THE EFFORT TO INCREASE THE PROBLEM SOLVING ABILITY OF STUDENT BY IMPLEMENTING PROBLEM BASED LEARNING (PBL) IN THE TOPIC OF TRIGONOMETRY IN GRADE X OF SMA NEGERI 1 PERBAUNGAN IN THE YEAR OF 2012/2013.

THE EFFORT TO INCREASE THE PROBLEM SOLVING ABILITY OF
STUDENT BY IMPLEMENTING PROBLEM BASED LEARNING
(PBL) IN THE TOPIC OF TRIGONOMETRY IN GRADE X
OF SMA NEGERI 1 PERBAUNGAN
IN THE YEAR OF 2012/2013

By:
Joy Juli Great Simanjuntak
Reg. Number 409312020
Bilingual Mathematics Education Program

THESIS
Submitted to Fulfill Requirement for
Sarjana Pendidikan Degree

MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2013

iv

ACKNOWLEDGMENTS
Firstly, writer would like to thanks be to Almighty God for His mercy and
blessing to writer thus because of His love to writer thus this research can be
finished well appropriate with time that has been planned.
Thesis entitled “The Effort to Increase the Problem Solving Ability of
Student by Implementing Problem Based Learning (PBL) in the Topic of
Trigonometry in Grade X of SMA Negeri 1 Perbaungan in the Year of
2012/2013” is compiled to fulfill requirement for Sarjana Pendidikan degree.
In this chance, writer wants to extend gratitude to Mr. Dr. Hasratuddin,
M.Pd as thesis advisor who has made his time for giving brief and guidance from
beginning until the end of writing process of this thesis. Gratitution also writer
delivers to Mr. Drs. H. Banjarnahor, M.Pd, Mr. Dr. E. Elvis Napitupulu, MS and
Mr. Dr. Edy Surya, M.Si as thesis examiner who have given advices and
suggestions from beginning of research planning until the compiling of this thesis
finished.
Thanks a lot also to Mr. Prof. Dr. Mukhtar, M.Pd as academic advisor and
as head of mathematics department who has given guidance, suggestion and even
facilitation along the study in State University of Medan. Thanks a lot also to Mr.

Prof. Dr. Ibnu Hajar, M.Si as head of State University of Medan, Mr. Prof. Drs.
Motlan, M.Sc, Ph.D as dean of mathematics and natural sciences faculty, Mr. Drs.
Yasifati Hia, M.Si as secretary of mathematics department, Mr. Drs. Syafari,
M.Pd as head of mathematics education program, Mr. Dr. rer. net. Binari
Manurung, M.Si as coordinator of bilingual program and also for all lecturer and
staff of mathematics department who has helped and facilitation during compiling
process of this thesis.
Thanks to Mr. Suhairi, M.Pd as principle of SMA Negeri 1 Perbaungan
whohas given permission to writer to do the research, Mr. Ishak Saragih, S.Pd as
mathematics teachers and all teacher and student in grade XU-1 of SMA Negeri 1
Perbaungan who has helped writer in conducting the research.

v

The special gratitude, writer wants deliver to dear loving father Alm.
Todung Simanjuntak and the dearest mother Lesman br Sihotang who have given
a lot of love, pray, motivation and spirit who help writer to finish the study until
now. Special thanks to my beloved sister Vickytri Afriani br Simanjuntak and all
family for all pray, motivation and support up to now.
Thanks to every member of IKBKM for all spirit, support and experience

that has been shared to writer. Thanks also for Adi, Ardianto, Reinojum,
Suprianto and Wes that united in Touring Team 2013 for all sprit, support and
time to have relax time together. Writer is indebted to bilingual mathematics
education 2009 big family for helping along the study in State University of
Medan, they are Dini, Enny, Evy, Epril, Faradilla, Iin, Iwan, Noya, Nurhabibah,
Qori, Retni, Rini, Rizki, Siska, Siti, and Widia. Big and special thanks to Siska
Nopa Tambunan that is one of writer best friend for helping and giving big
motivation, praying and even giving spirit in every activity that done by writer.
Moreover, thanks to all colleagues in PPLT Unimed 2012 in SMA Negeri 1
Perbaungan who always support and share their experience to writer.
Writer realized that there are still weaknesses in contents and grammar of
this thesis, so writer receives critics and advices from the reader to make this
thesis be better. Hopefully, this thesis can be useful for education world.

