach
and expository approach on the subject of system linear equation two
variables the categorized is good.
5.2.
Suggestion
Based on research result, then the suggestions that can be given by the
researchers are:
1.
For math teacher who want to use realistic mathematics education approach,
give more attention to time allocation for each phase so that learning process
can be done better.
2.
For math teacher, realistic mathematics education approach can be used as
alternative learning approach because it can be increase problem solving
ability of student.
3.
For math teacher who want to give some topic to student, make sure that
student has mastered prerequisite material so that learning process more
effective.
69
4.
For students, especially students in SMP Islam Al-Ulum Terpadu Medan are
suggested more brave in the expressing an opinion or ideas, can use the full
potential in math.
5.
For the next researcher, the results and device of this research can be
considered to apply realistic mathematics education approach on subtopic
system of linear equations two variables or other subject matter that can be
developed for future research.
68
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Menekankan Pada Representasi Matematik Melalui Pembelajaran
Berbasis Masalah Untuk Siswa Sekolah Menengah Pertama. Medan.
Unimed.
ABILITY OF STUDENTS’ THROUGH REALISTIC MATHEMATICS
EDUCATION APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM
TERPADU
OF MEDAN ACADEMIC YEAR 2012/2013
By:
Selvi Septiani Harahap
ID. Number 408 611 007
Mathematics Education Study Program
A THESIS
Submitted to fulfill the requirement for the degree of
Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATIC AND SCIENCE
STATE UNIVERSITY OF MEDAN
MEDAN
2013
BIBLIOGRAPHY
Selvi Septiani Harahap was born in Medan, September 24th 1989. Writer’s
father name is (Alm) Drs. H. Haridan Harahap and mother’s name is Hotnaria
Daulay. She is the first child from three children. She has two brothers. In 1995,
writer studied in primary school SD Inpres number 105288 Sei Rotan and was
graduated in 2001. In 2001, the writer continued her study in junior high school
MTS Negeri 2 Medan and was graduated in 2004. In 2004, writer also continued
her study in senior high school MAN 1 Medan and was graduated in 2007.
In 2008, the writer was accepted in Mathematics Education of Bilingual
class, Faculty of Mathematic and Natural Science, State University of Medan.
During the study.
ACKNOWLEDGEMENT
Praise be to Allah SWT, most gracious, most merciful and master of the
judgment. Thanks are to Allah who gave the strength and ability to the writer, so
that this thesis can be finished. An innovation and greeting to Rasulullah SAW,
who brought people from the darkness into lightness. The title of this research was
“The Increasing of Problem Solving Mathematical Ability Through Realistic
Mathematics Education Approach in VIII Grade at SMP Islam Al-Ulum Terpadu
of Medan Academic Year 2012/2013.” as a partial fulfillment of the requirements
for the degree Sarjana Pendidikan of the mathematic department, Faculty of
Mathematic and Natural Science State University of Medan.
In this occasion, the writer would like to express thank you very much to
her supervisor Prof. Dr. Sahat Saragih, M.Pd for his advice, motivation,
suggestion and guidance to finish this thesis. To her lecturer examinator
Prof.Asmin Panjaitan, M.Pd, Dr.W.Rajagukguk,M.Pd, and Dra. Katrina Samosir,
M.Pd, for their correction with valuable comments to correct the manuscript of
scientific writing, to her academic lecturer Drs. Syafari, M.Pd for his advice
support to her.
The writer also would like to express thank you to Mr. Prof.Ibnu
Hajar,M.Si as ahead of university and staff in office of university head, to Mr.
Prof. Motlan, M.Sc,Ph.D as a dean of mathematic and natural science faculty and
staff in mathematic and natural science faculty, to Mr. Dr Mukhtar,M.Pd as a head
of mathematic department, Mr.Drs. Syafari, M.Pd as ahead of mathematic
education program, Mr. Prof.Dr.Herbert Sipahutar, M.S, M.Sc as a coordinator of
Bilingual program, Mr. Drs.Yasifati Hia,M.Pd as secretary of mathematic
department, Mrs. Dr. IIs Siti Jahro, M.Si as secretary of Bilingual program, and
all staff in mathematic department and Bilingual program to help the writer.
