THE DIFFERENCE OF STUDENTS MATHEMATICAL REPRESENTATION ABILITY TAUGHT BY USING COOPERATIVE LEARNING TPS WITH STAD FOR GRADE X IN SMA NEGERI 7 MEDAN.
i
THE DIFFERENCE OF STUDENT’S MATHEMATICAL REPRESENTATION
ABILITY TAUGHT BY USING COOPERATIVE LEARNING TPS WITH
STAD FOR GRADE X IN SMA NEGERI 7 MEDAN
By:
Samantha Lidwina
ID 4113111070
Mathematics Education Study Program
THESIS
Submittedto 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
Praise and thanks to God Almighty who has give for all the graces and
blessings that provide health and wisdom to the author that this study can be
completed properly in accordance with the planned time.
Thesis entitled “The Difference of Student’s Mathematical Representation
Ability Taught By Using Cooperative Learning TPS With STAD Types For
Grade X In SMA Negeri 7 Medan”, prepared to obtain a Bachelor degree of
Mathematics Education, Faculty of Mathematics and Natural Sciences in State
University of Medan.
On this occasion the author like to thank Prof. Dr. Edi Syahputra, M.Pd. as
Thesis Supervisor who has provide guidance and suggestions to the author since
the beginning of the study until the completion of this thesis writing. Thanks also
to Prof. Dr. Mukhtar, M.Pd., Drs Zul Amry, M.Si,P.hD., Dr. Edy Surya, M.Si.
who have provided input the suggestions from the research plan until complete the
preparation of thesis. Thanks also to Prof. Dr. Sahat Saragih, M.Pd. as academic
supervisor and also the entire Lecturer and Staff in Mathematics Department.
Appreciation also present to Headmaster in SMA Negeri 7 Medan and Dra. Tinur
Purba as Mathematics teacher who has provide guidance when the research was
held. I would like say special thanks to my father Drs. Alisarles Hutabarat and
mother Dra. Rasmi Simanjuntak also my sister and lilbro Hanna Monika, S.Pd,
Gabriella Putri Sion, Alexandro Joshua, my Lovely Opung ST. Tinonggar br.
Pakpahan and all family who have supported, prayed, and gave me
encouragement and funding to complete the study in Mathematics Department.
Also thanks to my Best Friends Forever, Yeah! Jessica Ds, S.Ked, Margareth
Tambunan, Ruth Perangin-angin, Febryanty Simanjuntak who have made my life
is beautiful. Don’t forget to thanks for my Closest Friends Kristiani, Natalita,
Aprita, Yerni, Rony, Dewi, Lestari, Verawati, Anna who have made my study was
happy, enjoyable and memorable. Rock you guys! And also thanks to other
Bilmath ’11 member, Joe, Dwi, Leni, Wawa, Asifa, Tika, Widi, Nelly, Debby,
Ozy, Sapta, Acy, Evan, Galang and Elvi. And the end, I want to say thanks to my
iv
“Devil”, Angellyn, Poppy, Nurul, Asri, Sonia as my field study service colleagues
who make my life more powerful.
The Author has endeavored and maximally to complete this thesis. But
certainly there are still shortcomings that exist in this research. The author
welcome any suggestions and constructive criticism from readers for this thesis
perfectly. The author also hope the content of this research would be useful in
enriching the reader’s knowledge. Thank you.
Medan, August 2015
Author,
Samantha Lidwina
iii
THE DIFFERENCE OF STUDENT’S MATHEMATICAL REPRESENTATION
ABILITY TAUGHT BY USING COOPERATIVE LEARNING TPS WITH
STAD TYPES FOR GRADE X IN SMA NEGERI 7 MEDAN
Samantha Lidwina (ID. 4113111070)
ABSTRACT
The aim of this research is to know whether student’s Mathematical
Representation Ability taught by using Cooperative Learning TPS type is higher
than Cooperative Learning STAD Type for Grade X in SMA Negeri 7 Medan.
The population is all students of grade X in SMA Negeri 7 Medan A.Y.
2014/2015. Sampling Techniques that is used in this research is random sampling.
There are two samples in this research namely, Experimental class A is X MIA 4
taught by cooperative learning TPS and Experimental class B is X MIA 3 taught
by cooperative learning STAD. This research using pretest and posttest where,
data of pre test and post test are normal distribution and homogeneous. The result
of the research shows that the average score of pretest in experiment class A and
B are 39.58 and 45.9. After doing treatment in experiment class A and B obtained
average score of posttest are 85.48 and 80.45. Hypothesis testing that have been
conducted in this research is by calculating manually and results of hypothesis test
of data from both experimental class in post test was found that
� � �
.
> � � . 4 . It indicates that H₀ is rejected. So, we can
conclude that Students’ mathematical representation ability taught by using
cooperative learning TPS type is higher than cooperative learning STAD type.
