THE COMPARISON OF STUDENTS’ MATHEMATICAL REASONING ABILITYBETWEEN COOPEARTIVE LEARNING MODEL TPS (THINK-PAIR SHARE) WITH STAD (STUDENT TEAMACHIEVEMENTDIVISION) ON SUBJECT QUADRATIC EQUATION AT GRADE VIII SMPN 11 BINJAI ACADEMIC YEAR 2015/2016.
THE COMPARISON OF STUDENTS’ MATHEMATICAL REASONING
ABILITY BETWEEN COOPEARTIVE LEARNING MODEL TPS
(THINK-PAIR SHARE) WITH STAD (STUDENT TEAM
ACHIEVEMENT DIVISION) ON SUBJECT
QUADRATIC EQUATION AT GRADE
VIII SMPN11BINJAIACADEMIC
YEAR 2015/2016
By :
Windy Erlisa
Reg.Number 412312022
Bilingual Mathematics Education Study Program
SKRIPSI
Submitted in Partial Fulfillment of The Requirements for The
Degree of Sarjana Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2016
i
ii
BIOGRAPHY
Windy Erlisa was born in Samarinda, Mei 14th 1994. She is the second children from
Ali Akbar Ritonga and Ernawaty Siregar. In 2000, she started her study at SD
Muhammadiyah 2 Samarinda and graduated in 2006. In 2006, the author continued study to
SMPN 2 Binjai and graduated in 2009. The author continued study to SMAN 1 Binjai and
graduated in 2012. After graduated from Senior High School, she continued her study in
Unimed as student in Bilingual Class, Mathematics Education Study Program in 2012. She is
active in HMJ Matematika Unimed. Finally, the author completed her study of undergraduated (S-1) from Unimed in 2016.
iii
iv
PREFACE
Praise and great thanks to Allah SWT that given the amazing grace, love, strength
and health so that writer can finish this skripsi. The title of this skripsi is “The
Comparison Of Students’ Mathematical Reasoning Ability Between Coopeartive
Model TPS ( Think-Pair-Share) With STAD (Student Team Achievement
Division) On Subject Quadratic Equation At Grade VIII SMPN 11
Binjai”. This skripsi was arrenged to satisfy the requirement to obtain the Degree
of Sarjana Pendidikan from Faculty Mathematics and Natural Science in State
University of Medan.
In the completion of this skripsi , the writer received support various
parties, therefore it was appropriate writer big thanks to Mr. Drs. Zul Amry,
M.Pd, P.hD as my thesis supervisor who has provided guidance, direction, and
advice to the perfection of this thesis. Thanks are also due to Prof. Dr. B. Sinaga,
M.Pd, Dr, M. Manullang, M.Pd, Dra. Katrina Samosir,M.Pd as author’s
examiners who have provided input and suggestion from the planning to the
completion of the preparation of the research of this thesis. Thanks are also
extended to Drs. Yasifati Hia,M.Si as academic supervisor and then thankyou so
much for all author’s lecturer in FMIPA Unimed.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Si as rector of
Unimed, Dr. Asrin Lubis, M. Pd as Dean of Mathematics and Natural Science
Faculty and to coordinator of Bilingual Dr. Iis Siti Jahro, M.Si, Dr.Edi Surya,
M.Si as Chief of Mathematics Departement, Drs. Zul Amry,M.Si, P.hD as Chief
of Mathematics Education Study Program, Drs. Yasifati Hia, M.Si as sSecretary
of Mathematics Educarin, and all of employee staff who have helped the author.
Especially I would like to express my grtitude to my dear mother Mrs. Ernawaty
Siregar and my dear father Mr. Ali Akbar Ritonga continues to provide
motivation and prayers for the success of me completed this thesis. Special big
thanks to my beloved sister Winda Lestari Ritonga and also my brother M. Rizky
Rafsanjani Ritonga for giving support even moril or material and all my family
for all pray, motivation, and support until the end of my study. And never forget
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thanks to Fery Surya Perdana, the one who always giving his time to help me to
finish my thesis and also always motivating me to finish this thesis.
Also thanks to my bestfriend from PAMB until Graduation Day together Maulida
Hafni and Findi Septiani who always be there, always together and giving support
each other. And big thanks for my second family Girls Generation Rahima
Azzakiyya, Aisyah Tohar, Febby Faudina, Aida Syahfitri, Shinta Bella, Mutiara
Naibaho, Erika Simbolon, and also my classmate Friska Simbolon, Friska Elvita,
Rani S, Desi Agustina,Padillah, Is Wibowo, Mas Rudi, Satoto and Adi Sinambela
who always giving support from first semester until finishing this thesis in eight
semester.
And thanks to my senior sist Vivi always teach me to finish my thesis, and sist
Widi, Sist Debby, Sist Putri, Sist Mora and Bro Elfan and my Junior Sist Tia
Rizky, Sist Reyni, Sist Dhila, Sist Bita, Sist Nana, Sist Sherly for every support to
me.And also thanks to my sweet friends Tia Mariani, Inggri A, Ririn always help
me and thanks for every support to me.
At last, the Author has finished this thesis in maximum level but author realized
there are some imperfections. For that, the author asks for building comments and
suggestions in order to reach the perfection of this thesis. The author whises that
this thesis would be useful to improve the knowledge should give a big effort to
prepare this thesis, and the writer know that this thesis have so many weakness.
So that, the author needs some suggestions to make it this be better. And big
whises, it can be improve our knowledge, understanding, and enrich the science
education.
Medan, June
Author,
Windy Erlisa
ID. 4123312022
2016
iii
THE COMPARISON OF STUDENTS’ MATHEMATICAL REASONING
ABILITY BETWEEN COOPEARTIVE MODEL TPS ( THINK-PAIR
SHARE) WITH STAD (STUDENT TEAM ACHIEVEMENT
DIVISION) ON SUBJECT QUADRATIC EQUATION
AT GRADE VIII SMPN 11 BINJAI
ACADEMIC YEAR 2015/2016
Windy Erlisa (ID. 4123312022)
ABSTRACT
The type of this research is experiment. The objective of this research was to
know the comparison of mathematical reasoning ability which taught by TPS is
higher than STAD. Population of this research was 207 students of grade eight in
SMP Negeri 11 Binjai. Applying cluster-random-sampling, VIII 1 was taken as
Experiment Class I and taught by using TPS, meanwhile VIII 4 as Experiment
Class II and taught by using STAD. Each of class consist of 25 students.
Technique of analzying 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 co-variance and coefficient of determination index. The result of
ANCOVA show that Tstatistics = -3.089 and T(0.05;48) = 1.676. Consequently -tstatistics
< ttable, then H0 is rejected. It means there is significant effect of learning model
toward students’ problem solving ability. The coefficient of determination index
in TPS class is 0.5160 or 51.60 % meanwhile in STAD class is 0.4240 or 42.40%.
It means students’ mathematical reasoning ability of mathematics which taught by
TPS is higher than STAD. Furthermore, the comparison of both effect is equal to
9.2%. The result of this research contributes to suggest the using of TPS model to
increase students’ mathematical reasoning ability of mathematics.
