APPLICATION OF PROBLEM BASED LEARNING MODEL TO IMPROVE THE MATHEMATICAL CREATIVE THINKING ABILITY OF JUNIOR HIGH SCHOOL STUDENTS.
APPLICATION OF PROBLEM BASED LEARNING MODEL TO
IMPROVE THE MATHEMATICAL CREATIVE THINKING
ABILITY OF JUNIOR HIGH SCHOOL STUDENTS
by :
Dwi Ardy Dermawan
ID. 4103312013
Mathematics Education Study Program
THESIS
Submitted to Fulfill the Requirements for Getting the Degree of
Sarjana Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
PREFACE
Give thankfulness to Allah SWT that gives the God’s mercy and spirit so
that writer can finish this thesis. The title of this thesis is “Application of Problem
Based Learning Model to Improve The Mathematical Creative Thinking Ability of
Junior High School Students”. This thesis was compiled to satisfy the requirement
for Degree of Sarjana Pendidikan from Faculty of Mathematics and Natural Science
in Medan State University.
In the completion of this thesis, the writer received support from various
parts, therefore it was appropriate writer big thanks to Prof. Dr. Bornok Sinaga,
M.Pd. as academic supervisor and thesis supervisor who has provided guidance,
direction, and advice to the perfection of this thesis. Thanks are also due to Dr. E.
Elvis Napitupulu, M.S. and Dra. Ida Karnasih, M.Sc, Ph.D. and Dra. Katrina
Samosir, M.Pd as examiners who have provided input and suggestion from the
planning to the completion of the preparation of the research of this thesis and then
thank you so much for all lecturers and employee staff in FMIPA.
Thanks are extended to Prof. Dr. Ibnu Hajar Damanik, M.Si. as directorate
of State University of Medan and employee staff in directorate office, for Prof. Drs.
Motlan, M.Sc. Ph.D. as Dean of Mathematics and Natural Sciences Faculty, and to
coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy Surya,
M.Si. as Chief of Mathematics Department, Zul Amry, M.Si., Ph.D as Chief of
Mathematics Education Study Program, Drs. Yasifati Hia, M.Si. as Secretary of
Mathematics Education, and all of employee staff who have helped the author.
Thanks to Sugiarto, S.Pd as principle of SMP N 1 Rantau Selatan who had
given permission to writer do the research, Solo Sihombing, S.Pd as mathematics
teacher and all teacher, staffs and also the students in VII-3 Class SMP N 1 Rantau
Selatan who have helped writer conducting the research.
Especially the writer would like to express gratitude to his beloved father
Untung Riat Moko and beloved mother Rotua Lina Tambunan that always be hero
and angel for writer and always provide motivation and prayers for the success of
the writer completed this thesis. Writer also say big thanks to his beloved sister
Ririn Eko Febrina, S.Pd with her husband Syahrial Adam, S.T, his beloved sister
Tri Dewi Andani, and his beloved brother Ari Darma Prastio that always give
support even moril or material and all of family for all pray, motivation, and
support until the end of writer’s study.
Writer wants to say thanks to his best friends in Bilingual Mathematics
Class 2010, for the valuable support and motivation. Thanks also for friends,
teachers and students at SMA N 1 Tebing Tinggi, and all who have become family
while stayed in Tebing Tinggi, also thanks to beloved students Ira Putri Utami, Ika
Febri Chairawan, Indah Pratiwi, Tia Risdiana, and all my students in the world.
Thanks for friends under one roof (Zhul, Anggili, Anot, Liono, Iwan, Weli, Pian
and Ridho), and all friends who can’t be mentioned one by one, also thanks for all
stars that had shone all nights in this journey, and for the last is for the brightest
ever, special thanks to my special one, Dwi Kurnia Lestari for the motivations,
prayers, and love.
The writer should give a big effort to prepare this thesis, and the writer
know that this thesis have so many weakness. So that, the writer needs some
suggestions to make it be better. And big wishes, it can be improve our knowledge.
Medan, February
2015
Author,
Dwi Ardy Dermawan
ID. 4103312013
APPLICATION OF PROBLEM BASED LEARNING MODEL TO
IMPROVE THE MATHEMATICAL CREATIVE THINKING
ABILITY OF JUNIOR HIGH SCHOOL STUDENTS
Dwi Ardy Dermawan (4103312013)
ABSTRACT
The problem of this research was the low student’s creative thinking abilities. This
research aimed to improve students’ creative thinking ability by applying problem
based learning model. Problems were identified based on initial observation result
that consist of preliminary and interview test with mathematics teacher for grade
VII-3 in SMP N 1 Rantau Selatan. Initial ability test was done to know creative
thinking ability and references to grouping students in problem based learning that
will be done next. This research was Class Action Research (CAR), which is
implemented in SMP N 1 Rantau Selatan. The subject in this research were the
students of grade VII-3 academic year 2014/2015 that consists of 39 students. The
objects of this research were the students’ creative thinking ability which measured
by four indicators, namely fluency, flexibility, originality, and elaboration, and
problem based learning model. The level of problem solving capabilities planned in
this research was ≥ 80% of the total students that followed the test. This research
consisted of 2 cycles and from the first cycle consists of 2 meetings and the second
cycle consists of 2 meetings. Student’s creative thinking ability test was conducted
at the end of each cycle. The results of this research could be seen : (1) The
student’s creative thinking ability test in cycle 1, completed by 22 students and not
completed by 17 students, classical completeness was 56,41 %. (2) The student’s
creative thinking ability test in cycle 2, completed by 34 students and not completed
by only 5 students, classical completeness was 87,18%.
TABLE OF CONTENTS
Authentication Sheet ........................................................................................ i
Curriculum Vitae.............................................................................................. ii
Abstract ............................................................................................................ iii
Preface .............................................................................................................. iv
Table of Contents ............................................................................................. vi
List of Figures .................................................................................................. ix
List of Tables.................................................................................................... xi
List of Appendices ........................................................................................... xiv
CHAPTER I PRELIMINARY .........................................................................
1
1.1. Background .............................................................................................
1
1.2. Problem Identification ............................................................................
8
1.3. Problem Limitation .................................................................................
8
1.4. Problem Formulation ..............................................................................
8
1.5. Objectives of Research ...........................................................................
9
1.6. Benefits of Research ...............................................................................
9
1.7. Operational Definition ............................................................................
9
CHAPTER II LITERATURE REVIEW ..........................................................
11
2. 1. Theoritical Framework ...........................................................................
11
2.1.1. Mathematics Learning .......................................................................
11
2.1.2. Learning Model ..................................................................................
15
2.1.3. Problem Based Learning Model ........................................................
20
2.1.3.1. Learning Theories that Supports .................................................
29
2.1.4. Creative Thinking Ability ..................................................................
32
2.1.4.1. Definition of Thinking ................................................................
32
2.1.4.2. Definition of Creative .................................................................
33
2.1.4.3. Creative Thinking Ability ...........................................................
34
2.1.5. Learning Theory that Suport Subject Matter .....................................
37
2.1.6. Subject Matter ....................................................................................
38
2. 2. Relevant Researches ...............................................................................
44
2. 3. Conceptual Framework...........................................................................
46
2. 4. Hypothesis of Action ..............................................................................
47
CHAPTER III RESEARCH METHODS ........................................................
48
3.1. Types of Research...................................................................................
48
3.2. Location and Time of Research ..............................................................
48
3.3. Subject and Object of Research ..............................................................
48
3.4. Procedures of Research...........................................................................
48
3.5. Research Instruments ..............................................................................
51
3.6. Data Analysis Techniques ......................................................................
58
3.7. Indicators of Success ..............................................................................
61
CHAPTER IV RESEARCH RESULT AND DISCUSSION ..........................
