IMPLEMENTATION OF NUMBERED HEAD TOGETHER MODEL TO IMPROVE THE STUDENTS UNDERSTANDING OF MATHEMATICAL CONCEPT IN THE LINEAR EQUATION SYSTEM OF TWO VARIABLES CLASS VIII AT ACADEMIC YEAR 2013/2014.

IMPLEMENTATION OF NUMBERED HEAD TOGETHER MODEL TO IMPROVE THE STUDENT’S UNDERSTANDING OF

MATHEMATICAL CONCEPT IN THE TOPIC OF LINEAR EQUATION SYSTEM OF TWO

VARIABLES CLASS VIII AT THE ACADEMIC YEAR 2013/2014

By: Epril Parhusip Reg. Number 409312017

Bilingual Mathematics Education Program

THESIS

Submitted In Partial Fulfillment of the Requirements for the Sarjana Pendidikan Degree

MATHEMATICS DEPARTMENT

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

STATE UNIVERSITY OFMEDAN MEDAN

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ACKNOWLEDGEMENTS

First and foremost, praises and thanks to Jesus, the Almighty, for the wisdom and perseverance that He has been bestowed upon me during this research project, and indeed, throughout my life, I can do everything trough Him who gives me strength (Philippians 4:13) until this research being finished eventually.

I would like to express my deep and sincere gratitude to my research supervisor, Prof. Dr. Bornok Sinaga, M.Pd, for giving me the opportunity to do this research and providing me the invaluable assistance and insights leading throughout this research thesis. He has taught me the methodology how to carry out this research and how to present this research as clearly as possible. It was a great honor to work under his guidance. I am exteremely grateful for his understanding and also for his great sense of humor.

I would like to thank my academic supervisor, Prof. Dr. Dian Armanto, M.Pd.,M.Sc.,Ph.D for his caring and guidance. It was a great privilege to be his academic student. Thank you for encouraging me to face this honours programme. I would also like to thank him for his friendship and empathy.

I would also like to convey my heartfelt gratitude to the rector of State University of Medan, Prof. Dr. Ibnu Hajar Damanik, M.Si and also dean of mathematic and natural sciences faculty in State University of Medan, Prof. Drs. Motlan, M.Sc. Ph.D for their leadership and initiatives.

I would like to thank all my assesor, Prof. Dr. P. Siagian, M.Pd, Dr. E. Elvis Napitupulu, MS, Prof. Dr. Mukhtar, M.Pd. I am most grateful for their suggestion and referrals as the refinement of my thesis. I could not have imagined how to make better thesis without their invaluable advices

I would like to whole-heartedly thank head of math department, Drs. Syafari, M.Pd, the secretary of mathematics departement, Drs.Yasifati Hia, M. Si, and also head of study program, Dr. Zul Amry, M. Si, for their great helps, compassion and corrections. My appreciation also must be addressed to Mrs.Mutia Khairani for her extremely patient to helped me passionately and sincerely.

I am truly indebted to the coordinator of bilingual program, Dr.rer.nat.Binari Manurung, M.Si, for all his continuous help, support and assistance throughout my study in bilingual program.

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I would like thank the principle of SMP Negeri 5 Percut Sei Tuan, Mr. Effendi Tindaon for providing me the assistance to do the research on SMP Negeri 5 Percut Sei Tuan, and also for Mr. Amril Tambunan who entrustes me teaching on his class during my research project.

I am exteremely grateful to my beloved parents for their endless love, caring, prayers, and sacrificies for educating and preparing for my future education. They are the precious of my life who always support me on my way. Also my sincere gratitude to my beloved sisters, Junita Parhusip, Elisabeth Parhusip and Putri Parhusip for their support and valuable prayers, and my special gratitude addressed to my beloved little sister, Putri Parhusip, for her readiness to driving me to print my research thesis. Thank you Puputt.

My sincere thanks also goes to all my beloved classmates, Siska, Joy, Nurhabibah, Enny, Rizky, Rini, Siti, Noya, Iwan, Evi, Faradilla, Widia, Dini, Iin, Qoriyanti, Retni. Thanks for our togetherness during for years, for the sleepless nights we were working together before deadlines and for all the fun we had in the last four years, encouraging each other finish this thesis. Love to admit that I totally proud to have the kind-hearted friends like you all.

