COMPARISON OF STUDENTS MATHEMATICS ACHIEVEMENT BY IMPLEMENTING THINK PAIR SHARE (TPS) AND NUMBERED HEADS TOGETHER (NHT) ON TRIGONOMETRY FOR X GRADE STUDENTS IN SMA NEGERI 1 BATANG NATAL IN THE YEAR OF 2012/2013.

COMPARISON OF STUDENT’S MATHEMATICS ACHIEVEMENT BY
IMPLEMENTING THINK PAIR SHARE (TPS) AND NUMBERED
HEADS TOGETHER (NHT) ON TRIGONOMETRY FOR X
GRADE STUDENTS IN SMA NEGERI 1 BATANG
NATAL IN THE YEAR OF 2012/2013

By:
Nurhabibah Nasution
Reg. Number 409312021
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

iii

COMPARISON OF STUDENT’S MATHEMATICS ACHIEVEMENT BY
IMPLEMENTING THINK PAIR SHARE (TPS) AND NUMBERED
HEADS TOGETHER (NHT) ON TRIGONOMETRY FOR X
GRADE STUDENTS IN SMA NEGERI 1 BATANG
NATAL IN THE YEAR OF 2012/2013
Nurhabibah Nasution
Reg. Number 409312021
ABSTACT
Objective of this study is to know whether student’s mathematics
achievement who taught with TPS higher than student’s mathematics achievement
who taught with NHT on trigonometry.
The type of research which is used in this study is Quasi Experiment
Research with Posttest Only Design with two experiment classes. Population of
this study is all of students in X grade of SMA Negeri 1 Batang Natal. Sample of
this study is taken randomly of two classes. They are experiment class I (X2)
taught with TPS model and experiment class II (X3) taught with NHT model.
Hypothesis test method that is used is independent sample t-test.
Result of this study at = .05 shown that

>
namely
1.689 > 1.668. It means that student’s mathematics achievement who taught
with TPS higher than student’s mathematics achievement who taught with NHT
on trigonometry for X grade students in SMA Negeri 1 Batang Natal.

iv

PREFACE

Praise be to Allah the Lord of the universe for His blessings and mercy
so that the thesis with the title ”Comparison of Student’s Mathematics
Achievement by Implementing Think Pair Share (TPS) and Numbered Heads
Together (NHT) on Trigonometry for X Grade Students in SMA Negeri 1 Batang
Natal in the Year of 2012/2013” can be finished.
Making this thesis can not be separated from the support of various
parties. Writer thanks to Prof. Dr. Mukhtar, 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. Thank also to Dr. E. Elvis Napitupulu, MS, Drs. Syafari,
M.Pd, and Drs. Yasifati Hia as thesis assesor who has given advices and

suggestions from beginning of research planning until the compiling of this thesis
finished. Writer thankk also to Drs. H. Banjarnahor, M.Pd as academic advisor
who has given guidance and suggestion along the study in State University of
Medan.
Writer thanks to Prof. Dr. Ibnu Hajar, M.Si as head of State University
of Medan, Prof. Drs. Motlan, M.Sc, Ph.D as dean of mathematics and natural
sciences faculty, Drs. Syafari, M.Pd as head of mathematics department, Drs.
Yasifati Hia, M.Si as secretary of mathematics department, Drs. Zul Amry, M.Si
as head of mathematics education program, Dr.rer.nat. B. Manurung, M.Si as
coordinator of bilingual program and for all lecturers and staffs of mathematics
department who has helped and facilitated during compiling process of this thesis.
Thanks also to Drs. Darwin Nasution as principle of MAN Kase RaoRao who has given permission to do research instrument, Drs. Zainal Arifin, S.Pd
as principle of SMA Negeri 1 Batang Natal who has given permission to do
research, Asmara Dewi, S.Pd as mathematics teacher and all teachers and students
in X grade of SMA Negeri 1 Batang Natal who has helped writer in conducting
the research.
Special thanks to my dear loving father Ahmad Nasution, my dearest
mother Ramohot Delila Lubis, my great brothers Ali Napiah Nasution, S.Pi, Nur