v
CONTENT
Page
Validation Sheet
i
Biography
ii
Abstract
iii
Preface
iv
Content
v
Figure List
viii
Table List
ix
Appendix List
x
CHAPTER I INTRODUCTION
1.1
Background
1
1.2
Problem Identification
6
1.3
Problem Limitation
6
1.4
Problem Formulation
6
1.5
Research Purpose
7
1.6
Benefit of Research
7
1.7
Operational Definitions
7
CHAPTER II LITERATURE REVIEW
2.1
Theoretical Framework
10
2.1.1
Representation in Mathematics
10
2.1.2
Mathematical Representation Ability
12
2.1.3
Cooperative Learning
14
2.1.3.1
The Step of Cooperative Learning
16
2.1.3.2
Cooperative Learning
18
Think Pair Share (TPS) type
2.1.3.3
Cooperative Learning
Student Teams- Achievement Division
(STAD) Type
20
vi
2.1.4
The Comparison Between Cooperative Learning
24
TPS and STAD Types
2.1.5
The Relationship Between Cooperative Learning
25
TPS and STAD Types and Students’
Mathematical Representation Ability
2.2
Relevant Research
26
2.3
Conceptual Framework
26
2.4
Hypothesis
27
CHAPTER III RESEARCH METHOD
3.1
Time and Location of Research
3.2
Population and Sample
3.3
28
3.2.1 Population of Research
28
3.2.2 Sample Of Research
28
Variable of Research
3.3.1 Independent Variable
28
3.3.2 Dependent Variable
29
3.4
Type and Design of Research
29
3.5
Procedure of Research
29
3.6
Instrument of Research
3.6.1 Test Of Students’ Mathematical Representation
32
Ability
3.7
Data Analysis Techniques
3.7.1
Normality Test
34
3.7.2
Homogeneity test
35
3.7.3
Hypothesis Test
36
CHAPTER IV RESULT OF RESEARCH AND DISCUSSION
4.1
The result of Student’s Mathematical Representation Ability
37
4. 1. 1 Pre-test of Experiment Class A and B
37
4. 1. 2 Post-test of Experiment Class A and B
37
4. 1. 3 Normality Test of Student’s Mathematical
38
vii
Representation Ability
4. 1. 4 Homogeneity of Student’s Mathematical
39
Representation Ability
4. 1. 5 Hypothesis Test of Student’s Mathematical
39
Representation Ability
4.2 Discussion of Result
40
CHAPTER V CONCLUSION AND SUGGESTIONS
43
REFERENCES
44
viii
FIGURE LIST
Page
Figure 1.1 Observation Result of Student’s Answer Number 1
3
Figure 1.2 Observation Result of Student’s Answer Number 2
3
Figure 1.3 Observation Result of Student’s Answer Number 3
4
Figure 3.1 Procedure of research
31
Figure 4.1 Graph of Hypothesis Result
39
Figure 1. Pretest in Experiment Class A
118
Figure 2. Pretest in Experiment Class B
118
Figure 3. Researcher give treatment in Experiment Class A
118
Figure 4. Researcher give treatment in Experiment Class B
119
Figure 5. Group Activity in Experiment Class A (TPS)
119
Figure 6. Group Activity in Experiment Class B (STAD)
119
Figure 7. Post test in Experiment Class A
120
Figure 8. Post test in Experiment Class B
120
ix
TABLE LIST
Page
Table 2.1
Mathematical Representation Indicators
13
Table 2.2
Implementation Steps of Cooperative learning
17
Table 2.3
Implementation Steps Think-Pair-Share
19
Table 2.4
Score Calculation development
22
Table 2.5
Award level group
22
Table 2.6
Implementation Steps of Cooperative Learning
23
STAD Type
Table.2.7
Comparison of Cooperative Learning
25
TPS with STAD Types
Table 3.1
Research design of randomized control group only
29
Table 3.2
Blueprint of Mathematical Representation ability Problem
32
Table 3.3
The rubric of mathematical representation ability problem
33
Table 4.1
Data Pre-test
37
Table 4.2
Data Post-test
38
Table 4.3
Normality Test data result
38
Table 4.4
Homogeneity Test data result (manually)
39
Table 4.5
Hypothesis Test data result (manually)
39
x
APPENDIX LIST
page
Appendix 1
Diagnostic Test Sheet
47
Appendix 2
Blueprint of Pre Test
48
Appendix 3
Pre Test Sheet
59
Appendix 4
Solution of Pre Test Sheet
50
Appendix 5
Lesson Plan 1 for TPS
53
Appendix 6
Lesson Plan 2 for TPS
59
Appendix 7
Lesson Plan 1 for STAD
66
Appendix 8
Lesson Plan 2 for STAD
72
Appendix 9
Students Activity Sheet (SAS) 1 for TPS
78
Appendix 10 Students Activity Sheet (SAS) 2 for TPS
80
Appendix 11 Solution of SAS 1 for TPS
81
Appendix 12 Solution of SAS 2 for TPS
84
Appendix 13 Students Activity Sheet (SAS) 1 for STAD
87
Appendix 14 Students Activity Sheet (SAS) 2 for STAD
89
Appendix 25 Solution of SAS 1 for STAD
90
Appendix 16 Solution of SAS 2 for STAD
93
Appendix 17 Blueprint of Post Test
96
Appendix 18 Post Test Sheet
97
Appendix 19 Solution of Post Test Sheet
99
Appendix 20 Validation Sheet for Pretest and Post test
103
Appendix 21 Data of Student’s Pre test and Post test
109
Appendix 22 Calculation data Manually of Normality Test
112
Appendix 23 Calculation data Manually of Homogeneity Test
115
Appendix 24 Calculation data Manually of Hypothesis Test
116
Appendix 25 Documentation of Research
118
ix
TABLE LIST
Page
Table 2.1
Mathematical Representation Indicators
13
Table 2.2
Implementation Steps of Cooperative learning
17
Table 2.3
Implementation Steps Think-Pair-Share
19
Table 2.4
Score Calculation development
22
Table 2.5
Award level group
22
Table 2.6
Implementation Steps of Cooperative Learning
23
STAD Type
Table.2.7
Comparison of Cooperative Learning
25
TPS with STAD Types
Table 3.1
Research design of randomized control group only
29
Table 3.2
Blueprint of Mathematical Representation ability Problem
32
Table 3.3
The rubric of mathematical representation ability problem
33
Table 4.1
Data Pre-test
37
Table 4.2
Data Post-test
38
Table 4.3
Normality Test data result
38
Table 4.4
Homogeneity Test data result (manually)
39
Table 4.5
Hypothesis Test data result (manually)
39
viii
FIGURE LIST
Page
Figure 1.1 Observation Result of Student’s Answer Number 1
3
Figure 1.2 Observation Result of Student’s Answer Number 2
3
Figure 1.3 Observation Result of Student’s Answer Number 3
4
Figure 3.1 Procedure of research
31
Figure 4.1 Graph of Hypothesis Result
39
Figure 1. Pretest in Experiment Class A
118
Figure 2. Pretest in Experiment Class B
118
Figure 3. Researcher give treatment in Experiment Class A
118
Figure 4. Researcher give treatment in Experiment Class B
119
Figure 5. Group Activity in Experiment Class A (TPS)
119
Figure 6. Group Activity in Experiment Class B (STAD)
119
Figure 7. Post test in Experiment Class A
120
Figure 8. Post test in Experiment Class B
120
1
CHAPTER I
INTRODUCTION
1.1
Background
Progress of a nation can be seen from the quality of its human resources.
