THE COMPARISON OF STUDENTS’ MATHEMATICAL PROBLEM SOLVING ABILITY TAUGHT BY COOPERATIVE LEARNING
MODEL O F NUMB ERED HEADS TO GETHER AND THINK PAIR SHARE AT S MP NE GE RI 13
MEDAN ACADEMIC YEAR 2016/2017
By :
Febby Faudina Nestia ID 4123312008
Bilingual Mathematics Education Study Program
SKRIPSI
Submitted in Partial Fulfillment of The Requirement for The Degree of Sarjana Pendidikan
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
ii
BIOGRAPHY
Febby Faudina Nestia was born in Medan on July, 4th 1994. Her Father’s name is
Iklanuddin and her mother’s name is Jetty B. Pardede. She is the third child of
three siblings. She has brother and sister. In 1999, she started her study in TK
Melati Medan and graduated in 2000. In 2000, she continued her study in SD
Muhammadiyah 30 Medan and graduated in 2006. In 2006, she continued her
study in SMP N 12 Medan, then moved to SMP N 13 Medan in 2007 and
graduated in 2009. In 2009, she continued her study in SMA N 8 Medan and
graduated in 2012. In 2012, she continued her study in State University of
Medan, Faculty of Mathematics and Natural Sciences, Department of
iii
THE COMPARISON OF STUDENTS’ MATHEMATICAL PROBLEM SOLVING ABILITY TAUGHT BY COOPERATIVE LEARNING
MODEL O F NUMB ERED HEADS TO GETHER AND THINK PAIR SHARE AT S MP NE GE RI 13
MEDAN ACADEMIC YEAR 2016/2017
Febby Faudina Nestia (ID. 4123312008)
ABSTRACT
The aim of this research is to know whether students’ Mathematical Problem Solving Ability taught by Cooperative Learning model NHT type is higher than Cooperative Learning model TPS type in Grade IX at SMP Negeri 13 Medan. The population is all students of grade IX in SMP Negeri 13 Medan Academic Year 2016/2017. Sampling Techniques that is used in this research is random sampling. There are two samples in this research namely, Class A is IX-5 taught by NHT and Class B is IX-2 taught by TPS. Each of class consist of 32 students. Technique of analyzing data is consisted of normality, homogeneity, and hypothesis test. Based on normality and homogeneity test, the data was taken from normal distribution and homogeneous population. Hypothesis test is done by using analysis of T-test. The result of T-test show that tcalculated = 2.297 and t(0.5)(62) = 1.669. Consequently tcalculated > ttable, then H0 is rejected. So, we can conclude that students’ mathematical problem solving ability taught by cooperative learning model NHT type is higher than cooperative learning model TPS type.
iv
PREFACE
Praise and thanks to Allah Subhanallahu Wata’ala Who has give for all
the graces and blessings that provide health and wisdom to the author such that
the author could finish this thesis well. This thesis which entitled “The
Comparison of Students’ Mathematical Problem Solving Ability taught by
Cooperative Learning Model of Numbered Heads Together and Think Pair Share
in Grade IX SMPN 13 Medan Academic Year 2016/2017” is submitted in order to
get the academic title of Sarjana Pendidikan from Mathematics Department,
FMIPA Unimed.
In this part, the author would like to thank for all supports which gained
for completion of this thesis. Special thanks to Dr. Edy Surya, M.Si., as thesis
supervisor who has provided guidance, direction and advice from the beginning
until the finishing part of this thesis. Great thanks are also due to Prof. Dr.
Mukhtar, M.Pd., Dr. KMS Amin Fauzi, M.Pd., and Denny Haris, S.Si, M.Pd., as
thesis examiners who have provided builded suggestion and revision in the
completion of this thesis. Thanks also extended for Dr.Izwita Dewi, M.Pd as
academic supervisor and also for all lecturers in FMIPA Unimed.
The author also expressed sincerely thanks for Prof. Dr. Syawal Gultom,
M.Si as Rector of Unimed, Dr. Asrin Lubis, M.Pd as Dean of Mathematics and
Natural Sciences Faculty, Dr. Iis Siti Jahro, M.Si as Coordinator of Bilingual
Program, Dr. Edy Surya, M.Si as Head of Mathematics Department, Drs. Yasifati
Hia, M.Si as Secretary of Mathematics Education, and all staff employess which
supported in helping author.
Appreciation also present to Drs. Jaya Ginting as Headmaster in SMP
Negeri 13 Medan, Drs. Simaremare as Mathematics teacher who has provide
guidance when the research was held and all teachers and staff employes who
v
author to all of students in SMP Negeri 13 Medan for cooperative and helping
when the research.