62
4.1. Research Result .........................................................................................
62
4.1.1. The Result of Research in cycle 1 ...................................................
62
4.1.1.1. Problem 1............................................................................
62
4.1.1.2. Action Plan 1 ......................................................................
63
4.1.1.3. Action Implementation 1 ....................................................
63
4.1.1.4. Observation and Evaluation 1.............................................
64
4.1.1.5. Reflection 1.........................................................................
81
4.1.2. The Result of Research in cycle 2 ...................................................
85
4.1.2.1. Problem 2............................................................................
86
4.1.2.2. Action Plan 2 ......................................................................
86
4.1.2.3. Action Implementation 2 ....................................................
86
4.1.2.4. Observation and Evaluation 2.............................................
87
4.1.2.5. Reflection 2......................................................................... 103
4.2. Research Findings ..................................................................................... 107
4.3. Discussion of Research ............................................................................. 108
4.3.1. Students Creative Thinking Ability ................................................ 108
4.3.2. Students Activity Using Problem Based Learning ......................... 111
CHAPTER V CONCLUSIONS AND RECOMMENDATIONS ................... 114
5.1. Conclusion................................................................................................. 114
5.2. Recommendation ...................................................................................... 114
BIBLIOGRAPHY ............................................................................................ 116
LIST OF TABLES
Table 2.1. Syntax for Problem Based Learning Model
28
Table 2.2. Indicators of Creative Thinking Ability
36
Table 3.1. Lattice of Creative Thinking Ability I
52
Table 3.2. Lattice of Creative Thinking Ability II
53
Table 3.3. The Expert Validation Results of Creative Thinking Ability Test 1
54
Table 3.4. The Expert Validation Results of Creative Thinking Ability Test 2
54
Table 3.5. Validity Test of Instruments Test Cycle 1
55
Table 3.6. Validity Test of Instruments Test Cycle 2
56
Table 3.7. Reliability of Creative Thinking Ability Test
57
Table 3.8. List of Score’s Predicate and The Criteria
59
Table 3.9. Guidelines for Assessment of Teacher’s Ability to
manage learning
60
Table 3.10. Guidelines for Observation of Students’ Activity
60
Table 4.1. Observation Result of Teacher’s Activity Cycle 1
65
Table 4.2. Observation Result of Students’ Activity Cycle 1
66
Table 4.3. Result of Creative Thinking Ability Test for Fluency Indicator
70
Table 4.4. Percentage of Completeness for Fluency Indicator
71
Table 4.5. Result of Creative Thinking Ability Test for Flexibility Indicator
72
Table 4.6. Percentage of Completeness for Flexibility Indicator
72
Table 4.7. Result of Creative Thinking Ability Test for Originality Indicator
74
Table 4.8. Percentage of Completeness for Originality Indicator
75
Table 4.9. Result of Creative Thinking Ability Test for Elaboration Indicator 76
Table 4.10. Percentage of Completeness for Elaboration Indicator
77
Table 4.11. Percentage of Completeness for Each Indicator Cycle 1
78
Table 4.12. Result of Creative Thinking Ability Test Cycle 1
79
Table 4.13. Percentage of Completeness for Creative Thinking Ability Test 1
80
Table 4.14. Results Obtained from cycle 1
83
Table 4.15. Observation Result of Teacher’s Activity Cycle 2
88
Table 4.16. Observation Result of Students’ Activity Cycle 2
89
Table 4.17. Result of Creative Thinking Ability Test for Fluency
Indicator 2
Table 4.18. Percentage of Completeness for Fluency Indicator 2
92
93
Table 4.19. Result of Creative Thinking Ability Test for Flexibility
Indicator 2
Table 4.20. Percentage of Completeness for Flexibility Indicator 2
94
95
Table 4.21. Result of Creative Thinking Ability Test for Originality
Indicator 2
Table 4.22. Percentage of Completeness for Originality Indicator 2
96
96
Table 4.23. Result of Creative Thinking Ability Test for Elaboration
Indicator 2
Table 4.24. Percentage of Completeness for Elaboration Indicator 2
98
98
Table 4.25. Percentage of Completeness for Each Indicator Cycle 2
Table 4.26. Result of Creative Thinking Ability Test Cycle 2
99
101
Table 4.27. Percentage of Completeness for Creative Thinking Ability
Test 2
101
Table 4.28. Comparison between cycle 1 and cycle 2
104
Table 4.29. Results Obtained from cycle 2
105
LIST OF FIGURES
Figure 1.1.
Student’s answer on item no.1
4
Figure 1.2.
Student’s answer on item no.2
5
Figure 2.1.
Shape of Mr. Amal’s garden (example)
38
Figure 2.2.
Shape of Indah’s land (example)
40
Figure 2.3.
Models of Rectangle
42
Figure 2.4.
Illustration of rectangle’s properties
42
Figure 2.5.
Illustration of Square’s properties
43
Figure 3.1.
Procedures of Class Action Research
51
Figure 4.1.
Graph of category of students’ activity cycle 1
67
Figure 4.2.
Graph of percentage of students’ activity cycle 1
68
Figure 4.3.
Graph of Completeness for Fluency Indicator
71
Figure 4.4.
Graph of Completeness for Flexibility Indicator
73
Figure 4.5.
Graph of Completeness for Originality Indicator
75
Figure 4.6.
Graph of Completeness for Elaboration Indicator
77
Figure 4.7.
Graph of Completeness for Each Indicator Cycle 1
78
Figure 4.8.
Graph of Completeness of Creative Thinking Ability Test 1
80
Figure 4.9.
Graph of category of students’ activity cycle 2
90
Figure 4.10.
Graph of Completeness for Fluency Indicator 2
93
Figure 4.11.
Graph of Completeness for Flexibility Indicator 2
95
Figure 4.12.
Graph of Completeness for Originality Indicator 2
97
Figure 4.13.
Graph of Completeness for Elaboration Indicator 2
99
Figure 4.14.
Graph of Completeness for Each Indicator Cycle 2
100
Figure 4.15.
Graph of Completeness of Creative Thinking Ability Test 2 102
Figure 4.16.
Percentage of Students Creative Thinking Ability for Each
Indicator
Figure 4.17.
109
Increased of Percentage of Students Creative Thinking
Ability
110
LIST OF APPENDICES
Appendix 1. Lesson Plan 1
118
Appendix 2. Student Activity Sheet 1
125
Appendix 3. Lesson Plan 2
127
Appendix 4. Student Activity Sheet 2
134
Appendix 5. Lesson Plan 3
136
Appendix 6. Student Activity Sheet 3
143
Appendix 7. Lesson Plan 4
145
Appendix 8. Student Activity Sheet 4
152
Appendix 9. Initial Ability Test
154
Appendix 10. Alternative Solution of Initial Ability Test
155
Appendix 11. Guidance of Scoring for Initial Ability Test
162
Appendix 12. Lattice of Creative Thinking Ability Test I
163
Appendix 13. Lattice of creative Thinking Ability Test II
164
Appendix 14. Creative Thinking Ability Test I
165
Appendix 15. Creative Thinking Ability Test II
167
Appendix 16. Alternative Solution of Creative Thinking Ability Test 1
169
Appendix 17. Alternative Solution of Creative Thinking Ability Test 2
172
Appendix 18. Guidance of Scoring for Creative Thinking Ability Test
178
Appendix 19. The Validation Sheet of Creative Thinking Ability Test
179
Appendix 20. Validity of Creative Thinking Ability Test 1
191
Appendix 21. Validity of Creative Thinking Ability Test 2
194
Appendix 22. r table – Product Moment
197
Appendix 23. Reliability of Creative Thinking Ability Test 1
198
Appendix 24. Reliability of Creative Thinking Ability Test 2
200
Appendix 25. Teacher Observation Sheet
202
Appendix 26. Students’ Observation Sheet
214
Appendix 27. Result of Creative Thinking Ability Test 1
230
Appendix 28. Result of Creative Thinking Ability Test 2
232
Appendix 29. Documentations
244
1
CHAPTER I
PRELIMINARY
1.1. Background
Basically education is a process to help people in developing their
potential and thereby able to deal with any changes that occur. Through education
a person will get a variety of good science science science and technology.
