THE IMPLEMENTATION OF COOPERATIVE LEARNING MODEL TYPE NUMBER HEAD TOGETHER TO IMPROVE THE STUDENTS MATHEMATICAL COMMUNICATION ABILITY OF EIGHTH GRADE SMP N 2 SIDIKALANG ACADEMIC YEAR 2014/2015.
THE IMPLEMENTATION OF COOPERATIVE LEARNING MODEL TYPE NUMBER
HEAD TOGETHER TO IMPROVE THE STUDENTS’ MATHEMATICAL
COMMUNICATION ABILITY OF EIGHTH GRADE SMP N 2
SIDIKALANG ACADEMIC YEAR 2014/2015
By:
Dewi Bakara
ID 4113111018
Mathematics Education Study Program
THESIS
Submitted to Fulfill the Requirement for Getting
the Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
iv
PREFACE
Give thankfulness to Jesus Christ that gives the God’s mercy and spirit
so that writer can finish this thesis. The title of this thesis is “The Implementation
of Cooperative Learning Model Type Number Head Together to Improve the
Students’ Mathematical Communication Ability of Eight Grade SMP N 2
Sidikalang Academic Year 2014/2015”. This thesis was arranged 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 thesis, the writer received support from various
parties, therefore it was appropriate writer big thanks to Mr. Prof. Dr. Sahat
Saragih, M.Pd as my thesis supervisor who has provided guidance, direction, and
advice to the perfection of this thesis. Thanks are also due to Prof. Dr Asmin,
M.Pd and Dr. Edy Surya M.Si, and Muliono S.Si, M.Si, as my 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 Prof. Dr.
Bornok Sinaga, M.Pd as academic supervisor and then thank you so much for all
my lecturer in mathematics department in FMIPA UNIMED.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Pd. as rector of
State University of Medan and employee staff in office of university head, Prof.
Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural Sciences
and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy
Surya, M.Si as Chief of Mathematics Department, Drs. Zul Amry, M. Si. as Chief
of Mathematics Education Study Program, Drs. Yasifati Hia, M.Si as Secretary of
Mathematics Education, and all of employee staff who have helped the author.
Thanks to Mr. Rakut Sembiring S.Pd as principle of SMP N 2 Sidikalang
who has given permission to writer do research, Mrs. Rotua Sitio S.Pd as
mathematics teacher and all teacher, staffs and also the students in grade VIII-1
SMP N 2 Sidikalang who have helped writer conducting the research.
Especially the witer would like to express my gratitude to my dear father
Mr.Tumbur Bakara and my dear mother Mrs. Frosma Manik that always give me
v
motivation and continues to provide motivation and prayers for the success of the
writter completed this thesis. Special big thanks to my beloved sisters (Karlina
S.Pd, Junita SKM, Rominta A.Md, Tionarta, Tionarti, Futri, Siska,and Sonia) and
to my beloved brother (Sampit and Franklyn) and to my brother in law (Meratur
Siahaan S.Pd) and to my beloved nephew (Nino Siahaan) that always give me
support even moril or material and to all my family for all pray, motivation, and
support until the end of writer’s study.
Also thanks to big family in Bilingual Mathematics Education 2011 for
sadness and happiness in the class, especially to Natalita, Yerni, Kristiani, Lestari,
Samantha, Rony, Aprita, Vera and Anna, and to Widi, Debby, Joe, Evan, Oji,
Wawa, Leny, Mbak Tika, Sapta, Acy, Asifa, Nely, Elvi and Galang. Writer also
say thanks to the member of PPLT Sidikalang 2014, (Saut, Rusdi, Angela, Tresia,
Arta, Septe, Juwita, Mia and Vera) and to all students in SMA N 1 Sidikalang and
to my favorite teacher (Mr. Edwin Pasaribu), thanks for support the writer and
thanks for the story in Sidikalang, for our crazy and for our best memory.
. And big thanks to my best PK GMKI MB 2013/2014 (B’Kael, Elpa, Sri,
Eka, Yerni, Kristiani, Ivan, Novita, Lucia, Advent and Hendra), my best brother
and senior B’Jawalsen Pardede and B’Parles Sianturi and all members of GMKI,
thanks for our togetherness, memory, support and for everything that we have
done together. And special thanks to my beloved friend Ukap Liboy Pane for the
valuable love and support that given to the writer.
The writer should give a big effort to prepare this thesis, and the writer
know that this thesis have so many weakness. So that, the writer needs some
suggestions to make it this be better. And big wishes, it can be improve our
knowledge.
Medan, Juny 2015
Author,
Dewi Bakara
ID. 4113111018
iii
THE IMPLEMENTATION OF COOPERATIVE LEARNING MODEL TYPE NUMBER
HEAD TOGETHER TO IMPROVE THE STUDENTS’ MATHEMATICAL
COMMUNICATION ABILITY OF EIGHTH GRADE SMP N 2
SIDIKALANG ACADEMIC YEAR 2014/2015
Dewi Bakara (4113111018)
ABSTRACT
The purpose of this research were (1) to find out how the Number Head
Together learning model can improve the students' mathematical communication
ability, (2) to describe the process of answer toward mathematics learning by
using Number Head Together learning model.
The type of his research was belongs to Classroom Action Research
(CAR), which is implemented in SMP Negeri 2 Sidikalang. The subjects in this
research were students of VIII-1 class in academic year 2014/2015 that have total
of 39 students consisted of 9 male and 30 female. The object of this resarch were
the students’ mathematical communication ability and Number Head Together
learning model.
This research consisted of 2 cycles and each cycles consists of 2 meetings.
Students' mathematical communication ability test conducted at the end of each
cycle. Instrument used to collect the data is mathematical communication ability
test with the form of essay test as many three problems, and observation sheet.
The results of this study can be seen: (1) The results of students’
mathematical communication ability test in the first cycle known average value of
61.82, 15 students were completed and 24 students were uncompleted, the
classical completeness was 38,46% and the students’ mathematical
communication ability was categorized to low category categorized. (2) The
results of students’ mathematical communication ability test in the second cycle
known average value of 78.63, 35 students were completed and 4 students were
uncompleted, the classical completeness was 89.74% and the students’
mathematical communication ability was categorized to good category. (3)
Learning by using the Number Head Together learning model can make students’
activity were good categorized in learning, and (4) Learning by using the Number
Head Together learning model can make the process of student’s answer more
varied.
From the results of this research can be concluded that the implementation
of the Number Head Together learning model can improve the students’
mathematical communication ability. The suggestion that given for teachers is to
be able to implement the Number Head Together learning model as an alternative
in the learning process that can improve mathematical communication ability.
