THE DIFFERENCE OF STUDENT’S MATHEMATICAL UNDERST ANDI NG IN RE ALISTI C MATHEMATI CS
EDUCATION AND CONVENTIONAL CLASSROOM AT SMP NEGERI 1 LUBUK PAKAM
by:
Maria Priscillya Pasaribu IDN. 4103312018
Mathematics Education Study Program
Thesis
Submitted in fulfillment of the requirements for the degree of Sarjana Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND SCIENCESUNIVERSITAS NEGERI MEDAN
MEDAN
PREFACE
Praise to the God Almighty for His blessing, health, and opportunities in
every step I passed so that I could finish this thesis entitled The Difference of Student’s Mathematical Understanding in Realistic Mathematics Education and Conventional Classroom at SMP Negeri 1 Lubuk Pakam in time. This thesis is
submitted in partial fulfillment of the requirements for the degree of Sarjana
Pendidikan in Medan State University.
I want to express special thanks to my beloved family, my father, J.
Pasaribu, my mother, M. Tarigan, and my blood brother, Victor Patar Pasaribu,
for their everlasting support, patience, love, and their prayer throughout this
process. I dedicate this thesis for them. My warm thanks go to my cousin Maya
Silitonga and D. Supit, and their children, Ditya Andrean Supit, Yona Irene Supit,
and Cyrillus Ruben Supit, for their support and care. My special thanks are
extended to my family, my lovely grandmother, my sister, Sur, Nur, and Sum, my
brother, Bandot and Tugino for their prayer, care, and love.
Special thanks are extended to my supervisor, Mr. Dr. E. Elvis
Napitupulu, M.S. for his time, patience, a lot of advice, constructive criticism,
questioning and probing, and constant encouragement that were deeply
appreciated and valued. I also extend special thanks to Mrs. Dra. Ida Karnasih,
M.Sc., Ph.D., Mrs. Dra. Nerli Khairani, M.Si., and Mr. Denny Haris, S.Si., M.Pd.
as my examiners who gave me insightful suggestions from compiling proposal till
this thesis compilation was done. And also for my academic counselor, Mr. Prof.
Dr. Mukhtar, M.Pd., I want to express my special thanks for his guidance and
suggestion during the lecture period.
I would like to thank Mr. Prof. Dr. Ibnu Hajar, M.Si. as the Rector of
Medan State University as well as the staff employees in rector’s office, Mr. Prof.
Dr. Motlan, M.Sc., Ph.D. as the dean of Mathematics and Sciences Faculty, Mr.
Prof. Dr. rer.nat. Binari M., M.Si. as the coordinator of bilingual class, Mr. Drs.
Syafari, M.Pd. as the chief of Mathematics Department, Mr. Zul Amry, M.Si. as
M.Si., and all of staff employees in Mathematics Department of Mathematics and
Sciences Faculty that were involved in this thesis compilation.
I also express my deep gratitude to the principal of SMP Negeri 1 Lubuk
Pakam, Mr. Animan, S.Pd., as well as all of the clerical employees, Mr. Mahmud,
as the vice of principal, mathematics teacher, Mrs. T.N. Siregar, and all of
teachers in SMP Negeri 1 Lubuk Pakam, that gave me permit to conduct the
research, helped me from the beginning till the research done, and gave me
support throughout this process. I also want to thank all of students in class Bil-1
and Bil-2 for their collaboration, support, and passion when I was teaching them.
I would like to thank my best friends, Abdul, Anggi, Dian, Dwi, Erlyn,
Elfan, Kiki, Falni, Mila, Lia, Meiva, Martyanne, Melin, Surya, Nelly, Petra, Riny,
Rully, Sartika, Sheila, Siti, Uli, and Mimi, and also especially for my hometown
best friends Rabiatul Daulay and Winda Safitri, Firman Sibarani, friends of PPLT
in Balige, and all my friends i did not mention for their support and love
throughout this process. It would not have been possible without each of you.
I am also grateful for my senior Epril Parhusip, S.Pd. that has given me
some advice and support in the beginning of this thesis compilation.