Without an educated person will never know about the development of the outside
world can not even compete in the outside world. Therefore, education is
indispensable in everyday life. As well as that science will never be used up but
will grow if used.
Education has an important role in human life skills, education can affect
the development of the Human Resources in all aspects of the personality and life.
Trianto (2011 : 1) says that education is capable of supporting the development of
future educational atmospheres is to develop the potential of learners, so
concerned is able to face and solve life problems that it faces.
Arikunto (2011:115) argues that the purpose of education can be
formulated on three levels. First, the general objectives of education. This goal
determines whether or not something the program is held. In the daily practice in
schools, the goal is known as the General Instructional Objective. Second, the
purpose of which is based on behavior. In the period of the past twenty years,
many attempts have been made to find a method that can be used to analyze or
classify a view associated with the activities of daily education. The definition of
a successful education is in the form of behavior. This is what taxonomy. There
are three kinds of behavior are known in general, namely cognitive, affective, and
psychomotor (which in this case I use the term skill). Third, the purpose of which
is more clearly defined operationally.
Trianto (2011:1) explains that Law No. 20 of 2003 on the national
education system serves to develop skills and form the character and civilization
2
of dignity in the context of the intellectual life of the nation. Education aims to
develop potential students to become a man of faith and fear of God Almighty,
noble, healthy, knowledgeable, skilled, creative, independent, and become citizens
of a democratic and responsibilities.
In the world of education, mathematics as a subject in school was
considered quite an important role, both in shaping the patterns of thought and
qualified students into its application in everyday life and also because
mathematics is also a means to study something to think logically an
systematically.
Abdurrahman (2009 : 251) said that many people who view mathematics
as a field of study that is most difficult. Nonetheless, everyone should learn it as a
means to solve the problems of everyday life. Such as language, reading, and
writing, mathematics learning difficulties should be addressed as early as possible.
If not, the student will face a lot of problems because almost all fields of study
require the appropriate mathematics.
Mathematics is one of the areas of study that have an important role in
education. It can be seen from the number of hours these subjects than other
subjects. Mathematics lessons in the implementation of the education provided to
all levels of education starting from elementary school through college.
Mathematics is a science that is necessary to be taught. Cockroft (in
Abdurrahman, 2009 : 253) argues that mathematics should be taught because (1)
is always used in every facet of life, (2) All fields of study require appropriate
mathematical skills, (3) is a powerful means of communication, concise and clear,
(4) Can be used to present information in a variety of ways, (5) Enhancing the
ability to think logically, precision, spatial awareness, and (6) Provide satisfaction
with the efforts to solve challenging problems.
Mathematics as a science base, both aspects of its application as well as
aspects of reasoning, has an important role in the effort to control science and
technology. For that mathematics needs to function as a vehicle for school grow
3
and develop the intelligence, ability, skill and for shaping the personality of
students. Cornelius (in Abdurrahman , 2009: 253) also suggests five reasons for
studying mathematics because mathematics is (1) a means of clear and logical
thinking, (2) a means to solve the problems of everyday life, (3) the means to
know the patterns of relationships and generalization of experience, (4) the means
to develop creativity and (5) a means to raise awareness of cultural development.
However, learning mathematics is still in the spotlight, that mathematics is
seen is a difficult matter. Based on the experience of researchers at Teaching
Experience Program in School in August - November 2013 shows that the student
has a low learning spirit, and mastery of the mathematics learning of students is
low. Learning mathematics in school, have tended to focus on the teacher (teacher
centered). Teachers too dominating class , while students in the class only to be
the object. Events that stand out are the students just act as listeners, students are
less engaged and motivated to learn something about the learning, so thinking
ability is not creative that is just follow the steps or instructions that have been
there before.
Students' creativity or creative thinking ability of students often become
neglected in the teaching of mathematics. Generally people assume that creativity
and math has nothing to do with each other, and generally think that most
necessary logic in mathematics, while creativity is important in learning
mathematics.
Munandar (1999:7) also revealed the same picture appears in the field of
education. More emphasis on rote learning and looking for a right answer to the
questions given. The process of high thinking are rarely trained, including to think
creatively.
Before doing research, researcher make observation at July 8th 2014, the
researcher observe learning process in the class, and the researcher find the
students are less interested in learning mathematics, and in interwiew with some
students, answers that researcher got is the way of teacher to teach is boring and
4
another answer is the students don’t like mathematics subject because assumed
difficult. At the observation, researcher also find that model of learning that is
used by the teacher is not appropriate with goal of mathematics learning which is
make students be active in learning process and the learning model is not
supporting to make students have good mathematical creative thinking ability.
Indicators of creative thinking ability is fluency, flexibility, originality, and
elaboration. Indicator fluency is giving a lot of of ideas and flows of thought is
fluent. Indicator flexibility is giving ideas which is not uniform, able to change the
way or approach. Indicators original is giving answers that are not common,
different than the other, which is rarely given most people. Indicator elaboration is
developing and enriching an idea, specifyingthe details of idea and answers.
Lack of mathematical creative thinking ability is also evident from the
results of initial ability tests are given at the beginning of the observation to the
students of class VIII - 1 SMP Negeri 1 Rantau Selatan totaling 38 students,
obtained 100 % of all students are in the low category of creative thinking skills,
with a mean value average 23.24. The test given can be looked at appendix 6 page
101, with the alternative solution at appendix 7 page 102 and the guidance of
scoring at appendix 8 page 109. This test result shows that students are not able to
think creatively in solving mathematical problems.
Figure 1.1. Student’s answer on the item no.1
5
This picture above is one example of student’s answer, from this picture,
shown that in the item no.2, sthis student can only answer with one way, student’s
answer in second way is false.
Figure 1.2. Student’s answer on the item no.2
The second picture shows that in the item no.3, this student can only
answer with one way, this student can’t answer with the second way.
At the time of observation, Beside providing initial ability tests and
obervation of learning process, researchers also conducted interviews with
mathematic teacher Class VIII-1 namely, she said that students very rarely get
questions such as questions about the ability to think creatively or requesting more
than one answer. So that students are not able to answer as to what initial ability
tests are required in the matter . She also said that in the learning process, students
are less interested in learning mathematics, students are less active and
responsive, so just follow the formulas given teacher without being able to
develop it.
Issues regarding creativity can not be ignored given above is an aspect of
creativity needs to be developed in education. Creativity plays an important role
in a series of high - level mathematical thinking. Creative thinking can also be
viewed as a process that is used when an individual bring in or bring up a new
6
idea. The new idea is a combination of previous ideas that have never been
realized. Understanding creative thinking is characterized by a new idea that
emerged as a result of the thinking process.
Semiawan ( 1984 : 9 ) revealed that :
Success in education is often only assessed on the extent to which students
are able to produce a given material of knowledge. In mathematics ,
students are often required to solve the problems in only one way. It is
understandable that such an approach would lead to rigidity in thinking
and narrowness in reviewing an issue. Thus the power of creative thinking
as the ability to be able to see a problem from different angles review, it
inhibited
From the opinion, we can see that if someone is said creative so he can
think more than one idea or one way to solve problems he faced.
Relative to the need for a mathematical model of learning that can improve
students' understanding of a math problem. The use of problem-based learning
model is one alternative to improve the creativity of students.
Problem-Based Learning (PBL) is a learning model that is characterized
by the presence of the real problems that are not well structured as the context for
the learners to learn critical thinking and problem-solving skills and acquire
knowledge. Problem-based learning is one of the learning model associated with
contextual learning. Learning means confronted with a problem, which then
through problem solving, by through problems, students learn more basic skills.