v

Alamsyah Nasution, SE, Jufri Affandi Nasution, SH, M. Kholis Nasution, S.Pd,
Zuhairy, ST, Ismail Pahmi Rangkuti, S.Pd, and Zaki Irwan Rifai, S.Pd, my
beloved sister Nelly Asmidar, S.Keb, Nurdiana Nasution, S.Pd, Ilma Rosanna
Nasution, S.Pd, Asmidah Lubis, S.Pd, Ratna Wati Dalimunthe, Gema Sari Lubis,
Am.K., who have given a lot of love, pray, motivation, and spirit who help writer
to finish the study.
Thank also to all of my friends in Bilingual Mathematics Education
2009, Dini, Enny, Evy, Faradilla, Iin, Iwan, Noya, Qori, Retni, Rini, Rizki, Siti,
and Widia. Special thanks also to my beloved friends Joy Juli Great Simanjuntak,
S.Pd, Siska Nopa Tambunan, S.Pd, and Epril Parhusip, S.Pd who has helped and
given big motivation, spirit in every activity that done by writer.
Writer realized that there are still weaknesses in contents and grammar
of this thesis, so writer receives critics and advices from the reader that can make
this thesis be better. Hopefully, this thesis can be useful for education world.

Medan, September 05, 2013
Writer,

Nurhabibah Nasution

Reg.N. 409312021

vi

CONTENTS

Page
VALIDATION SHEET
CURRICULUM VITAE
ABSTRACT
PREFACE
CONTENTS
LIST OF FIGURES
LIST OF TABLES
LIST OF APPENDIX

i
ii
iii
iv

vi
viii
ix
x

CHAPTER I INTRODUCTION
1.1.
Rationale
1.2.
Problems Identification
1.3.
Problems Limitation
1.4.
Research Questions
1.5.
Research Objectives
1.6.
Research Benefits

1

1
5
5
5
5
6

CHAPTER II LITERATURE RIVIEW
2.1.
Theoretical Background
2.1.1. Learning Mathematics
2.1.2. Mathematics Achievement
2.1.3. Cooperative Learning
2.1.4. Think Pair Share Learning Model
2.1.5. Numbered Heads Together Learning Model
2.1.6. Differences of TPS Learning Model and NHT
2.2.
Trigonometry
2.2.1. Trigonometry Ratios of a Right Triangle
2.2.2. Trigonometry Identity

2.2.3. Value of Trigonometry Ratios for Specific Angles
2.2.4. Division of Angles in Trigonometry
2.2.5. Sign of Trigonometry Ratios in All Quadrants
2.2.6. Trigonometry Ratio Formulas of Related Angles
2.3.
Implementation of TPS in Learning Math
2.4.
Implementation of NHT in Learning Math
2.5.
Relevant Researches
2.6.
Conceptual Framework
2.7.
Research Hypotheses

7
7
7
8
9

12
13
14
15
15
16
17
18
18
19
21
23
25
26
27

CHAPTER III RESEARCH METHODOLOGY
3.1
Type of Research
3.2

Design of Research

28
28
28

vii

3.3
3.4
3.5
3.5.1
3.5.2
3.6
3.7
3.7.1.
3.7.1.1.
3.7.1.2.
3.7.2.
3.7.2.1.

3.7.2.2.
3.8.
3.8.1.
3.8.2.
3.8.3.
3.8.4.
3.8.5.
3.8.6.

Place and Time of Research
Population and Sample of Research
Variables of Research
Independent Variables
Dependent Variable
Procedures of Research
Collecting Data Instrument
Analysis of Test Quality
Validity Test
Reliability Test
Analysis of Test Items Quality
Difficulty Index Test
Discrimination Index Test
Data Analysis Techniques
Calculating Mean Score
Calculating Variance
Calculating Standard Deviation
Normality Test
Homogeneity Test
Hypothesis Test

28
28
29
29
30
30
32
32
33
33
34
35
35
36
36
36
36
36
37
38

CHAPTER IV RESULT AND DISCUSSION
4.1.
Result of Research
4.1.1. Description of Posttest Result
4.1.2. Test of Data Analysis
4.1.2.1. Normality Test
4.1.2.2. Homogeneity Test
4.1.3. Hypothesis Test
4.2.
Discussion