I have done the best for finishing this thesis, but I realize that this thesis
has its shortcomings either in contents, grammar, or technical writing. Hence, I
hope the constructive criticism and suggestion from the reader for the perfection
of this thesis. I hope this thesis could be useful for further researchers and useful
in enrichment the knowledge.
Medan, Agustus 2014
Author
THE DIFFERENCE OF STUDENT’S MATHEMATICAL
UNDERSTANDING IN REALISTIC MATHEMATICS EDUCATION AND CONVENTIONAL CLASSROOM AT SMP NEGERI 1 LUBUK PAKAM
Maria Priscillya Pasaribu (IDN 4103312018)
ABSTRACT
This research is quasi-experiment. The purpose of this research was to know if student’s mathematical concept understanding in RME classroom is better than student’s mathematical concept understanding in conventional classroom at SMP Negeri 1 Lubuk Pakam.
The population of this research was all students of SMP Negeri 1 Lubuk Pakam which consists of 24 classes, whereas the sample consisted of 2 classes, they are Bil-1 as experimental class consists of 28 students, Bil-2 as control class consists of 29 students. Experimental class used RME, whereas control class used conventional learning model. Collecting data technique of this research was mathematical concept understanding test that was given in the end of learning either in experimental class or control class. The type of this test is essay test.
Before doing hypothesis test, it would be done normality and homogeneity test beforehand. From the result of those tests, sample was taken from normal distributed and homogeneous population. From the data analysis of experimental class by using t-test with significance level α = 0.05, it was obtained that tcalculation > ttable then H0 is rejected and Ha is accepted.
So, it can be concluded that student’s mathematical concept understanding in Realistic Mathematics Education approach classroom is better than student’s mathematical concept understanding in conventional classroom at SMP Negeri 1 Lubuk Pakam
CONTENTS
Page
Authentication Sheet i
Biography ii
Abstract iii
Preface iv
Contents vi
Figure Lists vii
Table Lists viii
Appendix ix
CHAPTER I PRELIMINARY 1
1.1. Problem Background 1
1.2. Problem Identification 11
1.3. Problem Limitation 11
1.4. Problem Formulation 11
1.5. Research Objective 12
1.6. Research Benefit 12
1.7. Operational Defenition 12
CHAPTER II LITERATURE 14
2.1. Mathematical Concept 14
2.2. Mathematical Concept Understanding 14
2.3. Realistic Mathematics Education Approach 17
2.3.1. The Characteristics of RME Approach 20
2.3.2. RME Approach Steps 25
2.4. Conventional Learning Model 27
2.5. Cuboid and Cube Theory 29
2.6. Learning Theory Support 31
2.6.1. Learning Theory Support of Geometry 31
2.7. The Relevant Research 37
2.8. Conceptual Framework 38
2.9. Hypothesis of Research 39
CHAPTER III RESEARCH METHOD 40
3.1. Place and Time of Research 40
3.2. Population and Sample 40
3.2.1. The Population 40
3.2.2. The Sample 41
3.3. Variable and Instrument of Research 41
3.3.1. The Variable 41
3.3.2. The Instrument 41
3.3.2.1. Mathematical Concept Understanding Test 42
3.3.3. Instrument Try-Out 46
3.3.3.1. Instrument Validity 46
3.3.3.2. Instrument Reliability 47
3.4. Design of Research 49
3.5. Data Collection Techniques 49
3.6. Data Analysis Techniques 51
3.6.1. Quantitative Data Analysis 52
3.6.1.1. Analysis of Mathematical Concept Understanding Test 52
3.6.1.1.1. Data Analysis by Descriptive Statistic Technique 52
3.6.1.1.2. Data Analysis by Inferential Statistic Technique 52
CHAPTER IV RESULTS AND DISCUSSIONS 54
4.1. Research Result Description 54
4.1.1. Mathematical Concept Understanding Ability Test 54
4.1.2. The Description of Mathematical Concept Understanding Test 56
4.2. Analysis of Research Data 56
4.2.1. Analysis of Mathematical Concept Understanding Test 57
4.3. Research Discussion 62
CHAPTER V CONCLUSION 67
5.1. Conclusion 67