Delisle (1997 : 7) stated that troblem-based learning (PBL) works well
with all students, making its strategies ideal for heterogeneous classrooms where
students with mixed abilities can pool their talents collaboratively to invent a
solution. These techniques also lend themselves to an interdisciplinary orientation
since answering a problem frequently requires information from several academic
areas. By allowing children to direct their own activities and by giving them
greater responsibilities, teachers show them how to challenge themselves and
7
learn on their own. Teachers who use active learning say they have seen their
students learn more material, understand more ideas, and enjoy school more.
Problem-based learning model is a model of learning is done in the
presence of a stimulus giving problems then do problem solving by students is
expected to increase the skills of students in achieving the learning materials.
Before starting the process of teaching and learning in the classroom, students are
first asked to observe a phenomenon first. Then the students are required to record
the problems that arise. After that the teacher's task is to stimulate students to
think critically to solve problems. The task of the teacher is to guide students to
question, to prove the assumption, and listen to the different opinions of them.
Problem-based learning model that challenges students to "learn how to learn",
working in groups to seek solutions to real world problems. Given problem is
used to bind the learners in the learning curiosity question. Problems given to
students before the students learn the concepts or materials relating to the problem
to be solved.
As has been described previously about creative thinking ability students
of initial ability test, and observation of researcher to teaching and learning
activity in that class. Creative thinking ability of students is low, and after
observation and interview mathematics teacher, researcher look that students in
learning just listen what teacher said in front of class, so students are less
interested in learning mathematics, less active and responsive, and students are
very rarely find questions or problem that needs creativity to solve it. All of these
are cause of creative thinking ability of students is low. Researcher choose
Problem Based Learning model to be a solution for that because in Problem Based
Learning model, students will be divided in groups, so students can give their idea
and opinion in their groups about the problem given. From some learning model
that use groups in the process, Problem Based Learning model in the process
started with a problem, so teacher can use opened question in Student Activity
Sheet, so student’s brain is stimulated to think creatively.
8
By using PBL model, to get the competencies, at the beginning of
meeting, students are given one opened question orally, to make students can find
and can give idea to the class, from different students, other students will listen
various answers. Researcher divide students to be groups and give Student
Activity Sheet to all groups. In a group, will make students can work actively and
can find ideas to solve problems in Students Activity Sheet which consists of
opened question. In process investigating, researcher checks and guides students
in each group, motivating students to try to find other solution of a problem, to
find new ways and knowledge. Students are also given props, such as geoboard at
first meeting, to help students to create shapes of other planes and then cube and
cuboid so that can stimulate creativity of students. Students are given a quiz at the
end of each meeting, to practice students to solve open ended questions, and at the
end of cycles, students are given test which consists of open ended question, and
ask various and new ways to students through the direction of the question.
In problem-based learning model, the problem raised in the context of
realistic that may be encountered in the future students. Then students search for
information related to the problem before solving the problem. By working in a
group, students are taught to be critical and not blindly accept and follow the ideas
put forward by his colleagues. Learning and knowledge acquired in an effort to
solve the given problem helps students to explain their thinking and to formulate
an accurate conception. Finally, review, evaluation, and integration of learning in
the final stages of PBL allows students to understand the new knowledge that is
built as a result of solving the problem. When thinking of something for the first
time, one generates new ideas, new assumptions, and new concepts by asking new
questions, create a new conclusion, and allowing a view to forming a new
direction. It is essentially a creative act.
By applying this model, the expected learning that takes place can be more
meaningful and gives a strong impression on the students, and can certainly
improve the ability to think creatively math of students so that the learning
process is always demanding improvement efforts. Based on the description
above, the researchers wanted to conduct a study entitled "Application of
9
Problem-Based Learning Model to improve the mathematical creative thinking
ability of junior high school student".
1.2. Problem Identification
Based on the description that has been raised on the background of the
problem , the problem can be identified :
1. Students are less interested in learning mathematics
2. Learning model that used by teacher cause students are still less active during
the learning process.
3. The student’s mathematical creative thinking ability is low in solving
mathematical problems.
1.3. Problem Limitation
Because of the problems identified fairly wide, so that a more focused
study, the researchers made the extent of the problem in improving mathematical
creative thinking ability of junior high school students to solve mathematics
problem by applying problem-based learning model
1.4. Problem Formulation
Based on the above description of the problem limitation, the problem
formulation to be studied in this research are :
Whether the application of Problem-Based Learning model can improve the
mathematical creative thinking ability of junior high school students?
1.5. Objectives of Research
The objectives of this research are to know whether the application of
Problem-Based Learning model can improve the students' mathematical creative
thinking ability in solving mathematical problems
10
1.6. Benefits of Research
1 For students, through a model of problem-based learning is expected to
improve students' creativity in solving mathematical problems.
2 For teachers, providing an alternative to choose to use mathematical learning
model.
3 For schools, provide input for empower policy for implementation innovative
learning model for improving the quality of mathematics education
4 For researchers, as an input to develop the insight and knowledge as a teacher
candidate.
1.7. Operational Definition
To be able to study quantitatively the variables are defined as follows :
1. Learning is a process in the form of activities and efforts of an someone or
individual getting new knowledge/experience to make changes , both
aspects of knowledge and aspects of behavior in which these changes can
be observed , continuous , functional , positive , and active takes place in a
relatively long time.
2. Problem-based learning is a learning that begins with a problem in an
effort to stimulate and improve the thinking ability of students so that the
students construct their own knowledge. And problem-based learning have
5 phases, namely Orient students to the problem, Organize students for
study, Assist independent and group investigation, Develop and present
artifacts and exhibits, Analyze and evaluate the problem-solving process.
3. Creativity is the ability to bring something new , whether it be the idea
and the real work , both in the work of both new and existing things that
are relatively different. And there are four indicators used to measure
students' mathe
4. matical creative thinking ability, namely Ability to think fluently
(fluency), ability to think flexibly (flexibility), ability to think originally
(originality), ability to itemize (elaboration).
114
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusion
Based on the research results presented in the previous section can be
concluded that the application of problem-based learning model in learning on the
subject of Rectangle and Square can increase students' creative thinking abilities
of Grade VII-3 of SMP Negeri 1 Rantau Selatan. It is known from the result of
students’ creative thinking ability test in cycle 2 higher than cycle 1. Percentage of
many students who have minimal ability “medium” of 56,41% in cycle 1
increased to 87,18% in cycle 2. And Learning by using Problem Based Learning
Model also could make students’ activity in the learning was good category
5.2
Recommendation
Based on these results, the authors propose some suggestions for learning
mathematics, especially in secondary schools, namely:
1. Learning mathematics with problem-based learning model can be used as
an alternative learning effective in improving students' ability to think
creatively. But in the early learning, teachers will have difficulty in
preparing the child to make the process of cooperative learning, student is
difficult to accept the learning changes they have done so far with
constructivism learning through problem-based learning model. Therefore,
it is suggested that before learning to do, the teacher to familiarize the
learning with cooperative learning so that students will be accustomed to
the learning process
2. To support the successful implementation of problem-based learning
model required teaching materials an interesting, for the student activity
sheet should be designed based on the contextual issues are close to
everyday students and challenge students to solve.
115
3. Besides improving the students’ creative thinking abilities, problem-based
learning model also can stimulate the activity of students in learning and
can assist students in forming a positive perception towards learning
mathematics. Therefore this kind of learning is advisable to be developed
further other mathematics items and different levels of education.
4. This research only reveals the role of problem based learning model in
increasing students' creative thinking abilities, To complete the study of
the role of problem-based learning model as a whole needs to do further
research to see a role model of problem-based learning to improve
problem-solving abilities, reasoning, and mathematical connections.
5. The results of this research can be used as input for the school to improve
students' activity during the learning process.
6. The results of this research can also be used as input for the school
because it can give a positive response to the students' learning activities
through the application of problem-based learning.