39
39
39
40
40
40
41
42

CHAPTER V CONCLUSION
5.1.
Conclusion
5.2.
Suggestion

44
44
44

REFERENCES

45

viii

LIST OF FIGURES

Page
Figure 2.1. Variables Impacting Student Academic Achievement

9

Figure 2.2. Right Triangle

15

Figure 2.3. Right Triangles

17

Figure 2.4. Quadrants

18

Figure 3.1. Scheme of Research Procedures

31

ix

LIST OF TABLES

Page
Table 2.1. Differences Between TPS and NHT

14

Table 2.2. Value of Trigonometry Ratios

17

Table 2.3. Signs of Trigonometry Ratios

19

Table 2.4. Implementing TPS in Learning Math

21

Table 2.5. Implementing NHT in Learning Math

23

Table 3.1. Research Design

28

Table 3.2. Schedule of Research Activity

29

Table 3.3. Blue Print of Posttest items

32

Table 3.4. Criteria of Difficulty Index

35

Table 4.1. Posttest Scores of Two Experiment Classes

39

Table 4.2. Result of Normality Test

40

Table 4.3. Result of Homogeneity Test

40

Table 4.4. Result of Hypothesis Test

41

x

LIST OF APPENDIX
Page
Appendix 1. Lesson Plan 01 (TPS Class)

48

Appendix 2. Lesson Plan 02 (TPS Class)

54

Appendix 3. Lesson Plan 03 (TPS Class)

60

Appendix 4. Lesson Plan 01 (NHT Class)

66

Appendix 5. Lesson Plan 02 (NHT Class)

72

Appendix 6. Lesson Plan 03 (NHT Class)

79

Appendix 7. Student Activity Sheet (SAS-01)

85

Appendix 8. Problem Solving of SAS-01

90

Appendix 9. Student Activity Sheet (SAS-02)

94

Appendix 10. Problem Solving of SAS-02

98

Appendix 11. Student Activity Sheet (SAS-03)

101

Appendix 12. Problem Solving of SAS-03

107

Appendix 13. Blue Print of Posttest

112

Appendix 14. Posttest Items

113

Appendix 15. Key of Posttest Items

116

Appendix 16. Validity Test of Items

117

Appendix 17. Reliability Test of Items

120

Appendix 18. Test of Difficulty Index

122

Appendix 19. Test of Discrimination Index

124

Appendix 20. Mean, Variance, and Standard Deviation of Posttest Data

126

Appendix 21. Test of Normality

128

Appendix 22. Test of Homogeneity

132

Appendix 23. Test of Hypothesis

134

Appendix 24. Table of Critical Value for Pearson r

136

Appendix 25. Table of Critical Values for Liliefors Test

137

Appendix 26. Table of Normal Distribution

138

Appendix 27. Table of the F Distribution

140

Appendix 28. Table of the t Distribution

141

Appendix 29. Documentation

142

CHAPTER I
INTRODUCTION

1.1. Rationale
Mathematics is a subject that is very important at every level of
education, from primary to higher education. This is because mathematics can
train students to think logically, be responsible, have a good personality and have
skill in solving problems in real life. There are many reasons for students to learn
and master mathematics. As Cockroft (1982) (in Abdurrahman, 2009: 253) given
the reasons that mathematics always used in terms of education since all fields of
study require appropriate mathematical skills, it is a powerful means of
communication, it can be used to present information in a variety of ways, it can
improve the ability of logical thinking, accuracy, and spatial awareness, and to
give satisfaction to the efforts to solve challenging issues.
However, many students who still think that mathematics is a subject
which is frightening, because it is one of the main causes of failure of students in
the National Examination. Based on interview with one of mathematics teacher in
SMA Negeri 1 Batang Natal, Mrs. Dewi, conclude that student’s mathematics
achievement generally is still low. From the results of semester examination, there
are only about 70%-78% of students who achieve a minimum standard of mastery
learning. It means that there is still 22%-30% of students who have not been
thoroughly studied. If it is reviewed from their daily scores when conducting
learning process, not all of the subject matters have the low percentage of mastery
learning. But one of the subjects is trigonometry. Student’s math test score on
trigonometry is low. It is caused of there are many formulas that must be
memorized and used in trigonometry and students can not apply the formulas to
solve a problem, and they are also have difficulty to derive a formula to obtain a
new formula that can be used for certain problems.
Students' attitudes toward math and mathematics learning is closely
related to students’ achievement in mathematics. Suydam & Weaver (1975) (in
Turmudi, 2008: 87) conclude that students learn more effective when they are