5.2. Suggestion 67
TABLE LISTS
Page
Table 2.1. RME approach steps 25
Table 2.2. Conventional model learning step 27
Table 2.3. The difference between RME approach and conventional
model learning 28
Table 2.4. The activity of students in classroom according to Van Hiele’s
Theory 33
Table 3.1. Blue print of mathematical concept understanding test 42
Table 3.2. Scoring guideline of mathematical concept understanding
Test
Table 3.4. Validity testing of each instrument test 47
Table 3.4. The criteria of reliability 48
Table 4.1. Descriptive statistics of experimental and control class 55
Table 4.2. Mean percentage of experimental and control class of each
Indicator 56
Table 4.3. One-sample Kolmogorov-Smirnov test 57
Table 4.4. Homogeneity variance test 58
Table 4.5. Independent sample t-test 59
FIGURE LISTS
Page
Figure 1.1. Example 1 of student’s answer 5
Figure 1.2. A kite frame 6
Figure 1.3. Example 2 of student’s answer 6
Figure 1.4. Example 3 of student’s answer 6
Figure 3.1. Flowchart of data collection 51
Figure 4.1. Histogram of minimum score, maximum score, and mean in
APPENDIX LISTS
Page
Appendix 1. Lesson plan of experimental class 1 73
Appendix 2. Student activity sheet (SAS) 1 79
Appendix 3. Lesson plan of experimental class 2 87
Appendix 4. Student activity sheet (SAS) 2 93
Appendix 5. Lesson plan of experimental class 3 99
Appendix 6. Student activity sheet (SAS) 3 104
Appendix 7. Lesson plan of experimental class 4 112
Appendix 8. Student activity sheet (SAS) 4 118
Appendix 9. Lesson plan of control class 1 125
Appendix 10. Lesson plan of control class 2 128
Appendix 11. Lesson plan of control class 3 131
Appendix 12. Lesson plan of control class 4 134
Appendix 13. Blue print of mathematical concept understanding test 137
Appendix 14. Student’s mathematical concept understanding test 138
Appendix 15. Scoring guideline of mathematical concept understanding test 139
Appendix 16. Posttest score of experimental and control class 142
Appendix 17. Validity test of mathematical concept understanding test 143 Appendix 18. Reliability Test of Mathematical Concept Understanding Test 146
Appendix 19. Normality Test 148
Appendix 20. Homogeneity Test 149
Appendix 21. Compare Means Test 150
Appendix 22. Observation sheet 151
Appendix 23. r-table value of product moment 154
Appendix 24. t-table value of t-distribution 155
CHAPTER I
PRELIMINARY
1.1. Problem Background
The development of sciences and technologies which is rapidly increased
demands the qualified human resources who have high competences. One of the
competences is competence in mathematics. Mathematics is one of the subject
matters that are important and necessary because its concepts, principles, and
procedures are always used in solving problems in almost all subject matters in
school and even in daily life. Mathematics subject matter is expected to help
students to be able to think critically logic, and systematic. By mastering
mathematics, students are expected to have a competitive advantage, either in the
workplace or for further study to a higher level.
Mathematics has an important role because it has the advantage in
advanced of sciences and technologies as follows (Martono, et. al, 2007:vii)
1. The language and rule in mathematics is well designed and consistent.
2. The information network structure of mathematics is very strong by its clear
and systematic reasoning pattern.
3. Mathematics is an approach to learn sciences and technologies.
4. Mathematics is a tool in solving problems of other subject matters.
5. By mathematics, a problem can be seen in a compact model.
The importance of mathematics can also be seen from the position and
role of mathematics according to Adam and Hamm (Wijaya, 2012:5-6):
1. Mathematics as a way to think
Mathematics has role in the process of organizing ideas, analyzing
information, and drawing conclusions among data.
