THE DIFFERENCE OF STUDENTS’ MATHEMATICAL REPRESENTATION ABILITY BY USING PROBLEMBASED LEARNING AND INQUIRY
BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE VIII SMP NEGERI 1TANJUNG MORAWA
A C A D E M I C Y E A R 2 0 1 6 / 2 0 1 7
By:
Erika Agustina Simbolon ID. 4123312007
Mathematics Education Study Program
SKRIPSI
Submittedto Fulfill The Requirement for Getting The Degree of SarjanaPendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
ii
BIOGRAPHY
Erika Agustina Simbolon was born on August 29th, 1994 in Medan, North Sumatera.
She is the second child of Mr.Togar PandapotanSimbolon and Mrs.Megawati
br.Situmorang. She attended elementary school, SDN 101880Tanjung Morawa
in2000. After Graduated from elementary school in 2006, she continued her study to
SMP Negeri 1 Tanjung Morawa and graduated in 2009. Later, She continued her
study to SMA Negeri 1 Tanjung Morawa. In 2012, she finished her study in SMA
Negeri 1 Tanjung Morawa and accepted as a student in Mathematics Education
Bilingual, Mathematics Department, Faculty of Mathematics and Natural Sciences,
iii
THE DIFFERENCE OF STUDENTS’ MATHEMATICAL REPRESENTATION ABILITY BY USING PROBLEM BASED LEARNING AND INQUIRY
BASED LEARNING ON THE TOPIC OF STATISTICS IN GRADE VIII SMP NEGERI 1 TANJUNG MORAWA
A C A D E M I C Y E A R 2 0 1 6 / 2 0 1 7
Abstract
iv
PREFACE
Praise to God Almighty who I believed in Jesus Christ, who accompany
every step in life, including in education so that writer can finish this skripsi. The
title of this skripsi is “The Difference Of Students' Mathematical Representation
Ability By Using Problem Based Learning And Inquiry Based Learning On The
Topic Of Statistics In Grade VIII SMP Negeri 1 Tanjung Morawa”. This skripsi
was arranged to satisfy the requirement to obtain the Degree of Sarjana
Pendidikan from Faculty Mathematics and Natural Science in State University of
Medan.
During the process of the writing of this skripsi, the writer received
support from various parties. Special thanks go to Mr. Dr. Edy Surya, M.Si as my
skripsi supervisor who has provided guidance, direction, and advice to the
perfection of this skripsi. Thanks are also due to Prof. Dr. Asmin, M.Pd, Dr.
Mulyono, M.Si and Pardomuan N.J.M Sinambela, S.Pd, M.Pd as author’s
examiners who have provided input and suggestion from the planning to the
completion of the preparation of the research of this skripsi. Thanks are also
extended to Prof.Dr.Hasratuddin, M.Pd as academic supervisor and then thank you so much for all author’s lecturer in FMIPA Unimed.
Thanks to Mrs.Arwidah Parinduri, S.Pd. as principle of SMP Negeri 1
Tanjung Morawa, Mrs. Duena Maritha Sihotang, S.Pd as mathematics teacher
and all teachers, staffs and also the students in grade VIII-1 and VIII-2 SMP
Negeri 1 Tanjung Morawa who have helped writer conducting the research.
Most special thanks to my beloved parents, Togar Pandapotan Simbolon
and Megawati br. Situmorang, who take care of me from since I was born, who
always be there for me, who pray days and nights and giving me motivation and
all i need in finishing this skripsi. Big thanks to my beloved sister Rame
Novayanti Simbolon and my brother in law Fernando Cay Hasibuan, my brother
support even moril or material and all my family for all pray, motivation, and
support until the end of my study.