Medan, June

, 2013

Writer,

Joy Juli Great Simanjuntak
Reg. Number 409312020

iii

THE EFFORT TO INCREASE THE PROBLEM SOLVING ABILITY OF
STUDENT BYIMPLEMENTING PROBLEM BASED LEARNING
(PBL) IN THE TOPIC OF TRIGONOMETRY IN GRADE X
OF SMA NEGERI 1 PERBAUNGAN
IN THE YEAR OF 2012/2013
Joy Juli Great Simanjuntak (Reg. Number 409312020)

ABSTRACT
This research aims to increase the problem solving ability of student in
grade X of SMA Negeri 1 Perbaungan by implementing problem based learning
(PBL) model in trigonometry topic.
Type of this research is Classroom Action Research (CAR). Subject in
this research is student in class XU-1 of SMA Negeri 1 Perbaungan that consists
of 26 students. This research is conducted in two cycles. Data in this research is
obtained from learning implementation and student activity observation, problem

solving ability test, student response questionnaire and documentation.
Results of this research show that PBL can increase problem solving
ability of student. The increasing can be seen in three things such as, (1) average
of class score in cycle I is 71.04 becomes 78.35 in cycle II or increases 5.38
(10.29%), (2) total of student who completed in understanding problem step in
cycle I is 21 becomes 24 in cycle II or increases 3 students (14.29%), total of
student who completed in making a plan step in cycle I is 21 becomes 26 in cycle
II or increases 5 students (23.51%), total of student who completed in doing the
plan step in cycle I is 16 becomes 23 in cycle II or increases 7 students (43.75%),
total of student who completed in checking solution step in cycle I is 15 becomes
23 in cycle II or increases 8 students (53.33%) and (3) total of student who
completed to solve problem in cycle I is 13 becomes 23 in cycle II or increases 10
students (76.92%). Based on gain score criteria, the increasing of students’
problem solving ability is classified into low category.
Results of this research also show that level of student mastery is 88.46%
that means that completeness of student learning completes classically, attainment
of basic competence indicator at whole achieves 75% that means that
completeness attainment of basic competence indicator is achieved and
observation II shown that teacher ability is very good and student activity is good.
Those results shown that PBL is effective in trigonometry topic learning in grade

X. Response questionnaire result analysis shows that students feel interest, happy
and love learn mathematics by implementing PBL especially in trigonometry
topic.

vi

CONTENTS

Page
ENDORSEMENT PAGE
CURRICULUM VITAE
ABSTRACT
ACKNOWLEDGMENTS
CONTENTS
LIST OF FIGURE
LIST OF TABLE
LIST OF APPENDIX

i
ii

iii
iv
vi
ix
x
xii

CHAPTER I INTRODUCTION
1.1.
Background
1.2.
Problem Identification
1.3.
Problem Limitation
1.4.
Problem Formula
1.5.
Research Objective
1.6.
Research Benefit

1
1
5
5
6
6
6

CHAPTER II LITERATURE REVIEW
2.1.
Theoretical Background
2.1.1. Definition of Learning Mathematics
2.1.2. Learning Mathematics in School
2.1.3. Problem in Mathematics
2.1.4. Mathematics Problem Solving
2.1.5. Mathematics Problem Solving Ability
2.1.6. PBL Model
2.1.7. Summary of Subject Matter
2.1.7.1. Trigonometry Ratios that Formed by Angle of Right Triangle

2.1.7.2. Trigonometry Ratios Value of Specific Angles
2.2.
Relevant Research
2.3.
Theoretical Frame
2.4.
Action Hypothesis

8
8
8
9
11
12
17
18
22
22
23
25

26
29

CHAPTER III RESEARCH METHODOLOGY
3.1.
Type of Research
3.2.
Place and Time of Research
3.3.
Subject and Object of Research
3.3.1. Subject of Research
3.3.2. Object of Research
3.4.
Mechanism and Design of Research
3.5.
Technique in Collecting Data

30
30
30

30
30
30
30
34

vii

3.5.1.
3.5.2.
3.5.3.
3.5.4.
3.6.
3.6.1.
3.6.2.
3.6.2.1.
3.6.2.2.
3.6.3.
3.7.
3.7.1.
3.7.2.
3.7.3.
3.7.4.
3.8.
3.9.
3.9.1.
3.9.2.
3.9.3.
3.10.
3.11.