vi
TABLE OF CONTENTS
Page
Authentication Sheet
i
Curriculum Vitae
ii
Abstract
iii
Preface
iv
Table of contents
vi
List of Picture
ix
List of Tables
xi
List of Appendices
xiii
CHAPTER I INTRODUCTION
1
1.1
The Background of The Problems
1
1.2
The Identification of The Problems
12
1.3
The Limitations of The Problems
12
1.4
The Formulation of The Problems
12
1.5
The Purposes of The Research
13
1.6
The Benefits of The Research
13
1.7
The Definitions of Operational
14
CHAPTER II REVIEW OF LITERATURE
15
2.1
Theoritical Framework
15
2.1.1 Communication
15
2.1.2 Mathematics Communication
18
2.1.3 Mathematics Communication Ability
21
2.1.4 Students’ Answer Process
23
2.1.5 Cooperative Learning Model
25
2.1.6 Number Head Together Learning Model
28
2.2
Relevant Studies
30
2.3
Conceptual Framework
33
2.4
Hypothesis Action
36
vii
CHAPTER III RESEARCH METODOLOGY
37
3.1
Type of Research
37
3.2
Location of Research
37
3.3
Time of Research
37
3.4
Subject of Research
37
3.5
Object of Research
38
3.6
Design of Research
38
3.7
Procedures of Research
39
3.8
Data Collection Techniques
49
3.9
Data Resources
49
3.10
Research Instruments
50
3.11
Instrument Test
52
3.12
Scoring
55
3.13
Data Analysis Techniques
58
3.14
Indicator of Success
62
CHAPTER IV RESEARCH RESULT AND DISCUSSION
63
4.1
The Result Of Instrument Test
63
4.2
The Result Of Research
64
4.2.1 The Result of Research in Cycle I
65
4.2.2 The Result of Research in Cycle II
90
4.3
4.4
Research Discussion
109
4.3.1 Learning Factors
109
4.3.2 Students’ Mathematical Communication Ability
111
Research Limitation
114
CHAPTER V CONCLUSSION AND SUGGESTION
5.1
Conclussion
115
115
5.2
Suggestion
115
REFFERENCES
117
xi
LIST OF TABLE
Page
Table 2.1
Cooperative Learning Syntax
26
Table 3.1
The Steps in Cycle I
47
Table 3.2
The Steps in Cycle II
48
Table 3.3
Interpretation of r11 Value
54
Table 3.4
Interpretation of r Value
55
Table 3.5
The Scoring Criteria of Mathematical Communication Ability
55
Table 3.6
The Scoring Criteria of the Students’ Answer
57
Table 3.7
Criteria of Student’ Mathematical Communication Ability
Table 3.7
Interpretation of Gain Normalization
59
Table 3.8
Interpretation of Students’ Activity
60
Table 3.9
Interpretation of Teacher’s Activity
61
Table 4.1
The Validity Result of Mathematical Communication
Ability Test
Table 4.2
63
The Testing Result of Mathematical Communication
Ability’s Reliability
Table 4.5
63
The Testing Result of Mathematical Communication
Ability’s Validity Cycle II
Table 4.4
63
The Testing Result of Mathematical Communication
Ability’s Validity Cycle I
Table 4.3
58
64
The Result of Mathematical Communication Ability
On Initial Observation
66
Table 4.6
The Result of Teacher’s Observations in Cycle I
70
Table 4.7
The Result of Student’s Observations in Cycle I
71
Table 4.8
The Results of Students’ Mathematical Communication
Ability Cycle I
Table 4.9
Table 4.10
73
Data of Mastery Learning of Class to Communication
Ability Test I
75
The results of Cycle I
86
xii
Table 4.11
Observations of Teacher’s Activity in Cycle II
93
Table 4.12
Observations of Student’s Activity in Cycle II
94
Table 4.13
The Results of Students’ Mathematical Communication
Ability Cycle II
Table 4.14
Data of Mastery Learning of Class to Mathematical
Communication Ability Test II
Table 4.15
96
98
Description of the Improvement in Students’ Mathematical
Communication Based on Test Cycle I and Cycle II
100
Table 4.16
The Comparison Between Cycle I and Cycle II
106
Table 4.17
The results obtained from Cycle II
107
ix
LIST OF PICTURE
Page
Picture 1.1
Students’ answer to the first question
6
Picture 1.2
Students’ answer to the second question
7
Picture 1.3
Student’s answer to the third question
7
Picture 2.1
Relationship communicators and communicant
16
Picture 3.1
CAR cycle Kemmis Model adopted from Roza dkk
38
Picture 3.2
Action Research Process adopted from Hopkins
39
Picture 4.1
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in initial observation
Picture 4.2
Pie Chart of Persentation of Students’
mathematical communication Ability Level in cycle I
Picture 4.3
66
73
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in cycle I of Each Indicator
74
Picture 4.4
Pie Chart of Students’ Learning Complete in Cycle I
75
Picture 4.5
Process of Students’ Answer on SAS 1 No. 1
76
Picture 4.6
Process of Students’ Answer on SAS 1 No. 2
77
Picture 4.7
Process of Students’ Answer on SAS 1 No. 3
77
Picture 4.8
Process of Students’ Answer on SAS 2 No. 1
78
Picture 4.9
Process of Students’ Answer on SAS 2 No. 2
78
Picture 4.10
Process of Students’ Answer on SAS 2 No. 3
79
Picture 4.11
Process of Students’ Answer on SAS 2 No. 4
79
Picture 4.12
Process of Students’ Answer Number 1 in good category
80
Picture 4.13
Process of Students’ Answer Number 1 in enough category
81
Picture 4.14
Process of Students’ Answer Number 1 in not good category
81
Picture 4.15
Process of Students’ Answer Number 2 in good category
82
Picture 4.16
Process of Students’ Answer Number 2 in enough category
82
Picture 4.17
Process of Students’ Answer Number 2 in not good category
83
Picture 4.18
Process of Students’ Answer Number 3 in good category
83
Picture 4.19
Process of Students’ Answer Number 3 in enough category
84
x
Picture 4.20
Process of Students’ Answer Number 3 in not good category
Picture 4.21
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in cycle II
Picture 4.22
84
97
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in cycle II of Each Indicator
97
Picture 4.23
Pie Chart of Students’ Learning Complete in Cycle II
99
Picture 4.24
Pie Chart of Increasing Mathematical Communication Ability 100
Picture 4.25
Process of Students’ Answer on SAS 4 No. 1
101
Picture 4.26
Process of Students’ Answer on SAS 4 No. 2
101
Picture 4.27
Process of Students’ Answer on SAS 4 No. 3
102
Picture 4.28
Process of Students’ Answer on SAS 4 No. 4
102
Picture 4.29
Process of Students’ Answer in TKKM II No 1
103
Picture 4.30
Process of Students’ Answer in TKKM II No 2
104
Picture 4.31
Process of Students’ Answer in TKKM II No 3
105
xiii
LIST OF APPENDIX
Appendix 1 Lesson Plan I Cycle I
120
Appendix 2 Lesson Plan II Cycle I
129
Appendix 3 Lesson Plan III Cycle II
139
Appendix 4 Lesson Plan IV Cycle II
149
Appendix 5 Students’ Activities Sheet I
157
Appendix 6 Students Activities Sheet II
162
Appendix 7 Students Activities Sheet III
168
Appendix 8 Students Activities Sheet IV
173
Appendix 9 The Blueprint of Students’ Math Communication Ability Test I
178
Appendix 10 Students’ Math Communication Ability Test I
180
Appendix 11 Solution of Students’ Math Communication Ability Test I
181
Appendix 12 The Scoring Criteria of Students’ Math Communication Ability I 184
Appendix 13 The Blueprint of Students’ Math Communication Ability Test II 185
Appendix 14 Students’ Math Communication Ability Test II
187
Appendix 15 Solution of Students’ Math Communication Ability Test II
188
Appendix 16 The Testing Tesult of Mathematical Communication Ability I
191
Appendix 17 The Testing Tesult of Mathematical Communication Ability II
193
Appendix 18 The Result of Mathematical Communication Ability Test I
195
Appendix 19 The Result of Mathematical Communication Ability Test II
197
Appendix 20 The Result of Mathematical Communication Ability Test I of
Each Indicator
199
Appendix 21 The Result of Mathematical Communication Ability Test II of
Each Indicator
202
Appendix 22 The Calculation of Normalized Gain
205
Appendix 23 The Result of Teacher Observation Cycle I
207
Appendix 24 The Result of Teacher Observation Cycle II
208
Appendix 25 The Result of Student Observation Cycle I
209
Appendix 25 The Result of Student Observation Cycle II
210
Appendix 26 Observation Sheet Of Students’ Activity
211
Appendix 27 Observation Sheet Of Teacher’ Activity
213
1
CHAPTER I
INTRODUCTION
1.1.
The Background Of The Problems
The development of science and technology today has increased rapidly.
The development of science and technology makes us easier to communicate and
obtain information quickly from various parts of the world. Along with the
development of science and technology must be balanced with the development of
a qualified education.
Education is a very important sector in promoting the advance of a
country because an education can create qualified human resources and able to
compete in the era of globalization. Education is influenced and contribute
directly to the development of all aspects of human life especially in the
development of science and technology. We can say a country already developed
if the education and human resources quality of the country are better. This is
supported by Eni A and Tri H statement (in http://indikator negara maju dan
berkembang_ss belajar.htm, 2014) that: “The rate of advancement of a nation can
be seen from the six indicators, namely the economic conditions, the condition of
the population, the unemployment rate, the level of education, the condition of
socio-cultural and the progress of technological”.
Education can be obtained from formal or informal. Good education
should also be able to prepare students become qualified and reliable human
resources, and able to compete globally. Therefore, in education must have
requires high order thinking to realize this fact. The high order thinking can be
obtained through study of mathematics because mathematics can train someone to
think logically, creatively and skillfully. Trianto, 2011:1 stated that: “Education
that can support the future development is education that can develops students'
potentials, so they are able to face and solve the problems”.
Mathematics is one of the basic sciences that have an important role in the
mastery of science and technology. Mathematics is important to learn because
mathematics is a science that became the basic for understanding other sciences
2
both exact and non-exact. Mathematics is also one of the subjects that must be
followed by students from elementary school until college level.
The objective given in school mathematics courses have been described in
the SBC (BSNP, 2006: 388), namely that the student has the following
capabilities:
1.
Understand the mathematical concepts, explains the relationship between the
concept and apply it appropriately in problem solving.
2.
Use the pattern and nature of the reasoning, mathematical manipulation,
compile evidence or arrange ideas and mathematical statements.
3.
Solve the problems that include the ability to understand the problem, devised
a mathematical model, solve the model and interpret the obtained solution.
4.
Communicate the ideas with symbols, tables, diagrams or other media to
clarify the issue.
5.
Having a respect for the usefulness of mathematics in life, which has a
curiosity, attention and interest in studying mathematics and tenacious
attitude and confidence in solving problems.
After studying mathematics, is also expected five ability to be acquired,
namely, (1) learn to communicate, (2) learn to think logically, (3) learn to solve
problems, (4) learn to associate ideas, and (5) the establishment of positive
mathematics attitude. One of the ability that are important in learning mathematics
is learn to communicate, where communication is not only used in science but
also in the overall of human activity.