This Skripsi was compiled from the strength, spirit, and endless friendship ever given by author’s best partner Febby, Bella, Aisyah, Mutiara, Aida, Windy, Rahima, Ariyanto, Bowo, Adi, and Rudi. Thanks to my big family in Bilingual
Mathematics Education 2012, Dessy, Friska Simbolon, Friska Elvita, Rani,
Satoto, and Dilla for sadness and happiness in the class.For all partner of PPLT
Unimed Bilingual 2016 of SMA Negeri 2 Balige, for my senior and junior in
mathematics department, my students SPECTRO 24th generation when author
was doing practice in SMA Negeri 2 Balige, thanks for the support and motivation
to finish my study. Thanks for every one who cannot be mentioned one by one
who support and motivate the author.
This skripsi, of course, has its own advantages and limitations. Building
critics and suggestions are needed to improve the quality for this skripsi. The best
wish is that this skripsi is useful for those who use this skripsi now and future.
Medan, April 2017
Author,
vi
CONTENT
Ratification Sheet i
Biography ii
Abstract iii
Preface iv
Contents vi
List of Figure ix
List of Table x
List of Appendix xi
CHAPTER I INTRODUCTION
1.1 Background 1
1.2 Problem Identification 9
1.3 Problem Limitation 9
1.4 Problem Formulation 9
1.5 Research Purpose 10
1.6 Benefit of Research 10
1.7 Operational Definitions 10
CHAPTER II LITERATURE REVIEW
2.1 Theoretical Framework 12
2.1.1 Representation in Mathematics 12
2.1.2 Mathematical Representation Ability 13
2.1.3 Problem Based Learning 19
2.1.3.1 The Characteristic of PBL 21
2.1.3.2 Syntax of Problem Based Learning 23
2.1.3.3 Advantages and Disadvantages of PBL 23
vii
2.1.4.1The process of Learning by using Inquiry Methods 27
2.1.4.2Syntax of Inquiry Based Learning 28
2.1.4.3Advantages and Disadvantages of IBL 29
2.1.5 Summary of Subject Matter (Statistics) 30
2.2 Relevant Research 32
3.4.2 Test of Students’ Mathematical Representation Ability 37
3.5 Type and Design of Research 43
CHAPTER IV RESULT AND DISCUSSION
4.1. Research Results 49
viii
4.1.1.1. Students’ Mathematical Representation Ability in the
Problem Based Learning Classroom 50
4.1.1.2. Students’ Mathematical Representation Ability in the
Inquiry Based Learning Classroom 51
4.1.2 Result of Normality Test 52
4.1.3. Result of Homogeneity Test 52
4.1.4. Result of Hypothesis Test 53
4.2. Research Discussion 54
CHAPTER V CONCLUSION AND SUGGESTION
5.1. Conclusion 55
5.2. Suggestion 55
REFERENCES 58
APPENDICES 61
ix
LIST OF FIGURE
Figure 1.1 Observation Result of Student’s Answer Number 1 4 Figure 1.2 Observation Result of Student’s Answer Number 2 5
Figure 1.3 The Question of Observation Question Number 3 6
Figure 1.4 Observation Result of Student’s Answer Number 3 6
Figure 2.2 Bar Graphs 31
Figure 2.3 Pie Charts 31
Figure 2.4 Line Charts 32
x
LIST OF TABLE
Table 2.1 Operational Form of Mathematical Representation Ability 16 Table 2.2 Indicator of Mathematical Representation Ability 18
Table 2.3 Syntax Problem-Based Learning 23
Table 2.4 Syntax Inquiry Based Learning 28
Table 3.1 The Blueprint of Mathematical Representation Ability 36
Table 3.2 The Rubric of Mathematical Representation Ability 37
Table 3.3 Research design of randomized control group only 41
Table 3.3 The Statistical Validity Confirmation of Mathematical
Representation Ability Test 34
Table 3.4 The Reliability Confirmation of Mathematical
Representation Ability Test 35
Table 4.1 Descriptive Statistics Summary 49
Table 4.2 Descriptive Statistics for PBL Score 50
Table 4.3 Descriptive Statistics for iBL Score 51
Table 4.4 Kolmogorov – Smirnov Test of Normality 52
Table 4.5 Test of Homogeneity of Variances 52
xi
LIST OF APPENDICES Appendix 1. The Blueprint of Mathematical Representation
Ability Initial Test 61
Appendix 2. Initial Test of Mathematical Representation Ability 62
Appendix 3. Alternative Solution of Mathematical Representation
Ability Initial Test 64
Appendix 4. Lesson Plan of Experimental Class I 66