The writer also would like to express thank you to head master of SMP
Islam Al-Ulum Terpadu of Medan Mrs. Nur Rahima S, S.Pd who gave permission
to do the research, to math teacher Mrs. Herlina,S.Pd, Mr. Nurhadi, S.Pd and all
teacher and staff in SMP Islam Al-Ulum Terpadu of Medan that help the writer to
do the research.
The writer also would like to express her deepest love gratitude to her
father (Alm) Drs, H. M. Haridan Harahap, her mother Hj. Hotnaria Daulay, her
brother Imam Al-Rasyid Harahap and Sakti Rizki Fauzi Harahap affectionately
which gave birth and enlarge to writer, gave morale support, material and pray
and so all her family. To her friend Angelica Pardede and lovely all friends in
mathematic bilingual program 2008 thank you very much for your support,
helping to finish this thesis.
The writer has effort as maximal as she can in doing this thesis. But with
her humble heart, the writer hopes construct suggestion and critics from the reader
for perfection this thesis. The writer hopes this thesis can be useful and give many
function to the reader specifically about subject matter which was researched in
this thesis.
Medan,
February 2013
Writer
Selvi Septiani Harahap
THE INCREASING OF PROBLEM SOLVING MATHEMATICAL ABILITY OF
STUDENTS’ THROUGH REALISTIC MATHEMATICS EDUCATION
APPROACH IN VIII GRADE AT SMP ISLAM AL-ULUM TERPADU
OF MEDAN ACADEMIC YEAR 2012/2013
Selvi Septiani Harahap (ID. Number 408 611 007)
ABSTRACT
The purpose of this research to know increasing problem solving ability of
students that taught realistic mathematical education approach is better than the
mathematical problem-solving ability of students taught expository approach in VIII
grade at SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013. This type of
research is quasi-experimental research on first (odd) semester of VIII grade SMP Islam
Al-Ulum Terpadu Medan academic year 2012/2013. The population in this research is
all students of VIII grade SMP Islam Al-Ulum Terpadu School of Medan consisting of
118 students. Sample was taken by using random sampling; it means that each class had
the same chance to be sampled. The sample in this study consisted of two classes. The
experiment class in VIII-A was taught by applies Realistic Mathematics Education
(RME) approach and the control class in VIII-B was taught by applies Expository
approach. Research instrument in collecting data in this study were a test and an
observation sheet.
The kinds of test is essay test, contains four questions for pre-test and four
questions for post-test that related to the problem solving about Linear equation two
variables system. The instrument that arranged have legalized by expert validator
namely lecturer and mathematic teachers. Before hypothesis that will be test must be
done normality test and homogeneity test. For normality test used Liliefors normality
test and for homogeneity test is used F-test. From test can get the sample is distributes
normal and homogeneous. Data analysis technique that used T-test formula.
The average of pre test in experiment class is 26.0714 and the average of pre test
in control class is 26.0714. The average of posttest in experiment class is 85.1785 and
the average of post test in control class is 72.5. Analysis result of gain for problem
solving using t testing with significant level α=0.05 for the hypothesis is tcalculate =
3.9861 and ttable = 2.0048 so that -2.0048 < tcalculate < 2.0048, Because of that, the criteria
t-α/2 < tcal < tα/2 is rejected. It means H0 is rejected. So can be concluded, The increasing
problem solving ability that taught by using RME greater than solving math problems
that students taught with Expository approach in linear equation two variables system at
VIII SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013.