Intelligent nation is a people of nation that is able to use all its resources correctly
and the maximum is in the form of natural wealth, cultural diversity, ethnicity,
and language in order to support the country's progress. One of the things that
need to be considered to improve the intelligence and the quality of the nation is
to improve the education of all its human resources. One type of education that
needs to be improved in this time is a formal education.
Formal education occurs in a structured environment whose explicit
purpose is teaching students. Formal education usually takes place in a school
environment, with classrooms of multiple students learning together and taught by
professional teacher. As formal education institutions, schools are born and grow
effectively and efficiently to the community, It also as a tool to provide services to
young people in educating citizens. Of course, the service provided must be the
best and responsible. In this case, the teacher has an important role in the services.
Teachers must creative in teaching so that students are interested and active in
learning. One effort that can be done by the teacher is to implement learning
strategies.
Mathematics is a compulsory subject set by the government to be learned
by students ranging from elementary to high school. This is because mathematics
has an important role in the progress of a country. In Learning mathematics
students must have comprehension, skills, and knowledge which is this aspect are
known and can be done by teachers and students on learning mathematics in a
school. NCTM (2015) states that the expected goals in learning mathematics are
to set of five process standard that must be owned by student are problem
solving, Reasoning and Proof , Communication , Connection , Representation.
Representation is a form of interpretation of students' thinking of a
problem which is used as an aid to find solutions to these problems. Students can
2
be a form of interpretation of words or verbal, text, images, tables, graphs,
concrete objects, mathematical symbols, and others.
Representations should be treated as essential elements in supporting
students’ understanding of mathematical concepts and relationships; in
communicating mathematical approaches, arguments, and understandings to one’s
self and to others; in recognizing connections among related mathematical
concepts; and in applying mathematics to realistic problem situations through
modeling. New forms of representation associated with electronic technology
create a need for even greater instructional attention to representation. So,
representations
underpins
conceptual
understanding,
communications,
connections, and problem solving. All of these processes are assisted by an
effective representation. Students should engage with each of these in all of their
mathematics courses, so that be effective presentations.
create and use representations to organize, record, and communicate
mathematical ideas;
select, apply, and translate among mathematical representations to solve
problems;
use representations to model and interpret physical, social, and
mathematical phenomena.
At times, teachers should present a representation explicitly, while at other times,
they should guide students to “discover” how best to represent a mathematical
model.
But on last situation Mathematical representation ability of students is in
school less attention since many student don’t comprehend about their
mathematical representation ability. Though mathematical representation ability is
very important in learning mathematics since facilitating the students to represent
problem in form of mathematical visual object which is more interesting.
From the initial test which has been conducted by researchers to students,
it is known that the ability of students' mathematical representation is still low. it
can be seen from the answers that they make. Some of them are not able to create
a table of story problems correctly, not able to solve problems of the images
3
presented, and less able to write the conclusion of the diagram presented.
The following are some of the documentation of student test results.
Question 1.
The teacher return the semester exam scores of 25 students X IPA A. afterwards
where the data was obtained, Rani and Edi scored 90, Adi and Sinta and a friend
got the lowest score are 55. Ani, Devi, Gita scored 60. While Suci, Lea, and seven
others received a score of 70, on the other hand there were seven students scored
10 points lower than Rani and Edi. For the highest score, achieved by mina value
95. Based on the problems above, make X IPA A student scores into the table.
Answer 1.
Figure 1.1 Observation Result of Student’s Answer Number 1
From the answers above, we can see that the students have not been able to
represent story problems into the form of a table correctly. students are not able to
enter the data correctly into the table, the frequency of data which he wrote
different from the frequency of the data in question.
Question 2.
The following figure illustrates parents occupation of 48
students. Determine how many parents who work as:
a. PNS
b. Farmer
c. Entrepreneur
4
Answer 2
Figure 1.2 Observation Result of Student’s Answer Number 2
From the answers above, we can see that the students have not been able to
represent the image into the form of mathematical expressions. She can not
understand the questions well so that way represents the answer is
irrational
Question 3.
Consider the price of gold for 5
days in the month of May 2013
below. Give an appreciation of
the data and make the conclusion
from the diagram.
Answer 3
Figure 1.3 Observation Result of Student’s Answer Number 3
From the answers above, we can see that the students have not been able to
represent images into written text correctly because students are less able to
appreciate the graph based facts contained data. He just appreciate graph based
personal opinion.
5
Based on these problems, researchers can surmise that the students will
have difficulty in the future to manage the problem so that it will also affect
Student’s mastery and understanding in mathematics. Student’s Mathematical
Representation ability still low because the learning model used by mathematics
teachers poorly in developing student’s ability. They still using conventional
learning. It requires students to strive themselves in learning. it is not suitable to
be applied to the student in this modern era.
Students should be encouraged to play an active role in learning, teachers
must also be able to involve in technological sophistication in learning so that
students feel more passion and learning are more interesting. So, Student’s
Mathematical Representation ability will be improve well when teachers use the
right teaching methods. One of the right methods to improve that ability is
implementing cooperative learning method. This method of stimulating among
students to help each other in solving a problem, so that every student has the
opportunity to understand the learning well. As stated of Trianto (2009 : 59) that:
“Para ahli telah menunjukkan bahwa pembelajaran kooperatif dapat
meningkatkan kinerja siswa dalam tugas-tugas akademik unggul dalam
membantu siswa menumbuhkan kemampuan berpikir kritis. Pembelajaran
kooperatif dapat meningkatkan keuntungan baik bagi siswa kelompok
bawah maupun kelompok atas yang bekerja bersama menyelesaikan tugastugas akademik”.