My sincere thank also goes to every student that I ever taught before, student of SMA Negeri 1 Sidikalang and also student of SMP Negeri 5 Percut Sei Tuan. All of you ever take a part of my research success somehow.

Last but not least, I would like to thank all people who have helped me during the writing of this thesis and during my study but I can not mention their names one by one here. Hopefully this thesis can give a quite contribution for everyone. For any errors and inadequacies that may remain in this work, of course, the responsibility is entirely my own.

Medan, August 20, 2013

Epril Parhusip I.D. 409312017

ABSTRACT

Implementation of Numbered Head Together Model to Improve the Students Understanding of Mathematical Concept In the Linear Equation System of

Two Variables Class VIII at Academic Year 2013/2014

EPRIL PARHUSIP (409312017)

This research starts from low degree of student’s understanding of mathematical concept with the root of problem is irrelevance learning model which usually implemented by teacher. This research aimed to (1) knowing how is the degree of student’s conceptual understanding in linear equation of two variables system after Numbered Head Together model has been implemented, (2) describing the level of student’s activity in implementation of Numbered Head Together model.This research is class action research. The subject of this reseacrh is students in class VIII-5 SMP Negeri 5 Percut Sei Tuan with total students is 28 students.The object of this research is the conceptual understanding of students and also the student’s activity in linear equation of two variables system by implementing the cooperative learning strategy of Numbered Head Together model. The average score of prerequisite test based on data analysis is 67.25. The results of data analysis in cycle I are: (1) the average score of student’s conceptual understanding test in cycle I is 58, (2) student in very low category is 2 students (7%), (3) student in low category is 8 students (29%), (4) student in middle category is 12 students (43%), (5) student in high category is 6 students (21%), (6) and there is no student in very high category, (7) the used time for independent learning is 86.1% of available time and 13.2% of available time spent to interact with the teacher. The result of data analysis in cycle II is (1) the average score of conceptual understanding test is 72.57, (2) there is no student in very low and low category, (3) there are 11 students (39%) with middle prosperity, (4) there are 14 students (50%) in high category, (5) there are 3 students (11%) in very high category, (6) about 88.05% of available time, used by student to learn independently, and about 12.02% of available time used by students interact with a teacher. From the result of research concluded that implementation of Numbered Head Together model able to improve the student’s understanding of mathematical concept, and learning process are conducted well observed by student’s learning activity. Based on this conclusion, it is expected that this research can be used as reference to improve the student’s conceptual understanding.

Keywords: Student’s Conceptual Understanding, Numbered Head Together Model, Student’s Learning Activity

TABLE OF CONTENTS

PAGE

LEGALIZATION SHEET _i

CURRICULUM VITAE _ii

ABSTRACT _iii

ACKNOWLEDGEMENT _iv

TABLE OF CONTENTS _vi

LIST OF TABLES _x

LIST OF FIGURES _xi

APPENDIX _xii

Chapter

I INTRODUCTION 1

A. Rationale 1

B. Problem Identification 7

C. Problem Restriction 8

D. Problem Formulation 8

E. Research Goals 8

F. Research Benefits 9

G. Operational Definition 10

II LITERATURE REVIEW 12

A. Mathematical Learning 12

B. Learning Approach, Learning Strategy and Learning Model 14 C. Cooperative Learning Strategy 17 1. The Strength of Cooperative Learning Strategy 20 2. The Weakness of Cooperative Learning Strategy 21 C. Numbered Head Together Model 21 D. Understanding of Mathematical Concept 24

E. Student’s Learning Activity 27

F. Linear Equation Of Two Variables System 28 1. Linear Equation With One Variable 28

2. Linear Equation With Two Variables 28 3. Linear Equation Of two Variables System 29 4. Solving the Linear Equation of Two