In mathematics learning, a student is required not only have the ability in
learning concept but also able to communicate, so the knowledge can be
understood by others. Mathematic is not just a tool to think but also as a tool to
communicate between students and teachers with students. Everyone is expected
to use mathematical language to communicate information and ideas that have
gained. As Corwin in Bistari (2010: 14) argues that:
“Student’s mathematical communication ability allows students to be able
to measure the extent of their understanding of the material, enable
students to learn about the mathematical construction of the other students
3
and provide opportunities for students to reflect their mathematical
understanding. Mathematical concepts understanding are very strongly
associated with students' ability to communicate mathematically”.
Student must have communication ability in every process of learning,
especially in learning mathematics. This is accordance to Lindquist opinion based
on the National Council of Teachers of Mathematics (NCTM) revealed that
mathematics communication ability needs to be built so that students can:
1.
Reflecting and clarifying the thinking about mathematical ideas in a
variety of situations,
2.
Modeling the situation with verbal, written, graphic images and
algebraically,
3.
Developing an understanding of mathematical ideas, including the role of
definitions in various mathematical situations,
4.
Using the ability of reading, listening and writing, interpret and evaluate
mathematical ideas,
5.
Examining the mathematical ideas through conjecture and convincing
reasons,
6.
Understanding the value of notation and the role of mathematics in
development of mathematical ideas.
Communication should be improved in every student because the
communication process will help students to develop their ideas, publish ideas,
and can build a good social network in a classroom environment.
One thing that became determinant of qualified education is the success of
students in learning mathematics. Because mathematic is one of the subjects that
must be learnt. However, until today mathematics has always been considered a
difficult subject and creepy by students. In students soul is embedded an
assumption that mathematics was shut off and tend to memorize formulas. It
causes the interest of students in mathematics is low. One of the characteristics of
mathematic is abstract. This characteristic caused students difficulties in learning
mathematics, especially in understanding and completing mathematics problems.
As a result, students do not appreciate or understand the mathematical concepts
4
and have difficulties to apply mathematics in daily life. It makes learning
achievement also be low.
One of the factors that cause the results of students 'mathematics learning
becomes less is because of the students' mathematical ability communication that
can inhibit the understanding and mastery of concepts in mathematics learning
topic. This is supported by the opinion of Ansari (2009: 19) states: the higher
student's mathematical communication ability,
the higher the required
understanding to students.
To remember the important of mathematics role, the school must pay
attention to the development of learning mathematics itself and mathematics
learning outcomes in education needs to be improved. To be able to improve
learning outcomes as expected, it is require the participation from all supporting
aspects of the progress of learning, especially teachers and students.
However the reality is happens today, only teachers who play an active
role in the learning process. Teachers become a source of knowledge as a conduit
material and students to be good listeners who receive any material that is taught
by the teacher. To create teaching and learning condition was orderly and calm.
Communication happens tend to be one direction, from teacher to student. There
is no feedback from student to teacher. Generally, student is less to take the
opportunity to initiative and seek their own answer. Students are also not given
the opportunity to ask the teacher and to exchange ideas with classmates. Students
are accustomed to work individually and when they find a difficult problem,
students leave it alone until the lessons passed or hope teachers will solve it.
Teachers are too concentrated on procedural matters and mechanistic,
mathematical concepts presented in informative, and students are trained resolve
many problems without deep understanding.
Many things can cause communication ability in mathematics learning are
still low, that finally makes learning outcomes in mathematics are also low. One
of the method of teaching that is done by the teacher. The teaching methods are
almost applied by teachers is conventional teaching methods, where lectures
5
become the main choice in this learning method. Generally, students acquire
knowledge because “notified” by the teacher, not because of “find themselves”.
In conventional learning, a teacher is considers as a source of knowledge,
the teacher acts authoritarian and dominate the class. Teachers tend to be more
active and student is passive in receiving learning. Typically, teacher teaching
math materials directly, proving all their arguments and give examples, then ask
students to work on the problems similar to the problems that have been explained
by the teacher. While students just sit neatly, listen calmly and try to imitate the
ways of proving the proposition teachers and how teachers working on the
problems. Mathematics learning process that is done by the teachers do not
involve the activities of the students. So the learning process that occurs is teacher
centered.
Such learning process result students always depend on the teacher.
Students tend to imitate what the teacher worked. When the teacher gave
examples of questions to the students and then give the exact same problem and
just change the numbers, the students will tend to follow the way of teachers in
solving the problem. Usually the answer students in a class are the same and no
variations. And when different and difficult question given by the teacher than the
example question, the students will hard to find the answer of the question. This is
because of the knowledge that is gained by students do not come from themselves,
however came from the science sources that is teachers.
The low students' mathematical communication ability can be seen from
the example in the case of students of SMP N 2 Sidikalang class VIII-1. To
measure the students' communication ability, given the preliminary tests consist of
3 question about rectangular and Pythagorean theorem as a prerequisite materials
to learning cuboid and cube. As for the third questions is as follows:
1. A child raises a kite with the length of yarn is 250 meters. The distance of
child with a point just below the kite is 70 meters.
a. Draw a sketch of the problems above!
b. Calculate the height of the kite!
6
2. A rectangle with a length = (x) cm and width = (x - 4) cm. If the area of
the rectangle is 60 cm 2, find the length and width of the rectangle!
3. Is a triangle with the third sides consecutive 9 cm, 12 cm, and 18 cm a
right triangle? Explain!
After the results of the students' answers were analyzed, there were some
errors found were made by students. Communication indicator from the first
questions is the ability to write situation or mathematical idea into picture and
solve the problem. In question number 1, there are 22 student or only 66,41% of
students can answer the question rightly. This is one of incorrect picture from
student’s answer:
Figure 1.1.Student’s answer to the first question
From the pictures of the students' responses indicate that students are still
confused in describing a problem into mathematical models or into picture. In
question asked kites high, but the picture that the students showed that there has
been a height of kites. For the completion of answer part b, students unable to
communicate mathematical ideas of the images created. In the picture there is no
distance a, b, and c but in answer appear a, b, and c. In addition, students also still
failed to complete the final phase solution.
In question number 2 students failed to formulate a mathematical idea into
a mathematical model. In question number 2, there are 12 student or only 30.76%
of students can answer the question rightly. This is one of incorrect picture from
student answer:
7
Figure 1.2 Students' answers to the second question
From the pictures of the students' responses indicate that students are able
to describe a rectangle with the size of width is x and the size of length is x - 4,
and has been able to make known and were asked of a problem. However, student
failed to connect rectangular image with size into mathematical ideas. Student is
incorrect to write the formula of asked. The formula is supposed to area of the
rectangular, but that is written the circumference formula of rectangular. It is
show that the ability to communicate mathematical ideas of students is low so that
when making mathematical models and strategies for the final solution, students
still failed.
In question number 3, the indicator communication is responds to a
statement in the form of argument. In question number 3, there are only 9 student
or only 23.076% of students can answer the question rightly. Here's one of the
mistakes of the students' answers:
Figure 1.3 The students' answers to the third question
In question number 3, students are asked to provide a statement about right
triangles statement. From the picture above, we can see that the student’s
answered is “the triangle is not a right triangle because the length of all sides right
8
triangle is same”. The argument that given is certainly incorrect. Supposedly
students calculate the hypotenuse squared distance
equal to the sum of square
flat and upright side. If the student finally gets the result is larger or smaller or
equal, it
certain that it includes the type of acute triangle or obtuse triangle or
right triangle. However, these students do not give proof of that statement. This is
because understanding the concept of a right triangle that exist on these students is
still low, so in communicating their opinions about student right triangle is still
incorrect.The third incorrect answer example above can be used as concrete
evidence that mathematical communication ability of students is low.
The result of analyze show that from 39 students that follow the initial test,
the complete categorized who scored ≥ 65, only 9 students that complete or about
23.07%, while 76.92% students were not complete (30 students). Next can be seen
from the mathematical communication ability category, about 7.69% (3 students)
have very high mathematical communication ability and about 2.56% (one
student) have high mathematical communication ability, while 12.82% (5
students) were low and 76.92% (30 students) were very low. This show that the
communication ability is still low.
The results of the author's observation and interview by one of a math
teacher at SMP N 2 Sidikalang, Mrs. R.Sitio note that students are still difficulties
in solving mathematical problems, especially problems related to communicate
mathematics. It is characterized by the inability student to provide the correct
arguments or explanations about the problems they are answer. In addition,
student also unable to make the solving strategies steps, and unable to express a
mathematical idea in the form of images correctly. In directly learning, the
courage of students to submit the ideas and arguments correctly and clearly are
still less.
Recognizing that the level of students' mathematical communication
ability in the learning process is still low, it is required the participation of
students and teachers in the learning process. Students should be actively involved
in the learning process, for example in terms of finding information and try to find
more information about what will and has been studied in school, from teachers,
9
friends and other supporting books. Students who are actively involved in the
learning process will certainly have a positive impact on learning outcomes, this
will make the student will not quickly forget about the provided topic because in
the learning process the students also participated.
The role of teacher in the learning process is the most important thing. To
improve the communication ability of mathematics students, teachers must be able
to create a comfortable learning environment and choose strategies and learning
model that corresponds to the student's learning style. Teachers should be able to
make the students become actively involved during the learning process, because
the activeness in the learning is needed to improve the learning outcomes. Teacher
who is one of the main components in the learning process is expected to create
conditions that can motivate students to learn more active. One of the learning
model that is expected to improve communication ability is cooperative learning
model.