.
v
TABLE OF CONTENS
Pages
Sheet of Agreement
i
Biography
ii
Abstract
iii
Preface
iv
Contents
v
List of Figures
vi
List of Tables
vii
List of Appendices
viii
Chapter I
INTRODUCTION
1.1 Background
1
1.2 Problem Identification
10
1.3 Problem Limitation
11
1.4 Problem Formulation
11
1.5 Problem Objective
11
1.6 Research Benefits
11
1.7 Operational Definition
12
BAB II
LITERATURE REVIEW
2.1 Theoritical Framework
14
2.1.1
Definition of Learning and Learning Matheatics
14
2.1.2
Mathematics Problem
16
2.1.3
Reasoning Definition
17
2.1.4
Reasoning Ability
18
2.1.5
Reasoning in Mathematics
19
2.1.6
Learning Model
20
2.1.7
Cooperative Learning Model
23
2.1.8
Cooperative Learning Model type TPS
26
2.1.9
Cooperative Learning Model type STAD
28
vi
2.1.10
Comparison of Model Cooperative Learning TPS and STAD
30
2.1.11
Summary of Subject Matter
31
2.1.12
Quadratic Equation
31
2.1.13
Definition of Quadratic Equation
31
2.1.14 Determining Roots of Quadratic Equations by Factoring
32
2.1.15 Determining Roots of Quadratic Equations with Compliting Perfect
Square
33
2.1.16 Detemining Roots of Quadratic Equation by Formula abc
34
2.1.17 Kinds Roots of Quadratic Equation
35
2.1.18 Problem Involving Quadratic Equation
36
2.2.
Conceptual Framework
37
2.3
Relevant Research
39
2.4
Hypotesis Research
39
BAB III
RESEARCH METODOLOGY
3.1 Location and Time of Research
41
3.2 Population and Sample
41
3.2.1 Population
41
3.2.2 Sample
41
3.3 Research Variable
41
3.4 Operational Definition
41
3.5 Research Objectives
42
3.6 Research Procedure
43
3.7 Research Instrument
46
3.7.1 Ability Test
3.8 Data Analysis Technique
46
46
3.8.1 Mathematical Reasoning Ability Students
46
3.8.1.1 Normality Test
46
3.8.1.2 Homogenity Test
47
3.8.1.3 Hypothesis Analysis Testing
48
vii
CHAPTER IV: RESULT AND DISCUSSION
50
4.1. Result of Research
50
4.1.1 Result Data of Research
4.2. Analysis of Data
50
51
4.2.1. Normality Test
51
4.2.2. Homogenity Test
52
4.2.3. Hypothesis Test
53
4.3. Discussion of Result
54
CHAPTER V: CONCLUSION AND SUGGESTION
58
5.1. Conclusion
58
5.2. Suggestion
58
REFERENCES
59
ix
TABLE LIST
Pages
Table 1.1 Students’ Error in Solving Problem
Table 2.1 Steps of Cooperative Learning Model
5
25
Table 2.2 Comparison of Type Model Cooperative Learning Type TPS
and STAD
31
Table 3.1 Research Design
43
Table 4.2 Statistics Result
51
Table 4.3 Table of Nomality Test
52
Table 4.4 Table of Homogenity Test
52
Table 4.5 Table of Hypothesis Result
53
1
CHAPTER I
INTRODUCTION
1.1. Background
Education is one of the efforts to improve the quality of human resources
and that have certain characteristics such as insightful extensive knowledge,
ability to solve everyday problems it faces and the attitudes and behavior
positively to the surrounding natural environment. Trianto (2009: 1) states that:
"Good education is education that can support future development, which means
being able to develop the potential of learners, such as he would be able to face
and solve the problems by himself.”
Mathematics is the oldest science and basic science has an important role
in science and technology. The statement is supported by the statement Cockroft
(in Abdurrahman, 2009:253) argues that mathematics should be taught to students
because:
1.
2.
3.
4.
5.
6.
Mathematics always be used in all aspects of life.
All area studies require to math skills appropiate.
Can be strong, short and clear in communication.
Can be used for present information in various way.
Increase logical thinking, accuracy and awareness spatial.
Provide satisfaction against to solve challenging problems.
Mathematics education is one of study taught at every level of
education. Mathematics education has a very dominant role in educating students
for developing critical thinking skills, analytical and logical. One of the
problems that occur in the world of education in Indonesia is the low quality of
mathematics education, both in terms of process and learning outcomes, Thus
causing a low Indonesian student mathematics achievement.
Hamdani (2011: 79) said that:
The task of the teacher in order to optimize the learning process is a
facilitator who is able to develop the students' willingness to learn,
develop learning conditions, and impose restrictions on the positive for
himself as a teacher. Thus, the learning method is one factor or an
educational component that will determine the success or failure of a
lesson.
2
However, the reality has not been as expected. The study mentions that
the focus and attention on improving the ability of mathematical thinking still
rarely developed.
According Herman (in http://furahasekai.wordpress.com/2011/09/06/
permasalahanpembelajaran-matematika-di-sekolah/ ) said that:
The problem of the low mastery of math students are the teachers do not
provide adequate opportunity to the students to construct their own
knowledge. Math has studied by most students directly in the form of
ready-made. (formal), because mathematics is viewed by most teachers
as a process that procedural and mechanistic.
The mathematics problem is a matter of mathematics or mathematical
statement in which there is no procedure or algorithm that can be directly used or
used by students to solve the problems, and the statement must be solved by the
students. Teachers are required to encourage students to actively learn and can
improve the ability of solving mathematical problems which are important factors
in mathematics.
Mathematics is a field of study that is learned by everyone from an early
age. There are many reasons on the need for students to learn mathematics. As
stated by Cornelius (in Abdurrahman, 2012: 204):
“Five reasons for the need to learn math because math are
(1) the means to think clearly and logically,
(2) the means to solve the problems of everyday life,
(3) the means to know the relationship patterns and generalization of
experience,
(4) the means to develop creativity and
(5) the means to increase awareness of cultural development.”
Given the role of mathematics is very important in the process of
improving the quality of human resources in Indonesia, the efforts to improve the
quality of mathematics learning requires serious attention.
There are many reasons for the need to study mathematics. As proposed
by Cockroft (in Abdurrahman, 2009: 253):
The reasons of mathematics thaught to students because
3
(1) always used in our life,
(2) all fields of study require appropriate mathematical skills,
(3) a powerful means of communication, concise, and clear,
(4) can be used to present information in a variety of ways,
(5) improve the ability to think logically, accuracy, and spatial
awareness, and
(6) give satisfaction to the efforts to solve challenging problems.