Variables System 31

5. Solving the Narrative Problem 34

G. Conceptual Framework 36

H. Hypothesis of Action 37

III. METHODOLOGY OF RESEARCH 39

A. Type of Research 39

B. Research and Date of Location 40 C. Subject and Object of Research 40

D. Research Designs 41

1. Cycle I 41

a. Stage of Problem I 41

b. Stage of Planning I 41

c. Stage of Implementation of Action I 42

d. Stage of Observation I 42

e. Analysis of Data I 43

f. Stage of Reflection I 43

2. Cycle Continued 44

E. Technique of Data Collecting and Instrument of Research 45 1. Technique of Data Collecting 45

a. Observation 45

b. Documentation 45

2. Instrument of Research 45

a. Test of Conceptual Understanding 45

1) Reliability of Test 48

2) Validity of Test 49

F. Analyzing the Data of Test 50 1. Analyzing the Student’s Conceptual Understanding 50 2. Analyzing the Data of Student’s Activity 53

G. Indicator of Performance 55

IV. RESULT OF RESEARCH AND EXPLANATION

A. Result of Research 56

1. Result Description of Preliminary Class Action Research 56 2. Result Description of Class Action Research 59 a. Research Result of Cycle I 62

1) planning 62

2) implementing 63

a) data analysis of conceptual understanding test 64 b) description of students learning activity 73

3) reflection 77

b. Research Result of Cycle II 82

1) planning 83

2) implementing 83

3) result of research

a) description of conceptual understanding test 85 b) student’s learning activity 91

4) reflection 93

B. Explanation of Research Result 97 1. Student’s Conceptual Understanding 97 2. Student’s Learning Activity 99

3. Weakness of Research 100

V. Conclusion and Suggestion

A. Conclusion 101

B. Suggestion 102

LIST OF TABLES

Table 3.1 Table of Blueprints of Conceptual Understanding Test 46 Table 3.2 Table of Rubric of Criteria of Student’s Math 47

Conceptual Understanding

Table 3.3 Table of Category of Student’s Activity 50 Table 3.4 Table of Criteria of Scoring of Conceptual Understanding 51

Test

Table 3.5 Table of Category of Average Score in Class and 53 Conceptual Understanding

Table 4.1 Table of Score of Preliminary Test 57 Table 4.2 Table of Mastery Level of Preliminary Test 57 Table 4.3 Table of Mathematics Schedule Class VIII-5 59 Table 4.4 Table of Score of Prerequisite Test 60 Table 4.5 Table of Mastery Level of Prerequisite Test 60 Table 4.6 Table of Description of Conceptual Understanding Test 65

Result on Cycle I

Table 4.7 Table of Degree of Student Conceptual Understanding 65 On Cycle I

Table 4.8 Table of Score of Conceptual Understanding for Every 72 Aspect

Table 4.9 Table of Mastery Level of Students Conceptual 72 Understanding

Table 4.10 Table of Observation Result of Student’s Activity 75 In Cycle I

Table 4.11 Table of Comparison of Student’s Degree of Conceptual 80 Understanding in Preliminary Test and Cycle I

Table 4.12 Table of Amelioration list from cycle I to cycle II 81 Table 4.13 Table of General Description of Conceptual 85

Understanding Test of Cycle II

Table 4.14 Table of Degree of Student’s Conceptual Understanding 86 of Second Cycle

Table 4.15 Table of Conceptual Understanding for Every Aspect 88 Table 4.16 Table of Achievement of Mastery Concept in Cycle II 89 Table 4.17 Table of Improvement of Student’s Conceptual 90

Understanding in Cycle II

Table 4.18 Table of Observation Result of Student’s Activity 91 in Cycle II

Table 4.19 Table of The Comparison of Student’s Conceptual 96 Understanding from First Cycle to Second Cycle

LIST OF FIGURES

Figure 1.1 Graphic of Student’s Degree of Conceptual 4 Understanding In Math

Figure 1.2 The Student’s Answer of Preliminary Test 5 Figure 3.1 Design of Class Action Research 44 Figure 4.1 Percentage of Preliminary Test Score 58 Figure 4.2 Percentage of Prerequisite Test Mastery Level 61 Figure 4.3 Percentage of Degree of Student’s Conceptual 66