Observation
PSA Test
Questionnaire of Student Response
Documentation
Instrument in Collecting Data
Observation Guidance
PSA Test
Validity of Test
Reliability of Test
Questionnaire of Student Response Sheet
Data Analysis Techniques
Data analysis of Learning Implementation and Student Activity
in Learning by Using PBL
Analysis of Mathematics PSA
Questionnaire of Student Response Sheet
Documentation Result
Increasing Criteria of Mathematics PSA
Effectiveness of PBL
Calculating Level of Student Mastery
Calculating Completeness of Student Learning
Calculating Completeness Attainment of Basic Competence
Indicator
Data Explanation
Conclusion Drawing

CHAPTER IV RESULT AND EXPLANATION OF RESEARCH
4.1.
Description of Research Result
4.1.1.
Description of Diagnostic Test Result
4.1.2.
Description of Cycle I Result
4.1.2.1. Description of Student Initial Condition
4.1.2.2. Description of Action Planning I
4.1.2.3. Description of Action Implementation I
4.1.2.4. Description of Observation I
4.1.2.5. Description of Data Analysis I
4.1.2.5.1. Analysis of Observation Result Data
4.1.2.5.2. Analysis of PSA Test I Data
4.1.2.6. Description of Reflection I
4.1.3.
Description of Cycle II Result
4.1.3.1. Description of Student Initial Condition
4.1.3.2. Description of Action Planning II
4.1.3.3. Description of Action Implementation II
4.1.3.4. Description of Observation II
4.1.3.5. Description of Data Analysis II

34
34
34
34
34
35
35
35
36
37
37
37
38
41
42
43
43
43
44
44
44
45
45
46
46
46
49
49
49
50
51
52
52
56
58
70
70
70
71
72
73

viii

4.1.3.5.1.
4.1.3.5.2.
4.1.3.6.
4.1.4.
4.1.4.1.
4.1.4.2.
4.1.4.3.
4.1.5.
4.1.5.1.
4.1.5.2.
4.1.5.3.
4.1.6.
4.1.7.
4.1.8.

Analysis of Observation Result Data
Analysis of PSA Test II Data
Description of Reflection II
Effectiveness of PBL in Cycle I
Level of Student Mastery in Cycle I
Completeness of Student Learning in Cycle I
Completeness Attainment of Basic Competence Indicator in
Cycle I
Effectiveness of PBL in Cycle II
Level of Student Mastery in Cycle II
Completeness of Student Learning in Cycle II
Completeness Attainment of Basic Competence Indicator in
Cycle II
Result of Response Questionnaire
Research Result
Research Result Discussion

73
77
79
82
82
82
83
84
84
84
85
86
88
89

CHAPTER V CONCLUSION AND SUGGESTION
5.1. Conclusion
5.2. Suggestion

95
95
95

REFERENCES

97

x

LIST OF TABLE
Page
Table 1.1. Total of Students who Complete in Problem Solving Steps

4

Table 2.1. Value of Trigonometry Ratios

23

Table 2.2. Signs of Trigonometry Ratios

24

Table 3.1. Guideline of Class Score Average

38

Table 3.2. Scoring Guideline of Test

38

Table 3.3. Scoring for Each Category of Student Answer in
Questionnaire

41

Table 3.4. Criteria of Student Response Percentage

42

Table 3.5. Increasing Criteria

42

Table 3.6. Criteria of Percentage of Study Result Attainment

43

Table 4.1. Average of Class Score

46

Table 4.2. Total of Students who Complete in Problem Solving Steps

47

Table 4.3. Total of Student who Completes to Solve Problem

47

Table 4.4. Description of Observation Result of Teacher Ability in
Implementing the Learning in Cycle I

52

Table 4.5. Description of Observation Result of Student Activity in
Learning in Cycle I