7. It is hoped to further research with the application of problem-based
learning model in order to observe and increase the allocation of meeting
time.
IMPROVE THE MATHEMATICAL CREATIVE THINKING
ABILITY OF JUNIOR HIGH SCHOOL STUDENTS
by :
Dwi Ardy Dermawan
ID. 4103312013
Mathematics Education Study Program
THESIS
Submitted to Fulfill the Requirements for Getting the Degree of
Sarjana Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
PREFACE
Give thankfulness to Allah SWT that gives the God’s mercy and spirit so
that writer can finish this thesis. The title of this thesis is “Application of Problem
Based Learning Model to Improve The Mathematical Creative Thinking Ability of
Junior High School Students”. This thesis was compiled to satisfy the requirement
for Degree of Sarjana Pendidikan from Faculty of Mathematics and Natural Science
in Medan State University.
In the completion of this thesis, the writer received support from various
parts, therefore it was appropriate writer big thanks to Prof. Dr. Bornok Sinaga,
M.Pd. as academic supervisor and thesis supervisor who has provided guidance,
direction, and advice to the perfection of this thesis. Thanks are also due to Dr. E.
Elvis Napitupulu, M.S. and Dra. Ida Karnasih, M.Sc, Ph.D. and Dra. Katrina
Samosir, M.Pd as examiners who have provided input and suggestion from the
planning to the completion of the preparation of the research of this thesis and then
thank you so much for all lecturers and employee staff in FMIPA.
Thanks are extended to Prof. Dr. Ibnu Hajar Damanik, M.Si. as directorate
of State University of Medan and employee staff in directorate office, for Prof. Drs.
Motlan, M.Sc. Ph.D. as Dean of Mathematics and Natural Sciences Faculty, and to
coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy Surya,
M.Si. as Chief of Mathematics Department, Zul Amry, M.Si., Ph.D as Chief of
Mathematics Education Study Program, Drs. Yasifati Hia, M.Si. as Secretary of
Mathematics Education, and all of employee staff who have helped the author.
Thanks to Sugiarto, S.Pd as principle of SMP N 1 Rantau Selatan who had
given permission to writer do the research, Solo Sihombing, S.Pd as mathematics
teacher and all teacher, staffs and also the students in VII-3 Class SMP N 1 Rantau
Selatan who have helped writer conducting the research.
Especially the writer would like to express gratitude to his beloved father
Untung Riat Moko and beloved mother Rotua Lina Tambunan that always be hero
and angel for writer and always provide motivation and prayers for the success of
the writer completed this thesis. Writer also say big thanks to his beloved sister
Ririn Eko Febrina, S.Pd with her husband Syahrial Adam, S.T, his beloved sister
Tri Dewi Andani, and his beloved brother Ari Darma Prastio that always give
support even moril or material and all of family for all pray, motivation, and
support until the end of writer’s study.
Writer wants to say thanks to his best friends in Bilingual Mathematics
Class 2010, for the valuable support and motivation. Thanks also for friends,
teachers and students at SMA N 1 Tebing Tinggi, and all who have become family
while stayed in Tebing Tinggi, also thanks to beloved students Ira Putri Utami, Ika
Febri Chairawan, Indah Pratiwi, Tia Risdiana, and all my students in the world.
Thanks for friends under one roof (Zhul, Anggili, Anot, Liono, Iwan, Weli, Pian
and Ridho), and all friends who can’t be mentioned one by one, also thanks for all
stars that had shone all nights in this journey, and for the last is for the brightest
ever, special thanks to my special one, Dwi Kurnia Lestari for the motivations,
prayers, and love.
The writer should give a big effort to prepare this thesis, and the writer
know that this thesis have so many weakness. So that, the writer needs some
suggestions to make it be better. And big wishes, it can be improve our knowledge.
Medan, February
2015
Author,
Dwi Ardy Dermawan
ID. 4103312013
APPLICATION OF PROBLEM BASED LEARNING MODEL TO
IMPROVE THE MATHEMATICAL CREATIVE THINKING
ABILITY OF JUNIOR HIGH SCHOOL STUDENTS
Dwi Ardy Dermawan (4103312013)
ABSTRACT
The problem of this research was the low student’s creative thinking abilities. This
research aimed to improve students’ creative thinking ability by applying problem
based learning model. Problems were identified based on initial observation result
that consist of preliminary and interview test with mathematics teacher for grade
VII-3 in SMP N 1 Rantau Selatan. Initial ability test was done to know creative
thinking ability and references to grouping students in problem based learning that
will be done next. This research was Class Action Research (CAR), which is
implemented in SMP N 1 Rantau Selatan. The subject in this research were the
students of grade VII-3 academic year 2014/2015 that consists of 39 students. The
objects of this research were the students’ creative thinking ability which measured
by four indicators, namely fluency, flexibility, originality, and elaboration, and
problem based learning model. The level of problem solving capabilities planned in
this research was ≥ 80% of the total students that followed the test. This research
consisted of 2 cycles and from the first cycle consists of 2 meetings and the second
cycle consists of 2 meetings. Student’s creative thinking ability test was conducted
at the end of each cycle. The results of this research could be seen : (1) The
student’s creative thinking ability test in cycle 1, completed by 22 students and not
completed by 17 students, classical completeness was 56,41 %. (2) The student’s
creative thinking ability test in cycle 2, completed by 34 students and not completed
by only 5 students, classical completeness was 87,18%.
TABLE OF CONTENTS
Authentication Sheet ........................................................................................ i
Curriculum Vitae.............................................................................................. ii
Abstract ............................................................................................................ iii
Preface .............................................................................................................. iv
Table of Contents ............................................................................................. vi
List of Figures .................................................................................................. ix
List of Tables.................................................................................................... xi
List of Appendices ........................................................................................... xiv
CHAPTER I PRELIMINARY .........................................................................
1
1.1. Background .............................................................................................
1
1.2. Problem Identification ............................................................................
8
1.3. Problem Limitation .................................................................................
8
1.4. Problem Formulation ..............................................................................
8
1.5. Objectives of Research ...........................................................................
9
1.6. Benefits of Research ...............................................................................
9
1.7. Operational Definition ............................................................................
9
CHAPTER II LITERATURE REVIEW ..........................................................
11
2. 1. Theoritical Framework ...........................................................................
11
2.1.1. Mathematics Learning .......................................................................
11
2.1.2. Learning Model ..................................................................................
15
2.1.3. Problem Based Learning Model ........................................................
20
2.1.3.1. Learning Theories that Supports .................................................
29
2.1.4. Creative Thinking Ability ..................................................................
32
2.1.4.1. Definition of Thinking ................................................................
32
2.1.4.2. Definition of Creative .................................................................
33
2.1.4.3. Creative Thinking Ability ...........................................................
34
2.1.5. Learning Theory that Suport Subject Matter .....................................
37
2.1.6. Subject Matter ....................................................................................
38
2. 2. Relevant Researches ...............................................................................
44
2. 3. Conceptual Framework...........................................................................
46
2. 4. Hypothesis of Action ..............................................................................
47
CHAPTER III RESEARCH METHODS ........................................................
48
3.1. Types of Research...................................................................................
48
3.2. Location and Time of Research ..............................................................
48
3.3. Subject and Object of Research ..............................................................
48
3.4. Procedures of Research...........................................................................
48
3.5. Research Instruments ..............................................................................
51
3.6. Data Analysis Techniques ......................................................................
58
3.7. Indicators of Success ..............................................................................
61
CHAPTER IV RESEARCH RESULT AND DISCUSSION ..........................
