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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
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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.
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“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,
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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
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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 20
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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 28
3.2 Population and Sample 3.2.1 Population of Research 28
3.2.2 Sample Of Research 28
3.3 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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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:
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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
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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
tugas-tugas 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.
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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
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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.
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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
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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
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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.