Cooperative learning is learning that emphasizes on group collaboration
that built in small groups and consist of 4-5 students. The purpose of division’s
group is to make every student can to collaborate with friends, environment,
teachers and all part that involved in the learning process. Cooperative learning
model is effective in building the process of communication ability.
In accordance to Slavin (in Rusman, 2010: 201) says: “cooperative
learning promote student to interact actively and positively in the group”. By
using cooperative learning, teachers are expected to facilitate the students to
interact with other students, such as asking a problem, so that students are
encouraged to exchange information and informal discussion. The process of
implementation of cooperative learning can also change the old paradigm of
mathematics learning is teacher-centered learning to new learning paradigm of
mathematics that is student-centered learning, where the teacher is managers in
the classroom learning and manage small group activities, teachers are also
conditioned to enable students to actively communicate in learning.
One type of cooperative learning that can be applied to enhance the
students' mathematical communication is Number Heads Together (NHT). This
10
type was developed by Spencer Kagen 1993. NHT Model is a cooperative
learning model developed by Spencer Kagan where this learning model gives
learners the opportunity to exchange ideas and consider the right answer. This
model can be used for solving the problem that the level of difficulty is limited.
Kagan (2007) states that: “Cooperative Learning models Numbered Heads
Together (NHT) indirectly trains students to share information, listen carefully
and speak with the full calculation, so that students are more productive in
learning”.
The specific characteristic of Numbered Heads Together (NHT) is teacher
just appoint a student to mention a numbers that represent the group to present the
group's work without telling who will represent the group first. This is a very
good effort to increase the responsibility of individuals in group discussions, as
well as the interdependence between individuals in the member of group thus
improve students' communication ability in completing the task group.
Herdian (in Ngatini, 2012: 153) suggests three goals to be achieved in a
NHT cooperative learning namely:
1) The results of structural academic study, which aims to improve the
performance of students in academic tasks,
2) The recognition of the diversity, aims to enable students can receive friends
who have different backgrounds,
3) The development of social ability aims to develop students' social ability.
Ability among others to share tasks, actively ask, to respect the opinions of
others, to explain ideas or opinions and work in groups.
This learning model has been widely studied in order to promote and
develop the quality of education. One of the results of studies using this model is
done by Jatnika (2012). This research used experimental study to determine the
effect of the application of cooperative learning model type NHT on students
mathematical communication ability. From the research conducted showed that
students' response to NHT learning gained as much as 75% (18 students) who
responded positively. The average value of students' mathematical communication
11
gained 61.29, so it could be said that the level of mathematics communication
ability is in medium category.
In addition, the results of the research was conducted by Hadiyanti (2012)
to test the ability of understanding concept in three-dimensional topic class X
SMA Kesatrian 2 Semarang showed that the students learning outcomes of
understanding concept ability who was taught with cooperative learning model
NHT provide higher result than students who was taught with expository learning
model.
In addition, quasi-experimental study was conducted by Pradnyani (2013)
on the mathematics achievement of students in elementary school terms of study
habits gained that students who was taught with cooperative learning model type
Numbered Head Together on good study habits get the average score was higher
(28.18) than students who teach with conventional learning models in good study
habits with an average of 19.23. Thus, there is a difference in learning
achievement between students who was taught with cooperative learning model
type Numbered Head Together with the students who was taught with
conventional learning model.
Based on the above, researchers interested in conducting research reveal
whether cooperative learning model Number Head Together can improve the
students 'mathematical communication ability, which finally will improve the
learning outcomes of students as a form of contributing researcher to realize the
quality of education in Indonesia. Therefore, this research title is "The
Implementation of Cooperative Learning Model Type Number Head
Together to Improve The Student’s Mathematical Communication Ability Of
Grade Eight SMP N 2 Sidikalang Academic Year 2014/2015".
12
1.2. The Identification Of The Problems
Based on the background described above, we can identify some of the
issues as follows:
1.
Students difficult to solve the problem of mathematical communication.
2.
The students’ mathematical communication ability are generally low.
3.
The learning model used by teachers in teaching tends to be monotonous
and still teacher centered.
4.
The process of answer in solving mathematical communication problems in
class is not varied.
1.3. The Limitation of The Problems
From the problems above, the researcher limited this problem as follows:
1.
The implementation of cooperative learning model type Numbered Head
Together to improve the students’ mathematical communication ability in
cuboid and cube topic at eighth grade SMP N 2 Sidikalang Academic Year
2014/2015.
2.
The process of answer is made by the students in solving mathematical
communication problems by using cooperative learning model type Number
Head Together.
1.4. The Formulation Of The Problems
Based on the limitation of the problem above, the formulation of the
problem in this study as follows:
1.
How is the improvement of the students’ mathematical communication
ability with the implementation of cooperative learning model type
Number Head Together in cuboid and cube topic at eighth grade SMP N 2
Sidikalang Academic Year 2014/2015?
2.
How do the students make the process of answers in solving mathematical
communication problems by using cooperative learning model type
Number Head Together?
13
1.5. The Purposes of The Research
The purposes of this study are:
1.
To find out how is the improvement of the students’ mathematical
communication ability with the implementation of cooperative learning
model type Number Head Together in cuboid and cube topic at eighth grade
SMP N 2 Sidikalang academic year 2014/2015.
2.
To describe the process of answer is made by the students in solving
mathematical communication problems by using cooperative learning model
type Number Head Together.
1.6. The Benefits Of The Research
After the research is conducted, the results of this study are expected to
provide benefits such as:
1.
For students, can actively build knowledge up, able to develop
communication ability, an understanding in dealing with the problems and
can improve social relations and mutual responsibility for themselves and
their environment.
2.
For teachers, in order to improve the quality of mathematics learning
outcomes by improving the ability of students in learning mathematics
through the creation of mathematical communication and as an alternative
learning models that can be used in the learning of mathematics.
3.
For the researchers, to be a comparative material on the topic of the role of
mathematical communication, learning motivation, achievement motivation
on the acquisition of learning outcomes in mathematics, and add the
experience and insight into the thinking of the authors of scientific research.
4.
For schools and quality of education, is expected to be considered to apply
learning with learning model Number Head Together and is expected to
improve the quality of education in Indonesia.
14
1.7. The Definitions of Operational
To avoid differences in interpretation of the terms contained in the
formulation of the problem in this study, it should be noted the following
operational definition
1.
The mathematical communication ability is the ability of the student (1) to
connect the images, tables, diagrams and daily events into mathematical
ideas, (2) to declare a situation in the form of images or graphics (drawing),
and (3) to formulate a mathematical idea into a mathematical model
(mathematical expression) and do calculation.
2.
Learning Model of Number Head Together type is a learning model more
forward to the activities of students in searching, processing, and reporting
of information from various sources that finally presented to the class. This
learning model consists of four phases, they are: (1) Numbering, (2) Asking
questions, (3) Thinking together, and (4) Answering.
3.
The process of answer is how the form or the composition of the students'
answers performance in solving mathematical communication problems to
see the variation process of the answer or solution resulted by the students.
115
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1
CONCLUSION
Based on the research results presented in the previous section can be
concluded that:
1. The improvement of students’ mathematical communication ability by the
implementation Number Head Together learning model belongs to
medium category with the normalized gain value is 0.46 where the average
of students’ mathematical communication ability in cycle I is 62.11 or
categorized to low category and in cycle II the average is improved
become 77.92 or categorized to medium category. As mastery learning
students classical in the first cycle reached 38.46% and in the second cycle
improved become 89.74%.
2. The process of student’s answer in solving a problem through
implementation Number Head Together learning model on the subject
cuboid and cube were more varied.
5.2
RECOMMENDATIONS
The recommendations in this research are as follows:
1.
Learning mathematics learning model Number Head Together can be used
as an alternative learning effective to improving the student’s mathematical
communication ability. But in the early learning teachers will have difficulty
in preparing children to make the process of cooperative learning, student
learning is difficult to accept the changes they have done so far with
constructivism learning through Number Head Together learning model. It
is therefore advisable that before learning process performed, learning
familiarize teachers with cooperative learning so that students will get used
116
to communicate both orally and in writing in conveying the idea of
mathematics.
2.
When learn with Number Head Together, teacher must be give more
attention in answering question activity, because in this phases students will
give their answer and became the appointment that students have understand
about the problem or not.
3.
From three indicators of mathematical communication ability, teacher must
be more pay attention in drawing an idea into a picture, so that the students
will produced the correct and complete picture
4.
When learning in cuboid and cube topics, teacher must be give more
attention in drawing a cuboid/cube and showing the parts of it. Because it is
the first material that students must be obtained and understanding so that
there is no problem happened when it continue into others topic.
5.
For teacher and school practitioner is equitable to change the learning
custom which is dominated by teacher and starting to involve students more
actively in the learning process, as well as give more attention to students’
mathematical communication ability. For this case, Number Head Together
learning model can be one of learning alternative to improve students’
mathematical communication ability.
6.