62
4.1. Research Result .........................................................................................
62
4.1.1. The Result of Research in cycle 1 ...................................................
62
4.1.1.1. Problem 1............................................................................
62
4.1.1.2. Action Plan 1 ......................................................................
63
4.1.1.3. Action Implementation 1 ....................................................
63
4.1.1.4. Observation and Evaluation 1.............................................
64
4.1.1.5. Reflection 1.........................................................................
81
4.1.2. The Result of Research in cycle 2 ...................................................
85
4.1.2.1. Problem 2............................................................................
86
4.1.2.2. Action Plan 2 ......................................................................
86
4.1.2.3. Action Implementation 2 ....................................................
86
4.1.2.4. Observation and Evaluation 2.............................................
87
4.1.2.5. Reflection 2......................................................................... 103
4.2. Research Findings ..................................................................................... 107
4.3. Discussion of Research ............................................................................. 108
4.3.1. Students Creative Thinking Ability ................................................ 108
4.3.2. Students Activity Using Problem Based Learning ......................... 111
CHAPTER V CONCLUSIONS AND RECOMMENDATIONS ................... 114
5.1. Conclusion................................................................................................. 114
5.2. Recommendation ...................................................................................... 114
BIBLIOGRAPHY ............................................................................................ 116
LIST OF TABLES
Table 2.1. Syntax for Problem Based Learning Model
28
Table 2.2. Indicators of Creative Thinking Ability
36
Table 3.1. Lattice of Creative Thinking Ability I
52
Table 3.2. Lattice of Creative Thinking Ability II
53
Table 3.3. The Expert Validation Results of Creative Thinking Ability Test 1
54
Table 3.4. The Expert Validation Results of Creative Thinking Ability Test 2
54
Table 3.5. Validity Test of Instruments Test Cycle 1
55
Table 3.6. Validity Test of Instruments Test Cycle 2
56
Table 3.7. Reliability of Creative Thinking Ability Test
57
Table 3.8. List of Score’s Predicate and The Criteria
59
Table 3.9. Guidelines for Assessment of Teacher’s Ability to
manage learning
60
Table 3.10. Guidelines for Observation of Students’ Activity
60
Table 4.1. Observation Result of Teacher’s Activity Cycle 1
65
Table 4.2. Observation Result of Students’ Activity Cycle 1
66
Table 4.3. Result of Creative Thinking Ability Test for Fluency Indicator
70
Table 4.4. Percentage of Completeness for Fluency Indicator
71
Table 4.5. Result of Creative Thinking Ability Test for Flexibility Indicator
72
Table 4.6. Percentage of Completeness for Flexibility Indicator
72
Table 4.7. Result of Creative Thinking Ability Test for Originality Indicator
74
Table 4.8. Percentage of Completeness for Originality Indicator
75
Table 4.9. Result of Creative Thinking Ability Test for Elaboration Indicator 76
Table 4.10. Percentage of Completeness for Elaboration Indicator
77
Table 4.11. Percentage of Completeness for Each Indicator Cycle 1
78
Table 4.12. Result of Creative Thinking Ability Test Cycle 1
79
Table 4.13. Percentage of Completeness for Creative Thinking Ability Test 1
80
Table 4.14. Results Obtained from cycle 1
83
Table 4.15. Observation Result of Teacher’s Activity Cycle 2
88
Table 4.16. Observation Result of Students’ Activity Cycle 2
89
Table 4.17. Result of Creative Thinking Ability Test for Fluency
Indicator 2
Table 4.18. Percentage of Completeness for Fluency Indicator 2
92
93
Table 4.19. Result of Creative Thinking Ability Test for Flexibility
Indicator 2
Table 4.20. Percentage of Completeness for Flexibility Indicator 2
94
95
Table 4.21. Result of Creative Thinking Ability Test for Originality
Indicator 2
Table 4.22. Percentage of Completeness for Originality Indicator 2
96
96
Table 4.23. Result of Creative Thinking Ability Test for Elaboration
Indicator 2
Table 4.24. Percentage of Completeness for Elaboration Indicator 2
98
98
Table 4.25. Percentage of Completeness for Each Indicator Cycle 2
Table 4.26. Result of Creative Thinking Ability Test Cycle 2
99
101
Table 4.27. Percentage of Completeness for Creative Thinking Ability
Test 2
101
Table 4.28. Comparison between cycle 1 and cycle 2
104
Table 4.29. Results Obtained from cycle 2
105
LIST OF FIGURES
Figure 1.1.
Student’s answer on item no.1
4
Figure 1.2.
Student’s answer on item no.2
5
Figure 2.1.
Shape of Mr. Amal’s garden (example)
38
Figure 2.2.
Shape of Indah’s land (example)
40
Figure 2.3.
Models of Rectangle
42
Figure 2.4.
Illustration of rectangle’s properties
42
Figure 2.5.
Illustration of Square’s properties
43
Figure 3.1.
Procedures of Class Action Research
51
Figure 4.1.
Graph of category of students’ activity cycle 1
67
Figure 4.2.
Graph of percentage of students’ activity cycle 1
68
Figure 4.3.
Graph of Completeness for Fluency Indicator
71
Figure 4.4.
Graph of Completeness for Flexibility Indicator
73
Figure 4.5.
Graph of Completeness for Originality Indicator
75
Figure 4.6.
Graph of Completeness for Elaboration Indicator
77
Figure 4.7.
Graph of Completeness for Each Indicator Cycle 1
78
Figure 4.8.
Graph of Completeness of Creative Thinking Ability Test 1
80
Figure 4.9.
Graph of category of students’ activity cycle 2
90
Figure 4.10.
Graph of Completeness for Fluency Indicator 2
93
Figure 4.11.
Graph of Completeness for Flexibility Indicator 2
95
Figure 4.12.
Graph of Completeness for Originality Indicator 2
97
Figure 4.13.
Graph of Completeness for Elaboration Indicator 2
99
Figure 4.14.
Graph of Completeness for Each Indicator Cycle 2
100
Figure 4.15.
Graph of Completeness of Creative Thinking Ability Test 2 102
Figure 4.16.
Percentage of Students Creative Thinking Ability for Each
Indicator
Figure 4.17.
109
Increased of Percentage of Students Creative Thinking
Ability
110
LIST OF APPENDICES
Appendix 1. Lesson Plan 1
118
Appendix 2. Student Activity Sheet 1
125
Appendix 3. Lesson Plan 2
127
Appendix 4. Student Activity Sheet 2
134
Appendix 5. Lesson Plan 3
136
Appendix 6. Student Activity Sheet 3
143
Appendix 7. Lesson Plan 4
145
Appendix 8. Student Activity Sheet 4
152
Appendix 9. Initial Ability Test
154
Appendix 10. Alternative Solution of Initial Ability Test
155
Appendix 11. Guidance of Scoring for Initial Ability Test
162
Appendix 12. Lattice of Creative Thinking Ability Test I
163
Appendix 13. Lattice of creative Thinking Ability Test II
164
Appendix 14. Creative Thinking Ability Test I
165
Appendix 15. Creative Thinking Ability Test II
167
Appendix 16. Alternative Solution of Creative Thinking Ability Test 1
169
Appendix 17. Alternative Solution of Creative Thinking Ability Test 2
172
Appendix 18. Guidance of Scoring for Creative Thinking Ability Test
178
Appendix 19. The Validation Sheet of Creative Thinking Ability Test
179
Appendix 20. Validity of Creative Thinking Ability Test 1
191
Appendix 21. Validity of Creative Thinking Ability Test 2
194
Appendix 22. r table – Product Moment
197
Appendix 23. Reliability of Creative Thinking Ability Test 1
198
Appendix 24. Reliability of Creative Thinking Ability Test 2
200
Appendix 25. Teacher Observation Sheet
202
Appendix 26. Students’ Observation Sheet
214
Appendix 27. Result of Creative Thinking Ability Test 1
230
Appendix 28. Result of Creative Thinking Ability Test 2
232
Appendix 29. Documentations
244
1
CHAPTER I
PRELIMINARY
1.1. Background
Basically education is a process to help people in developing their
potential and thereby able to deal with any changes that occur. Through education
a person will get a variety of good science science science and technology.