Understanding on First Cycle

Figure 4.4 Percentage of Mastery Level in Conceptual Understanding 73 First Cycle

Figure 4.5 Percentage of Student Activity in Cycle I 77 Figure 4.6 Percentage of Student’s Conceptual Understanding 80

Cycle I and Preliminary Research

Figure 4.7 Percentage of Student’s Conceptual Understanding 86 Cycle II

Figure 4.8 Percentage of Mastery Level on Understanding Concept 89 In Second Cycle

Figure 4.9 Percentage of Conceptual Understanding Improvement 90 From First Cycle to Second Cycle

Figure 4.10 Percentage of Student’s Learning Activity in 93 Second Cycle

Figure 4.11 Comparison of Student’s Conceptual Understanding 96 From First Cycle to Second Cycle

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APPENDIX

Appendix 1.1 Lesson Plan (Cycle I) 106 Appendix 1.2 Lesson Plan (Cycle II) 116 Appendix 2.1 Student’s Activity Worksheet I 125 Appendix 2.2 Student’s Activity Worksheet II 141 Appendix 2.3 Student’s Activity Worksheet III 156 Appendix 2.4 Student’s Activity Worksheet IV 164 Appendix 2.5 Alternative Solution of Student’s Activity Worksheet I 171 Appendix 2.6 Alternative Solution of Student’s Activity Worksheet II 184 Appendix 2.7 Alternative Solution of Student’s Activity Worksheet III 198 Appendix 2.8 Alternative Solution of Student’s Activity Worksheet IV 203 Appendix 3.1 Blueprints of Conceptual Understanding Test of Cycle I 208 Appendix 3.2 Blueprints of Conceptual Understanding Test of Cycle II 209 Appendix 3.3 The Rubric of Criteria of Student’s Conceptual 210

Understanding In Mathematics

Appendix 3.4 Validation Sheet of Conceptual Understanding Test 212 On Cycle I

Appendix 3.5 Validation Sheet of Conceptual Understanding Test 214 On Cycle II

Appendix 3.6 Conceptual Understanding Test of Cycle I 224 Appendix 3.7 Conceptual Understanding Test of Cycle II 225

Appendix 3.7 Prerequisite Test 226

Appendix 3.8 Preliminary Test 227

Appendix 3.6 Observation Sheet of Student Activity in Cooperative 228 Learning Strategy Numbered Head Together Model

Appendix 4.1 Score of Preliminary Test 232 Appendix 4.2 Score of Conceptual Understanding Test Cycle I 234 Appendix 4.3 Score of Conceptual Understanding Test Cycle II 236 Appendix 5.1 Research Documentation 238

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CHAPTER 1 INTRODUCTION A. Rationale

Mathematic is a fundamental human activity – a way of making sense of the world. Children possess a natural curiosity and interest in mathematics, and come to school with an understanding of mathematical concepts and problem solving strategies that they have discovered through explorations of the world around them (Ginsburg, 2002)

Stodolsky (1985) stated that mathematics is an area in which ability, in the sense of a stable trait is believed to play a dominant role in performance, either one has the ability or one does not. And if one lacks ability in mathematics, nothing can be done about it. By contrast, people generally believ that performance in in other subjects, like raeding or social studies, can be improved with practice and effort, they hold an incremental theory of ability

But actually mathematics is generally considered as a most difficult subject, boring and scarry subject indeed. This opinion may not too redundancy, beside its abstract properties, mathematics should needs a good conceptual understanding. So that, no wonder if students don’t like to learn mathematics. It may just because they hard to understand the Mathematics. Another reason why Mathematics called as difficult subject can be observed from the mastery of Mathematics of students in Indonesia that still low. As Balitbang Depdiknas proposed that just look to the test results of Trends in International Mathematics and Science Study (TIMSS) 2003 which are coordinated by International for Evaluation of Education Achievement (IEA), the test results put Indonesia students in 36th rank of Science mastery. Compare to neighboring countries of Indonesia, like Singapore and Malaysia, this position still far behind their position. Singapore is in first rank in both of

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Mathematics and Science and Malaysian is in 10th rank in Mathematics and 20th rank in Science.