From the statement above, can be concluded that cooperative learning can
improve Student’s Mathematical Representation ability. This is also reinforced by
the relevant research conducted by Tri Fauji in 2014, the results showed that the
implementation of
Cooperative learning TPS type can improve students'
mathematical representation ability. As well as research conducted by Tyas
Wardani in 2015 states that Cooperative Learning STAD type can improve
students' mathematical representation ability. It’s mean that, cooperative learning
TPS and STAD are two types of cooperative learning that can improve students'
mathematical representation ability.
Think- Pair- Share (TPS) is a cooperative learning that a combination of
self-learning and learning in groups which students work together to solve a
6
problem or answer a question about an assigned reading. This technique requires
students to (1) think individually about a topic or answer to a question (it is
possible that students can solve these problems own); and (2) share ideas with
classmates. Discussing an answer with a partner serves to maximize participation,
focus attention and engage students in comprehending the reading material.
While, Student Teams Achievement Division (STAD) is a type of
cooperative learning with learning team- work. The main idea behind the model
STAD is to motivate the students to encourage and help each other to master the
skills presented by the teacher.
Based on background above, research interested in conducting research entitled:
“The Difference Of Student’s Mathematical Representation Ability Taught
By Using Cooperative Learning TPS With STAD Types For Grade X in SMA
Negeri 7 Medan”
1.2
Problem Identification
Based on the background presented above, can be identified issue:
1. Student’s Mathematical Representation Ability is still low
2. Lack of Student’s activeness in Learning Mathematics
1.3
Problem Limitation
The problems limitation in this research are as follow:
1. The author focus with The Difference Of Student’s Mathematical
Representation Ability Taught By Using Cooperative Learning TPS With
Cooperative Learning STAD Types For Grade X in SMA Negeri 7 Medan.
2. Learning in this Research topic is Statistics
1.4
Problem Formulation
The problems formulation in this research is : “Whether Student’s Mathematical
Representation Ability taught by using Cooperative Learning TPS type is higher
than Cooperative Learning STAD Type for Grade X in SMA Negeri 7 Medan ?
7
1.5
Research Purpose
Research purpose in this research are : to know whether student’s Mathematical
Representation Ability taught by using Cooperative Learning TPS type is higher
than Cooperative Learning STAD Type for Grade X in SMA Negeri 7 Medan.
1.6
Benefit of Research
The benefit of this research are:
1. For Teachers and prospective teachers, can be used as a references to choose a
better learning model not only in Statistics but also in another topics.
2. For Students, to use the cooperative learning Think-Pair-Share type can
improve the student’s mathematical representation ability.
3. For School, is expected to be source of information or contribute ideas for
improvement of mathematics teaching and learning.
4. For Researches, can be used to increase the knowledge about both of
cooperative learning model so it will be easier to apply them to other learning
topics.
1.7
Operational definitions
To avoid difference of meaning clarity about important terms contained in this
research, The operational definition be stated as follow:
1. Mathematical representation ability is the ability of students in the depiction,
translation, disclosure, re-appointment, figuratively, or modeling, the idea of a
concept in mathematics as an effort to gain clarity of meaning, show
understanding or looking for a solution of his problems. which can be
interpreted in the form of words or verbal, text, images, tables, graphs,
concrete objects, mathematical symbols etc.
2. Cooperative Learning Think- Pair-Share (TPS) type: The think, pair, share
strategy is a cooperative learning technique that encourages individual
participation and is applicable across all grade levels and class sizes. Students
think through questions using three distinct steps:
8
Think: Students think independently about the question that has been posed,
forming ideas of their own.
Pair: Students are grouped in pairs to discuss their thoughts. This step allows
students to articulate their ideas and to consider those of others.
Share: Student pairs share their ideas with a larger group, such as the whole
class. Often, students are more comfortable presenting ideas to a group with
the support of a partner. In addition, students' ideas have become more refined
through this three-step process.
3. Cooperative Learning Student Teams Achievement Division (STAD) type is
one of the simple and effective method in cooperative learning.
In the process of learning, STAD cooperative learning consist of four steps as
follow:
Step I: Teach (Class Presentation)
The class presentation is a teacher-directed presentation of the material--concepts, skills, and processes---that the students are to learn.
Step II: Team Study
a. In STAD teams are composed of four students who represent a balance in
terms of academic ability, gender, and ethnicity.
b.Team members work together with prepared worksheets and make sure that
each member of the team can answer all questions on the worksheet
c. Students have the responsibility to make sure that their teammates have
learned the material. No one is finished studying until all teammates have
mastered the subject.
d.Ask all teammates for help before asking the teacher.
Step III: Test
After the team study is completed, the teacher administers a test to measure
the knowledge that students have gained. Students take the individual tests and
are not permitted to help each other.
9
Step IV: Team Recognition (Giving Award)
Team averages are reported in the weekly recognition chart. Teachers can use
special words to describe the teams' performance such as science stars,
science geniuses, or Einstein's. Recognition of the work of each team can
occur by means of a newsletter, handout, or bulletin board that reports the
ranking of each team within the class.
43
CHAPTER V
CONCLUSION AND SUGGESTIONS
5.1
Conclusion
In Hypothesis test, the data are processed based on post test shows that
�
(2.67) >
�
�
(1.66462) that it’s
mean H₀ rejected. So, can be
concluded that Students’ mathematical representation ability taught by using
cooperative learning TPS type is higher than cooperative learning STAD type.
5.2
Suggestions
Related to the writer’s research, some suggestions are pointed out as
follows:
a.
For Teachers, can be used as a references to choose a Think-Pair-Share not
only in Statistics but also in another topics, Teachers are expected to be
active in guiding students in learning process so that weak student can be
helped to improving their mathematical representation ability, and teachers
should be able to guide and provide more detail to the students about how to
present the random data into the correct distribution table groups
b.
For prospective teachers, during the learning process takes place, the teacher
must be able to control the class so no student is making noise in the
classroom that can interfere with other students' concentration.
c.