Most special thanks especially would like to express for my beloved
father Mr. Iklanuddin, SE., and my mother Mrs. Drs. Jetty B. Pardede also older
brother Fajar Ferdian Nugraha S.Kom and older sister Fanny Fairinanadya
Ningrum S.Kom and all family who have supported, material, prayed, and gave
the author encouragement and funding to complete the study in Mathematics
Department.
The author also thanks to Girls’ Generation members Shinta Bella G.S,
Rahima Azzakiya, Mutiara Naibaho, Windy Erlisa, Aisyah Tohar, Aida Syahfitri,
Erika A. Simbolon, and who have made my life was happy, enjoyable and
memorable. Also big thanks for second family of BilMath 2012: Adi, Desy,
Friska Elvita, Friska Simbolon, Bowo, Rudi, Dillah, Rani, and Totok for all
support, sadness, happiness and togetherness during first semester until eight
semester. Thanks for author’s bestfriends when author was in school until now
angkatan Sepuluh, Derin P. Sianipar and Ririn Darianto then the oldest friend
Riza Fadillah. For all of PPLT Unimed 2016 SMA Negeri Plus Matauli Pandan
especially Anggi, Anis, Miyzan, Nida, Lia, Rosyadi and also all of my students
when I was doing practice. Thanks for the supports and the motivation.
At last, the author has finished and maximally to complete this thesis. But
certainly there are still some imperfection in this research. The author welcome
any suggestions and constructive criticism from readers for this thesis perfectly.
The author also hope the content of this research would be useful in enriching the reader’s knowledge. Thank you.
Medan, January 2017 Author,
Febby Faudina Nestia
vi
1.3 Problem Formulation 7
1.4 Problem Limitation 7
2.1.1 Problem in Mathematics 9
2.1.2 Mathematical Problem Solving 10
2.1.3 Mathematical Problem Solving Ability 11
2.1.4 Cooperative Learning Model 14
2.1.4.1 Component of Cooperative Learning 16
2.1.4.2 Learning Theories of Cooperative Learning 17
2.1.4.3 The Benefit of Cooperative Learning 18
vii
2.1.5.1 Advantages and Disadvantages of NHT 21
2.1.6 Cooperative Learning TPS 22
2.1.6.1 Advantages and Disadvantages of TPS 25
2.2. Conceptual Framework 25
2.3 Relevant of Research 26
2.4 Hypotesis Research 24
BAB III RESEARCH METODOLOGY
3.1 Type of Research 28
3.2 Location and Time of Research 28
3.3 Population and Sample 28
3.3.1 Population of Research 28
3.3.2 Sample of Research 29
3.4 Variable and The Instrument Research 29
3.4.1 Variable of Research 29
3.4.1.1 Independent Variable 29
3.4.1.2 Dependent Variable 30
3.4.2 Instrumens of Research 30
3.5 Design of Research 35
3.5.1 Procedure of Research 36
3.6 Techniques of Analysis Data 38
3.6.1 Problem Solving Ability 38
3.6.2 Data Analysis by Inferential Statistics Technique 38
3.6.2.1 Normality Test 38
3.6.2.2 Homogeneity Test 39
3.6.2.3 Hypothesis Test 40
CHAPTER IV RESULT AND DISCUSSION
4.1 The result of Students’ Mathematical Problem Solving 42
4.1.1 Posttest Class A and Class B 42
viii
4.1.3 Homogeneity Test of Students 44
4.1.4 Hypothesis Test of Students 45
4.2 Discussion of Result
CHAPTER V CONCLUSION AND SUGGESION
5.1 Conclusion 49
5.2 Suggestion 49
REFERENCES 50
ix
LIST OF TABLES
Pages
Table 2.1 Indicators Problem Solving Ability Based on Phase
Problem Solving by Polya 13
Table 2.2 Steps of Cooperative Learning 16
Table 2.3 Example of Steps Cooperative Learning Model of
Numbered Heads Together in a Class 20
Table 2.4 Example of Steps Cooperative Learning Model of
Think Pair Share in a Class 23
Table 3.1 Guidelines of Scoring for Problem Solving
Ability Test 31
Table 3.2 Criterion of Stuents’ Problem Solving Ability 32
Table 3.3 Criterion of Validity 33
Table 3.4 Result of Validy Test 33
Table 3.5 Criterion of Reliability 34
Table 3.6 The Reliability Confirmation 35
Table 3.7 Design of Research
Table 4.1 Statistics Data of Post-test Students 42
Table 4.2 Data of Post-test Student’ Class A and Class B 43
Table 4.3 Result of Normality Data Posttest Both Classes 44
Table 4.4 Homogeneity Test of Student’ Mathematical Problem
Solving Ability 44