Without an educated person will never know about the development of the outside
world can not even compete in the outside world. Therefore, education is
indispensable in everyday life. As well as that science will never be used up but
will grow if used.
Education has an important role in human life skills, education can affect
the development of the Human Resources in all aspects of the personality and life.
Trianto (2011 : 1) says that education is capable of supporting the development of
future educational atmospheres is to develop the potential of learners, so
concerned is able to face and solve life problems that it faces.
Arikunto (2011:115) argues that the purpose of education can be
formulated on three levels. First, the general objectives of education. This goal
determines whether or not something the program is held. In the daily practice in
schools, the goal is known as the General Instructional Objective. Second, the
purpose of which is based on behavior. In the period of the past twenty years,
many attempts have been made to find a method that can be used to analyze or
classify a view associated with the activities of daily education. The definition of
a successful education is in the form of behavior. This is what taxonomy. There
are three kinds of behavior are known in general, namely cognitive, affective, and
psychomotor (which in this case I use the term skill). Third, the purpose of which
is more clearly defined operationally.
Trianto (2011:1) explains that Law No. 20 of 2003 on the national
education system serves to develop skills and form the character and civilization
2
of dignity in the context of the intellectual life of the nation. Education aims to
develop potential students to become a man of faith and fear of God Almighty,
noble, healthy, knowledgeable, skilled, creative, independent, and become citizens
of a democratic and responsibilities.
In the world of education, mathematics as a subject in school was
considered quite an important role, both in shaping the patterns of thought and
qualified students into its application in everyday life and also because
mathematics is also a means to study something to think logically an
systematically.
Abdurrahman (2009 : 251) said that many people who view mathematics
as a field of study that is most difficult. Nonetheless, everyone should learn it as a
means to solve the problems of everyday life. Such as language, reading, and
writing, mathematics learning difficulties should be addressed as early as possible.
If not, the student will face a lot of problems because almost all fields of study
require the appropriate mathematics.
Mathematics is one of the areas of study that have an important role in
education. It can be seen from the number of hours these subjects than other
subjects. Mathematics lessons in the implementation of the education provided to
all levels of education starting from elementary school through college.
Mathematics is a science that is necessary to be taught. Cockroft (in
Abdurrahman, 2009 : 253) argues that mathematics should be taught because (1)
is always used in every facet of life, (2) All fields of study require appropriate
mathematical skills, (3) is a powerful means of communication, concise and clear,
(4) Can be used to present information in a variety of ways, (5) Enhancing the
ability to think logically, precision, spatial awareness, and (6) Provide satisfaction
with the efforts to solve challenging problems.
Mathematics as a science base, both aspects of its application as well as
aspects of reasoning, has an important role in the effort to control science and
technology. For that mathematics needs to function as a vehicle for school grow
3
and develop the intelligence, ability, skill and for shaping the personality of
students. Cornelius (in Abdurrahman , 2009: 253) also suggests five reasons for
studying mathematics because mathematics is (1) a means of clear and logical
thinking, (2) a means to solve the problems of everyday life, (3) the means to
know the patterns of relationships and generalization of experience, (4) the means
to develop creativity and (5) a means to raise awareness of cultural development.
However, learning mathematics is still in the spotlight, that mathematics is
seen is a difficult matter. Based on the experience of researchers at Teaching
Experience Program in School in August - November 2013 shows that the student
has a low learning spirit, and mastery of the mathematics learning of students is
low. Learning mathematics in school, have tended to focus on the teacher (teacher
centered). Teachers too dominating class , while students in the class only to be
the object. Events that stand out are the students just act as listeners, students are
less engaged and motivated to learn something about the learning, so thinking
ability is not creative that is just follow the steps or instructions that have been
there before.
Students' creativity or creative thinking ability of students often become
neglected in the teaching of mathematics. Generally people assume that creativity
and math has nothing to do with each other, and generally think that most
necessary logic in mathematics, while creativity is important in learning
mathematics.
Munandar (1999:7) also revealed the same picture appears in the field of
education. More emphasis on rote learning and looking for a right answer to the
questions given. The process of high thinking are rarely trained, including to think
creatively.
Before doing research, researcher make observation at July 8th 2014, the
researcher observe learning process in the class, and the researcher find the
students are less interested in learning mathematics, and in interwiew with some
students, answers that researcher got is the way of teacher to teach is boring and
4
another answer is the students don’t like mathematics subject because assumed
difficult. At the observation, researcher also find that model of learning that is
used by the teacher is not appropriate with goal of mathematics learning which is
make students be active in learning process and the learning model is not
supporting to make students have good mathematical creative thinking ability.
Indicators of creative thinking ability is fluency, flexibility, originality, and
elaboration. Indicator fluency is giving a lot of of ideas and flows of thought is
fluent. Indicator flexibility is giving ideas which is not uniform, able to change the
way or approach. Indicators original is giving answers that are not common,
different than the other, which is rarely given most people. Indicator elaboration is
developing and enriching an idea, specifyingthe details of idea and answers.
Lack of mathematical creative thinking ability is also evident from the
results of initial ability tests are given at the beginning of the observation to the
students of class VIII - 1 SMP Negeri 1 Rantau Selatan totaling 38 students,
obtained 100 % of all students are in the low category of creative thinking skills,
with a mean value average 23.24. The test given can be looked at appendix 6 page
101, with the alternative solution at appendix 7 page 102 and the guidance of
scoring at appendix 8 page 109. This test result shows that students are not able to
think creatively in solving mathematical problems.
Figure 1.1. Student’s answer on the item no.1
5
This picture above is one example of student’s answer, from this picture,
shown that in the item no.2, sthis student can only answer with one way, student’s
answer in second way is false.
Figure 1.2. Student’s answer on the item no.2
The second picture shows that in the item no.3, this student can only
answer with one way, this student can’t answer with the second way.
At the time of observation, Beside providing initial ability tests and
obervation of learning process, researchers also conducted interviews with
mathematic teacher Class VIII-1 namely, she said that students very rarely get
questions such as questions about the ability to think creatively or requesting more
than one answer. So that students are not able to answer as to what initial ability
tests are required in the matter . She also said that in the learning process, students
are less interested in learning mathematics, students are less active and
responsive, so just follow the formulas given teacher without being able to
develop it.
Issues regarding creativity can not be ignored given above is an aspect of
creativity needs to be developed in education. Creativity plays an important role
in a series of high - level mathematical thinking. Creative thinking can also be
viewed as a process that is used when an individual bring in or bring up a new
6
idea. The new idea is a combination of previous ideas that have never been
realized. Understanding creative thinking is characterized by a new idea that
emerged as a result of the thinking process.
Semiawan ( 1984 : 9 ) revealed that :
Success in education is often only assessed on the extent to which students
are able to produce a given material of knowledge. In mathematics ,
students are often required to solve the problems in only one way. It is
understandable that such an approach would lead to rigidity in thinking
and narrowness in reviewing an issue. Thus the power of creative thinking
as the ability to be able to see a problem from different angles review, it
inhibited
From the opinion, we can see that if someone is said creative so he can
think more than one idea or one way to solve problems he faced.
Relative to the need for a mathematical model of learning that can improve
students' understanding of a math problem. The use of problem-based learning
model is one alternative to improve the creativity of students.
Problem-Based Learning (PBL) is a learning model that is characterized
by the presence of the real problems that are not well structured as the context for
the learners to learn critical thinking and problem-solving skills and acquire
knowledge. Problem-based learning is one of the learning model associated with
contextual learning. Learning means confronted with a problem, which then
through problem solving, by through problems, students learn more basic skills.