For School, is expected to be source of information or contribute ideas for
improvement of mathematics teaching and learning.
d.
Researcher expecting of this research can be enhanced by next researcher.
THE DIFFERENCE OF STUDENT’S MATHEMATICAL REPRESENTATION
ABILITY TAUGHT BY USING COOPERATIVE LEARNING TPS WITH
STAD FOR GRADE X IN SMA NEGERI 7 MEDAN
By:
Samantha Lidwina
ID 4113111070
Mathematics Education Study Program
THESIS
Submittedto 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
Praise and thanks to God Almighty who has give for all the graces and
blessings that provide health and wisdom to the author that this study can be
completed properly in accordance with the planned time.
Thesis entitled “The Difference of Student’s Mathematical Representation
Ability Taught By Using Cooperative Learning TPS With STAD Types For
Grade X In SMA Negeri 7 Medan”, prepared to obtain a Bachelor degree of
Mathematics Education, Faculty of Mathematics and Natural Sciences in State
University of Medan.
On this occasion the author like to thank Prof. Dr. Edi Syahputra, M.Pd. as
Thesis Supervisor who has provide guidance and suggestions to the author since
the beginning of the study until the completion of this thesis writing. Thanks also
to Prof. Dr. Mukhtar, M.Pd., Drs Zul Amry, M.Si,P.hD., Dr. Edy Surya, M.Si.
who have provided input the suggestions from the research plan until complete the
preparation of thesis. Thanks also to Prof. Dr. Sahat Saragih, M.Pd. as academic
supervisor and also the entire Lecturer and Staff in Mathematics Department.
Appreciation also present to Headmaster in SMA Negeri 7 Medan and Dra. Tinur
Purba as Mathematics teacher who has provide guidance when the research was
held. I would like say special thanks to my father Drs. Alisarles Hutabarat and
mother Dra. Rasmi Simanjuntak also my sister and lilbro Hanna Monika, S.Pd,
Gabriella Putri Sion, Alexandro Joshua, my Lovely Opung ST. Tinonggar br.
Pakpahan and all family who have supported, prayed, and gave me
encouragement and funding to complete the study in Mathematics Department.
Also thanks to my Best Friends Forever, Yeah! Jessica Ds, S.Ked, Margareth
Tambunan, Ruth Perangin-angin, Febryanty Simanjuntak who have made my life
is beautiful. Don’t forget to thanks for my Closest Friends Kristiani, Natalita,
Aprita, Yerni, Rony, Dewi, Lestari, Verawati, Anna who have made my study was
happy, enjoyable and memorable. Rock you guys! And also thanks to other
Bilmath ’11 member, Joe, Dwi, Leni, Wawa, Asifa, Tika, Widi, Nelly, Debby,
Ozy, Sapta, Acy, Evan, Galang and Elvi. And the end, I want to say thanks to my
iv
“Devil”, Angellyn, Poppy, Nurul, Asri, Sonia as my field study service colleagues
who make my life more powerful.
The Author has endeavored and maximally to complete this thesis. But
certainly there are still shortcomings that exist in this research. The author
welcome any suggestions and constructive criticism from readers for this thesis
perfectly. The author also hope the content of this research would be useful in
enriching the reader’s knowledge. Thank you.
Medan, August 2015
Author,
Samantha Lidwina
iii
THE DIFFERENCE OF STUDENT’S MATHEMATICAL REPRESENTATION
ABILITY TAUGHT BY USING COOPERATIVE LEARNING TPS WITH
STAD TYPES FOR GRADE X IN SMA NEGERI 7 MEDAN
Samantha Lidwina (ID. 4113111070)
ABSTRACT
The aim of this research is to know whether student’s Mathematical
Representation Ability taught by using Cooperative Learning TPS type is higher
than Cooperative Learning STAD Type for Grade X in SMA Negeri 7 Medan.
The population is all students of grade X in SMA Negeri 7 Medan A.Y.
2014/2015. Sampling Techniques that is used in this research is random sampling.
There are two samples in this research namely, Experimental class A is X MIA 4
taught by cooperative learning TPS and Experimental class B is X MIA 3 taught
by cooperative learning STAD. This research using pretest and posttest where,
data of pre test and post test are normal distribution and homogeneous. The result
of the research shows that the average score of pretest in experiment class A and
B are 39.58 and 45.9. After doing treatment in experiment class A and B obtained
average score of posttest are 85.48 and 80.45. Hypothesis testing that have been
conducted in this research is by calculating manually and results of hypothesis test
of data from both experimental class in post test was found that
� � �
.
> � � . 4 . It indicates that H₀ is rejected. So, we can
conclude that Students’ mathematical representation ability taught by using
cooperative learning TPS type is higher than cooperative learning STAD type.