For the further researcher is recommended to continue the research in more
complex aim. Because the students’ success in learning can’t be measured
only with the written test and also expected to use the research result as
comparison matter and to implement Number Head Together learning
model in the other topic.
HEAD TOGETHER TO IMPROVE THE STUDENTS’ MATHEMATICAL
COMMUNICATION ABILITY OF EIGHTH GRADE SMP N 2
SIDIKALANG ACADEMIC YEAR 2014/2015
By:
Dewi Bakara
ID 4113111018
Mathematics Education Study Program
THESIS
Submitted to Fulfill the Requirement for Getting
the Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
iv
PREFACE
Give thankfulness to Jesus Christ that gives the God’s mercy and spirit
so that writer can finish this thesis. The title of this thesis is “The Implementation
of Cooperative Learning Model Type Number Head Together to Improve the
Students’ Mathematical Communication Ability of Eight Grade SMP N 2
Sidikalang Academic Year 2014/2015”. This thesis was arranged 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 thesis, the writer received support from various
parties, therefore it was appropriate writer big thanks to Mr. Prof. Dr. Sahat
Saragih, M.Pd as my thesis supervisor who has provided guidance, direction, and
advice to the perfection of this thesis. Thanks are also due to Prof. Dr Asmin,
M.Pd and Dr. Edy Surya M.Si, and Muliono S.Si, M.Si, as my 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 Prof. Dr.
Bornok Sinaga, M.Pd as academic supervisor and then thank you so much for all
my lecturer in mathematics department in FMIPA UNIMED.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Pd. as rector of
State University of Medan and employee staff in office of university head, Prof.
Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural Sciences
and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy
Surya, M.Si as Chief of Mathematics Department, Drs. Zul Amry, M. Si. as Chief
of Mathematics Education Study Program, Drs. Yasifati Hia, M.Si as Secretary of
Mathematics Education, and all of employee staff who have helped the author.
Thanks to Mr. Rakut Sembiring S.Pd as principle of SMP N 2 Sidikalang
who has given permission to writer do research, Mrs. Rotua Sitio S.Pd as
mathematics teacher and all teacher, staffs and also the students in grade VIII-1
SMP N 2 Sidikalang who have helped writer conducting the research.
Especially the witer would like to express my gratitude to my dear father
Mr.Tumbur Bakara and my dear mother Mrs. Frosma Manik that always give me
v
motivation and continues to provide motivation and prayers for the success of the
writter completed this thesis. Special big thanks to my beloved sisters (Karlina
S.Pd, Junita SKM, Rominta A.Md, Tionarta, Tionarti, Futri, Siska,and Sonia) and
to my beloved brother (Sampit and Franklyn) and to my brother in law (Meratur
Siahaan S.Pd) and to my beloved nephew (Nino Siahaan) that always give me
support even moril or material and to all my family for all pray, motivation, and
support until the end of writer’s study.
Also thanks to big family in Bilingual Mathematics Education 2011 for
sadness and happiness in the class, especially to Natalita, Yerni, Kristiani, Lestari,
Samantha, Rony, Aprita, Vera and Anna, and to Widi, Debby, Joe, Evan, Oji,
Wawa, Leny, Mbak Tika, Sapta, Acy, Asifa, Nely, Elvi and Galang. Writer also
say thanks to the member of PPLT Sidikalang 2014, (Saut, Rusdi, Angela, Tresia,
Arta, Septe, Juwita, Mia and Vera) and to all students in SMA N 1 Sidikalang and
to my favorite teacher (Mr. Edwin Pasaribu), thanks for support the writer and
thanks for the story in Sidikalang, for our crazy and for our best memory.
. And big thanks to my best PK GMKI MB 2013/2014 (B’Kael, Elpa, Sri,
Eka, Yerni, Kristiani, Ivan, Novita, Lucia, Advent and Hendra), my best brother
and senior B’Jawalsen Pardede and B’Parles Sianturi and all members of GMKI,
thanks for our togetherness, memory, support and for everything that we have
done together. And special thanks to my beloved friend Ukap Liboy Pane for the
valuable love and support that given to the writer.
The writer should give a big effort to prepare this thesis, and the writer
know that this thesis have so many weakness. So that, the writer needs some
suggestions to make it this be better. And big wishes, it can be improve our
knowledge.
Medan, Juny 2015
Author,
Dewi Bakara
ID. 4113111018
iii
THE IMPLEMENTATION OF COOPERATIVE LEARNING MODEL TYPE NUMBER
HEAD TOGETHER TO IMPROVE THE STUDENTS’ MATHEMATICAL
COMMUNICATION ABILITY OF EIGHTH GRADE SMP N 2
SIDIKALANG ACADEMIC YEAR 2014/2015
Dewi Bakara (4113111018)
ABSTRACT
The purpose of this research were (1) to find out how the Number Head
Together learning model can improve the students' mathematical communication
ability, (2) to describe the process of answer toward mathematics learning by
using Number Head Together learning model.
The type of his research was belongs to Classroom Action Research
(CAR), which is implemented in SMP Negeri 2 Sidikalang. The subjects in this
research were students of VIII-1 class in academic year 2014/2015 that have total
of 39 students consisted of 9 male and 30 female. The object of this resarch were
the students’ mathematical communication ability and Number Head Together
learning model.
This research consisted of 2 cycles and each cycles consists of 2 meetings.
Students' mathematical communication ability test conducted at the end of each
cycle. Instrument used to collect the data is mathematical communication ability
test with the form of essay test as many three problems, and observation sheet.
The results of this study can be seen: (1) The results of students’
mathematical communication ability test in the first cycle known average value of
61.82, 15 students were completed and 24 students were uncompleted, the
classical completeness was 38,46% and the students’ mathematical
communication ability was categorized to low category categorized. (2) The
results of students’ mathematical communication ability test in the second cycle
known average value of 78.63, 35 students were completed and 4 students were
uncompleted, the classical completeness was 89.74% and the students’
mathematical communication ability was categorized to good category. (3)
Learning by using the Number Head Together learning model can make students’
activity were good categorized in learning, and (4) Learning by using the Number
Head Together learning model can make the process of student’s answer more
varied.
From the results of this research can be concluded that the implementation
of the Number Head Together learning model can improve the students’
mathematical communication ability. The suggestion that given for teachers is to
be able to implement the Number Head Together learning model as an alternative
in the learning process that can improve mathematical communication ability.
vi
TABLE OF CONTENTS
Page
Authentication Sheet
i
Curriculum Vitae
ii
Abstract
iii
Preface
iv
Table of contents
vi
List of Picture
ix
List of Tables
xi
List of Appendices
xiii
CHAPTER I INTRODUCTION
1
1.1
The Background of The Problems
1
1.2
The Identification of The Problems
12
1.3
The Limitations of The Problems
12
1.4
The Formulation of The Problems
12
1.5
The Purposes of The Research
13
1.6
The Benefits of The Research
13
1.7
The Definitions of Operational
14
CHAPTER II REVIEW OF LITERATURE
15
2.1
Theoritical Framework
15
2.1.1 Communication
15
2.1.2 Mathematics Communication
18
2.1.3 Mathematics Communication Ability
21
2.1.4 Students’ Answer Process
23
2.1.5 Cooperative Learning Model
25
2.1.6 Number Head Together Learning Model
28
2.2
Relevant Studies
30
2.3
Conceptual Framework
33
2.4
Hypothesis Action
36
vii
CHAPTER III RESEARCH METODOLOGY
37
3.1
Type of Research
37
3.2
Location of Research
37
3.3
Time of Research
37
3.4
Subject of Research
37
3.5
Object of Research
38
3.6
Design of Research
38
3.7
Procedures of Research
39
3.8
Data Collection Techniques
49
3.9
Data Resources
49
3.10
Research Instruments
50
3.11
Instrument Test
52
3.12
Scoring
55
3.13
Data Analysis Techniques
58
3.14
Indicator of Success
62
CHAPTER IV RESEARCH RESULT AND DISCUSSION
63
4.1
The Result Of Instrument Test
63
4.2
The Result Of Research
64
4.2.1 The Result of Research in Cycle I
65
4.2.2 The Result of Research in Cycle II
90
4.3
4.4
Research Discussion
109
4.3.1 Learning Factors
109
4.3.2 Students’ Mathematical Communication Ability
111
Research Limitation
114
CHAPTER V CONCLUSSION AND SUGGESTION
5.1
Conclussion
115
115
5.2
Suggestion
115
REFFERENCES
117
xi
LIST OF TABLE
Page
Table 2.1
Cooperative Learning Syntax
26
Table 3.1
The Steps in Cycle I
47
Table 3.2
The Steps in Cycle II
48
Table 3.3
Interpretation of r11 Value
54
Table 3.4
Interpretation of r Value
55
Table 3.5
The Scoring Criteria of Mathematical Communication Ability
55
Table 3.6
The Scoring Criteria of the Students’ Answer
57
Table 3.7
Criteria of Student’ Mathematical Communication Ability
Table 3.7
Interpretation of Gain Normalization
59
Table 3.8
Interpretation of Students’ Activity
60
Table 3.9
Interpretation of Teacher’s Activity
61
Table 4.1
The Validity Result of Mathematical Communication
Ability Test
Table 4.2
63
The Testing Result of Mathematical Communication
Ability’s Reliability
Table 4.5
63
The Testing Result of Mathematical Communication
Ability’s Validity Cycle II
Table 4.4
63
The Testing Result of Mathematical Communication
Ability’s Validity Cycle I
Table 4.3
58
64
The Result of Mathematical Communication Ability