Table 4.5 Hypothesis Test of Students’ Mathematical Problem
x
LIST OF FIGURES
Pages
xi
APPENDICES LIST
Pages
Appendix 1. Lesson Plan I Class NHT 53
Appendix 2. Lesson Plan II Class NHT 56
Appendix 3. Lesson Plan I Class TPS 59
Appendix 4. Lesson Plan II Class TPS 62
Appendix 5. Worksheet I 65
Appendix 6. Worksheet II 70
Appendix 7. Blueprint of Post Test 75
Appendix 8. Post Test 76
Appendix 9. Alternative Solution of Post Test 77
Appendix 10. Statistical Validity of The Test 82
Appendix 11. Reliability of The Test 85
Appendix 12. Procedure to Calculate Normality Test 87
Appendix 13. Procedure to Calculate Homogenity Test 89
Appendix 14. Procedure to Calculate Hypothesis Test 90
Appendix 15. List of Critical Value for Liliefors 92
Appendix 16. Table of t-Distribution 93
Appendix 17. F Distribution Values 96
Appendix 18. Critical r-table 106
1
CHAPTER I
INTRODUCTION
1.1 Background
Mathematics is a study that be the basic of science and technology that is
very important in every aspect of human life. Threfore, mathematics is very
important to teach in every level of educatioan such as SD, SMP, SMA and
university. Beside of that mathematics is mother of all science, so mathematics is
very important to teach. The statement is supported by the statement Cockroft (in
Abdurrahman, 2012:204) said that :
Matematika perlu di ajarkan kepada siswa karena (1) selalu digunakan dalam segi kehidupan; (2) semua bidang studi memerlukan keterampilan matematika yang sesuai; (3) merupakan sarana komunikasi yang kuat, singkat dan jelas; (4) dapat digunakan untuk menyajikan informasi dalam berbagai cara; (5) meningkatkan kemampuan berpikir logis, ketelitian, dan kesadaran keuangan; dan (6) memberikan kepuasan terhadap usaha memcahkan masalah yang menantang.
Beside that statement above, Cornelius (in Abdurahman , 2012:204) also
said that:
Lima alasan perlunya belajar matematika karena matematika merupakan (1) sarana berpikir yang jelas dan logis; (2) sarana untuk memecahkan masalah kehidupan sehari-hari; (3) sarana mengenal pola-pola hubungan dan generalisasi pengalaman; (4) sarana untuk mengembangkan kreativitas; dan (5) sarana untuk meningkatkan kesadaran terhadap perkembangan budaya.
Meanwhile, based on the outcomes of mathematics, Lerner (in
Abdurrahman, 2012: 204) argues that "mathematics studies curriculum should
include three elements: (1) concept, (2) skills and (3) problem solving ".
From the above statement, one aspect that is emphasized of the
curriculum is to improve students' problem solving ability. Problem solving is a
part of mathematics curriculum which very important because in the learning
2
and skills already possessed to be applied to solve problems that are not
considered routine.
The importance of problem solving ability was explained too by Hudojo (2005: 133)
Pemecahan masalah merupakan suatu hal yang esensial dalam pembelajaran matematika di sekolah, disebabkan antara lain (1) siswa menjadi terampil menyeleksi informasi yang relevan, kemudian menganalisisnya dan akhirnya meneliti kembali hasilnya; (2) keputusan intelektual akan timbul dari dalam merupakan hadiah intrinsik bagi siswa; (3) potensi intelektual siswa mengingkat; (4) siswa belajar bagaimana melakukan penemuan dengan melalui poses melakukan penemuan.
Cooney et.al (in Hudojo, 2005: 130) states that:
Bila seorang siswa dilatih untuk menyelesaikan masalah, maka siswa itu akan mampu mengambil keputusan sebab siswa itu menjadi mempunyai keterampilan tentang bagaimana mengumpulkan informasi yang relevan, menganalisis informasi dan menyadari betapa perlunya meneliti kembali hasil yang telah diperolehnya.
And then in additional Husna, dkk (2013 :82) state that :
The purpose of teaching problem solving in general is to (1) build knowledge of new math, (2) solve problems that arise in mathematics and in other contexts, (3) implement and customize a variety of appropriate strategies to solve problems and (4) monitor and reflect on the process of mathematical problem solving.