From the above statement it is seen the purpose of learning mathematics
is to make all parties must continue to improve the quality of education. One of
the capabilities that are expected to be achieved by students is the mathematical
reasoning ability. It is stated in the Ministerial Regulation No.22 of 2006 on
Subjects Mathematics Content Standards, the purpose of learning mathematics is
that the students are able to:
(1) understanding mathematical concept, explaining the relationship
of concepts and applying concepts or algorithms, are flexible, accurate,
efficient, and precise in solving the problem,
(2) using reasoning on patterns and properties, perform mathematical
manipulation in making generalizations, compile evidence, or explain
ideas and statements of mathematics,
(3) solving problems that include the ability to understand the problem,
devised a mathematical model, solve the model and men afsirkan
obtained solution,
(4) communicating the ideas with symbols, tables, diagrams, or other
media to clarify the situation or problem, and
(5) having respect usefulness of mathematics in life, curiousity, concerns
and interests in learning mathematics and a tenacious attitude and
confidence in solving problems.
Various reasons for the need for schools to teach math to students in
essence can be summarized as problems of everyday life. According exposure
Liebeck (in Abdurrahman, 2003: 253) "There are two kinds of mathematics
4
mathematical reasoning abilitythat must be mastered by the student, mathematical
calculations and mathematical reasoning".
Reasoning in mathematics has a very important role in the process of
thinking of a person. Reasoning is also a foundation in mathematics. If the
students do not develop the ability to reasoning, then for math students will only
be a matter that follow set procedures and emulate the examples without knowing
its meaning.
Mathematics and reasoning are two things that can not be separated, that
is mathematics theory understanding through reasoning and mathematical
reasoning can be understood and be trained through learn math. Students are able
to think and make sense of a mathematical problem if it had been able to
understand the math problems. A point of view of students about math problems
influence the thought patterns of settlement that will be done. In addition to
mathematics is a science which is understood through reasoning, also because one
of the goals of mathematics learning is that the students are able to use our
reasoning in the patterns and character, manipulation mathematics in making
generalizations,
compile
evidence,
or
explain
mathematical
ideas
and
statements. This is similar to the Directorate General of Primary and Secondary
Education Regulations explanation No. 506 / C / PP / 2004 (in Sadiq, 2009: 14)
states
of
the
indicators
of
reasoning
that
should
be
achieved
by
students. Indicators show the reasoning, among others:
(1) ability to present mathematical statement in writing, and drawing,
(2) ability to manipulate the math,
(3) ability to check the validity of an argument,
(4) ability to draw conclusions from the statement.
From the research in field observations were carried out in SMP Negeri
11 Binjai shows that the ability of mathematical reasoning students still low seen
from students who do not understand the problem, confused associating with
known what was asked so difficult to manipulate formulas to be used, and many
students are less rigorous in calculation so that the effect on the end result. This is
evident from the questions given to students:
5
1. Determine the roots of a quadratic equation x2 - 15x + 36 = 0
2. Perimeter of a rectangular garden is 70 m. If area of the garden is 300
m2, Find the length and breadth of the garden!
Tabel 1.1
Students Error In Solving Problem
No.
Student’s Answer
Student’s Mistaken
1
o Students can not change
the results of factoring in
the form of roots.
o Students are less precise in
the calculation .
6
No.
Student’s Answer
Student’s Mistaken
2
o
Lack of understanding of
the
basic
concepts
/
material precondition of a
quadratic equation is an
algebraic seen from the
students
who
are
still
confuse with factoring.
o
Did not understand the
question
3
o Did not written where are
the known and questioned.
o In this question, students
could not identifying the
question which can be seen
that
student
just
remembering the formula
7
4
o The steps of answering th
question almost right but
student still confuse to
connect
between
equations obtained from
the
circumference
of
square with the width of
the square
Based on the examples above, it can be concluded that there are still many
students who have difficulty in solving mathematical problems that reasoning
math
student
can
not
be
increased
as
expected
of
teachers.
This illustrates the mathematical reasoning problems, hence the need for an action
to be able to train and develop the skills of mathematical reasoning students in
order to increase the learning of mathematics.
Connecting with these problems shows that the reasoning of students is
important, it is supported by the general aim of providing reasoning structuring
and formation of student attitudes and skills in the application of
mathematics. Recognizing the importance of mathematical reasoning for students,
it is necessary that learning can improve students' mathematical reasoning. One
step that can be done by teachers as mentors are appropriate learning models, one
of which is to implement cooperative learning model. According Artzt &
Newman (in Trianto, 2009: 56) states that in a cooperative learning students learn
together as a team to accomplish the tasks of the group to achieve a common
goal. Thus, each member of the group has the same responsibility for the group's
8
success. Some experts claim that this model is not only excel in helping students
understand difficult concepts, but also very useful to cultivate the ability to think
critically, work together, and help a friend.
This is also supported by the results of interviews with teachers of
mathematics at SMP Negeri 11 Binjai (on January 16th 2016) says that, generally
there are difficulties in learning mathematics when a given problem is not the
same as the example, this would mean a lack of understanding of the students in
understanding the concept of bringing the ability to think they are not too
maximal and its effects reasoning ability also becomes low, the implementation of
learning mathematics dominated by teacher makes student involvement for this
study is still not optimal. He also said that students are not too interested in math
so that students easily forget and understand only when he explains.
One
of
solutions
that
can
be
applied
to
solve
the
low mathematical reasoning skills students is to apply the model of cooperative
learning. Character of cooperative learning is students learn together as a team to
accomplish the tasks of the group to achieve a common goal. Thus, each member
of the group has the same responsibility for the group's success. Some experts
claim that this model is not only success in helping students to understand the
difficult concepts, but also very useful for the kind of critical thinking, working
together, and help a friend. This is supported by the results of research conducted
by Slavin (in Rusman, 2012 : 205) said that:
(1) Using the cooperative learning can improve student achievement
while increasing social relationships, cultivate a tolerance
and respect for the opinions of others,
(2) Cooperative learning can solve the needs of students in critical
thinking, reasoning, and integrate knowledge with experience.
In this model of cooperative learning, teachers not only impart knowledge
to students, but also have to build knowledge in his mind. Students have the
opportunity to gain direct experience in implementing their ideas, this is an
opportunity for students to find and implement their own ideas (Rusman,
2012:201).
There were 4 of cooperative learning approach according to Trianto
(2011: 67), "That Student Teams-Achievement Division (STAD), JIGSAW,
9
Investigation Group (Teams Games Tournaments or TGT), and the Structural
approaches include Think - Pair-Share (TPS) and Numbered Head Together
(NHT)”.
Because teachers' mastery of the learning model is still not optimal, the
researcher tried to introduce cooperative learning models for math teachers in
SMPN 11 Binjai. One of the cooperative learning model to improve mathematical
reasoning abilityis cooperative learning model type Think-Pair-Share (TPS). The
reason the researchers chose this learning model because TPS is a type of
cooperative learning that is designed to influence the pattern of interaction that
occurs between students in learning activities. In this case the student is expected
to work in small groups to help each other and be identified with a pattern of
cooperation rather than individuals. The advantages of TPS models are shaping
individual and a pair group responsibility, because in this model there are
individual tasks and task groups. So also with cooperative learning model Student
Teams-Achievement Division (STAD) is the simplest cooperative learning, with
4-5 people heterogeneously discussions. STAD cooperative learning created
between student interaction with the students and also between students and
teachers to create a learning community. Students not only learn from teachers
but also from fellow students. In STAD cooperative learning requires active
student participation in group discussions. According to Istarani (2011: 68-69),
think-pair-share has strength:
1. Be able to improve students’ reasoning, critical power of students, the
students’ imagination and power of analysis to a problem;
2. Promote cooperation among the students as they work in groups;
3. Improve the ability of students to understand and appreciate other
opinions;
4. Improve students’ ability to express opinions as implementation of
his/her knowledge;
5. Teacher is more likely to increase students’ knowledge when they
finished with the discussion.