ii
TABLE OF CONTENTS
Page
Sheet agreement ........................................................................................ i
Table of contents ....................................................................................... ii
Table list .................................................................................................... iii
List of appendix......................................................................................... iv
Figure list ................................................................................................. v
CHAPTER 1: INTRODUCTION .......................................................... 1
1.1 Background ........................................................................................ 1
1.2 Problem Identification......................................................................... 7
1.3 Problem Limitation ............................................................................. 7
1.4 Problem Formulation .......................................................................... 8
1.5 Research Objectives ........................................................................... 8
1.6 Operational defenition......................................................................... 8
1.7 Benefit of Researh................................................................................ 9
CHAPTER 2: LITERATURE REVIEW .............................................. 10
2.1. Theoretical Background ..................................................................... 10
2.1.1 Mathematical Problem Solving Ability.................................. 10
2.1.2 Understanding of Realistic Mathematics Education approach 17
2.1.3 Principles and Characteristics of RME ................................. 19
2.1.4 Steps of Realistic Mathematics Education ............................. 24
2.1.5 The Excess and Complexity of RME ..................................... 27
2.1.6 Expository Approach.............................................................. 29
2.1.7 The Difference of RME and Expository ................................ 33
2.1.8 The lesson material................................................................. 34
2.2 The Relevant Research ........................................................................ 40
2.3 Conceptual Framework ....................................................................... 41
2.4 Hypothesis ........................................................................................... 42
iii
CHAPTER 3: RESEARCH METHODS .............................................. 43
3.1 Type of research .................................................................................. 43
3.2 Place and Time of research ................................................................. 43
3.3 Population and Sample........................................................................ 43
3.3.1 Population of Research ............................................................. 43
3.3.2 Sample of Research................................................................... 43
3.4 Research Variables .............................................................................. 44
3.5 Research Design ................................................................................. 44
3.6 Research Procedure ............................................................................ 45
3.7 Instrument Analysis Technique .......................................................... 50
3.8. Data Analysis ..................................................................................... 52
1 Hypothesis test ................................................................................ 52
a. Mean score .............................................................................. 52
b. Standard deviation .................................................................. 52
c. Normality test .......................................................................... 53
d. Homogeneity test .................................................................... 54
e. Hypothesis test ........................................................................ 54
CHAPTER 4: RESULT AND DISCUSSION ...................................... 56
4.1 The Result of Problem Solving .......................................................... 56
4.1.1 Pre Test of Experiment and Control classes ................................... 56
4.1.2 Post Test of Experiment and Control Classes .................................. 57
4.1.3 Gain of Experiment and Control Classes ........................................ 59
4.1.4 Normality Testing of Data .............................................................. 61
4.1.5 Homogeniety Testing of Data ......................................................... 62
4.1.6. Hypotesis Testing ........................................................................... 62
4.2 Discussion ......................................................................................... 64
CHAPTER 5 : CONCLUTION AND SUGGESTION ....................... 68
5.1 Conclution .......................................................................................... 68
5.2 Suggestion .......................................................................................... 68
REFERENCES ........................................................................................ 68
Appendix .................................................................................................. 69
TABLE LIST
Page
Table 2.1 Cooperative Learning Phase
12
Table 2.2 Approaches to Cooperative Learning
14
Table 2.3 The Steps of Think Pair Share (TPS)
19
Table 2.4 Calculating of Gaining Score
21
Table 2.5 Example of Giving Gaining Score
22
Table 2.6 Technique of Giving Score For Each Step in Problem Solving
24
Table 3.1 Research Design
33
Table 3.2 Criteria of Student Mastering Level
44
Table 4.1 Pretest result of the first and second experiment classes
46