54

Table 4.6. Average of Class Score

56

Table 4.7. Total of Students who Complete in Problem Solving Steps

56

Table 4.8. Total of Students who Complete to Solve Problem

57

Table 4.9. Investigation of Reflection I Result in Cycle I

63

Table 4.10. Description of Observation Result of Teacher Ability in
Implementing the Learning in Cycle II

74

Table 4.11. Description of Observation Result of Student Activity in
Learning in Cycle II

76

Table 4.12. Average of Class Score

77

Table 4.13. Total of Students who Complete in Problem Solving Steps

78

Table 4.14. Total of Students who Complete to Solve Problem

78

Table 4.15. Increasing Criteria of Students’ Problem Solving Ability

81

xi

Table 4.16. Level of Student Mastery

82

Table 4.17. Completeness of Student Learning

83

Table 4.18. Completeness Attainment of BCI

83

Table 4.19. Level of Student Mastery

84

Table 4.20. Completeness of Student Learning

84

Table 4.21. Completeness Attainment of BCI

85

Table 4.22. Result of Student Response Questionnaire

86

Table 4.23. Student Response for Each Indicator

87

ix

LIST OF FIGURE

Page
Figure 2.1. Problem Solving Process by Polya

15

Figure 2.2. Right Triangle

22

Figure 2.3. Scheme of Problem Solving with PBL

28

Figure 3.1. CAR Design

33

Figure 4.1. Student Difficulty in Understanding Problem Step

59

Figure 4.2. Student Difficulty in Making a Plan Step

60

Figure 4.3. Student Difficulty in Doing the Plan Step

61

Figure 4.4. Student Difficulty in Doing the Plan Step

62

CHAPTER I
INTRODUCTION

1.1. Background
Education is one form of human culture manifestation that dynamic and
full of development. Therefore, a change or a development of education is indeed
should be in line with the change of life culture. Education that can support future
development is education that able to develop potential of learners, so the
concerned is able to face and to solve the life problems that he/she is faced.
Education should touch the inner potential and the competence potential of
learners (Trianto, 2011:1).
Mathematics is a subject that very important in every level of education,
from primary to high education. This is because mathematics can train students to
think logically, to be responsible and to have a good personality and skill in
solving problems in real life.
As one of basic sciences, mathematics has an essential value that can be
applied in various fields of life. Mathematics learning is qualified or not, it cannot
be separated from role of teachers and students. Teachers are required to create an
active learning situation, innovative, creative, effective and fun in the learning
process that the result will be reflected in student achievement that high.
Trigonometry is type of mathematics that deals with the relationship
between the sides and angles of triangles (Oxford English Dictionary, 2000:1444).
Trigonometry has a very close relationship in our lives, both directly and
indirectly. Astrology and building construction is greatly helped by presence of
trigonometry. With changing of times, trigonometry keeps to be developed,
combined with other disciplines in order to be useful together. Originally,
trigonometry comes as solution of solving of simple planes, with the growing of
time, trigonometry is often used in world of applied sciences, the development of
other sciences, and the development of mathematics itself. Here are some
examples of trigonometry applications in daily life, such as: to calculate angle of

2

attack which is the most optimal from a launcher weapon, to be able to throw the
projectile as far as possible; determine how the highest gradient of a hill on a
public road in the mountains, so that all vehicles can pass it safely; and the
simplest example of the daily events, when we walk in the stairs, we do not want
to make the gradient of the stair to be too big or the angle is too small because its
range is low (Bawazir, 2012).
However, what happened today is contrary to the expectations; it was
indicated by low of students' mathematics achievement. Generally, the learning of
mathematics in Indonesia, including learning trigonometry in high school is still
far from satisfactory and sometimes can be said still disappointing. (Setiawan,
2004:1).
Based on survey data of Trends in International Mathematics and
Sciences Study (TIMSS) 2003 under the International Association for the
Evaluation of Educational Achievement (IEA) that: "Indonesia in the position 34
for field of mathematics and in position 36 for field of science of 45 countries
surveyed" (Karwono, 2009).
The success of mathematics learning can be measured by the success of
students who follow learning activity. That success can be seen from student’s
activity in participating in classroom activities and learning mathematics
achievement. The better activity and mathematics learning achievement, then
level of success of learning mathematics process is higher.
Many things affect the low mathematics learning achievement of
students. One of them is the use of approaching or the learning model which is
irrelevant to topic that taught by teacher. Generally, learning model that
implemented is conventional learning model that often called with teacher center.
Suherman (2012) expresses the same thing:
It is said that in the current implementation of learning mathematics in
general teacher is still using conventional methods where teacher still
dominates the class, the students passive (come, sit, watch, practice, ...,
and forget). Teacher tells concepts, so students receive materials.
Similarly in practice, from year to year the problem which is given is the
almost the same problem and it also does not vary. To follow the lessons
in the school, most students do not prepare themselves by reading the