2. Mathematics as an understanding of pattern and relation
Connecting a mathematical concept with existing knowledge of students is
concept they are learning has similarities and differences with the concepts
they have learned.
3. Mathematics as a tool
We have to view mathematics as a tool that we can use every day. Plenty of
mathematical concepts can be found and used in daily life. For instance, the
concept of the area of circle is useful to determine the price of circular food
that has the same height, i.e. pizzas are often advertised according to their
diameter.
4. Mathematics as a language or a tool to communicate
Symbols in mathematics have the same meaning for certain terms from
different languages. Therefore, mathematics is the universal language. For example, when we say “empat dikali tiga sama dengan dua belas”, then only Indonesian knows that statement. But if we state that statement as “4 x 3 =
12”, then people who have different language knowledge will understand that
statement.
Regarding to the role and position of mathematics above, greater
understanding of mathematics will be important of today’s school-children. They
must be able to learn new concepts and skills in order that they can use them in
daily life. Student with a poor understanding in mathematics will have fewer
opportunities to pursue higher levels of education and to compete a good job
(National Research Council (NRC), 2002:3).
The importance of student’s conceptual understanding also can be seen from the learning objectives of mathematics according to Content Standard in
Kurikulum Tingkat Satuan Pendidikan (Badan Standar Nasional Pendidikan
(BSNP), 2006:146), that is mathematics subject matter intended that learners have
the following abilities:
1. Memahami konsep matematika, menjelaskan keterkaitan antar konsep dan
mengaplikasikan konsep atau logaritma secara luwes, akurat, efisien dan tepat
2. Menggunakan penalaran pada pola dan sifat, melakukan manipulasi
matematika dalam membuat generalisasi, menyusun bukti atau menjelaskan
gagasan dan pernyataan matematika.
3. Memecahkan masalah yang meliputi kemampuan memahami masalah,
merancang model matematika, menyelesaikan model dan menafsirkan solusi
yang diperoleh.
4. Mengomunikasikan gagasan dengan simbol, tabel, diagram, atau media lain
untuk memperjelas keadaan atau masalah.
5. Memiliki sikap menghargai kegunaan matematika dalam kehidupan, yaitu
memiliki rasa ingin tahu, perhatian, dan minat dalam mempelajari
matematika, serta sikap ulet dan percaya diri dalam pemecahan masalah.”
If we notice the above learning objectives of mathematics, we can see
that mathematics education in Indonesia is already noticed the development of
mathematical thinking ability. One of those abilities that have to be possessed is
mathematical concept ability. Understanding the concepts and theories well is
getting emphasis in mathematics (Martono, et. al, 2007:viii). This ability is a
fundamental ability to achieve other higher abilities.
Understanding may consist of a variety of other things as well. If the
object of understanding is a phenomenon then its understanding may consist in
finding an explanation of why the phenomenon occurs. A person may feel she
understands an action because she knows how to perform it successfully. Piaget
asserts that understanding focuses neither on the goals that the action is expected
to attain, nor on the means that can be used to reach them (Sierpinska, 2005:5-6).
Learning mathematics with understanding is essential and makes
subsequent learning easier. Knowledge learned with understanding provides a
foundation for remembering or reconstructing mathematical facts and methods,
for solving new and unfamiliar problems, and for generating new knowledge
(NRC, 2002:11). Mathematics makes more sense and is easier to remember and to
apply when students connect new language to existing knowledge in meaningful
be aimed at developing mathematical connection ability among ideas, how ideas
interconnected to each other so that will be built the understanding thoroughly,
and use mathematics in context out of mathematics (NCTM, 2000:20). Getting
students to see connections between the mathematics they are learning and what
they already know also aids them in conceptual understanding. According to
Ansari (2009:28), mathematical understanding is the level of student’s knowledge
about concepts, principles, algorithm, and skillfulness of students in using solving
strategy to the presented problems. Therefore, all students should be expected to
understand and be able to apply procedures, concepts, and processes mathematics
(NCTM, 2000:20). Mathematical understanding can be gained by experience
about the owned characteristics and not possessed of a set of objects (abstraction).