Thus, problem solving should get more attention, considering the role in
developing the intellectual potential of students. To find a solution of
mathematical problem solving the students must utilize their knowledge, and
through this process they will often develop new mathematical understanding.
A student is called having problem solving ability in mathematics when
students have criteria, or commonly known as the indicator. There are four
important phase to solve mathematics problem. In this research problem solving
ability will be measured through students' ability to complete a problem by using
3
1. Understanding the problem
In this step, students should be able to point out the principal parts of the problem include the unknown and the data.
2.Devising a plan
In second steps, there are some alternatives to do include students can find the connection between the data and the unknown.
3.Carrying out the plan
Students be able to implementing problem solving strategies based on plan and operate of integers correct.
4.Looking back
Student be able to look back at the complered solution, by reconsidering and reexamining the result and the path that led.
(Polya, 1973).
During the learning of mathematics impressed not touching the substance
of problem solving. Students tend to memorize math concepts, so that the
students’ ability to solve problems is lacking. Because students are not always
motivated to want to look for his own ideas, only the teacher who has always
played an active role in the learning process.
And in other occasions, Arends said that (in Trianto, 2009 : 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.”
The above statements are also supported by researcher’s preliminary of
students at SMP Negeri 13 Medan in eighth grade. In this observation, students
given problem indicating the mathematical problem solving. There are 23 students
who took the test, the students are not able to fulfill the indicator of mathematical
problem solving ability from the problem given. It can be seen from students’
answer sheet when the students have the test about students’ mathematical
problem solving ability where the average score is 37,39. While based on the
mastery level in problem solving ability, there is none get very high level (0%), 1
person (4,34%) who has high ability, 1 person (4,34%) who has medium ability,
12 person (52,17%) who have low ability, and 9 persons (39,13%) who have a
very low ability. There are only 2 persons (8,69%) who achieve the learning
4
Based on the above explanation that became one of the main problems is
the students are not taught about the steps to resolve mathematical problems and
questions given is a problem that can be resolved through existing procedures.
There were indications that the mathematical problem solving ability of students
is still relatively low.
To anticipate such problems, a teacher should be able to choose
appropriate learning models that can improve students' mathematical problem
solving abilitiy. The learning model used must be able to make students active,
because the student activity capable of influencing their knowledge.
And the statement above added by Zulkarnain (2016 : 390), he said that :
In this case students who possess basic skills require teachers’ ability to shift their
teaching from traditional to become active and innovative so that the learning
process runs according to educational development that suits the present needs.
Innovative learning leads the students to become creative, independent and able to
develop their thinking to overcome existing problems.
Duren and Cherrington (in Yusuf, 2002 : 82) investigated the effects of
cooperative group work versus individualistic effort on the learning problem
solving strategies. They summarized that students in cooperative groups were
more active in problem solving process and more open to solve the problems in different ways”
In group problem solving has the advantage, among others: (1)
problem-solving strategies, which are arranged more powerful and complex. Problem
solving in groups give students the opportunity to practice the strategy; (2) the
group can resolve more complex problems than individuals (3) each member can
practice planning and monitoring capabilities they need to make himself a better
problem solver; (4) in the discussion, each member of a turn in the opinion and
can double check their misconceptions; (5) when it got into trouble, the students
are not so afraid to deal with it, because basically they do not independent but in
5
Maheady, dkk (2006) said that:
A clear and consistent finding of educational research has been the importance of active student responding. During lectures and discussions, active responding most often takes the form of student responses to teacher questions. This whole group responding to questions, however, does not permit every student to respond and does not assure that all students are actively engaged. Previous research has shown that Numbered Heads Together is an afficient and effective intructional technique to increase student responding and to improve achievement.
In mathematical problem solving, can be done by working together. One model of learning that applies the principles of cooperation is a cooperative learning model of Numbered Heads Together (NHT).NHT is a model of learning by using a problem-solving approach, which is also able to involve students actively in learning. By using NHT, students are expected to help each other in order to develop mathematical problem solving abilities that increase their academic achievement (Dalud, 2014 : 303).
NHT learning model is the kind of cooperative learning that is designed
to influence the pattern of interaction of students and as an alternative to the
traditional class structure.Numbered Head Together (NHT) developed by spencer
Kagen in 1993 to involve more students in reviewing the material covered in the
lesson and check their understanding of the subject content (in Trianto 2009: 82) .