Table 4.2 Post test result of the first and second experiment classes
47
Table 4.3 Gain of the first and second experiment classes
48
Table 4.4 Result of Normality Testing
50
Table 4.5 Result of Homogeneity Testing
50
Table 4.6 The Result of Hypothesis Testing
52
Table 4.7 Description of Student Misatake for number 1using jigsaw
53
approach
Table 4.8 Description of Student Misatake for number 2 using jigsaw
54
approach
Table 4.9 Description of Student Misatake for number 3 using jigsaw
55
approach
Table 4.10 Description of Student Misatake for number 4 using jigsaw
56
approach
Table 4.11 Description of Student Misatake for number 1using TPS
58
approach
Table 4.12 Description of Student Misatake for number 2using TPS
59
approach
Table 4.13 Description of Student Misatake for number 3using TPS
61
approach
Table 4.14 Description of Student Misatake for number 4using TPS
62
approach
Table 4.15 Level of Problem solving Skills
63
Table 4.16 The average of observation result of learning process
66
FIGURE LIST
Page
Figure 2.1 Jigsaw Teams
15
Figure 2.2 Jigsaw Steps
17
Figure 2.3 Example of prism
26
Figure 2.4 Triangular Prism and its nets
27
Figure 2.5 Dividing Cuboids become Two Triangular Prisms
28
Figure 3.1 Research Procedures Scheme
36
Figure 4.1 Average of pre test, post test and gain
48
Figure 4.2 Level of Problem Solving
64
Figure 4.3 Students Mistake in Understanding Problem Number 2,3,1,and
69
4 using Jigsaw
Figure 4.4 Student Mistake for arranging Strategy using Jigsaw Approach
70
Figure 4.5 Mistake in calculating using Jigsaw
71
Figure 4.6 Mistake in Putting Some Values
71
Figure 4.7 Student’s Mistake for Understanding Problem using TPS
73
Approach
Figure 4.8 Student’s Mistake for Arranging Strategy to Solve Problem
74
Figure 4.9 Student’s Mistake in Implementing the Planning
74
APPENDIX LIST
Page
Appendix 1 First Lesson Plan for Experiment Class A
81
Appendix 2 Second Lesson Plan for Experiment Class A
88
Appendix 3 First Lesson Plan for Experiment Class B
95
Appendix 4 Second Lesson Plan for Experiment Class B
101
Appendix 5 Student Work Sheet I
107
Appendix 6 Student Work Sheet II
113
Appendix 7 Latticework of Pre-test
119
Appendix 8 Latticework of Post-test
120
Appendix 9 Pre-test Question
121
Appendix 10 Alternative Solution of Pre-test
123
Appendix 11 Post-test Question
126
Appendix 12 Alternative Solution of Post-test
128
Appendix 13 Observer Assessment Scale
131
Appendix 14 Validator Assessment Paper
133
Appendix 15 Validator Names
134
Appendix 16 Observation Paper of Learning Process Using Cooperative
135
Learning Jigsaw Approach
Appendix 17 Observation Paper of Teacher Activity for cooperative
137
learning Think Pair Share (TPS) Approach
Appendix 18 Technique of Giving Score For Mathematic Problem
139
Solving
Appendix 19 Validation Analysis of Validator Agreement for Pre Test
140
Appendix 20 Validation Analysis of Validator Agreement for Post Test
142
Appendix 21 Reliability Analysis of Pre Test
144
Appendix 22 Reliability Analysis of Post Test
146
Appendix 23 Pre Test for the First Experiment Class
148
Appendix 24 Pre Test for the Second Experiment Class
150
Appendix 25 Post Test for the First Experiment Class
152
Appendix 26 Post Test for the Second Experiment Class
154
Appendix 27 Pre Test and Post Test Mark for the First and Second
156
Experiment Classes
Appendix 28 Calculation of Normality Testing
157
Appendix 29 Calculation of HomogenietyTesting
161
Appendix 30 Calculation of Gain Score
164
Appendix 31 Calculation of Hypothesis Testing
165
Appendix 31 Documentation of Research
169
CHAPTER I
INTRODUCTION
1.1. Background
Education is one of very important aspects of life. Giving the role of
education is an effort to form a high quality human, then the problem of education
in the spotlight, especially in Indonesia. One of the goals of national development
in the field of education is the intellectual life of the nation and to improve the
quality of Indonesian human. Through improving the quality of education at all
levels of education, which enables its citizens to develop themselves as whole
human beings Indonesia. To realize the national development in the field of
education needed improvement and refinement of education in accordance with
the development of science and technology (Science and Technology).
Mathematics is one of the basic sciences in school curriculum and must be
learned in educational institutions. Based on the data above, Indonesia ranks are
located in 39th of the 41 states and this must be very worrying. This problem must
be improved immediately and be seriously handled because the usefulness of
mathematics and very important both in development thinking, mastery of science
and technology and its role in several other scientific subjects. It is also expressed
by the Daniel Muijs and David Reynolds (2008: 332) which states mathematics is
the main means for developing the ability of logical thinking and higher cognitive
skills in children and plays an important role in several other scientific fields such
as physics, engineering, statistics and others. Therefore, it is necessary teach
students to mastery the mathematics early on creating, face and master modern
technology for globalization era. Then, Cornelius in Abdurrahman (2003: 253)
show several reasons for studying mathematics, namely:
1.
2.
3.
4.
5.
Means of a distinct and logical thinking
Means to solve problems of daily life
Means to know the patterns, relationships and generalization of experience
Means to develop creativity
Means to increase awareness of cultural development.
Based on the above quotation through the learning of mathematics is
expected that students can develop the ability to think, reason, develop creativity,
communicate and present ideas and information and solve problems in daily
activities. According to the National Council of Teacher Mathematics (NCTM)
and its agenda for action in Alfred S. Posamentier Jay Stepelman (1990: 109) state
that problem solving as primary goals for mathematics education and teacher are
urged to:
1.