2

interested in what they learn and they achieve well if they loved math. To be
positive attitudes toward mathematics, concern should be directed towards the
continuous creation, development, maintenance, and encouragement.
This is certainly part of the math teachers’ roles to improve students’
attitudes and achievement. Mathematics teacher needs to guide learners to engage
in higher levels of cognition when using meaningful materials and relevant
strategies for learners (Rao, 2005: 121). In order for students to be positive in
math, the attractive strategies is needed to motivate them in learn, give a sense of
security to learn, and fun for them. In addition, teachers should also be able to
choose more effective strategies in implementing the learning. But, learning
model which is used by teachers sometimes is not relevant with the subject or
topic that is learned.
Killen (1998) (in Sanjaya, 2006: 131) suggested that: “No teaching
strategy is better than others in all circumstances, so you have to be able to use a
variety of teaching strategies, and make rational decisions about when each of the
teaching strategies is likely to most effective”.
Learning strategies that is used by teachers are extremely diverse. There
are teacher-centered and student-centered approaches. The National Council of
Teachers of Mathematics (NCTM) (in Macpherson , 2007) recommends that:
Students be provided opportunities to work together cooperatively in
large and small groups on significant problems that arise out of their
experiences and frames of reference. Group assignments should help
learners combine new knowledge with prior knowledge, leading to the
construction of new ideas within the group. Students should question,
discuss, make mistakes, listen to the ideas of others, provide constructive
criticism and summarize discoveries.
Education experts recently gave attention to learning strategies and
encouraged to use the student-centered strategy, one of the strategies is
cooperative learning. Cooperative learning is a series of learning activities
undertaken by students in heterogeneous groups to achieve a common goal. Some
studies show that using cooperative learning can improve student achievement

3

while increasing the ability of social relationships, growing acceptance of self and
others lack, and enhancing self-esteem. Cooperative learning also can realize
students need in learning to think, solving problems, and integrating knowledge
with skills.
More clearly, Slavin (1995) (in Biehler & Snowman, 2009) argued that:
Students who learn cooperatively tend to be more highly motivated to
learn because of increased self-esteem, the proacademic attitudes of
group mates, appropriate attributions for success and failure, and greater
on-task behavior. They also score higher on tests of achievement and
problem solving and tend to get along better with classmates of different
racial, ethnic, and social class backgrounds. This last outcome should be
of particular interest to those of you who expect to teach in areas marked
by cultural diversity.
Cooperative learning strategy is developed in an effort to increase
student’s participation and generate effective interaction among group members
through discussion. Cooperative small group as learning atmosphere where
students interact with others in small group to complete academic task and to
accomplish a common goal.
Cooperative learning refers to work done by student teams producing a
product of some sort under conditions that satisfy five criteria: (1)
positive interdependence, (2) individual accountability, (3) face to face
interaction for at least part of the work, (4) appropriate use of
interpersonal skills, and (5) regular self-assessment of team functioning.
(Richard & Rebecca: 2007)
Cooperative learning has many variations of model. Based on research of
Dotson (2003) found that cooperative learning structures could increase student
achievement. Two of the cooperative learning structures are Think Pair Share and
Numbered Heads Together Models.
Think Pair Share is a learning model which proposed by Franklin Lyman
(1985), aims to teach students to be more independent in solving problems which
can generate students' self-confidence. In addition, TPS also teaches students to
accept differences and work together with others. TPS is a learning model
indicating how to think and share with group.