Teachers divide students into three to five member teams and have them number
off on them so each student has a number between 1 and 5. Teachers ask students
a queation. After that, students put their heads together to figure out and make
sure everyone knows the answer. Finally, the the teachers call a anumber an
dsyudent from each group with that number raise hands and provide answer to the
whole class(Arends, 2011 :371)
6
Cooperative learning model TPS (Think Pair Share) is a type of
cooperative learning designed to influence students' interaction patterns. First
developed by Frag Lyman and colleagues at University of Maryland accordance
Arends in 1997, states that think pair share an effective way to create an
atmosphere of variation patterns of a class discussion. "Assuming that all of
recitation or discussion needs settings for controlling the class as a whole, the
procedure used in think pair share can give a better student to think, to respond
and help each other" (in Trianto 2009: 81). Thinking : the teacher poses a question
associated with the lesson and ask students thinking alone about the answer.
Pairing :the teacher asks students to pair off and discuss what they have been
thinking about. Sharing : in teh final step, the teacher asks the pairs to share what
they have been talking about with the whole class. It is effective to simply go
around the form pair to pair and continue until about fourth or half of the pairs
have had a chance to report ( Arends, 2011 : 370-371).
Based on the above background, the researcher intends to conduct a
research entitled : “The Comparison of Students’ Mathematical Problem
Solving Ability Taught by Cooperative Learning Model of Numbered Heads
Together and Think Pair Share at SMP Negeri 13 Medan Academic Year 2016/2017”.
1.2 Problem Identification
Based on the background of the problems that have been described
problem identification in this research are
1. Most of students in SMP Negeri 13 Medan had low mathematical problem
solving ability
2. The conventional way is often used in SMP Negeri 13 Medan student
centered learning has not been applied fully in the teaching and learning
process of mathematics.
3. Teacher in SMP Negeri 13 Medan rare using cooperative learning in Learning
7
1.3 Problem Limitation
This research needs to restrict to get targets as expected. The limitation of
this research are :
1. Students’ problem solving ability on the topic of Similarity for Class IX in
SMP Negeri 13 Medan for odd Semester 2016/2017.
2. The learning activities for this study are given by using numbered heads
together and Think Pair Share.
1.4 Problem Formulation
Based in the background above, the author formulates the problems of
the study as follows :
1. Is students’ mathematical problem solving ability taught by cooperative
learning model of Numbered Heads Together is higer than cooperative
1. To know whether students' mathematical problem solving ability taught by
cooperative learning model of Numbered Head Together is higer than
cooperative learning model of Think Pair Share in IX grade SMP Negeri 13
Medan Academic Year 2016/2017.
1.6 Research Benefit
After the research is expected to result of research can provide significant
benefits, namely:
1. For the teacher, as a material consideration in choosing a model of learning
that can improve students' mathematical problem solving ability.
2. For students, it can make-students having enthusiasm to improve mathematical
problem solving ability.
3. For the school, it can be used as consideration and suggestion to improve the
8
4. For researchers, as reference materials to improve teaching and learning as
future teachers and as study materials for further research.
1.7 Operational Definition
To avoid differences or lack of meaning clarity, the following operational
definition are important terms in this research :
1. Students’ mathematical problem solving ability is students abilities in solving
mathematical problem with regard the process of understanding the problem,
planning to solving the problem, implement solving plan and looking back.
2. The syntaxes of NHT are:
a. Phase 1 : Numbering : teachers divide students into three to five member
teams and have them number off so each student on them has a number
between 1 and 5.
b. Phase 2 : Questioning : Teachers ask students a queation.
c. Phase 3 : Heads Together : After that, students put their heads together to
figure out and make sure everyone knows the answer.
d. Phase 4 : Answering : Finally, the the teachers call a anumber a student
talking about with the whole class. It is effective to simply go around the
form pair to pair and continue until about fourth or half of the pairs have
49 CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion
Based on the result and discussion of research in the previous chapters,
can be concluded that In Hypothesis test, the data are processed based on post-test
shows � � = 2.297 and � = 1.669 then � � > � which mean
H₀ rejected. So, can be concluded that students’ mathematical problem solving
ability taught by cooperative learning model of NHT is higher than cooperative
learning model of TPS.
5.2 Suggestion
Based on the conclusion and relevant study of this research, there are
some suggestions as follows:
1. For mathematics teacher, use cooperative learning model of Numbered Heads
Together or cooperative learning model of Think Pair Share as an alternative learning model in improving students’ mathematical problem solving ability. 2. For students, to cooperate with teachers by following the steps of learning
process and do not ignore the steps of problem solving ability.
3. For next researcher, base on problem solving ability aspect which will be
achieved, cooperative learning model of Numbered Heads Together is more
effective than cooperative learning model of Think Pair Share.
4. Because in this research the learning models are implemented to subtopic
50
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