Appendix 5. Lesson Plan of Experimental Class II 76
Appendix 6. Worksheet of Experimental Class I 85
Appendix 7. Worksheet of Experimental Class II 90
Appendix 8. The Blueprint of Students’ Mathematical Representation
Ability 96
Appendix 9. Test of Mathematical Representation Ability (Post Test) 97
Appendix 10. Alternative Solution Of Mathematical Representation
Ability (Post Test) 101
Appendix 11. Validity Of Students Mathematical Representation
Ability Sheet 104
Appendix 12. Statistical Validity of The Test 110
Appendix 13. Reliability of The Test 113
Appendix 14. The Scores of PBL and IBL Classroom 115
Appendix 15. Normality Test 116
Appendix 16. Homogeneity Test 119
Appendix 17. Hypothesis Test 121
Appendix 18. Critical r –table 124
Appendix 19. t – table
126
CHAPTER I
Lima alasan perlunya belajar matematika karena matematika merupakan (1) sarana bepikir yang jelas dan logis, (2) sarana utuk memecahkan masalah kehidupan sehari-hari, (3)sarana mengenal pola-pola hubungan dan generalisasi pengalaman, (4) sarana untuk mengembangkan kreativitas, dan (5) sarana untuk meningkatkan kesadaran terhadap perkembangan budaya.
Mastery of mathematics by students become a necessity that can not be bargained
in structuring reasoning and decision-making in an increasingly competitive era of
competition at this time.Mathematics learning activities is expected to be able
makes students ability to resolve the problems it faces, both in mathematics and
outside of mathematics, and makes students developing their reasoning, so that
students able to think critically, logically, systematically and finally expected that
students able to be objective, honest and discipline.
Mathematics as a very important science should have been the lesson that
favored by students that being learned mathematics. However, in reality the
math including lessons that disliked a lot of students.Fears of students are not only
caused by the students themselves, but rather the lack of ability of teachers
in creating a situation that could bring students interested inmathematics.The main
cause of the failure of a teacher in teaching in front of the class is superficiality of
knowledge of teachers against whom students and how their learning ways. So
every action learning that programmed even more mistakes than a policy
taken.Due to fears of the students, the purpose of mathematical education is not
2
According to National (NCTM, 2000: 206) that learning mathematics with
understanding is the main thing. Conceptual understanding and procedural isan
inseparable part of mathematicsproblemssolving.In NCTM (2000) also described
there are five standardsmathematical ability should be owned by students, namely:
problem solving, communication, connection, reasoning, and
repreprsentation.Based on the description, NCTM contains representations as one
of the standards that must be owned by students so that mathematical
representation of student really need to developed.
The mathematical representation ability is one of the general objectives of
learning mathematics in school. This ability is particularly important for students
and closely related to communication skills and problem-solving. To
communicate something, someone needs a good representation in the form of
pictures, graphs, charts, and other forms of representation. With representation,
problems that initially seem difficult and complicated can be seen more easily and
simply, so that the issues presented can be solved more easily.Goldin (2002: 208)
state that:
Representasiadalahelemen yang
sangatpentinguntukteoribelajarmengajarmatematika,
tidakhanyakarenapemakaian system simbolis yang
jugapentingdalammatematikadan kaya akankalimatdan kata, beragamdan
universal, tetapijugauntuk 2 alasanpentingyaitu (1)
matematikamempunyaiperananpentingdalammengkonseptualisasiduniany
ata; (2) matematikamembuathomomorphis yang
merupakanpenurunandaristrukturhal-hal lain dari yang pokok.