On Initial Observation
66
Table 4.6
The Result of Teacher’s Observations in Cycle I
70
Table 4.7
The Result of Student’s Observations in Cycle I
71
Table 4.8
The Results of Students’ Mathematical Communication
Ability Cycle I
Table 4.9
Table 4.10
73
Data of Mastery Learning of Class to Communication
Ability Test I
75
The results of Cycle I
86
xii
Table 4.11
Observations of Teacher’s Activity in Cycle II
93
Table 4.12
Observations of Student’s Activity in Cycle II
94
Table 4.13
The Results of Students’ Mathematical Communication
Ability Cycle II
Table 4.14
Data of Mastery Learning of Class to Mathematical
Communication Ability Test II
Table 4.15
96
98
Description of the Improvement in Students’ Mathematical
Communication Based on Test Cycle I and Cycle II
100
Table 4.16
The Comparison Between Cycle I and Cycle II
106
Table 4.17
The results obtained from Cycle II
107
ix
LIST OF PICTURE
Page
Picture 1.1
Students’ answer to the first question
6
Picture 1.2
Students’ answer to the second question
7
Picture 1.3
Student’s answer to the third question
7
Picture 2.1
Relationship communicators and communicant
16
Picture 3.1
CAR cycle Kemmis Model adopted from Roza dkk
38
Picture 3.2
Action Research Process adopted from Hopkins
39
Picture 4.1
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in initial observation
Picture 4.2
Pie Chart of Persentation of Students’
mathematical communication Ability Level in cycle I
Picture 4.3
66
73
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in cycle I of Each Indicator
74
Picture 4.4
Pie Chart of Students’ Learning Complete in Cycle I
75
Picture 4.5
Process of Students’ Answer on SAS 1 No. 1
76
Picture 4.6
Process of Students’ Answer on SAS 1 No. 2
77
Picture 4.7
Process of Students’ Answer on SAS 1 No. 3
77
Picture 4.8
Process of Students’ Answer on SAS 2 No. 1
78
Picture 4.9
Process of Students’ Answer on SAS 2 No. 2
78
Picture 4.10
Process of Students’ Answer on SAS 2 No. 3
79
Picture 4.11
Process of Students’ Answer on SAS 2 No. 4
79
Picture 4.12
Process of Students’ Answer Number 1 in good category
80
Picture 4.13
Process of Students’ Answer Number 1 in enough category
81
Picture 4.14
Process of Students’ Answer Number 1 in not good category
81
Picture 4.15
Process of Students’ Answer Number 2 in good category
82
Picture 4.16
Process of Students’ Answer Number 2 in enough category
82
Picture 4.17
Process of Students’ Answer Number 2 in not good category
83
Picture 4.18
Process of Students’ Answer Number 3 in good category
83
Picture 4.19
Process of Students’ Answer Number 3 in enough category
84
x
Picture 4.20
Process of Students’ Answer Number 3 in not good category
Picture 4.21
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in cycle II
Picture 4.22
84
97
Pie Chart of Persentation of Students’ mathematical
communication Ability Level in cycle II of Each Indicator
97
Picture 4.23
Pie Chart of Students’ Learning Complete in Cycle II
99
Picture 4.24
Pie Chart of Increasing Mathematical Communication Ability 100
Picture 4.25
Process of Students’ Answer on SAS 4 No. 1
101
Picture 4.26
Process of Students’ Answer on SAS 4 No. 2
101
Picture 4.27
Process of Students’ Answer on SAS 4 No. 3
102
Picture 4.28
Process of Students’ Answer on SAS 4 No. 4
102
Picture 4.29
Process of Students’ Answer in TKKM II No 1
103
Picture 4.30
Process of Students’ Answer in TKKM II No 2
104
Picture 4.31
Process of Students’ Answer in TKKM II No 3
105
xiii
LIST OF APPENDIX
Appendix 1 Lesson Plan I Cycle I
120
Appendix 2 Lesson Plan II Cycle I
129
Appendix 3 Lesson Plan III Cycle II
139
Appendix 4 Lesson Plan IV Cycle II
149
Appendix 5 Students’ Activities Sheet I
157
Appendix 6 Students Activities Sheet II
162
Appendix 7 Students Activities Sheet III
168
Appendix 8 Students Activities Sheet IV
173
Appendix 9 The Blueprint of Students’ Math Communication Ability Test I
178
Appendix 10 Students’ Math Communication Ability Test I
180
Appendix 11 Solution of Students’ Math Communication Ability Test I
181
Appendix 12 The Scoring Criteria of Students’ Math Communication Ability I 184
Appendix 13 The Blueprint of Students’ Math Communication Ability Test II 185
Appendix 14 Students’ Math Communication Ability Test II
187
Appendix 15 Solution of Students’ Math Communication Ability Test II
188
Appendix 16 The Testing Tesult of Mathematical Communication Ability I
191
Appendix 17 The Testing Tesult of Mathematical Communication Ability II
193
Appendix 18 The Result of Mathematical Communication Ability Test I
195
Appendix 19 The Result of Mathematical Communication Ability Test II
197
Appendix 20 The Result of Mathematical Communication Ability Test I of
Each Indicator
199
Appendix 21 The Result of Mathematical Communication Ability Test II of
Each Indicator
202
Appendix 22 The Calculation of Normalized Gain
205
Appendix 23 The Result of Teacher Observation Cycle I
207
Appendix 24 The Result of Teacher Observation Cycle II
208
Appendix 25 The Result of Student Observation Cycle I
209
Appendix 25 The Result of Student Observation Cycle II
210
Appendix 26 Observation Sheet Of Students’ Activity
211
Appendix 27 Observation Sheet Of Teacher’ Activity
213
1
CHAPTER I
INTRODUCTION
1.1.
The Background Of The Problems
The development of science and technology today has increased rapidly.
The development of science and technology makes us easier to communicate and
obtain information quickly from various parts of the world. Along with the
development of science and technology must be balanced with the development of
a qualified education.
Education is a very important sector in promoting the advance of a
country because an education can create qualified human resources and able to
compete in the era of globalization. Education is influenced and contribute
directly to the development of all aspects of human life especially in the
development of science and technology. We can say a country already developed
if the education and human resources quality of the country are better. This is
supported by Eni A and Tri H statement (in http://indikator negara maju dan
berkembang_ss belajar.htm, 2014) that: “The rate of advancement of a nation can
be seen from the six indicators, namely the economic conditions, the condition of
the population, the unemployment rate, the level of education, the condition of
socio-cultural and the progress of technological”.
Education can be obtained from formal or informal. Good education
should also be able to prepare students become qualified and reliable human
resources, and able to compete globally. Therefore, in education must have
requires high order thinking to realize this fact. The high order thinking can be
obtained through study of mathematics because mathematics can train someone to
think logically, creatively and skillfully. Trianto, 2011:1 stated that: “Education
that can support the future development is education that can develops students'
potentials, so they are able to face and solve the problems”.
Mathematics is one of the basic sciences that have an important role in the
mastery of science and technology. Mathematics is important to learn because
mathematics is a science that became the basic for understanding other sciences
2
both exact and non-exact. Mathematics is also one of the subjects that must be
followed by students from elementary school until college level.
The objective given in school mathematics courses have been described in
the SBC (BSNP, 2006: 388), namely that the student has the following
capabilities:
1.
Understand the mathematical concepts, explains the relationship between the
concept and apply it appropriately in problem solving.
2.
Use the pattern and nature of the reasoning, mathematical manipulation,
compile evidence or arrange ideas and mathematical statements.
3.
Solve the problems that include the ability to understand the problem, devised
a mathematical model, solve the model and interpret the obtained solution.
4.
Communicate the ideas with symbols, tables, diagrams or other media to
clarify the issue.
5.
Having a respect for the usefulness of mathematics in life, which has a
curiosity, attention and interest in studying mathematics and tenacious
attitude and confidence in solving problems.
After studying mathematics, is also expected five ability to be acquired,
namely, (1) learn to communicate, (2) learn to think logically, (3) learn to solve
problems, (4) learn to associate ideas, and (5) the establishment of positive
mathematics attitude. One of the ability that are important in learning mathematics
is learn to communicate, where communication is not only used in science but
also in the overall of human activity.
In mathematics learning, a student is required not only have the ability in
learning concept but also able to communicate, so the knowledge can be
understood by others. Mathematic is not just a tool to think but also as a tool to
communicate between students and teachers with students. Everyone is expected
to use mathematical language to communicate information and ideas that have
gained. As Corwin in Bistari (2010: 14) argues that:
“Student’s mathematical communication ability allows students to be able
to measure the extent of their understanding of the material, enable
students to learn about the mathematical construction of the other students
3
and provide opportunities for students to reflect their mathematical
understanding. Mathematical concepts understanding are very strongly
associated with students' ability to communicate mathematically”.