v
CONTENT
Page
Validation Sheet
i
Biography
ii
Abstract
iii
Preface
iv
Content
v
Figure List
viii
Table List
ix
Appendix List
x
CHAPTER I INTRODUCTION
1.1
Background
1
1.2
Problem Identification
6
1.3
Problem Limitation
6
1.4
Problem Formulation
6
1.5
Research Purpose
7
1.6
Benefit of Research
7
1.7
Operational Definitions
7
CHAPTER II LITERATURE REVIEW
2.1
Theoretical Framework
10
2.1.1
Representation in Mathematics
10
2.1.2
Mathematical Representation Ability
12
2.1.3
Cooperative Learning
14
2.1.3.1
The Step of Cooperative Learning
16
2.1.3.2
Cooperative Learning
18
Think Pair Share (TPS) type
2.1.3.3
Cooperative Learning
Student Teams- Achievement Division
(STAD) Type
20
vi
2.1.4
The Comparison Between Cooperative Learning
24
TPS and STAD Types
2.1.5
The Relationship Between Cooperative Learning
25
TPS and STAD Types and Students’
Mathematical Representation Ability
2.2
Relevant Research
26
2.3
Conceptual Framework
26
2.4
Hypothesis
27
CHAPTER III RESEARCH METHOD
3.1
Time and Location of Research
3.2
Population and Sample
3.3
28
3.2.1 Population of Research
28
3.2.2 Sample Of Research
28
Variable of Research
3.3.1 Independent Variable
28
3.3.2 Dependent Variable
29
3.4
Type and Design of Research
29
3.5
Procedure of Research
29
3.6
Instrument of Research
3.6.1 Test Of Students’ Mathematical Representation
32
Ability
3.7
Data Analysis Techniques
3.7.1
Normality Test
34
3.7.2
Homogeneity test
35
3.7.3
Hypothesis Test
36
CHAPTER IV RESULT OF RESEARCH AND DISCUSSION
4.1
The result of Student’s Mathematical Representation Ability
37
4. 1. 1 Pre-test of Experiment Class A and B
37
4. 1. 2 Post-test of Experiment Class A and B
37
4. 1. 3 Normality Test of Student’s Mathematical
38
vii
Representation Ability
4. 1. 4 Homogeneity of Student’s Mathematical
39
Representation Ability
4. 1. 5 Hypothesis Test of Student’s Mathematical
39
Representation Ability
4.2 Discussion of Result
40
CHAPTER V CONCLUSION AND SUGGESTIONS
43
REFERENCES
44
viii
FIGURE LIST
Page
Figure 1.1 Observation Result of Student’s Answer Number 1
3
Figure 1.2 Observation Result of Student’s Answer Number 2
3
Figure 1.3 Observation Result of Student’s Answer Number 3
4
Figure 3.1 Procedure of research
31
Figure 4.1 Graph of Hypothesis Result
39
Figure 1. Pretest in Experiment Class A
118
Figure 2. Pretest in Experiment Class B
118
Figure 3. Researcher give treatment in Experiment Class A
118
Figure 4. Researcher give treatment in Experiment Class B
119
Figure 5. Group Activity in Experiment Class A (TPS)
119
Figure 6. Group Activity in Experiment Class B (STAD)
119
Figure 7. Post test in Experiment Class A
120
Figure 8. Post test in Experiment Class B
120
ix
TABLE LIST
Page
Table 2.1
Mathematical Representation Indicators
13
Table 2.2
Implementation Steps of Cooperative learning
17
Table 2.3
Implementation Steps Think-Pair-Share
19
Table 2.4
Score Calculation development
22
Table 2.5
Award level group
22
Table 2.6
Implementation Steps of Cooperative Learning
23
STAD Type
Table.2.7
Comparison of Cooperative Learning
25
TPS with STAD Types
Table 3.1
Research design of randomized control group only
29
Table 3.2
Blueprint of Mathematical Representation ability Problem
32
Table 3.3
The rubric of mathematical representation ability problem
33
Table 4.1
Data Pre-test
37
Table 4.2
Data Post-test
38
Table 4.3
Normality Test data result
38
Table 4.4
Homogeneity Test data result (manually)
39
Table 4.5
Hypothesis Test data result (manually)
39
x
APPENDIX LIST
page
Appendix 1
Diagnostic Test Sheet
47
Appendix 2
Blueprint of Pre Test
48
Appendix 3
Pre Test Sheet
59
Appendix 4
Solution of Pre Test Sheet
50
Appendix 5
Lesson Plan 1 for TPS
53
Appendix 6
Lesson Plan 2 for TPS
59
Appendix 7
Lesson Plan 1 for STAD
66
Appendix 8
Lesson Plan 2 for STAD
72
Appendix 9
Students Activity Sheet (SAS) 1 for TPS
78
Appendix 10 Students Activity Sheet (SAS) 2 for TPS
80
Appendix 11 Solution of SAS 1 for TPS
81
Appendix 12 Solution of SAS 2 for TPS
84
Appendix 13 Students Activity Sheet (SAS) 1 for STAD
87
Appendix 14 Students Activity Sheet (SAS) 2 for STAD
89
Appendix 25 Solution of SAS 1 for STAD
90
Appendix 16 Solution of SAS 2 for STAD
93
Appendix 17 Blueprint of Post Test
96
Appendix 18 Post Test Sheet
97
Appendix 19 Solution of Post Test Sheet
99
Appendix 20 Validation Sheet for Pretest and Post test
103
Appendix 21 Data of Student’s Pre test and Post test
109
Appendix 22 Calculation data Manually of Normality Test
112
Appendix 23 Calculation data Manually of Homogeneity Test
115
Appendix 24 Calculation data Manually of Hypothesis Test
116
Appendix 25 Documentation of Research
118
ix
TABLE LIST
Page
Table 2.1
Mathematical Representation Indicators
13
Table 2.2
Implementation Steps of Cooperative learning
17
Table 2.3
Implementation Steps Think-Pair-Share
19
Table 2.4
Score Calculation development
22
Table 2.5
Award level group
22
Table 2.6
Implementation Steps of Cooperative Learning
23
STAD Type
Table.2.7
Comparison of Cooperative Learning
25
TPS with STAD Types
Table 3.1
Research design of randomized control group only
29
Table 3.2
Blueprint of Mathematical Representation ability Problem
32
Table 3.3
The rubric of mathematical representation ability problem
33
Table 4.1
Data Pre-test
37
Table 4.2
Data Post-test
38
Table 4.3
Normality Test data result
38
Table 4.4
Homogeneity Test data result (manually)
39
Table 4.5
Hypothesis Test data result (manually)
39
viii
FIGURE LIST
Page
Figure 1.1 Observation Result of Student’s Answer Number 1
3
Figure 1.2 Observation Result of Student’s Answer Number 2
3
Figure 1.3 Observation Result of Student’s Answer Number 3
4
Figure 3.1 Procedure of research
31
Figure 4.1 Graph of Hypothesis Result
39
Figure 1. Pretest in Experiment Class A
118
Figure 2. Pretest in Experiment Class B
118
Figure 3. Researcher give treatment in Experiment Class A
118
Figure 4. Researcher give treatment in Experiment Class B
119
Figure 5. Group Activity in Experiment Class A (TPS)
119
Figure 6. Group Activity in Experiment Class B (STAD)
119
Figure 7. Post test in Experiment Class A
120
Figure 8. Post test in Experiment Class B
120
1
CHAPTER I
INTRODUCTION
1.1
Background
Progress of a nation can be seen from the quality of its human resources.