3

material to be studied, students come without sufficient knowledge as
bringing an empty container.
According to Arends (in Trianto, 2011:90): “It is strange that we expect
students to learn yet seldom teach then about learning, we expect student to solve
problems yet seldom teach then about problem solving”.
Teachers are required to make the students learn actively. This is an
important factor in the outcome of teaching and learning activities. Learning
mathematics still does not reach the substance of problem solving. Students are
more likely to memorize concept than to understand the meaning thus students'
ability in solving mathematical problems is low. Prayudi (2008) states that:
One of KTSP advantages is declared that problem solving, reasoning,
communication as a goal of learning mathematics in elementary school,
junior high school, senior high school, and vocational school beside goals
which are related to concept of understanding which has been known by
teacher.
Problem solving can be considered as a method of learning in which
students are trained to solve problems. The problem may come from the teacher, a
phenomenon or real problems that encountered by students. Problem solving
refers to child's brain function, develops creative thinking to recognize problem
and seek alternative solutions. Mathematics problem solving includes "problem
solving" as cognitive behavior and "mathematics" as the object of being studied.
Process thinking in mathematical problem solving requires a certain intellectual
skills that will organize strategy that pursued in accordance with data and problem
that encountered. Therefore, it can be understood that before mastering
mathematical problem solving, it is required to mastery lower cognitive aspects
firstly, namely memory, understanding and application.
Based on the interview (January 22, 2013) of researcher with
mathematics teacher of grade X of SMA Negeri 1 Perbaungan, Mr. Ishak Saragih,
said that:
Students are less able to solve problems in trigonometry material; it is
occurred because students think that trigonometry topic is a difficult
material to understand, so that concentration level of students during

4

learning process is not maximal. This might be due to methods which are
used do not appropriate or methods do not make students be motivated to
learn, so problem solving ability of students in trigonometry topic is low.
From result of survey that conducted by researcher (February 4, 2013) by
giving the problem solving diagnostic test to students of grade XU-1 of SMA
Negeri 1 Perbaungan, in topic of Angle Size and Angle Triangle as a prerequisites
matter of trigonometry topic. From 26 students who took the test, the average of
class score that obtained is 54.23 (score scale 0 – 100). Based on the test result is
also obtained that total of student who complete in understanding the problem step
is 10 students (38.46%), in making a plan step is 13 students (50%), in doing the
plan step is 4 students (15.39%) and in checking solution step is 0 student (0%).
The complete result can be seen in the following table:
Table 1.1. Total of Students who Complete in Problem Solving Steps
No.

Problem Solving Step

Diagnostic Test
Total of Student

Percentage

1.

Understanding problem

10

38.46%

2.

Making a plan

13

50%

3.

Doing the plan

4

15.39%

4.

Checking solution

0

0%

Diagnostic test result also shown that there was not student who
completed to solve problem.
From some of descriptions above, it can be seen that many of students
who are not able to solve problem because learning process is less meaningful to
students that cause to low ability of students in solving problems. The reality is
students just memorize the concepts and less able to use these concepts if it is
encountered in real life problems that associated with concept that owned.
Furthermore, students even are not able to determine problem and formulate it
(Trianto, 2011: 89). Mathematics teachers have a duty to help students to improve
students' problem-solving abilities. Teachers should strive harder to enable