4

Educational research on the use cooperative learning type TPS has been
studied previously. Ahyar (2011) said that there is significant differences in
student’s achievement who are taught by TPS and Snowball Throwing models.
Students’ mean score in statistics taught by TPS and Snowball Throwing
respectively are 79.123 and 68.889. It concludes that average value of students on
the subject of statistics by implementing TPS is higher than Snowball Throwing.
Another educational study about TPS is research of Rahim (2010) which also
found the improvement of students achievement on the subject of algebra
factorizes.
Numbered Heads Together is a learning model developed by Kagan
(1998) to involve more students in examining a variety of subject matter in a
lesson and to examine their understanding about content of the lesson.
Educational research on the use cooperative learning type NHT has also been
studied previously. Tambunan (2011) found that students mathematics problem
solving on the topic of algebra by implementing NHT and STAD respectively
have average value of 75.475 and 72.456. It indicates that NHT better than STAD
in the topic of algebra.
Since not all learning models are suitable to achieve all the goals and
circumstances and each learning model has its own characteristics. As well as in
mathematics, then not all learning models are effective used for each topic in
mathematics such as trigonometry. Therefore, the selection of in appropriate
learning model will be able to make effectiveness of learning decreases that
indicates the decreasing of students achievement, thus there needs to be concern to
the model that is used by teachers in learning process.
Based on the above explanation, it should be conducted further study
which entitled: “Comparison of Student’s Mathematics Achievement by
Implementing Think Pair Share (TPS) and Numbered Heads Together
(NHT) on Trigonometry for X Grade Students in SMA Negeri 1 Batang
Natal in the Year of 2012/2013”

5

1.2. Problems Identification
Based on the background, some issues that can be identified as follows:
1. Mathematics is a frightening lesson for students
2. Student’s achievement on math test scores especially on trigonometry is
low
3. Learning model which is used by teachers is not relevant

1.3. Problems Limitation
Based on the identification of the research problems, the scope of this
study is limited on:
1. Learning models which is used in this study are Think Pair Share (TPS)
and Numbered Heads Together (NHT)
2. Objects of this study are students in X grade of SMA Negeri 1 Batang
Natal
3. Data in this study is data of student’s math scores that is got from students’
math posttest scores.
4. Study is focused on topic of Trigonometry

1.4. Research Question
Research question in this study is: “Is student’s mathematics achievement
who taught with TPS higher than student’s mathematics achievement who taught
with NHT on trigonometry for X grade students in SMA Negeri 1 Batang Natal in
the year of 2012/2013?”

1.5. Research Objective
Objective of this study is to know whether student’s mathematics
achievement who taught with TPS higher than student’s mathematics achievement
who taught with NHT on trigonometry for X grade students in SMA Negeri 1
Batang Natal in the year of 2012/2013.

6

1.6. Research Benefits
The results of this study are expected to provide benefits for:
1. Teachers
a. It helps math teachers in effort to find the effective learning to improve
student’s achievement in math.
b. It can be study reference for teachers and motivates them to conduct
many research in others subject.
2. Students
a. Students achieve math better by applying effective learning model in
learning process.
b. It can improve students’ learning creativity, collaboration, and
responsibility to make learning more qualified.
3. Researchers
a. It can be an input for a similar study
b. It can serve as guidelines in performing their teaching duties in the
future.

44

CHAPTER V
CONCLUSION AND SUGGESTION

5.1. Conclusion
Based on study result and data analysis then the conclusion of the
research is: “Student’s mathematics achievement who taught with TPS higher
than student’s mathematics achievement who taught with NHT on trigonometry
for X grade students in SMA Negeri 1 Batang Natal in the year of 2012/2013”.

5.2. Suggestions
Based on result of the research, then the suggestions are:
1.

To mathematics teachers especially to mathematics teachers in SMA Negeri 1
Batang Natal, implementation of TPS model can be one alternative to
increase student’s mathematics achievement especially in the topic of
trigonometry.

2.

To students, teachers and all school party of SMA Negeri 1 Batang Natal in
order to keep trying to develop and to find creative innovation mathematics
learning especially relates to TPS model such as combine TPS with others
supported media.

3.

To advance researchers is hoped conducting more study for this research not
only to see the student’s achievement in cognitive domain but also student’s
achievement in affective and psychomotor domains.

45

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