10
And there are some of the strength of cooperative learning model STAD
(Student Teams-Achievement Division), according Nurgayah (2011: 86-88) are:
a. In STAD cooperative learning model, learners are not overly relied on
teachers, but also increased confidence in the ability to think
independently, finding information from a variety of sources as well
as learning from other learners.
b. STAD cooperative learning model develops the ability to express an
idea or ideas verbally and compare with other people's ideas.
c. STAD cooperative learning model can help learners to appreciate
others and aware to the limitations as well as receiving all the
difference.
d. STAD cooperative learning model can help learners to take more
responsibility in learning.
STAD cooperative learning model improves academic achievement and
social, including developing a sense of self-esteem.
Based on the background described above, the researchers intend to
conduct a study entitled: "Comparative Ability of Reasoning Math Students Using
Cooperative Learning TPS Model (Think-Pair-Share) With Learning STAD
(Student Teams Achievement Division) Model In Class VIII SMP Negeri 11
Binjai TA 2015/2016 "
1.2. Problem Identification
Based on the problems in background that have been mentioned above,
can be identified several problems as follows:
1. Teacher dominated in Math study
2. Teacher have to establish knowledge and encouradge students
Mathematics Reasoning.
3. Teacher does not encourage the students to be more active thinking
bounce ideas off so the reasoning ability is still low.
4. Teacher is no use cooperative learning model for TPS (Think-PairShare) and STAD (Student Team Achievement Divisions) yet.
11
5. Students’ ability to solve problem is lack.
6. Students are not always motivated to want to look for his own ideas.
7. Students lack of ability to associate,organize and define the concepts.
1.3. Problem Limitation
Based on the background and the problem identification above, the
research problem is limited only to compare the ability of mathematical reasoning
students taught by cooperative learning model TPS (Think-Pair-Share) and STAD
(Student Team Achievement Divisions) on the subject of quadratic equations in
Class VIII SMP Negeri 11 Binjai.
1.4. Problem Formulation
Based on the identification and scope of problem above, then that becomes
the problem in this research is : How the comparison reasoning abilities
mathematics students taught by cooperative learning model TPS (Think-PairShare) and STAD (Student Team Achievement Divisions) on the subject of
quadratic equations in class VIII SMP Negeri 11 Binjai?
1.5. Problem Objctives
As for the purpose of this research is to know how to compare the ability
of reasoning math students taught by cooperative learning model TPS (ThinkPair-Share) and taught by cooperative learning model STAD (Student Team
Achievement Divisions) on the subject of the equation squares in class VIII SMP
Negeri 11 Binjai.
1.6. Research Benefit
This research was conducted with the hope to provide the following
benefits:
1. For
teachers,
it
can
expand
the
knowledge
of cooperative
learning model Think-Pair-Share and Student
Team
Divisions in
improve mathematical
helping
students
to
Achievement
reasoning abilities
2. For students, through cooperative learning model can help students
improve their mathematical reasoning abilities.
12
3. For schools, as consideration in the development and improvement of
mathematics teaching programs in schools.
4. For researchers, as information material as well as a handbook for
investigators in performing duties as a prospective teacher in the future.
5. As the material information to readers or other researchers who want to
conduct similar research.
1.7. Operational Definition
The operational definition in this research are:
1. Mathematical reasoning is important to know and to do math. The
ability to reason make the students solve problems in life, inside and
outside the school. Whenever we use reasoning to validate our
thinking,
then
we
increase
confidence
in
mathematics
and
mathematical thinking.
2. Cooperative
learning
model
STAD (Student Team
Achievement Divisions) is a cooperative learning model using small
groups with the number of each member of each group of 4-5 students
heterogeneously. Beginning with pen y ampaian learning objectives,
delivery of material, group activities, quizzes and awards groups. The
teacher presents a lesson, and then students work on their team to make
sure that all team members have mastered the lesson. Then, all students
are given a test on the material, at the time of this test they are not
allowed to help each other.
3. The learning model Think Pair Share or think in pairs is a type of
cooperative learning designed to influence students' interaction patterns.
The step of learning Think Pair Share types as follows:
i.
ii.
Step 1: Thinking (Thinking)
Teachers ask a question or problem that is associated with the lesson,
and ask students to use a few minutes to think for themselves answer or
problem.
Step 2: Pairing (Pairing)
13
The teacher asks the students to pair up and discuss what they have
acquired. Interaction during the time provided unite answer questions if
a unifying idea or if a particular problem is identified.
Normally teachers give no more than 4 or 5 minutes for pairs.
iii.
Step 3: Sharing (Sharing)
In the final step, the teacher asks the pairs to share with the whole class
that they are talking about. It is effective to go around the room from
partner to partner and continued until about most couples have the
opportunity to report.
58
CHAPTER V
CONCLUSION AND SUGGESTION
5.1.
Conclusion
Based on the research and processing of data it can be concluded that the
comparison of mathematical reasoning ability taught by cooperative learning
model TPS type is better than mathematical reasoning ability taught by STAD
type.
5.2.
Suggestion
Based on these results it is suggested that researchers can provide are as
follows:
1. To mathematics teachers are suggested to use cooperative learning model
TPS type or STAD type as learning model alternative in improving
students’ mathematical reasoning ability.
2. Based on mathematical reasoning aspect that will be achieved, cooperative
learning model TPS type is more effective that cooperative learning model
STAD type with the requirement teachers should be handle allocation time
in the classroom.
3. For prospective teachers to apply cooperative learning model TPS type in
improving the average value of students' mathematical reasoning abilities.
59
REFERENCES
Abbdurahman, M., (2009), Pendidikan Bagi Anak Berkesulitan Belajar, Penerbit
Rineka Cipta, Jakarta.
http://id.wikipedia.org/wiki/penalaran ( accessed on March, 1st 2016 )
http://furahasekai.wordpress.com/2011/09/06/permasalahanpembelajaranmatematika-di-sekolah/ ( Accessed September, 6th 2015)
Isjoni., (2009), Cooperative Learning, Penerbit Alfabeta, Bandung.
Istarani, (2011), 58 Model Pembelajaran Inovatif, Media Persada, Medan.
Hartati,(2011), Upaya Meningkatkan Kemampuan Pemecahan Masalah Siswa
dengan pendekatan TPS pada pokok Bahasan Pecahan di kelas V SD
Negeri No. 016505 Taman Sari Kab. Asahan Tahun Ajaran
2011/2012,Skripsi,FMIPA,UNIMED,Medan.
Hudojo,Herman.(2005),Pengembangan Kurikulum dan Pengajaran Matematika,
UM Press, Malang.