By doing observation of examples and non-examples, students could gain the
meaning of a concept (Suherman, 2001:55). So that, when students understand
mathematically, they are able to classify the objects based on its concept by their
own words, give example and non-example, and use the concepts in solving
routine exercises.
To know the ability of student’s understanding of mathematical concept
in the field, researcher should do the preliminary study. Arikunto (2007:26)
asserts that preliminary study is the activity of researcher to conduct the
temporary data collection for the certainty of the next step in research. Regarding to Arikunto’s opinion, we can say that preliminary study is useful for researcher to collect the data and information and also to know how to analyze the data
(Sahayu, 2012).
In the preliminary study that has been done by researcher, researcher
conducted the preliminary test. The preliminary test is compiled by researcher
based on three indicators of understanding of mathematical concept, they are, be
able to classify the object according to its concept, be able to give example and
non-example, and to use the concept in the routine exercises. Preliminary test that
conducted to 28 students of class VIII Bil-2 at SMP Negeri 1 Lubuk Pakam
indicates that conceptual understanding ability of certain students is still low. This
junior high school students as the population, that is, the students’ understanding
of mathematical concept is not sufficient. In addition, since stage of junior high
school students' cognitive development has reached the stage of formal
operations, which is asserted by Piaget's theory (Trianto, 2011:30) that the level of
formal operation development of students at the age of 11-15 old years. In this
step, students begin to think concept that is out of their knowledge and try to
connect it with their own knowledge so that it is possible to implement the RME
approach. Besides that, it is few studies conducted in the schools, especially in the
field of mathematics education research.
This case also can be seen from several student’s answers when this
following problem was given: “A ship sailed from point A to the east as far as 3
km. After that, the ship turned to the north as far as 4 km then arrived at point B.
From point B, the sailing ship continued its journey to the east as far as 6 km and
turn toward the north as far as 8 km. Finally, the ship arrived at the point C.
Define the distance from point A to C through point B.” Example of student’s answer for the above problem is
Fig. 1.1. Example 1 of student’s answer
From the student’s answer above, we can say that the ability of student in understanding the problem given and using Pythagorean Theorem is low.
The longest bamboo is made into a perpendicular frame. If the end of each bamboo is connected with ropes, then calculate the required ropes (winding ropes are ignored).”
Fig. 1.2. A kite frame
Example of student’s answer for the above problem is
Fig. 1.3. Example 2 of student’s answer
From the student’s answer above, we can say that the ability of student in using the Pythagorean Theorem in problem is low.
For another example:
Write down the triangle’s sizes that is triple of Pythagoras or not triple
Fig. 1.4. Example 3 of student’s answer
From the above answer, we can say that the ability of student to classify
the object according to its concept is low.
The decline of mathematical understanding ability of students in class are
because the teacher often exemplifies to students how to solve problems, students
learn by listening and watching the teacher do the mathematics, then teacher tries
to solve it by his/himself, and when teaching mathematics, the teacher explains
the topics that will be directly studied, followed by giving examples, and
problems for practice. Brooks and Brooks call the above learning is as
conventional, because the most activities in learning activities are still dominated
by teacher (Ansari, 2009:2). Learning activities like those can not fulfill the
students’ needs for developing their ability in mathematical understanding. The
teacher explains the material is only targeting on learning outcomes rather than on
learning process (Arifin, 2009:85). One of the reasons of this happens because the
density of the material which is explained and completed based on the applicable
curriculum. It is realized by researcher at the time of the Program Pengalaman
Lapangan Terpadu (PPLT). This conventional or mechanistic learning emphasizes
on exercise or drill by repeating the procedure and more using a formula or a more
specific algorithm (Ansari, 2009:2). When learning mathematics emphasizes on
rules and procedures, it can give the impression that math is to memorize.