Intelligent nation is a people of nation that is able to use all its resources correctly
and the maximum is in the form of natural wealth, cultural diversity, ethnicity,
and language in order to support the country's progress. One of the things that
need to be considered to improve the intelligence and the quality of the nation is
to improve the education of all its human resources. One type of education that
needs to be improved in this time is a formal education.
Formal education occurs in a structured environment whose explicit
purpose is teaching students. Formal education usually takes place in a school
environment, with classrooms of multiple students learning together and taught by
professional teacher. As formal education institutions, schools are born and grow
effectively and efficiently to the community, It also as a tool to provide services to
young people in educating citizens. Of course, the service provided must be the
best and responsible. In this case, the teacher has an important role in the services.
Teachers must creative in teaching so that students are interested and active in
learning. One effort that can be done by the teacher is to implement learning
strategies.
Mathematics is a compulsory subject set by the government to be learned
by students ranging from elementary to high school. This is because mathematics
has an important role in the progress of a country. In Learning mathematics
students must have comprehension, skills, and knowledge which is this aspect are
known and can be done by teachers and students on learning mathematics in a
school. NCTM (2015) states that the expected goals in learning mathematics are
to set of five process standard that must be owned by student are problem
solving, Reasoning and Proof , Communication , Connection , Representation.
Representation is a form of interpretation of students' thinking of a
problem which is used as an aid to find solutions to these problems. Students can
2
be a form of interpretation of words or verbal, text, images, tables, graphs,
concrete objects, mathematical symbols, and others.
Representations should be treated as essential elements in supporting
students’ understanding of mathematical concepts and relationships; in
communicating mathematical approaches, arguments, and understandings to one’s
self and to others; in recognizing connections among related mathematical
concepts; and in applying mathematics to realistic problem situations through
modeling. New forms of representation associated with electronic technology
create a need for even greater instructional attention to representation. So,
representations
underpins
conceptual
understanding,
communications,
connections, and problem solving. All of these processes are assisted by an
effective representation. Students should engage with each of these in all of their
mathematics courses, so that be effective presentations.
create and use representations to organize, record, and communicate
mathematical ideas;
select, apply, and translate among mathematical representations to solve
problems;
use representations to model and interpret physical, social, and
mathematical phenomena.
At times, teachers should present a representation explicitly, while at other times,
they should guide students to “discover” how best to represent a mathematical
model.
But on last situation Mathematical representation ability of students is in
school less attention since many student don’t comprehend about their
mathematical representation ability. Though mathematical representation ability is
very important in learning mathematics since facilitating the students to represent
problem in form of mathematical visual object which is more interesting.
From the initial test which has been conducted by researchers to students,
it is known that the ability of students' mathematical representation is still low. it
can be seen from the answers that they make. Some of them are not able to create
a table of story problems correctly, not able to solve problems of the images
3
presented, and less able to write the conclusion of the diagram presented.
The following are some of the documentation of student test results.
Question 1.
The teacher return the semester exam scores of 25 students X IPA A. afterwards
where the data was obtained, Rani and Edi scored 90, Adi and Sinta and a friend
got the lowest score are 55. Ani, Devi, Gita scored 60. While Suci, Lea, and seven
others received a score of 70, on the other hand there were seven students scored
10 points lower than Rani and Edi. For the highest score, achieved by mina value
95. Based on the problems above, make X IPA A student scores into the table.
Answer 1.
Figure 1.1 Observation Result of Student’s Answer Number 1
From the answers above, we can see that the students have not been able to
represent story problems into the form of a table correctly. students are not able to
enter the data correctly into the table, the frequency of data which he wrote
different from the frequency of the data in question.
Question 2.
The following figure illustrates parents occupation of 48
students. Determine how many parents who work as:
a. PNS
b. Farmer
c. Entrepreneur
4
Answer 2
Figure 1.2 Observation Result of Student’s Answer Number 2
From the answers above, we can see that the students have not been able to
represent the image into the form of mathematical expressions. She can not
understand the questions well so that way represents the answer is
irrational
Question 3.
Consider the price of gold for 5
days in the month of May 2013
below. Give an appreciation of
the data and make the conclusion
from the diagram.
Answer 3
Figure 1.3 Observation Result of Student’s Answer Number 3
From the answers above, we can see that the students have not been able to
represent images into written text correctly because students are less able to
appreciate the graph based facts contained data. He just appreciate graph based
personal opinion.
5
Based on these problems, researchers can surmise that the students will
have difficulty in the future to manage the problem so that it will also affect
Student’s mastery and understanding in mathematics. Student’s Mathematical
Representation ability still low because the learning model used by mathematics
teachers poorly in developing student’s ability. They still using conventional
learning. It requires students to strive themselves in learning. it is not suitable to
be applied to the student in this modern era.
Students should be encouraged to play an active role in learning, teachers
must also be able to involve in technological sophistication in learning so that
students feel more passion and learning are more interesting. So, Student’s
Mathematical Representation ability will be improve well when teachers use the
right teaching methods. One of the right methods to improve that ability is
implementing cooperative learning method. This method of stimulating among
students to help each other in solving a problem, so that every student has the
opportunity to understand the learning well. As stated of Trianto (2009 : 59) that:
“Para ahli telah menunjukkan bahwa pembelajaran kooperatif dapat
meningkatkan kinerja siswa dalam tugas-tugas akademik unggul dalam
membantu siswa menumbuhkan kemampuan berpikir kritis. Pembelajaran
kooperatif dapat meningkatkan keuntungan baik bagi siswa kelompok
bawah maupun kelompok atas yang bekerja bersama menyelesaikan tugastugas akademik”.