Another opinion proposed by Rahim (2012) that Indonesia students’ achievement in Mathematics still under standard average scores of TIMSS (500). Indonesia only gets 307 points. As for other countries like Singapore, Malaysia, and Thailand respectively get 593, 474, 444 with minimal standard score is 500.

In mathematics learning, mathematics conceptual understanding is important for students, because one mathematics concept related with another concept, so that, to learn mathematics should continuously. If students already understanding about mathematics concept ease them to understand the more complex concept.

Hiebert and Carpenter (1992) specifically defined mathematical understanding as involving the building up of the conceptual ‘context’ or ‘structure’ mentioned above

The mathematics is understood if its mental representation is part of a network of representations. The degree of understanding is determined by the number and strength of its connections. A mathematical idea, procedure, or fact is understood thoroughly if it is linked to existing network with stronger or more numerous connections (Andreas, 2007). According to Bruner, Goodnow, and Austin (1956) a concept is learned by testing hypotheses about the correct solution. If the first hypothesis formed is correct, the individual has learned the concept. However, if the hypothesis is incorrect, another hypothesis will be generated and tested. Hypothesis testing will continue until a correct solution is discovered (Klein, 1991)

Many things that considered makes students lack of math conceptual understanding are (1) students relying on rote memorized without understanding the material. That will cause the lack of student’s creativity to find the concept so that they will easily forget the material; (2) the material which are taught has float concept, so that students hard to find the keywords to understand the material and;(3) educator (teacher) may not too success to explain the keywords of material concept of existing subjects so that student

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not attract to study and causes the low conceptual understanding (Lynch and Waters, 1980, Nakhleh, 1992, 1994).

According to Debora Stipek (Johnson & Johnson, 1985b) students tend to find cooperative learning groups more enjoyable than working independently. Some studies suggest that girls respond particularly well to math and science instruction when it is taught in a cooperative manner (Eccles & Roesser, 1999). Debora Stipek proposed that individual accountability is important, and cooperative learning activities need to be planned and implemented thoughfully to ensure that all students are actively participating in substantive intelectual work. Students can collaborate in pairs for a few minutes to solve a single math problem during whole-class instruction (Stigler & Stevenson, 1991)

Based on observation result which conducted in SMP Negeri 5 Percut Sei Tuan on July 15th 2013 in class VIII-5 year academic 2013/2014, linear equation system of two variables considered as difficult subject matter. Actually, linear equation system of two variables is basic knowledge that should be mastered because too often to use in daily life problems and relate to the next subject matter. Students have low prosperity in understanding the concepts that inflict students not able to create mathematic model and solving the problems.

Conceptual understanding of mathematic may observed from 3 aspects. The first aspect is define the concept by own words, second is give the example and counter example of concepts, and third is apply the concept to solve the problem. Observer gave the preliminary test about linear equation system of two variables which test the students’ conceptual understanding. The conceptual understanding score after preliminary test was given, the lowest score is 14 and the highest score is 76, with average score is 48.14. For 36% or 10 students have very low degree of conceptual understanding in math, 21% or 6 students have low degree of math conceptual understanding, 9 students or 32% have enough score conceptual understanding degree in math, 3 students

or 11% have high deg high degree of concep

Figure 1.1. Gra

From above res of linear equation of result can concluded linear equation of tw this problem.

When the probl The total price fo 6 oranges and 5 app model and find the pr 36%

degree of conceptual understanding and no studen eptual understanding. The graphic will be shown

raphic of degree of conceptual understanding

esults obviously observed that the score of prelimi of two variables system not too satisfy. Based ed that student’s conceptual understanding esp two variables system still low and need any actio

blem as follow given:

for 8 oranges and 6 apples is Rp 25.000, while th pples is Rp 20.000,-. Make this problem into ma

price for one orange! 36%

21%

32%

11%

0%

PERCENTAGE OF STTDENT'S

CONCEPTTAL DEGREE

4

ent has very n as below:

g in math

iminaary test ed on above especially in tion to solve

the price for mathematic VERY LOW LOW MIDDLE HIGH VERY HIGH

5

And one of the students’ answers is:

The above answer shows that student disable to define the concept of linear equation system of two variables and also disable to apply the concept to solve the mathematics problem. This case shows that the conceptual understanding of students in linear equation system of two variables still low.