Student must have communication ability in every process of learning,
especially in learning mathematics. This is accordance to Lindquist opinion based
on the National Council of Teachers of Mathematics (NCTM) revealed that
mathematics communication ability needs to be built so that students can:
1.
Reflecting and clarifying the thinking about mathematical ideas in a
variety of situations,
2.
Modeling the situation with verbal, written, graphic images and
algebraically,
3.
Developing an understanding of mathematical ideas, including the role of
definitions in various mathematical situations,
4.
Using the ability of reading, listening and writing, interpret and evaluate
mathematical ideas,
5.
Examining the mathematical ideas through conjecture and convincing
reasons,
6.
Understanding the value of notation and the role of mathematics in
development of mathematical ideas.
Communication should be improved in every student because the
communication process will help students to develop their ideas, publish ideas,
and can build a good social network in a classroom environment.
One thing that became determinant of qualified education is the success of
students in learning mathematics. Because mathematic is one of the subjects that
must be learnt. However, until today mathematics has always been considered a
difficult subject and creepy by students. In students soul is embedded an
assumption that mathematics was shut off and tend to memorize formulas. It
causes the interest of students in mathematics is low. One of the characteristics of
mathematic is abstract. This characteristic caused students difficulties in learning
mathematics, especially in understanding and completing mathematics problems.
As a result, students do not appreciate or understand the mathematical concepts
4
and have difficulties to apply mathematics in daily life. It makes learning
achievement also be low.
One of the factors that cause the results of students 'mathematics learning
becomes less is because of the students' mathematical ability communication that
can inhibit the understanding and mastery of concepts in mathematics learning
topic. This is supported by the opinion of Ansari (2009: 19) states: the higher
student's mathematical communication ability,
the higher the required
understanding to students.
To remember the important of mathematics role, the school must pay
attention to the development of learning mathematics itself and mathematics
learning outcomes in education needs to be improved. To be able to improve
learning outcomes as expected, it is require the participation from all supporting
aspects of the progress of learning, especially teachers and students.
However the reality is happens today, only teachers who play an active
role in the learning process. Teachers become a source of knowledge as a conduit
material and students to be good listeners who receive any material that is taught
by the teacher. To create teaching and learning condition was orderly and calm.
Communication happens tend to be one direction, from teacher to student. There
is no feedback from student to teacher. Generally, student is less to take the
opportunity to initiative and seek their own answer. Students are also not given
the opportunity to ask the teacher and to exchange ideas with classmates. Students
are accustomed to work individually and when they find a difficult problem,
students leave it alone until the lessons passed or hope teachers will solve it.
Teachers are too concentrated on procedural matters and mechanistic,
mathematical concepts presented in informative, and students are trained resolve
many problems without deep understanding.
Many things can cause communication ability in mathematics learning are
still low, that finally makes learning outcomes in mathematics are also low. One
of the method of teaching that is done by the teacher. The teaching methods are
almost applied by teachers is conventional teaching methods, where lectures
5
become the main choice in this learning method. Generally, students acquire
knowledge because “notified” by the teacher, not because of “find themselves”.
In conventional learning, a teacher is considers as a source of knowledge,
the teacher acts authoritarian and dominate the class. Teachers tend to be more
active and student is passive in receiving learning. Typically, teacher teaching
math materials directly, proving all their arguments and give examples, then ask
students to work on the problems similar to the problems that have been explained
by the teacher. While students just sit neatly, listen calmly and try to imitate the
ways of proving the proposition teachers and how teachers working on the
problems. Mathematics learning process that is done by the teachers do not
involve the activities of the students. So the learning process that occurs is teacher
centered.
Such learning process result students always depend on the teacher.
Students tend to imitate what the teacher worked. When the teacher gave
examples of questions to the students and then give the exact same problem and
just change the numbers, the students will tend to follow the way of teachers in
solving the problem. Usually the answer students in a class are the same and no
variations. And when different and difficult question given by the teacher than the
example question, the students will hard to find the answer of the question. This is
because of the knowledge that is gained by students do not come from themselves,
however came from the science sources that is teachers.
The low students' mathematical communication ability can be seen from
the example in the case of students of SMP N 2 Sidikalang class VIII-1. To
measure the students' communication ability, given the preliminary tests consist of
3 question about rectangular and Pythagorean theorem as a prerequisite materials
to learning cuboid and cube. As for the third questions is as follows:
1. A child raises a kite with the length of yarn is 250 meters. The distance of
child with a point just below the kite is 70 meters.
a. Draw a sketch of the problems above!
b. Calculate the height of the kite!
6
2. A rectangle with a length = (x) cm and width = (x - 4) cm. If the area of
the rectangle is 60 cm 2, find the length and width of the rectangle!
3. Is a triangle with the third sides consecutive 9 cm, 12 cm, and 18 cm a
right triangle? Explain!
After the results of the students' answers were analyzed, there were some
errors found were made by students. Communication indicator from the first
questions is the ability to write situation or mathematical idea into picture and
solve the problem. In question number 1, there are 22 student or only 66,41% of
students can answer the question rightly. This is one of incorrect picture from
student’s answer:
Figure 1.1.Student’s answer to the first question
From the pictures of the students' responses indicate that students are still
confused in describing a problem into mathematical models or into picture. In
question asked kites high, but the picture that the students showed that there has
been a height of kites. For the completion of answer part b, students unable to
communicate mathematical ideas of the images created. In the picture there is no
distance a, b, and c but in answer appear a, b, and c. In addition, students also still
failed to complete the final phase solution.
In question number 2 students failed to formulate a mathematical idea into
a mathematical model. In question number 2, there are 12 student or only 30.76%
of students can answer the question rightly. This is one of incorrect picture from
student answer:
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Figure 1.2 Students' answers to the second question
From the pictures of the students' responses indicate that students are able
to describe a rectangle with the size of width is x and the size of length is x - 4,
and has been able to make known and were asked of a problem. However, student
failed to connect rectangular image with size into mathematical ideas. Student is
incorrect to write the formula of asked. The formula is supposed to area of the
rectangular, but that is written the circumference formula of rectangular. It is
show that the ability to communicate mathematical ideas of students is low so that
when making mathematical models and strategies for the final solution, students
still failed.
In question number 3, the indicator communication is responds to a
statement in the form of argument. In question number 3, there are only 9 student
or only 23.076% of students can answer the question rightly. Here's one of the
mistakes of the students' answers:
Figure 1.3 The students' answers to the third question
In question number 3, students are asked to provide a statement about right
triangles statement. From the picture above, we can see that the student’s
answered is “the triangle is not a right triangle because the length of all sides right
8
triangle is same”. The argument that given is certainly incorrect. Supposedly
students calculate the hypotenuse squared distance
equal to the sum of square
flat and upright side. If the student finally gets the result is larger or smaller or
equal, it
certain that it includes the type of acute triangle or obtuse triangle or
right triangle. However, these students do not give proof of that statement. This is
because understanding the concept of a right triangle that exist on these students is
still low, so in communicating their opinions about student right triangle is still
incorrect.The third incorrect answer example above can be used as concrete
evidence that mathematical communication ability of students is low.
The result of analyze show that from 39 students that follow the initial test,
the complete categorized who scored ≥ 65, only 9 students that complete or about
23.07%, while 76.92% students were not complete (30 students). Next can be seen
from the mathematical communication ability category, about 7.69% (3 students)
have very high mathematical communication ability and about 2.56% (one
student) have high mathematical communication ability, while 12.82% (5
students) were low and 76.92% (30 students) were very low. This show that the
communication ability is still low.
The results of the author's observation and interview by one of a math
teacher at SMP N 2 Sidikalang, Mrs. R.Sitio note that students are still difficulties
in solving mathematical problems, especially problems related to communicate
mathematics. It is characterized by the inability student to provide the correct
arguments or explanations about the problems they are answer. In addition,
student also unable to make the solving strategies steps, and unable to express a
mathematical idea in the form of images correctly. In directly learning, the
courage of students to submit the ideas and arguments correctly and clearly are
still less.
Recognizing that the level of students' mathematical communication
ability in the learning process is still low, it is required the participation of
students and teachers in the learning process. Students should be actively involved
in the learning process, for example in terms of finding information and try to find
more information about what will and has been studied in school, from teachers,
9
friends and other supporting books. Students who are actively involved in the
learning process will certainly have a positive impact on learning outcomes, this
will make the student will not quickly forget about the provided topic because in
the learning process the students also participated.
The role of teacher in the learning process is the most important thing. To
improve the communication ability of mathematics students, teachers must be able
to create a comfortable learning environment and choose strategies and learning
model that corresponds to the student's learning style. Teachers should be able to
make the students become actively involved during the learning process, because
the activeness in the learning is needed to improve the learning outcomes. Teacher
who is one of the main components in the learning process is expected to create
conditions that can motivate students to learn more active. One of the learning
model that is expected to improve communication ability is cooperative learning
model.