Lie, A., (2010), Cooperative Learning: Mempraktikkan Cooperative Learning di
Ruang-Ruang Kelas, PT Grasindo, Jakarta.
Nurgayah,(2011),Strategi dan Metode Pembelejaran, Cipta Pustaka Media
Perintis, Bandung
Ross., (2008), Penggunaan Pola Pikir Induktif-Deduktif Dalam Pembelajaran
Matematika
Beracuan
Konstruktivisme,
http://rochmadunnes.blogspot.com/2008/01/penggunaan-pola-pikir-induktif-deduktif.html
Shadiq, Fadjar., (2009), Kemahiran Matematika, Pusat Perkembangan dan
Pemberdayaan Pendidik dan Tenaga Kependididkan Matematika,
Yogyakarta.
Shadiq, Fadjar., (2009), Model-Model Pembelajaran Matematika SMP, Pusat
Perkembangan dan Pemberdayaan Pendidik dan Tenaga Kependididkan
Matematika, Yogyakarta.
Slavin, Robert E,(2010),Cooperative Learning : Teori, Riset, Praktik, PT. Rineka
Cipta, Jakarta
Sudjana., (2005), Metoda Statistika, Tarsito, Bandung.
60
Sumedi, Pudjo., (2008), http://achmadsudrajat.wordpress.com/penalaran ( diakses
1 Maret 2016 )
Trianto, (2010), Mendesain Model Pembelajaran Inovatif-Progressif: Konsep,
Landasan, dan Implementasinya pada Kurikulum Tingkat Satuan
Pendidikan (KTSP), Kencana, Jakarta.
ABILITY BETWEEN COOPEARTIVE LEARNING MODEL TPS
(THINK-PAIR SHARE) WITH STAD (STUDENT TEAM
ACHIEVEMENT DIVISION) ON SUBJECT
QUADRATIC EQUATION AT GRADE
VIII SMPN11BINJAIACADEMIC
YEAR 2015/2016
By :
Windy Erlisa
Reg.Number 412312022
Bilingual Mathematics Education Study Program
SKRIPSI
Submitted in Partial Fulfillment of The Requirements for The
Degree of Sarjana Pendidikan
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2016
i
ii
BIOGRAPHY
Windy Erlisa was born in Samarinda, Mei 14th 1994. She is the second children from
Ali Akbar Ritonga and Ernawaty Siregar. In 2000, she started her study at SD
Muhammadiyah 2 Samarinda and graduated in 2006. In 2006, the author continued study to
SMPN 2 Binjai and graduated in 2009. The author continued study to SMAN 1 Binjai and
graduated in 2012. After graduated from Senior High School, she continued her study in
Unimed as student in Bilingual Class, Mathematics Education Study Program in 2012. She is
active in HMJ Matematika Unimed. Finally, the author completed her study of undergraduated (S-1) from Unimed in 2016.
iii
iv
PREFACE
Praise and great thanks to Allah SWT that given the amazing grace, love, strength
and health so that writer can finish this skripsi. The title of this skripsi is “The
Comparison Of Students’ Mathematical Reasoning Ability Between Coopeartive
Model TPS ( Think-Pair-Share) With STAD (Student Team Achievement
Division) On Subject Quadratic Equation At Grade VIII SMPN 11
Binjai”. This skripsi was arrenged to satisfy the requirement to obtain the Degree
of Sarjana Pendidikan from Faculty Mathematics and Natural Science in State
University of Medan.
In the completion of this skripsi , the writer received support various
parties, therefore it was appropriate writer big thanks to Mr. Drs. Zul Amry,
M.Pd, P.hD as my thesis supervisor who has provided guidance, direction, and
advice to the perfection of this thesis. Thanks are also due to Prof. Dr. B. Sinaga,
M.Pd, Dr, M. Manullang, M.Pd, Dra. Katrina Samosir,M.Pd as author’s
examiners who have provided input and suggestion from the planning to the
completion of the preparation of the research of this thesis. Thanks are also
extended to Drs. Yasifati Hia,M.Si as academic supervisor and then thankyou so
much for all author’s lecturer in FMIPA Unimed.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Si as rector of
Unimed, Dr. Asrin Lubis, M. Pd as Dean of Mathematics and Natural Science
Faculty and to coordinator of Bilingual Dr. Iis Siti Jahro, M.Si, Dr.Edi Surya,
M.Si as Chief of Mathematics Departement, Drs. Zul Amry,M.Si, P.hD as Chief
of Mathematics Education Study Program, Drs. Yasifati Hia, M.Si as sSecretary
of Mathematics Educarin, and all of employee staff who have helped the author.
Especially I would like to express my grtitude to my dear mother Mrs. Ernawaty
Siregar and my dear father Mr. Ali Akbar Ritonga continues to provide
motivation and prayers for the success of me completed this thesis. Special big
thanks to my beloved sister Winda Lestari Ritonga and also my brother M. Rizky
Rafsanjani Ritonga for giving support even moril or material and all my family
for all pray, motivation, and support until the end of my study. And never forget
v
thanks to Fery Surya Perdana, the one who always giving his time to help me to
finish my thesis and also always motivating me to finish this thesis.
Also thanks to my bestfriend from PAMB until Graduation Day together Maulida
Hafni and Findi Septiani who always be there, always together and giving support
each other. And big thanks for my second family Girls Generation Rahima
Azzakiyya, Aisyah Tohar, Febby Faudina, Aida Syahfitri, Shinta Bella, Mutiara
Naibaho, Erika Simbolon, and also my classmate Friska Simbolon, Friska Elvita,
Rani S, Desi Agustina,Padillah, Is Wibowo, Mas Rudi, Satoto and Adi Sinambela
who always giving support from first semester until finishing this thesis in eight
semester.
And thanks to my senior sist Vivi always teach me to finish my thesis, and sist
Widi, Sist Debby, Sist Putri, Sist Mora and Bro Elfan and my Junior Sist Tia
Rizky, Sist Reyni, Sist Dhila, Sist Bita, Sist Nana, Sist Sherly for every support to
me.And also thanks to my sweet friends Tia Mariani, Inggri A, Ririn always help
me and thanks for every support to me.
At last, the Author has finished this thesis in maximum level but author realized
there are some imperfections. For that, the author asks for building comments and
suggestions in order to reach the perfection of this thesis. The author whises that
this thesis would be useful to improve the knowledge should give a big effort to
prepare this thesis, and the writer know that this thesis have so many weakness.
So that, the author needs some suggestions to make it this be better. And big
whises, it can be improve our knowledge, understanding, and enrich the science
education.
Medan, June
Author,
Windy Erlisa
ID. 4123312022
2016
iii
THE COMPARISON OF STUDENTS’ MATHEMATICAL REASONING
ABILITY BETWEEN COOPEARTIVE MODEL TPS ( THINK-PAIR
SHARE) WITH STAD (STUDENT TEAM ACHIEVEMENT
DIVISION) ON SUBJECT QUADRATIC EQUATION
AT GRADE VIII SMPN 11 BINJAI
ACADEMIC YEAR 2015/2016
Windy Erlisa (ID. 4123312022)
ABSTRACT
The type of this research is experiment. The objective of this research was to
know the comparison of mathematical reasoning ability which taught by TPS is
higher than STAD. Population of this research was 207 students of grade eight in
SMP Negeri 11 Binjai. Applying cluster-random-sampling, VIII 1 was taken as
Experiment Class I and taught by using TPS, meanwhile VIII 4 as Experiment
Class II and taught by using STAD. Each of class consist of 25 students.