Hudiono (2005:19) state that the representation ability can support students to
understand mathematical concepts that learned and the relationship; to
communicate mathematical ideas of students, to know more about the relationship
(connection) between mathematical concepts; or apply mathematics in realistic
mathematical problems through modeling.The role of representations is
alsodescribed by NCTM (2000: 280)
3
Representations should be treated as essential elements in supporting
students’ understanding of mathematical concepts and relationships; in
communicating mathematical approaches, arguments, and understandings to one’s self and to others; in recognizing connections among related mathematical
concepts; and in applying mathematics to realistic problem situations through
modeling. New forms of representation associated with electronic technology
create a need for even greater instructional attention to representation. So,
representations underpinconceptual understanding, communications, connections,
and problem solving. All of these processes are assisted by an effective
representation. Students should engage with each of these in all of their
mathematics courses, so that effective presentations.
Create and use representations to organize, record, and communicate mathematical ideas;
Select, apply, and translate among mathematical representations to solve problems;
Use representations to model and interpret physical, social, and mathematical phenomena
Based on explanation above can be concluded that representationis one of
the important thing in understanding mathematics. Mathematics can be
understood if the students have good representation. So they able to describe,
interpret, express, symbolize or even modeling ideas, mathematical concepts and
the coherence among them and contained in a configuration, construction or
certain situations that appear in various forms in order to obtain clarity of
meaning, show understanding or looking for a solution of the problems.But on last
situation Mathematical representation ability of students is in school less attention
since many studentsdon’t comprehend about their mathematical representation
ability. Though mathematical representation ability is very important in learning
mathematics since facilitating the students to represent problem in form of
4
From the initial test which has been conducted by researchers to students,
it is known that the ability of students' mathematical representation is still low. It
can be seen from the answers that they make. Some of them are notable to create a
table of story problems correctly, notable to solve problems of the images
presented, and less able to write the conclusion of the diagram presented.
The following are some of the documentation of student test results.
Question 1
Given a following data
7, 9, 3, 6, 6, 8, 4, 5, 8, 7, 4, 5, 6, 9, 3
a. Calculate the mean values
b. Median and mode of data
Answer:
Figure 1.1Observation Result of Student’s Answer Number 1
From the answers above, we can conclude that the students have not been able to
represent the data into the form of mathematical expressions. Theydon’t
understandhow to calculate the mean of data and also don’t understand how to
find mode and median.
5
Sinchan body temperature for 10 days is shown by the following table.
Table 1.1The Question of Observation Question Number 2
Harike 1 2 3 4 5 6 7 8 9 10
Suhu (o C) 35 36 37 36 37.5 38 37 38 38.5 37
a.Draw a line diagram of the above data
b. How many days sinchan’s body temperature is above normal(36.5o C)??
Answer :
Figure 1.2Observation Result of Student’s Answer Number 2
From the answers above, we can conclude that the students have not been able to
represent the data into the form of graph. Students are not able to enter the data
correctly into the graph, data which he wrotedifferent from the data in question
and also don’t understand how to put the datafrom tables that given, so the student
feel so difficult to answer the question.
Question 3
The bar chart below shows the acquisition value math test grade VII-A. Minimal
6
Figure 1.3The Question of Observation Question Number 3 a. Calculate how much students that must follow the remedy
b. Make a conclusion from the above bar chart math scores
Answer :
Figure 1.4 Observation Result of Student’s Answer Number 3
From theanswersabove, wecanconcludethat thestudentshave not beenable to
representimagesinto written text correctlybecausestudents areless ableto
appreciatethe diagram basedfactscontaineddata. Hejustunderstand
thegraphbasedpersonal opinion.