2.
3.
4.
Create a classroom environment and develop appropriate curricular
materials in which problem solving can flourish
Give priority to identification and analysis of specific problem solving
strategies
Develop examples of good problem
Encourage students to question , experiment, estimate, explore and
suggest explanations
KEMDIKNAS 2006 in http://pmat.uad.ac.id/perkembangan-pembelajaranmatematika-di-indonesia.html then stated:
"The goal of learning mathematics, namely: (1) understand math concepts,
explain the relationship among concepts and apply the concepts or
algorithms in widely, accurate, efficient, and appropriately in problem
solving, (2) using the pattern and characteristics of reasoning, mathematical
manipulations in making generalization, arrange evidence, or explain
mathematical ideas and statements, (3) solve problems that include the
ability to understand the problem, design mathematical model, complete
model and interpreting solution obtained, (4) communicate ideas with
symbols, table, diagrams, or other media to explain the situation and
problem, (5) respect of the usefulness of mathematics in life, which has the
curiosity, attention, and interest in studying mathematics and a competent
attitude and confidence in problem solving.”
From the above statement, one of the aspects emphasized in the goal of
learning mathematics is problem solving ability. It is very important because in
solving the problem usually involves some of the concepts and skills in new
situations or different that in the process possible the students’ learning gain
experience in using knowledge and skills to be applied in problem solving.
Learning of mathematics and its evaluation system have been less provides
an opportunity for students to come up with ideas for students to learn
mathematics. This is because learning is more focused on the teacher (teacher
centered) are generally directly transferring his knowledge to students so that
students become passive. More emphasis on learning outcomes (product) in which
students live using formula rather than emphasizing the process. Thus some
actives to learn mathematic is to be trained in order to solve the problems.
This is also reinforced one of them by the results of The Third International
Mathematics and Science Study (TIMSS) that the junior high school students in
Indonesia are very weak, but pretty good problem solving in procedural
skills. (Al-jupri & kartika). In addition Hudojo (2003: 152) states that teaching
students to solve problems allow students to become more analytical in taking
decisions for life. In other words if a student is trained to resolve problems, the
students were able to make decisions for the students to have skills on how to
gather relevant information, analyze information and realize the need to reexamine the results already obtained. But most of mathematics educators are
concerned about the narrow focus of many schools programs, the limited
treatment of content that they view as important for students, and the lack of
attention given to developing in reasoning and problem solving (Lindquist, 1980:
9).
Furthermore, Tarwiyah (2011) explains that solving problems in
mathematics learning is an approach and goals to be achieved. As an approach,
problem solving is used to discover and understand the material and mathematical
concepts. Meanwhile, as the goal, it is expected that students can identify the
unknown elements, and asked the necessary elements of adequacy, formulating
the problem of everyday situations in mathematics, implement strategies to solve
problems (similar and new problems) within or outside of mathematics, describes
the results as origin of the problem, develop a meaningful mathematical
model. As the implications of the problem-solving skills should be possessed by
all the children who learn mathematics. In learning process, students are passive,
fearful, some are bored and some even feel that mathematics is a terrible
lesson. In other words the students have not responded well to the challenges that
exist in math. As a result, students are not able to be independent and do not know
what to do. It can be concluded that the increase in students ability in solving
mathematical problems have a considerable role for students. However, the
problem-solving is an activity in the learning process has not become a major
activity so that there are many students who find it difficult when faced with
problem solving.
Mathematical problem solving ability has get attention because it is a
necessary capability in learning. Mathematical problem solving ability to
encourage students in meaningful learning and togetherness, but it can help
students in dealing with mathematical problems and issues of everyday life in
general. Weak student math problem-solving ability is not out of lack of
opportunity and not frequently students do problem solving. Mathematical
problems presented in the classroom tend to routine problems. So that the students
are not accustomed to solving problems in determining what is known and what is
asked on the matter and to what to use.
The Causes of low mathematical problem-solving ability is due to intake of
students who have previously not met the standards. Knowledge and experience
of the material previously learned material will affect the learning process
further. This is reinforced by Herman Hudojo statement that: "Studying the
concept B is based on the concept of A, that person may not understand the
concept of B. This means, learning mathematics should be gradual and sequential,
and then based on their learning experience."