Technique of analzying 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 co-variance and coefficient of determination index. The result of
ANCOVA show that Tstatistics = -3.089 and T(0.05;48) = 1.676. Consequently -tstatistics
< ttable, then H0 is rejected. It means there is significant effect of learning model
toward students’ problem solving ability. The coefficient of determination index
in TPS class is 0.5160 or 51.60 % meanwhile in STAD class is 0.4240 or 42.40%.
It means students’ mathematical reasoning ability of mathematics which taught by
TPS is higher than STAD. Furthermore, the comparison of both effect is equal to
9.2%. The result of this research contributes to suggest the using of TPS model to
increase students’ mathematical reasoning ability of mathematics.
.
v
TABLE OF CONTENS
Pages
Sheet of Agreement
i
Biography
ii
Abstract
iii
Preface
iv
Contents
v
List of Figures
vi
List of Tables
vii
List of Appendices
viii
Chapter I
INTRODUCTION
1.1 Background
1
1.2 Problem Identification
10
1.3 Problem Limitation
11
1.4 Problem Formulation
11
1.5 Problem Objective
11
1.6 Research Benefits
11
1.7 Operational Definition
12
BAB II
LITERATURE REVIEW
2.1 Theoritical Framework
14
2.1.1
Definition of Learning and Learning Matheatics
14
2.1.2
Mathematics Problem
16
2.1.3
Reasoning Definition
17
2.1.4
Reasoning Ability
18
2.1.5
Reasoning in Mathematics
19
2.1.6
Learning Model
20
2.1.7
Cooperative Learning Model
23
2.1.8
Cooperative Learning Model type TPS
26
2.1.9
Cooperative Learning Model type STAD
28
vi
2.1.10
Comparison of Model Cooperative Learning TPS and STAD
30
2.1.11
Summary of Subject Matter
31
2.1.12
Quadratic Equation
31
2.1.13
Definition of Quadratic Equation
31
2.1.14 Determining Roots of Quadratic Equations by Factoring
32
2.1.15 Determining Roots of Quadratic Equations with Compliting Perfect
Square
33
2.1.16 Detemining Roots of Quadratic Equation by Formula abc
34
2.1.17 Kinds Roots of Quadratic Equation
35
2.1.18 Problem Involving Quadratic Equation
36
2.2.
Conceptual Framework
37
2.3
Relevant Research
39
2.4
Hypotesis Research
39
BAB III
RESEARCH METODOLOGY
3.1 Location and Time of Research
41
3.2 Population and Sample
41
3.2.1 Population
41
3.2.2 Sample
41
3.3 Research Variable
41
3.4 Operational Definition
41
3.5 Research Objectives
42
3.6 Research Procedure
43
3.7 Research Instrument
46
3.7.1 Ability Test
3.8 Data Analysis Technique
46
46
3.8.1 Mathematical Reasoning Ability Students
46
3.8.1.1 Normality Test
46
3.8.1.2 Homogenity Test
47
3.8.1.3 Hypothesis Analysis Testing
48
vii
CHAPTER IV: RESULT AND DISCUSSION
50
4.1. Result of Research
50
4.1.1 Result Data of Research
4.2. Analysis of Data
50
51
4.2.1. Normality Test
51
4.2.2. Homogenity Test
52
4.2.3. Hypothesis Test
53
4.3. Discussion of Result
54
CHAPTER V: CONCLUSION AND SUGGESTION
58
5.1. Conclusion
58
5.2. Suggestion
58
REFERENCES
59
ix
TABLE LIST
Pages
Table 1.1 Students’ Error in Solving Problem
Table 2.1 Steps of Cooperative Learning Model
5
25
Table 2.2 Comparison of Type Model Cooperative Learning Type TPS
and STAD
31
Table 3.1 Research Design
43
Table 4.2 Statistics Result
51
Table 4.3 Table of Nomality Test
52
Table 4.4 Table of Homogenity Test
52
Table 4.5 Table of Hypothesis Result
53
1
CHAPTER I
INTRODUCTION
1.1. Background
Education is one of the efforts to improve the quality of human resources
and that have certain characteristics such as insightful extensive knowledge,
ability to solve everyday problems it faces and the attitudes and behavior
positively to the surrounding natural environment. Trianto (2009: 1) states that:
"Good education is education that can support future development, which means
being able to develop the potential of learners, such as he would be able to face
and solve the problems by himself.”
Mathematics is the oldest science and basic science has an important role
in science and technology. The statement is supported by the statement Cockroft
(in Abdurrahman, 2009:253) argues that mathematics should be taught to students
because:
1.
2.
3.
4.
5.
6.
Mathematics always be used in all aspects of life.
All area studies require to math skills appropiate.
Can be strong, short and clear in communication.
Can be used for present information in various way.
Increase logical thinking, accuracy and awareness spatial.
Provide satisfaction against to solve challenging problems.
Mathematics education is one of study taught at every level of
education. Mathematics education has a very dominant role in educating students
for developing critical thinking skills, analytical and logical. One of the
problems that occur in the world of education in Indonesia is the low quality of
mathematics education, both in terms of process and learning outcomes, Thus
causing a low Indonesian student mathematics achievement.
Hamdani (2011: 79) said that:
The task of the teacher in order to optimize the learning process is a
facilitator who is able to develop the students' willingness to learn,
develop learning conditions, and impose restrictions on the positive for
himself as a teacher. Thus, the learning method is one factor or an
educational component that will determine the success or failure of a
lesson.
2
However, the reality has not been as expected. The study mentions that
the focus and attention on improving the ability of mathematical thinking still
rarely developed.
According Herman (in http://furahasekai.wordpress.com/2011/09/06/
permasalahanpembelajaran-matematika-di-sekolah/ ) said that:
The problem of the low mastery of math students are the teachers do not
provide adequate opportunity to the students to construct their own
knowledge. Math has studied by most students directly in the form of
ready-made. (formal), because mathematics is viewed by most teachers
as a process that procedural and mechanistic.
The mathematics problem is a matter of mathematics or mathematical
statement in which there is no procedure or algorithm that can be directly used or
used by students to solve the problems, and the statement must be solved by the
students. Teachers are required to encourage students to actively learn and can
improve the ability of solving mathematical problems which are important factors
in mathematics.
Mathematics is a field of study that is learned by everyone from an early
age. There are many reasons on the need for students to learn mathematics. As
stated by Cornelius (in Abdurrahman, 2012: 204):
“Five reasons for the need to learn math because math are
(1) the means to think clearly and logically,
(2) the means to solve the problems of everyday life,
(3) the means to know the relationship patterns and generalization of
experience,
(4) the means to develop creativity and
(5) the means to increase awareness of cultural development.”