Based onthese problems, researcherscansurmisethat thestudentswillhave
difficultyin the futureto managethe problemso thatitwillalsoaffect
7
Student’smasteryand understanding inmathematics.Student’s Mathematical
Representation ability still low because thelearning modelused bymathematics
teacherspoorlayin developing student’s ability.They still using conventional
learning. It requires studentstostrivethemselvesin learning. Itis not suitableto be
applied tothe studentinthismodernera.There are many factors can lead to low
mathematics student learning achievements. Prasad (2008) said:
There are three dimensions – school environment, teacher-student relations and value orientation among teachers’ influence the whole educational process in the classroom situation. School environment is an external factor and teacher-student relation is an internal factor. We know that values among teacher decide and control both the factors.
Students should been courage to play an active role in learning, teachers
must also be able to involve in technological sophistication in learning so that
students feel more passion and learning are more interesting. So, Student’s
Mathematical Representation ability will be improving well when teachers use the
right teaching methods.Therefore, while efforts should be made to improve the
ability of the student representation is to increase the competence of teachers in
selecting a learning model.Preferably learning model chosen is to increase student
engagement in the learning process because until now there are still many students
which complain even make mathematics as a frightening specter.So that they
become lazy to further explore more math.This tends to make students less active
that cause actions or behavior of the students are less skilled in communicating
ideas or their ideas.
Relating with the above description it is necessary to think about ways and
strategies to overcome the above problems. One model of learning which applied
in learning mathematics is the Problem-based learning.ProblemBased Learning is
effective to improve students' mathematical representation based on multi-level
and overall student achievement. According Tall (1995) in mathematical thinking,
someone will be faced with an object (a problem in the form of numbers, symbols,
statements, or other) in a learning environment, and it will have a perception of
this object and perform an internal process to an action. This action in the form of
verbal-8
deductive) through an object, or in the process of-concept with a conceptual link
between them. Problem-based learning that begins with the real concept enables
students to more easily understood better when working in groups as well as
classical. Each student is required to undertake the completion of a variety of
practice questions that had been prepared in the work sheet. PBL models can
facilitate the conceptual change on students because of cognitive conflict through
the exposed concrete problems.
The findings show that there is a change in the students’ misconceptions in
understanding mathematical representation. Problem Based Learning can facilitate
students' conceptual change because this model gives students opportunity to
syntesize the concept. Problem-based learning can facilitate changes of student
misconceptions about multi mathematical representation for problem-based
learning poses a challenge for students to develop a strategy to prove his
hypothesis. Once the strategy is used, the teacher role is to support students in
syntesizing of new concepts through questions support (scaffolding).
The learning model that can be applied in learning mathematics is
Inquiry-Based Learning.Inquiry-Inquiry-Based Learning is well suited to helping students become
active learners because it situates learning in real-world problems and makes
students responsible for their learning. It has the dual emphasis of helping learners
develop strategies and construct knowledge. Allowing students to interact with
materials, models, manipulate variables, explore phenomena, and attempt to apply
principle affords them with opportunities to notice patterns, discover underlying
causalities, and learn in ways that are seemingly more robust. Learning by using
Problem Based Learning (PBL) and Inquiry Based Learning (IBL) gives greater
opportunities for students to develop students' mathematical representation ability.
PBL and IBL learning model is expected to improve the ability of students'
mathematical representation is low, especially in the statistics.Statistics not
onlylearn the ability to find the truth and the absolute final answer, but also to
obtain a conceptual understanding and application of learning in life. But,between
both of models are definitely one better model applied to the topic statisticsand
9
the other models. Based on the general description above, then the researcher has
interested to do research entitled “The Difference of Students' Mathematical
Representation Ability By Using Problem Based Learning And Inquiry Based Learning on The Topic of Statistics in Grade VIII SMP Negeri 1 TanjungMorawa A.Y2016/2017.”