Delisle (1997 : 7) stated that troblem-based learning (PBL) works well
with all students, making its strategies ideal for heterogeneous classrooms where
students with mixed abilities can pool their talents collaboratively to invent a
solution. These techniques also lend themselves to an interdisciplinary orientation
since answering a problem frequently requires information from several academic
areas. By allowing children to direct their own activities and by giving them
greater responsibilities, teachers show them how to challenge themselves and
7
learn on their own. Teachers who use active learning say they have seen their
students learn more material, understand more ideas, and enjoy school more.
Problem-based learning model is a model of learning is done in the
presence of a stimulus giving problems then do problem solving by students is
expected to increase the skills of students in achieving the learning materials.
Before starting the process of teaching and learning in the classroom, students are
first asked to observe a phenomenon first. Then the students are required to record
the problems that arise. After that the teacher's task is to stimulate students to
think critically to solve problems. The task of the teacher is to guide students to
question, to prove the assumption, and listen to the different opinions of them.
Problem-based learning model that challenges students to "learn how to learn",
working in groups to seek solutions to real world problems. Given problem is
used to bind the learners in the learning curiosity question. Problems given to
students before the students learn the concepts or materials relating to the problem
to be solved.
As has been described previously about creative thinking ability students
of initial ability test, and observation of researcher to teaching and learning
activity in that class. Creative thinking ability of students is low, and after
observation and interview mathematics teacher, researcher look that students in
learning just listen what teacher said in front of class, so students are less
interested in learning mathematics, less active and responsive, and students are
very rarely find questions or problem that needs creativity to solve it. All of these
are cause of creative thinking ability of students is low. Researcher choose
Problem Based Learning model to be a solution for that because in Problem Based
Learning model, students will be divided in groups, so students can give their idea
and opinion in their groups about the problem given. From some learning model
that use groups in the process, Problem Based Learning model in the process
started with a problem, so teacher can use opened question in Student Activity
Sheet, so student’s brain is stimulated to think creatively.
8
By using PBL model, to get the competencies, at the beginning of
meeting, students are given one opened question orally, to make students can find
and can give idea to the class, from different students, other students will listen
various answers. Researcher divide students to be groups and give Student
Activity Sheet to all groups. In a group, will make students can work actively and
can find ideas to solve problems in Students Activity Sheet which consists of
opened question. In process investigating, researcher checks and guides students
in each group, motivating students to try to find other solution of a problem, to
find new ways and knowledge. Students are also given props, such as geoboard at
first meeting, to help students to create shapes of other planes and then cube and
cuboid so that can stimulate creativity of students. Students are given a quiz at the
end of each meeting, to practice students to solve open ended questions, and at the
end of cycles, students are given test which consists of open ended question, and
ask various and new ways to students through the direction of the question.
In problem-based learning model, the problem raised in the context of
realistic that may be encountered in the future students. Then students search for
information related to the problem before solving the problem. By working in a
group, students are taught to be critical and not blindly accept and follow the ideas
put forward by his colleagues. Learning and knowledge acquired in an effort to
solve the given problem helps students to explain their thinking and to formulate
an accurate conception. Finally, review, evaluation, and integration of learning in
the final stages of PBL allows students to understand the new knowledge that is
built as a result of solving the problem. When thinking of something for the first
time, one generates new ideas, new assumptions, and new concepts by asking new
questions, create a new conclusion, and allowing a view to forming a new
direction. It is essentially a creative act.
By applying this model, the expected learning that takes place can be more
meaningful and gives a strong impression on the students, and can certainly
improve the ability to think creatively math of students so that the learning
process is always demanding improvement efforts. Based on the description
above, the researchers wanted to conduct a study entitled "Application of
9
Problem-Based Learning Model to improve the mathematical creative thinking
ability of junior high school student".
1.2. Problem Identification
Based on the description that has been raised on the background of the
problem , the problem can be identified :
1. Students are less interested in learning mathematics
2. Learning model that used by teacher cause students are still less active during
the learning process.
3. The student’s mathematical creative thinking ability is low in solving
mathematical problems.
1.3. Problem Limitation
Because of the problems identified fairly wide, so that a more focused
study, the researchers made the extent of the problem in improving mathematical
creative thinking ability of junior high school students to solve mathematics
problem by applying problem-based learning model
1.4. Problem Formulation
Based on the above description of the problem limitation, the problem
formulation to be studied in this research are :
Whether the application of Problem-Based Learning model can improve the
mathematical creative thinking ability of junior high school students?
1.5. Objectives of Research
The objectives of this research are to know whether the application of
Problem-Based Learning model can improve the students' mathematical creative
thinking ability in solving mathematical problems
10
1.6. Benefits of Research
1 For students, through a model of problem-based learning is expected to
improve students' creativity in solving mathematical problems.
2 For teachers, providing an alternative to choose to use mathematical learning
model.
3 For schools, provide input for empower policy for implementation innovative
learning model for improving the quality of mathematics education
4 For researchers, as an input to develop the insight and knowledge as a teacher
candidate.
1.7. Operational Definition
To be able to study quantitatively the variables are defined as follows :
1. Learning is a process in the form of activities and efforts of an someone or
individual getting new knowledge/experience to make changes , both
aspects of knowledge and aspects of behavior in which these changes can
be observed , continuous , functional , positive , and active takes place in a
relatively long time.
2. Problem-based learning is a learning that begins with a problem in an
effort to stimulate and improve the thinking ability of students so that the
students construct their own knowledge. And problem-based learning have
5 phases, namely Orient students to the problem, Organize students for
study, Assist independent and group investigation, Develop and present
artifacts and exhibits, Analyze and evaluate the problem-solving process.
3. Creativity is the ability to bring something new , whether it be the idea
and the real work , both in the work of both new and existing things that
are relatively different. And there are four indicators used to measure
students' mathe
4. matical creative thinking ability, namely Ability to think fluently
(fluency), ability to think flexibly (flexibility), ability to think originally
(originality), ability to itemize (elaboration).
114
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusion
Based on the research results presented in the previous section can be
concluded that the application of problem-based learning model in learning on the
subject of Rectangle and Square can increase students' creative thinking abilities
of Grade VII-3 of SMP Negeri 1 Rantau Selatan. It is known from the result of
students’ creative thinking ability test in cycle 2 higher than cycle 1. Percentage of
many students who have minimal ability “medium” of 56,41% in cycle 1
increased to 87,18% in cycle 2. And Learning by using Problem Based Learning
Model also could make students’ activity in the learning was good category
5.2
Recommendation
Based on these results, the authors propose some suggestions for learning
mathematics, especially in secondary schools, namely:
1. Learning mathematics with problem-based learning model can be used as
an alternative learning effective in improving students' ability to think
creatively. But in the early learning, teachers will have difficulty in
preparing the child to make the process of cooperative learning, student is
difficult to accept the learning changes they have done so far with
constructivism learning through problem-based learning model. Therefore,
it is suggested that before learning to do, the teacher to familiarize the
learning with cooperative learning so that students will be accustomed to
the learning process
2. To support the successful implementation of problem-based learning
model required teaching materials an interesting, for the student activity
sheet should be designed based on the contextual issues are close to
everyday students and challenge students to solve.
115
3. Besides improving the students’ creative thinking abilities, problem-based
learning model also can stimulate the activity of students in learning and
can assist students in forming a positive perception towards learning
mathematics. Therefore this kind of learning is advisable to be developed
further other mathematics items and different levels of education.
4. This research only reveals the role of problem based learning model in
increasing students' creative thinking abilities, To complete the study of
the role of problem-based learning model as a whole needs to do further
research to see a role model of problem-based learning to improve
problem-solving abilities, reasoning, and mathematical connections.
5. The results of this research can be used as input for the school to improve
students' activity during the learning process.
6. The results of this research can also be used as input for the school
because it can give a positive response to the students' learning activities
through the application of problem-based learning.
7. It is hoped to further research with the application of problem-based
learning model in order to observe and increase the allocation of meeting
time.