Given the role of mathematics is very important in the process of
improving the quality of human resources in Indonesia, the efforts to improve the
quality of mathematics learning requires serious attention.
There are many reasons for the need to study mathematics. As proposed
by Cockroft (in Abdurrahman, 2009: 253):
The reasons of mathematics thaught to students because
3
(1) always used in our life,
(2) all fields of study require appropriate mathematical skills,
(3) a powerful means of communication, concise, and clear,
(4) can be used to present information in a variety of ways,
(5) improve the ability to think logically, accuracy, and spatial
awareness, and
(6) give satisfaction to the efforts to solve challenging problems.
From the above statement it is seen the purpose of learning mathematics
is to make all parties must continue to improve the quality of education. One of
the capabilities that are expected to be achieved by students is the mathematical
reasoning ability. It is stated in the Ministerial Regulation No.22 of 2006 on
Subjects Mathematics Content Standards, the purpose of learning mathematics is
that the students are able to:
(1) understanding mathematical concept, explaining the relationship
of concepts and applying concepts or algorithms, are flexible, accurate,
efficient, and precise in solving the problem,
(2) using reasoning on patterns and properties, perform mathematical
manipulation in making generalizations, compile evidence, or explain
ideas and statements of mathematics,
(3) solving problems that include the ability to understand the problem,
devised a mathematical model, solve the model and men afsirkan
obtained solution,
(4) communicating the ideas with symbols, tables, diagrams, or other
media to clarify the situation or problem, and
(5) having respect usefulness of mathematics in life, curiousity, concerns
and interests in learning mathematics and a tenacious attitude and
confidence in solving problems.
Various reasons for the need for schools to teach math to students in
essence can be summarized as problems of everyday life. According exposure
Liebeck (in Abdurrahman, 2003: 253) "There are two kinds of mathematics
4
mathematical reasoning abilitythat must be mastered by the student, mathematical
calculations and mathematical reasoning".
Reasoning in mathematics has a very important role in the process of
thinking of a person. Reasoning is also a foundation in mathematics. If the
students do not develop the ability to reasoning, then for math students will only
be a matter that follow set procedures and emulate the examples without knowing
its meaning.
Mathematics and reasoning are two things that can not be separated, that
is mathematics theory understanding through reasoning and mathematical
reasoning can be understood and be trained through learn math. Students are able
to think and make sense of a mathematical problem if it had been able to
understand the math problems. A point of view of students about math problems
influence the thought patterns of settlement that will be done. In addition to
mathematics is a science which is understood through reasoning, also because one
of the goals of mathematics learning is that the students are able to use our
reasoning in the patterns and character, manipulation mathematics in making
generalizations,
compile
evidence,
or
explain
mathematical
ideas
and
statements. This is similar to the Directorate General of Primary and Secondary
Education Regulations explanation No. 506 / C / PP / 2004 (in Sadiq, 2009: 14)
states
of
the
indicators
of
reasoning
that
should
be
achieved
by
students. Indicators show the reasoning, among others:
(1) ability to present mathematical statement in writing, and drawing,
(2) ability to manipulate the math,
(3) ability to check the validity of an argument,
(4) ability to draw conclusions from the statement.
From the research in field observations were carried out in SMP Negeri
11 Binjai shows that the ability of mathematical reasoning students still low seen
from students who do not understand the problem, confused associating with
known what was asked so difficult to manipulate formulas to be used, and many
students are less rigorous in calculation so that the effect on the end result. This is
evident from the questions given to students:
5
1. Determine the roots of a quadratic equation x2 - 15x + 36 = 0
2. Perimeter of a rectangular garden is 70 m. If area of the garden is 300
m2, Find the length and breadth of the garden!
Tabel 1.1
Students Error In Solving Problem
No.
Student’s Answer
Student’s Mistaken
1
o Students can not change
the results of factoring in
the form of roots.
o Students are less precise in
the calculation .
6
No.
Student’s Answer
Student’s Mistaken
2
o
Lack of understanding of
the
basic
concepts
/
material precondition of a
quadratic equation is an
algebraic seen from the
students
who
are
still
confuse with factoring.
o
Did not understand the
question
3
o Did not written where are
the known and questioned.
o In this question, students
could not identifying the
question which can be seen
that
student
just
remembering the formula
7
4
o The steps of answering th
question almost right but
student still confuse to
connect
between
equations obtained from
the
circumference
of
square with the width of
the square
Based on the examples above, it can be concluded that there are still many
students who have difficulty in solving mathematical problems that reasoning
math
student
can
not
be
increased
as
expected
of
teachers.
This illustrates the mathematical reasoning problems, hence the need for an action
to be able to train and develop the skills of mathematical reasoning students in
order to increase the learning of mathematics.
Connecting with these problems shows that the reasoning of students is
important, it is supported by the general aim of providing reasoning structuring
and formation of student attitudes and skills in the application of
mathematics. Recognizing the importance of mathematical reasoning for students,
it is necessary that learning can improve students' mathematical reasoning. One
step that can be done by teachers as mentors are appropriate learning models, one
of which is to implement cooperative learning model. According Artzt &
Newman (in Trianto, 2009: 56) states that in a cooperative learning students learn
together as a team to accomplish the tasks of the group to achieve a common
goal. Thus, each member of the group has the same responsibility for the group's
8
success. Some experts claim that this model is not only excel in helping students
understand difficult concepts, but also very useful to cultivate the ability to think
critically, work together, and help a friend.
This is also supported by the results of interviews with teachers of
mathematics at SMP Negeri 11 Binjai (on January 16th 2016) says that, generally
there are difficulties in learning mathematics when a given problem is not the
same as the example, this would mean a lack of understanding of the students in
understanding the concept of bringing the ability to think they are not too
maximal and its effects reasoning ability also becomes low, the implementation of
learning mathematics dominated by teacher makes student involvement for this
study is still not optimal. He also said that students are not too interested in math
so that students easily forget and understand only when he explains.
One
of
solutions
that
can
be
applied
to
solve
the
low mathematical reasoning skills students is to apply the model of cooperative
learning. Character of cooperative learning is students learn together as a team to
accomplish the tasks of the group to achieve a common goal. Thus, each member
of the group has the same responsibility for the group's success. Some experts
claim that this model is not only success in helping students to understand the
difficult concepts, but also very useful for the kind of critical thinking, working
together, and help a friend. This is supported by the results of research conducted
by Slavin (in Rusman, 2012 : 205) said that:
(1) Using the cooperative learning can improve student achievement
while increasing social relationships, cultivate a tolerance
and respect for the opinions of others,
(2) Cooperative learning can solve the needs of students in critical
thinking, reasoning, and integrate knowledge with experience.
In this model of cooperative learning, teachers not only impart knowledge
to students, but also have to build knowledge in his mind. Students have the
opportunity to gain direct experience in implementing their ideas, this is an
opportunity for students to find and implement their own ideas (Rusman,
2012:201).