From the statement above, can be concluded that cooperative learning can
improve Student’s Mathematical Representation ability. This is also reinforced by
the relevant research conducted by Tri Fauji in 2014, the results showed that the
implementation of
Cooperative learning TPS type can improve students'
mathematical representation ability. As well as research conducted by Tyas
Wardani in 2015 states that Cooperative Learning STAD type can improve
students' mathematical representation ability. It’s mean that, cooperative learning
TPS and STAD are two types of cooperative learning that can improve students'
mathematical representation ability.
Think- Pair- Share (TPS) is a cooperative learning that a combination of
self-learning and learning in groups which students work together to solve a
6
problem or answer a question about an assigned reading. This technique requires
students to (1) think individually about a topic or answer to a question (it is
possible that students can solve these problems own); and (2) share ideas with
classmates. Discussing an answer with a partner serves to maximize participation,
focus attention and engage students in comprehending the reading material.
While, Student Teams Achievement Division (STAD) is a type of
cooperative learning with learning team- work. The main idea behind the model
STAD is to motivate the students to encourage and help each other to master the
skills presented by the teacher.
Based on background above, research interested in conducting research entitled:
“The Difference Of Student’s Mathematical Representation Ability Taught
By Using Cooperative Learning TPS With STAD Types For Grade X in SMA
Negeri 7 Medan”
1.2
Problem Identification
Based on the background presented above, can be identified issue:
1. Student’s Mathematical Representation Ability is still low
2. Lack of Student’s activeness in Learning Mathematics
1.3
Problem Limitation
The problems limitation in this research are as follow:
1. The author focus with The Difference Of Student’s Mathematical
Representation Ability Taught By Using Cooperative Learning TPS With
Cooperative Learning STAD Types For Grade X in SMA Negeri 7 Medan.
2. Learning in this Research topic is Statistics
1.4
Problem Formulation
The problems formulation in this research is : “Whether Student’s Mathematical
Representation Ability taught by using Cooperative Learning TPS type is higher
than Cooperative Learning STAD Type for Grade X in SMA Negeri 7 Medan ?
7
1.5
Research Purpose
Research purpose in this research are : to know whether student’s Mathematical
Representation Ability taught by using Cooperative Learning TPS type is higher
than Cooperative Learning STAD Type for Grade X in SMA Negeri 7 Medan.
1.6
Benefit of Research
The benefit of this research are:
1. For Teachers and prospective teachers, can be used as a references to choose a
better learning model not only in Statistics but also in another topics.
2. For Students, to use the cooperative learning Think-Pair-Share type can
improve the student’s mathematical representation ability.
3. For School, is expected to be source of information or contribute ideas for
improvement of mathematics teaching and learning.
4. For Researches, can be used to increase the knowledge about both of
cooperative learning model so it will be easier to apply them to other learning
topics.
1.7
Operational definitions
To avoid difference of meaning clarity about important terms contained in this
research, The operational definition be stated as follow:
1. Mathematical representation ability is the ability of students in the depiction,
translation, disclosure, re-appointment, figuratively, or modeling, the idea of a
concept in mathematics as an effort to gain clarity of meaning, show
understanding or looking for a solution of his problems. which can be
interpreted in the form of words or verbal, text, images, tables, graphs,
concrete objects, mathematical symbols etc.
2. Cooperative Learning Think- Pair-Share (TPS) type: The think, pair, share
strategy is a cooperative learning technique that encourages individual
participation and is applicable across all grade levels and class sizes. Students
think through questions using three distinct steps:
8
Think: Students think independently about the question that has been posed,
forming ideas of their own.
Pair: Students are grouped in pairs to discuss their thoughts. This step allows
students to articulate their ideas and to consider those of others.
Share: Student pairs share their ideas with a larger group, such as the whole
class. Often, students are more comfortable presenting ideas to a group with
the support of a partner. In addition, students' ideas have become more refined
through this three-step process.
3. Cooperative Learning Student Teams Achievement Division (STAD) type is
one of the simple and effective method in cooperative learning.
In the process of learning, STAD cooperative learning consist of four steps as
follow:
Step I: Teach (Class Presentation)
The class presentation is a teacher-directed presentation of the material--concepts, skills, and processes---that the students are to learn.
Step II: Team Study
a. In STAD teams are composed of four students who represent a balance in
terms of academic ability, gender, and ethnicity.
b.Team members work together with prepared worksheets and make sure that
each member of the team can answer all questions on the worksheet
c. Students have the responsibility to make sure that their teammates have
learned the material. No one is finished studying until all teammates have
mastered the subject.
d.Ask all teammates for help before asking the teacher.
Step III: Test
After the team study is completed, the teacher administers a test to measure
the knowledge that students have gained. Students take the individual tests and
are not permitted to help each other.
9
Step IV: Team Recognition (Giving Award)
Team averages are reported in the weekly recognition chart. Teachers can use
special words to describe the teams' performance such as science stars,
science geniuses, or Einstein's. Recognition of the work of each team can
occur by means of a newsletter, handout, or bulletin board that reports the
ranking of each team within the class.
43
CHAPTER V
CONCLUSION AND SUGGESTIONS
5.1
Conclusion
In Hypothesis test, the data are processed based on post test shows that
�
(2.67) >
�
�
(1.66462) that it’s
mean H₀ rejected. So, can be
concluded that Students’ mathematical representation ability taught by using
cooperative learning TPS type is higher than cooperative learning STAD type.
5.2
Suggestions
Related to the writer’s research, some suggestions are pointed out as
follows:
a.
For Teachers, can be used as a references to choose a Think-Pair-Share not
only in Statistics but also in another topics, Teachers are expected to be
active in guiding students in learning process so that weak student can be
helped to improving their mathematical representation ability, and teachers
should be able to guide and provide more detail to the students about how to
present the random data into the correct distribution table groups
b.
For prospective teachers, during the learning process takes place, the teacher
must be able to control the class so no student is making noise in the
classroom that can interfere with other students' concentration.
c.
For School, is expected to be source of information or contribute ideas for
improvement of mathematics teaching and learning.
d.
Researcher expecting of this research can be enhanced by next researcher.