5

students to solve problems because one focus of learning mathematics is problem
solving, so that basic competencies that should be owned by every student is a
minimum standard of knowledge, skills, attitudes and values which is reflected in
learning of mathematics with habits of thought and action to solve problem.
Powerful learning model that believed can enhance students' problem
solving abilities are learning models that require students to seek their own
solution problem independently that will give a concrete experience, the
experience can be used also to solve the similar problem because experience will
give meaning itself for the learners. Learning model that has the characteristics
above is problem based learning (PBL). PBL model is a learning model that based
on a number of issues that require authentic investigation that is an investigation
that require a real solution from the real issues (Trianto, 2011: 90).
Based on the explanations above, researcher is interested to conduct a
research which entitled: The Effort to Increase the Problem Solving Ability of
Student by Implementing Problem Based Learning (PBL) in the Topic of
Trigonometry in Grade X of SMA Negeri 1 Perbaungan in the Year of
2012/2013

1.2. Problem Identification
Based on background, some issues that can be identified as follows:
1. Learning approaches which is used by teachers is irrelevant.
2. Learning activities are still centered on teacher.
3. Student ability in solving mathematics problem is low.
4. Implementation of PBL is an effort to increase mathematics problem
solving ability of students.

1.3. Problem Limitation
Based on identification of problems that has been described above, scope
of this study is limited to implementation of PBL in topic of trigonometry in grade
X of SMA Negeri 1 Perbaungan in the year of 2012/2013, as an effort to improve

6

mathematics problem solving ability of student and to know difficulties which is
faced by students in doing trigonometry problem.

1.4. Problem Formula
Based on problem limitation above, then problems formula of this
research are
1. How increasing of students’ problem solving ability by implementing
PBL in trigonometry topic?
2. Is PBL effective in learning of trigonometry topic?
3. How do students response to implementation of PBL in learning of
trigonometry topic?

1.5. Research Objective
The objective of this research such as
1. To find out the increasing of students' problem solving ability with
implementation of trigonometry topic.
2. To know effectiveness of PBL in trigonometry topic learning.
3. To know the response of student to implementation of PBL in learning of
trigonometry topic.

1.6. Research Benefit
After this research is done, it is expected to be beneficial to all people,
including:
1. For teacher/teacher candidate that is as information about student
achievement in solving problems by implementing PBL in trigonometry
topic.
2. For principal that can be considered matter for teacher to implement PBL
in teaching and learning activities in school.
3. For students that are by implementing PBL can help students to increase
problem solving ability.

7

4. For researchers that are results of this research and instrument can be
material information and considered to implement PBL in subject matter
of trigonometry and other subjects and can be developed for future
research.

CHAPTER V
CONCLUSION AND SUGGESTION
5.1. Conclusion
Based on result of analysis and observation, so it can be taken some
conclusions such as:
1.

Based on problem solving ability test I in cycle I and problem
solving ability test II in cycle II, there exist increasing of average of
class score. Average of class score increases 10.29%. By using gain
score formula, it is obtained that the gain score is 0.25. Based on
gain score criteria, increasing of mathematics problem solving ability
of student is classified into low category.

2.

Based on problem solving ability test II in cycle II and observation
II, got that level of student mastery is 88.46% that means that
completeness of student learning is complete classically, attainment
of basic competence indicator at whole achieves 75% that means that
completeness attainment of basic competence indicator is achieved
and observation II shown that teacher ability is very good and
student activity is good. So, problem based learning model is
effective in learning of trigonometry topic in grade X.

3.

Based on response questionnaire result, students are interested,
happy and love learns mathematics by implementing problem based
learning model especially in trigonometry topic.

5.2. Suggestion
Based on the conclusion above, researcher proposes some suggestions
such as:
1.

To mathematics teacher, especially to mathematics teacher of SMA
Negeri 1 Perbaungan, implementation of PBL model can be one
alternative to increase mathematics problem solving ability of
student, especially in topic of trigonometry.

96

2.

To teacher and all school party of SMA Negeri 1 Perbaungan, in
order to keep trying to develop and to find creative innovation of
mathematics learning especially that relates to PBL model such as
combine PBL model

with cooperative learning such that

mathematics learning in class be more interesting and please.
3.

To advance researcher, in order to make result and instrument in this
research as consideration material to implement learning by using
PBL model in topic of trigonometry or another topic and can be
developed for advance research.