From the observation of the junior high school Al-Ulum Islamic Terpadu
Academic Year 2012/2013, students tend not to like math because of lack of
delivery of material related to everyday life so that academic concepts are difficult
to understand. The teachers still teach and learn conventional learning models as a
center of learning where the teacher (teacher cantered). Conventional learning
gives effect to the inactivity of learning actors. Thus resulting to a total mastery of
Mathematics and ultimately affect the competences and learning outcomes of
students in mathematics.
One of the subjects of mathematics involved in this problem is Linear
Equation of Variables system. Students have difficulty in learning the subject
matter of linear equation of variables system, the majority of students are difficult
to understand the concept of the linear equation of variables system. Students are
less able to translate the linear equation of variables system itself in everyday life.
As the initial observations by the author on Islam Al-Ulum Terpadu in VIII class
academic year 2012/2013 that most of the students were unable to resolve the
problem concerning the complete linear equation of variables system. One
problem, the ratio of rika and rido’s money is 3:2, if the amount of their money is
Rp.20.000, their money is the difference? Of course the problem can be regarded
as a social arithmetic. But it would be better if we look as a problem in linear
Equation of variables system. In linear equation of variables system, the problem
above can be seen as a problem with two equations and two unknown
variables. But in fact most students are not able to solve algebra problems
thoroughly.
Based on these observations it can be identified that many mistakes which
made by students at SMP VIII Al-Ulum Islam Terpadu Medan for solving
problem of linear equation two variables system. caused by the weakness of
students in aspects of pouring, declaring, disclosing, or making a model of ideas,
mathematical concepts, and relationships among them into a new mathematical
form variety in the form of words (written text), graphics, tables, diagrams,
drawings, equations (mathematical expression), or a form of concrete (props) and
use them in solving problems with the sort of things are known, asked, then
answered.
In an effort to improve students' problem-solving skills, teachers should
strive to train and familiarize students to the form of problem solving in learning
activities, such as giving students the chance to hold a conversation in order to use
the scientific opinions, conclusions or develop alternative solutions to a
problem. Therefore, teachers need to select appropriate learning approaches to
encourage students to learn to do math problem solving. Make learning math is
boring and students do not think that mathematics is an abstract lesson in class,
the teacher needs to choose a learning approach that requires an active
involvement of students and also develop thinking skills by using the real thing
around them, so that the learning objectives can be achieved. Learning math will
head in the right direction and managed to find out if the characteristics of
mathematics. Mathematics has its own characteristics in terms of both aspects of
competency to be achieved, as well as from the aspect of the material being
studied to support the achievement of competence.
Realistic Mathematics Education (RME) is a learning system based on the
philosophy that one will be able to absorb the subject matter if they can grasp the
meaning of learning. RME is a comprehensive system that consists of five
components, namely the contextual issues, modeling, production and contribution
of students, interactions, linkages. If any parts of the RME intertwined with each
other it will produce effects that exceed the results given in the parts separately
and involve different processes as well, when it is used together to enable the
students to make connections with each other produce. Learning mathematics
using Realistic Mathematics Education approach (RME), which concerned local
conditions (culture or environment or context) shows that students are not afraid
to express their ideas, has begun to dare to give a different problem solving with
their
peers,
grow
their
creativity
in
doing
problem
solving(problem
solving) together.
The purpose of Realistic Mathematics Education is to solve the problems
facing students by linking the material to the real world so that students can solve
problems. This method is cooperative so to enhance cooperation among of
student, all students are guided and directed to an active and creative condition so
that the learning becomes more effective and efficient. Realistic Mathematics
approach is expected to make the students know the importance of mathematics in
everyday life. Learning innovations with Realistic Mathematics approach is
expected to foster a new spirit to be more enterprising students to learn
mathematics so that mathematical problem solving ability of students can be
increased. Based on the above background, the writer is interested in doing
research on "The Increasing of Problem Solving Mathematical Ability That
Taught Realistic Mathematics Education Approach in VIII grade at SMP Islam
Al-Ulum Terpadu of Medan Academic Year 2012/2013"
1.2.Problems Identification
Based on the background of problems it can be identified some problems, as
follows
1. Teachers who taught using teacher centered make students as passive
objects in the study.