There were 4 of cooperative learning approach according to Trianto
(2011: 67), "That Student Teams-Achievement Division (STAD), JIGSAW,
9
Investigation Group (Teams Games Tournaments or TGT), and the Structural
approaches include Think - Pair-Share (TPS) and Numbered Head Together
(NHT)”.
Because teachers' mastery of the learning model is still not optimal, the
researcher tried to introduce cooperative learning models for math teachers in
SMPN 11 Binjai. One of the cooperative learning model to improve mathematical
reasoning abilityis cooperative learning model type Think-Pair-Share (TPS). The
reason the researchers chose this learning model because TPS is a type of
cooperative learning that is designed to influence the pattern of interaction that
occurs between students in learning activities. In this case the student is expected
to work in small groups to help each other and be identified with a pattern of
cooperation rather than individuals. The advantages of TPS models are shaping
individual and a pair group responsibility, because in this model there are
individual tasks and task groups. So also with cooperative learning model Student
Teams-Achievement Division (STAD) is the simplest cooperative learning, with
4-5 people heterogeneously discussions. STAD cooperative learning created
between student interaction with the students and also between students and
teachers to create a learning community. Students not only learn from teachers
but also from fellow students. In STAD cooperative learning requires active
student participation in group discussions. According to Istarani (2011: 68-69),
think-pair-share has strength:
1. Be able to improve students’ reasoning, critical power of students, the
students’ imagination and power of analysis to a problem;
2. Promote cooperation among the students as they work in groups;
3. Improve the ability of students to understand and appreciate other
opinions;
4. Improve students’ ability to express opinions as implementation of
his/her knowledge;
5. Teacher is more likely to increase students’ knowledge when they
finished with the discussion.
10
And there are some of the strength of cooperative learning model STAD
(Student Teams-Achievement Division), according Nurgayah (2011: 86-88) are:
a. In STAD cooperative learning model, learners are not overly relied on
teachers, but also increased confidence in the ability to think
independently, finding information from a variety of sources as well
as learning from other learners.
b. STAD cooperative learning model develops the ability to express an
idea or ideas verbally and compare with other people's ideas.
c. STAD cooperative learning model can help learners to appreciate
others and aware to the limitations as well as receiving all the
difference.
d. STAD cooperative learning model can help learners to take more
responsibility in learning.
STAD cooperative learning model improves academic achievement and
social, including developing a sense of self-esteem.
Based on the background described above, the researchers intend to
conduct a study entitled: "Comparative Ability of Reasoning Math Students Using
Cooperative Learning TPS Model (Think-Pair-Share) With Learning STAD
(Student Teams Achievement Division) Model In Class VIII SMP Negeri 11
Binjai TA 2015/2016 "
1.2. Problem Identification
Based on the problems in background that have been mentioned above,
can be identified several problems as follows:
1. Teacher dominated in Math study
2. Teacher have to establish knowledge and encouradge students
Mathematics Reasoning.
3. Teacher does not encourage the students to be more active thinking
bounce ideas off so the reasoning ability is still low.
4. Teacher is no use cooperative learning model for TPS (Think-PairShare) and STAD (Student Team Achievement Divisions) yet.
11
5. Students’ ability to solve problem is lack.
6. Students are not always motivated to want to look for his own ideas.
7. Students lack of ability to associate,organize and define the concepts.
1.3. Problem Limitation
Based on the background and the problem identification above, the
research problem is limited only to compare the ability of mathematical reasoning
students taught by cooperative learning model TPS (Think-Pair-Share) and STAD
(Student Team Achievement Divisions) on the subject of quadratic equations in
Class VIII SMP Negeri 11 Binjai.
1.4. Problem Formulation
Based on the identification and scope of problem above, then that becomes
the problem in this research is : How the comparison reasoning abilities
mathematics students taught by cooperative learning model TPS (Think-PairShare) and STAD (Student Team Achievement Divisions) on the subject of
quadratic equations in class VIII SMP Negeri 11 Binjai?
1.5. Problem Objctives
As for the purpose of this research is to know how to compare the ability
of reasoning math students taught by cooperative learning model TPS (ThinkPair-Share) and taught by cooperative learning model STAD (Student Team
Achievement Divisions) on the subject of the equation squares in class VIII SMP
Negeri 11 Binjai.
1.6. Research Benefit
This research was conducted with the hope to provide the following
benefits:
1. For
teachers,
it
can
expand
the
knowledge
of cooperative
learning model Think-Pair-Share and Student
Team
Divisions in
improve mathematical
helping
students
to
Achievement
reasoning abilities
2. For students, through cooperative learning model can help students
improve their mathematical reasoning abilities.
12
3. For schools, as consideration in the development and improvement of
mathematics teaching programs in schools.
4. For researchers, as information material as well as a handbook for
investigators in performing duties as a prospective teacher in the future.
5. As the material information to readers or other researchers who want to
conduct similar research.
1.7. Operational Definition
The operational definition in this research are:
1. Mathematical reasoning is important to know and to do math. The
ability to reason make the students solve problems in life, inside and
outside the school. Whenever we use reasoning to validate our
thinking,
then
we
increase
confidence
in
mathematics
and
mathematical thinking.
2. Cooperative
learning
model
STAD (Student Team
Achievement Divisions) is a cooperative learning model using small
groups with the number of each member of each group of 4-5 students
heterogeneously. Beginning with pen y ampaian learning objectives,
delivery of material, group activities, quizzes and awards groups. The
teacher presents a lesson, and then students work on their team to make
sure that all team members have mastered the lesson. Then, all students
are given a test on the material, at the time of this test they are not
allowed to help each other.
3. The learning model Think Pair Share or think in pairs is a type of
cooperative learning designed to influence students' interaction patterns.
The step of learning Think Pair Share types as follows:
i.
ii.
Step 1: Thinking (Thinking)
Teachers ask a question or problem that is associated with the lesson,
and ask students to use a few minutes to think for themselves answer or
problem.
Step 2: Pairing (Pairing)
13
The teacher asks the students to pair up and discuss what they have
acquired. Interaction during the time provided unite answer questions if
a unifying idea or if a particular problem is identified.
Normally teachers give no more than 4 or 5 minutes for pairs.
iii.
Step 3: Sharing (Sharing)
In the final step, the teacher asks the pairs to share with the whole class
that they are talking about. It is effective to go around the room from
partner to partner and continued until about most couples have the
opportunity to report.
58
CHAPTER V
CONCLUSION AND SUGGESTION
5.1.
Conclusion
Based on the research and processing of data it can be concluded that the
comparison of mathematical reasoning ability taught by cooperative learning
model TPS type is better than mathematical reasoning ability taught by STAD
type.
5.2.
Suggestion
Based on these results it is suggested that researchers can provide are as
follows:
1. To mathematics teachers are suggested to use cooperative learning model
TPS type or STAD type as learning model alternative in improving
students’ mathematical reasoning ability.
2. Based on mathematical reasoning aspect that will be achieved, cooperative
learning model TPS type is more effective that cooperative learning model
STAD type with the requirement teachers should be handle allocation time
in the classroom.
3. For prospective teachers to apply cooperative learning model TPS type in
improving the average value of students' mathematical reasoning abilities.
59
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