1.2 Problem Identification
Based on the explanation in the background, the problem identification:
a. Students of in SMP Negeri 1 TanjungMorawa still have difficulties in
solving mathematical represetation tests, especially on the topic of
statistics.
b. Students are not actively involved in the learning process.
c. Teacher in SMP Negeri 1 Tanjung Morawa never using a variety of
learning models (PBL or IBL) on the topic of statistics so that are not
visible differences better model used in topic of statistics because the
learning is still teacher centered.
d. The learning process in the classroom rarely train and develop the skills of
communication and interaction among students.
1.3 Problem Limitation
The problem limitation in this research are as follows:
1. The author sofocus with The Difference Of Student’s Mathematical
Representation Ability Taught By Using Problem based learning With
Inquiry based learning For Grade VIII in SMP Negeri 1 TanjungMorawa.
2. Learning in this Research topic is Statistics.
1.4 Problem Formulation
Based on the problem limitation and background above, the problem is
formulated: Whether Student’s Mathematical Representation Ability taught by
using Problem Based learning is higher than Inquiry Based Learning for Grade
10
1.5 Research Purpose
The purpose of this research: to know whether student’s Mathematical
Representation Ability taught by using Problem Based Learning is higher
thanInquiry Based Learning for grade VIII SMPNegeri 1 TanjungMorawa.
1.6 Benefit of Research
The benefits of this research are:
1. For students: Helping students of SMP Negeri 1 TanjungMorawa for
increasing their conceptual understanding in mathematics.
2. For teachers and prospective teachers: This study could be a reference in
planning learning of statistics subject.
3. For school: Expectto be a source of information or contribute ideas for
improvement of mathematics teaching, especially in school where the
researcher conducted and the school in general.
4. For researcher: The result of research can be used as reference in
developing the appropriate learning approach in learning process.
1.7 Operational definitions
In order to avoid the differences of clarity meaning about important terms
contained in this research, the operational definitions will be noted as following :
1. Mathematical representation ability is students’ ability to express
mathematical ideas (problem, statement, definition, and so on) into form:
(1) Picture, diagram, graph, or table; (2) Mathematical notation,
numerical/algebra symbol; (3) Written texts/words the interpretation of
their mind.
2. Problem-based learning that begins with the real concept enables students
to more easily understood better when working in groups as well as
11
of practice questions that had been prepared in the work sheet. PBL
models can facilitate the conceptual change on students because of
cognitive conflict through the exposed concrete problems.The findings show that there is a change in the students’ misconceptions in understanding mathematical representation. Problem Based Learning can
facilitate students' conceptual change because this model gives students
opportunity to syntesize the concept. Problem-based learning can facilitate
changes of student misconceptions about multi mathematical
representation for problem-based learning poses a challenge for students to
develop a strategy to prove his hypothesis.
3. Inquiry-based learning (IBL) is a pedagogy which best enables students to
experience the processes of knowledge creation and the key attributes are
learning stimulated by inquiry, a student-centred approach, a move to
CHAPTER V
CONCLUSION AND SUGGESTIONS
5.1 Conclusion
In Hypothesis test, the data are processed based on post test shows that
(2.284) > (1.671) that it’s mean H₀ rejected. So, can be
concluded that Students’ mathematical representation ability taught by using
Problem Based Learning is higher than Inquiry Based Learning.
5.2 Suggestions
Related to the writer’s research, some suggestions are pointed out as follows:
a. For Teachers, can be used as a references to choose a Problem Based
Learning not only in Statistics but also in another topics, Teachers are
expected to be active in guiding students in learning process so that weak
student can be helped to improving their mathematical representation ability,
and teachers should be able to guide and provide more detail to the students
about how to present the random data into the correct distribution table
groups
b. For prospective teachers, during the learning process takes place, the teacher
must be able to control the class so no student is making noise in the
classroom that can interfere with other students' concentration.
c. For School, is expected to be source of information or contribute ideas for
improvement of mathematics teaching and learning.
d. Researcher expecting of this research can be enhanced by next researcher.
58
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