2. Many mistakes which made by students in VIII grade at SMP Islam AlUlum
Terpadu Medan for solving problem of linear equation two
variables system.
3. The students are not yet accustomed to solve problems in mathematics
learning in the classroom.
4. Realistic mathematical approach has not been implemented in the school,
in general, teachers tend to prefer the conventional approach in teaching
mathematics.
1.3.Problem Limitation
Seeing the wide scope of issues identified and comparing the ability of the
researcher, the writer feels the need to limits the problems that are examined for
the results in this study that can be performed and directed.
In this study the problem under study is limited to the influence of Realistic
Mathematics Education for mathematical problem solving ability of students the
subject of linear equation of variables system in VIII grade at SMP Islam AlUlum Terpadu Medan Academic Year 2012/2013
1.4.Problem formulation
Dictated by the above problems, the formulation of the problem in the study
is "Is the increasing problem-solving mathematical ability of students that taught
realistic mathematical education approach is better than the mathematical
problem-solving ability of students taught by expository approach in VIII grade at
SMP Islam Al-Ulum Terpadu Medan Academic Year 2012/2013.”
1.5.Research Objectives
Based on the above problem formulation, the objective of this study is "To
know the increased problem solving abilities of students that taught realistic
mathematical education approach is better than the mathematical problem-solving
ability of students taught by expository approach in VIII grade at SMP Islam AlUlum Terpadu Medan Academic Year 2012/2013.”
1.6.Operational definition
So that the terminology in this study is more clearly so that the objectives
and research directions to be is specific, then the variables are defined as follows:
a. Realistic Mathematics Education is an approach to learning mathematics
that has five characteristics: (1) using contextual problems as a first step,
(2) using a mathematical model developed by students, (3) consider the
contribution of students, (4) optimize the interaction with his students,
students with teachers and other supporting facilities, and (5) consider the
relationship between the topics.
b. Expository approach is a procedure commonly used by teachers in
teaching. The steps are the teachers prepare teaching materials in a
systematic and organized, explaining the subject matter, students are given
the opportunity to ask questions, students are given exercises that work on
the problems of teachers, students and teachers discuss the exercise, then
the teacher give homework.
c. Problem-solving ability is the ability of students in solving mathematical
problems by considering the process of finding answers based on problemsolving steps, namely: (1) understanding the problem, (2) making a plan
strategy, (3) Carrying out the plan (4) Looking back or checking the
answer.
1.7. Benefits of research
This study is expected to be useful:
1. As input material for teachers, especially SMP Islam Al-Ulum Terpadu
Medan is a way to improve students' mathematical problem solving
ability.
2. As input and consideration for prospective teachers in implementing the
teaching and learning activities
3. As input for other researchers to conduct further research. RME learning
implementation is expected to increase student learning outcomes for
mathematics courses
68
CHAPTER V
CONCLUSSION AND SUGGESTION
5.1.
Conclusion
Based on the result research from data analysis, can be obtained some conclusion,
those are
1.
By testing hypothesis using t-test of the gain average in the control and
experiment classes, then can be concluded the increasing of problem solving
mathematical ability students that taught realistic mathematics education
approach is better than the mathematical problem solving ability of students
taught with expository approach on subtopic system of linear equations two
variables in VIII grade at SMP Islam Al-Ulum Terpadu Medan Academic
Year 2012/2013.
2.
Based on the observation of the application of realistic mathematics approach
and expository approach on the subject of system linear equation two
variables the categorized is good.
5.2.
Suggestion
Based on research result, then the suggestions that can be given by the
researchers are:
1.
For math teacher who want to use realistic mathematics education approach,
give more attention to time allocation for each phase so that learning process
can be done better.
2.
For math teacher, realistic mathematics education approach can be used as
alternative learning approach because it can be increase problem solving
ability of student.
3.
For math teacher who want to give some topic to student, make sure that
student has mastered prerequisite material so that learning process more
effective.
69
4.
For students, especially students in SMP Islam Al-Ulum Terpadu Medan are
suggested more brave in the expressing an opinion or ideas, can use the full
potential in math.
5.
For the next researcher, the results and device of this research can be
considered to apply realistic mathematics education approach on subtopic
system of linear equations two variables or other subject matter that can be
developed for future research.
68
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