Cooperative learning is learning that emphasizes on group collaboration
that built in small groups and consist of 4-5 students. The purpose of division’s
group is to make every student can to collaborate with friends, environment,
teachers and all part that involved in the learning process. Cooperative learning
model is effective in building the process of communication ability.
In accordance to Slavin (in Rusman, 2010: 201) says: “cooperative
learning promote student to interact actively and positively in the group”. By
using cooperative learning, teachers are expected to facilitate the students to
interact with other students, such as asking a problem, so that students are
encouraged to exchange information and informal discussion. The process of
implementation of cooperative learning can also change the old paradigm of
mathematics learning is teacher-centered learning to new learning paradigm of
mathematics that is student-centered learning, where the teacher is managers in
the classroom learning and manage small group activities, teachers are also
conditioned to enable students to actively communicate in learning.
One type of cooperative learning that can be applied to enhance the
students' mathematical communication is Number Heads Together (NHT). This
10
type was developed by Spencer Kagen 1993. NHT Model is a cooperative
learning model developed by Spencer Kagan where this learning model gives
learners the opportunity to exchange ideas and consider the right answer. This
model can be used for solving the problem that the level of difficulty is limited.
Kagan (2007) states that: “Cooperative Learning models Numbered Heads
Together (NHT) indirectly trains students to share information, listen carefully
and speak with the full calculation, so that students are more productive in
learning”.
The specific characteristic of Numbered Heads Together (NHT) is teacher
just appoint a student to mention a numbers that represent the group to present the
group's work without telling who will represent the group first. This is a very
good effort to increase the responsibility of individuals in group discussions, as
well as the interdependence between individuals in the member of group thus
improve students' communication ability in completing the task group.
Herdian (in Ngatini, 2012: 153) suggests three goals to be achieved in a
NHT cooperative learning namely:
1) The results of structural academic study, which aims to improve the
performance of students in academic tasks,
2) The recognition of the diversity, aims to enable students can receive friends
who have different backgrounds,
3) The development of social ability aims to develop students' social ability.
Ability among others to share tasks, actively ask, to respect the opinions of
others, to explain ideas or opinions and work in groups.
This learning model has been widely studied in order to promote and
develop the quality of education. One of the results of studies using this model is
done by Jatnika (2012). This research used experimental study to determine the
effect of the application of cooperative learning model type NHT on students
mathematical communication ability. From the research conducted showed that
students' response to NHT learning gained as much as 75% (18 students) who
responded positively. The average value of students' mathematical communication
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gained 61.29, so it could be said that the level of mathematics communication
ability is in medium category.
In addition, the results of the research was conducted by Hadiyanti (2012)
to test the ability of understanding concept in three-dimensional topic class X
SMA Kesatrian 2 Semarang showed that the students learning outcomes of
understanding concept ability who was taught with cooperative learning model
NHT provide higher result than students who was taught with expository learning
model.
In addition, quasi-experimental study was conducted by Pradnyani (2013)
on the mathematics achievement of students in elementary school terms of study
habits gained that students who was taught with cooperative learning model type
Numbered Head Together on good study habits get the average score was higher
(28.18) than students who teach with conventional learning models in good study
habits with an average of 19.23. Thus, there is a difference in learning
achievement between students who was taught with cooperative learning model
type Numbered Head Together with the students who was taught with
conventional learning model.
Based on the above, researchers interested in conducting research reveal
whether cooperative learning model Number Head Together can improve the
students 'mathematical communication ability, which finally will improve the
learning outcomes of students as a form of contributing researcher to realize the
quality of education in Indonesia. Therefore, this research title is "The
Implementation of Cooperative Learning Model Type Number Head
Together to Improve The Student’s Mathematical Communication Ability Of
Grade Eight SMP N 2 Sidikalang Academic Year 2014/2015".
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1.2. The Identification Of The Problems
Based on the background described above, we can identify some of the
issues as follows:
1.
Students difficult to solve the problem of mathematical communication.
2.
The students’ mathematical communication ability are generally low.
3.
The learning model used by teachers in teaching tends to be monotonous
and still teacher centered.
4.
The process of answer in solving mathematical communication problems in
class is not varied.
1.3. The Limitation of The Problems
From the problems above, the researcher limited this problem as follows:
1.
The implementation of cooperative learning model type Numbered Head
Together to improve the students’ mathematical communication ability in
cuboid and cube topic at eighth grade SMP N 2 Sidikalang Academic Year
2014/2015.
2.
The process of answer is made by the students in solving mathematical
communication problems by using cooperative learning model type Number
Head Together.
1.4. The Formulation Of The Problems
Based on the limitation of the problem above, the formulation of the
problem in this study as follows:
1.
How is the improvement of the students’ mathematical communication
ability with the implementation of cooperative learning model type
Number Head Together in cuboid and cube topic at eighth grade SMP N 2
Sidikalang Academic Year 2014/2015?
2.
How do the students make the process of answers in solving mathematical
communication problems by using cooperative learning model type
Number Head Together?
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1.5. The Purposes of The Research
The purposes of this study are:
1.
To find out how is the improvement of the students’ mathematical
communication ability with the implementation of cooperative learning
model type Number Head Together in cuboid and cube topic at eighth grade
SMP N 2 Sidikalang academic year 2014/2015.
2.
To describe the process of answer is made by the students in solving
mathematical communication problems by using cooperative learning model
type Number Head Together.
1.6. The Benefits Of The Research
After the research is conducted, the results of this study are expected to
provide benefits such as:
1.
For students, can actively build knowledge up, able to develop
communication ability, an understanding in dealing with the problems and
can improve social relations and mutual responsibility for themselves and
their environment.
2.
For teachers, in order to improve the quality of mathematics learning
outcomes by improving the ability of students in learning mathematics
through the creation of mathematical communication and as an alternative
learning models that can be used in the learning of mathematics.
3.
For the researchers, to be a comparative material on the topic of the role of
mathematical communication, learning motivation, achievement motivation
on the acquisition of learning outcomes in mathematics, and add the
experience and insight into the thinking of the authors of scientific research.
4.
For schools and quality of education, is expected to be considered to apply
learning with learning model Number Head Together and is expected to
improve the quality of education in Indonesia.
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1.7. The Definitions of Operational
To avoid differences in interpretation of the terms contained in the
formulation of the problem in this study, it should be noted the following
operational definition
1.
The mathematical communication ability is the ability of the student (1) to
connect the images, tables, diagrams and daily events into mathematical
ideas, (2) to declare a situation in the form of images or graphics (drawing),
and (3) to formulate a mathematical idea into a mathematical model
(mathematical expression) and do calculation.
2.
Learning Model of Number Head Together type is a learning model more
forward to the activities of students in searching, processing, and reporting
of information from various sources that finally presented to the class. This
learning model consists of four phases, they are: (1) Numbering, (2) Asking
questions, (3) Thinking together, and (4) Answering.
3.
The process of answer is how the form or the composition of the students'
answers performance in solving mathematical communication problems to
see the variation process of the answer or solution resulted by the students.
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CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1
CONCLUSION
Based on the research results presented in the previous section can be
concluded that:
1. The improvement of students’ mathematical communication ability by the
implementation Number Head Together learning model belongs to
medium category with the normalized gain value is 0.46 where the average
of students’ mathematical communication ability in cycle I is 62.11 or
categorized to low category and in cycle II the average is improved
become 77.92 or categorized to medium category. As mastery learning
students classical in the first cycle reached 38.46% and in the second cycle
improved become 89.74%.
2. The process of student’s answer in solving a problem through
implementation Number Head Together learning model on the subject
cuboid and cube were more varied.
5.2
RECOMMENDATIONS
The recommendations in this research are as follows:
1.
Learning mathematics learning model Number Head Together can be used
as an alternative learning effective to improving the student’s mathematical
communication ability. But in the early learning teachers will have difficulty
in preparing children to make the process of cooperative learning, student
learning is difficult to accept the changes they have done so far with
constructivism learning through Number Head Together learning model. It
is therefore advisable that before learning process performed, learning
familiarize teachers with cooperative learning so that students will get used
116
to communicate both orally and in writing in conveying the idea of
mathematics.
2.
When learn with Number Head Together, teacher must be give more
attention in answering question activity, because in this phases students will
give their answer and became the appointment that students have understand
about the problem or not.
3.
From three indicators of mathematical communication ability, teacher must
be more pay attention in drawing an idea into a picture, so that the students
will produced the correct and complete picture
4.
When learning in cuboid and cube topics, teacher must be give more
attention in drawing a cuboid/cube and showing the parts of it. Because it is
the first material that students must be obtained and understanding so that
there is no problem happened when it continue into others topic.
5.
For teacher and school practitioner is equitable to change the learning
custom which is dominated by teacher and starting to involve students more
actively in the learning process, as well as give more attention to students’
mathematical communication ability. For this case, Number Head Together
learning model can be one of learning alternative to improve students’
mathematical communication ability.
6.
For the further researcher is recommended to continue the research in more
complex aim. Because the students’ success in learning can’t be measured
only with the written test and also expected to use the research result as
comparison matter and to implement Number Head Together learning
model in the other topic.