Most learners are only able to memorize the concepts (rote learning) and
using the formula without knowing why they are using that formula and even they
rote learning can be caused students feel difficult to transfer knowledge into other
situations. In addition, the learning process is still dominated by the role of the
teacher while the students tend to be passive (teacher-centered). Passive role of
students in the learning process can make students quickly forgot the knowledge
they have just been receiving. And also most of students consider mathematics is
the most difficult lesson, bored, even their biggest enemy.
Actually, these are the crucial problems since the up-to-date curriculum
or curriculum of 2013 demands learning system that was teacher-centered
becomes students-centered, students become more interactive, active, and
observant in the learning process, students may get the knowledge from whoever
and wherever they get, and passive learning system becomes critical one
(Kementrian Pendidikan dan Kebudayaan (Kemendikbud), 2013:68). Therefore,
to increase students' understanding of mathematical concepts and achieve one of
the learning objectives in Indonesia, it is necessary to change the less effective
methods to be more effective, making the role of students in learning activities
that were passive to be active, and more using the experiences of students and
contextual problems in learning mathematics so that learning mathematics can be
more meaningful for students.
Problem that is faced by students is difficult to relate the knowledge they
already had with the material they are learning in school. Knowledge they already
had can take the form of contextual problems and their experiences in daily life.
And they are also difficult to relate the mathematical material in classroom with
the real situation out of classroom. Using real situations can strengthen their
ability to see those relationships and generate informal mathematical knowledge.
Connecting the real situation with the actual experience of students can make
learning more effective (Muijs, 2008:343).
Learning strategies that begin learning by using examples and realistic
situations, then change the realistic situation into a mathematical model, direct
that model to the mathematics solution and then re-interpret as a realistic solution
that would be useful in relating knowledge and application of mathematics and the
One approach that is appropriate with the above strategy is the Realistic
Mathematics Education (RME) approach. The approach which is introduced and
developed by the Freudenthal Institute in the Netherlands emphasizes how to
learn real mathematics, beginning with simple problems that exist in real life so
that students can be more understood the concepts that are being taught.
Freudenthal’s view that the basis in the development of RME approach is
mathematics is a human activity. Based on his view, mathematics is a form of
activity or process. Students are given the opportunity to construct or re-invent a
mathematical concept in their own way. In other words, students are not given a
ready-made product that is ready to use, but rather construct their own knowledge
of mathematics. This is caused students become more active in the learning
process.
The word realistic in the RME approach is not only referring to the
real-world. But it also refers to the real problems experienced by students and can be
imagined. The problems are presented based on the experience and knowledge
that is already had by students made learning becomes more meaningful. The
differences in the level of experience of each student are useful so that each
student complement their knowledge based on the experience of the individual.
Realistic Mathematics Education approach has five characteristics in
learning. The first characteristic is using contextual problems. The use of
contextual problems gives students an experienced and motivating way so that
students can build or re-invent mathematical concepts. Contextual problems here
are not always a real world problem, but could be other situations that can still be
imagined by students. By using contextual problem in the beginning of learning, it
intends to stimulate students to construct or invent the defenitions, concepts,
operations, and the way of solving problems. So they could be more understood
concepts of the topic they are learning.
The second characteristic is the use of models for progressive
mathematization. Since students have understood the concepts by using contextual
The third characteristic is the use of student’s own production and contribution. Student-centered learning aims to stimulate students in generating
ideas, variation of answer, and variation of informal problem solving.
The fourth characteristic is the interactive. By interactivity in learning
process, that is interaction between student and teacher, among students, and
students and their environment, causes students have active roles in sharing their
own knowledge so that the learning process becomes meaningful.
The fifth characteristic is the intertwinement. Concepts, topics,
procedures in mathematics have intertwinement (Suryanto, et. al, 2010:45). The
intertwinement made integration among the concepts, even between mathematics
and other subjects. By this integration, learning time becomes more efficient and
easier for students to solve problems.
Besides having five characteristics above, RME approach also has three
principles; they are guided reinvention and progressive mathematization,
didactical phenomenology, and self-developed model.
Based on the above RME characteristics and principles, RME fulfills the
criteria of scientific approach in curriculum of 2013 (Kemendikbud, 2013:182),
such as, 1) subject matter is based on the facts and explainable phenomena by
logic and certain reasoning; 2) encourage and inspire students to think critically,
annalistically, and exactly in identifying, understanding, solving problems, and
applying the subject matter; 3) encourage and inspire students to be able to
understand, apply, and develop rational and objective thinking system in
responding subject matter, etc. Besides that, in 2013 curriculum, teacher-centered
becomes student-centered, students more interactive
(teacher-student-people-environment), students is active in learning process, self-study system becomes
group-study, students may get the knowledge from whoever and wherever they
get, etc. It is appropriate with the characteristics of RME in the learning process.
By implementing learning syntax which is based on the characteristics
and principles of RME, they are understanding the contextual problems, solving
contextual problems, comparing or discussing the answers, and concluding
learning activity can be more fun because student is actively participated in
learning activities. The activeness of each student can be seen when they state
his/her knowledge based on his/her experience to teacher and his/her classmates.
Those activities could be made students able to classify the object based on its
concepts, give examples and non-examples, and use the concepts in solving
routine exercises. And also reinvention the concept by themselves is better than
recitation since students could apply the concept directly.
Based on the above explanation of problem background, researcher
attracts to conduct a research entitled “The Difference of Student’s
Mathematical Understanding in Realistic Mathematics Education and
Conventional Classroom of Grade VIII at SMP Negeri 1 Lubuk Pakam”
1.2. Problem Identification
Based on the background above, the matters that considered as problem
identification are:
a. Students considered that mathematics is a difficult subject.
b. Students are rarely involved in the learning process.
c. The student’s understanding of mathematical concept is low, so that they feel
hard to solve mathematics problem by their own way.
d. Most learners are only able to memorize the concepts and using the formula
without knowing why they are using that formula and even they do not know
the benefits of his knowledge into daily life.
e. Teacher often exemplifies to students how to solve problems.
f. Teacher explains the material is only targeting on learning outcomes rather
than on learning process.
g. The most activities in learning activities are still dominated by teacher.
1.3. Problem Limitation
Based on the above background and identification of problem, the
research problem is limited only to know the difference of student’s
understanding of mathematical concept in RME and in conventional classroom at
SMP Negeri 1 Lubuk Pakam in the topic of cube and cuboid.
1.4. Problem Formulation
Based on the above identification and limitation of problem, then the
problem formulation is: is student’s understanding of mathematical concept in
RME better than student’s understanding of mathematical concept in conventional
classroom at SMP Negeri 1 Lubuk Pakam?
1.5. Objective of Research
Based on problem formulation above, then the problem objective is: to
know whether student’s understanding of mathematical concept in RME
classroom is better than student’s understanding of mathematical concept in
conventional classroom at SMP Negeri 1 Lubuk Pakam.
1.6. Research Benefit
This research is expected to be useful for all people, including:
1. For students. Helping students of SMP Negeri 1 Lubuk Pakam for increasing
their conceptual understanding in mathematics.
2. For teacher. As consideration for teacher in implementing the Realistic Mathematics Education Approach to increase student’s understanding of mathematical concept in learning mathematics.
3. For researcher. The results of research can be used as reference in developing
1.7. Operational Defenition
1. Understanding of mathematical concept is students' ability to classify the
objects based on its concept, give example and non-example, and use the
concepts in solving routine exercises.
2. The syntaxes of realistic mathematics education are:
Step 1: Understanding the contextual problem
Teacher gives contextual problems to students.
Step 2: Solving the contextual problem
Teacher assists and enhances the results of the students by asking the
questions to lead students to construct their knowledge about the
possibility of appropriate model of.
Step 3: Comparing or discussing the answer
Teacher asks one of students to present model of and its solution in front of
the class, give opportunity to other students to present different model of,
and let students to respond and choose the appropriate model of.
Step 4: Summarizing
Teacher helps students to make a summary and conclusion.
3. Conventional learning model is a common learning which is done by most
teachers in school is marked by lecturing, explanation, and giving examples