Based on interview with mathematics teacher in class VIII-5 SMP Negeri 5 Percut Sei Tuan, Mr. Amril, learning model which often used is teacher-centered learning which learning process mostly focuses only to the teacher. Teacher most often to explain and to give the information about the concepts of learned material. One of asked question in interview is “What do you think about the conceptual understanding in mathematics?” and teacher answered that the students conceptual understanding is very low. It can observed by their difficulty to solve their problem using concepts, students were soon forgotten with the material that has been taught, and difficult to answer the test with has little different with the explained test before. Based on Mr.Amril, students often waste their chance to ask or to express their mind when teacher prompted. They seems easier to express their idea or ask the question to their friend with their own words and make them understand then help each other. It shows that students need to learn cooperatively.

Cooperative learning is a generic term that is used to describe an instructional arrangement for teaching academic and collaborative skills to small, heterogeneus group of students (Rich, 1993; Sharan, 1980). Cooperative

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learning is deemed highly desirable because of its tendency to reduce peer competition and isolation, and to promote academic achievement and positive interrelationship. A benefit of cooperative learning, therefore, is to provide students with learning disabilities (LD), who have math disabilities and social interaction difficulties, an instructional arrangement that fosters the application and practice of mathematics and collaborative skills within a natural setting (i.e., group activity). Thus, cooperative learning has been used extensively to promote mathematics achievement of students both with and without learning disabilities (Slavin, Leavey, &Madden, 1984; Slavin, Madden, &Leavey, 1984) According to the National Council of Teachers of Mathematics (NCTM; 1991), learning environtments should be created that promote active learning and teaching; classroom discourse; and individual, small group, and whole group learning. Cooperative learning is one example of an instructional arrangement that can be used to foster active student learning, which is an important dimension of mathematics learning and highly endorsed by math educators and researchers. Students can be given tasks to discuss, problem solve, and accomplish.

Numbered Head Together (NHT) is one of cooperative learning type. This model can be used as alternative model of previous learning model. By that condition of underprivileged students in understanding the mathematical concepts, so Numbered Head Together expected to improve the students’ spirit in understanding the mathematics concept and to facilitate students to learn mathematics, so that it can improve the students’ understanding of mathematical concept.

Numbered Head Together is cooperative learning strategy that holds each students accountable for learning the material. Students are occupied in groups and each person be given a number (from one to the highest number in each group). The teacher poses a question and students “put their heads together” to figure out the answers. The teacher calls a spesific number to respond as spokesperson for the group. By having students work together in a group, this strategy ensures that each member knows the answer of the problems or

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questions which asked by teacher. Because no one knows which number will be called, all team members must prepare their selves.

This cooperative learning strategy promotes discussion and both individual and group accountability. This strategy is beneficial for reviewing and integrating subject matter. Students with special needs often benefit when this strategy is used. In learning strategy Numbered Head Together, students not only learn from what teacher teach, but also discuss and share with their friend. Beside of that, students easier to interact to figure out the difficult concept when they discuss that problem to their friend. And also, Numbered Head Together never used before in SMP NEGERI 5 Percut Sei Tuan as learning model for mathematics subject.

By Numbered Head Together model, researcher expected to make a great change for students in SMP Negeri 5 Percut Sei Tuan to learn Linear Equation of Two Variables System until conceptual understanding increase year by year, and help the teacher especially to teach Linear Equation of two variables System in class VIII

Based on above, the researcher attract to did the observation whose entitled “IMPLEMENTATION OF NUMBERED HEAD TOGETHER MODEL TO IMPROVE THE UNDERSTANDING OF MATHEMATICAL CONCEPTS IN THE TOPIC OF LINEAR EQUATION OF TWO VARIABLES SYSTEM CLASS VIII AT THE ACADEMIC YEAR 2013/2014”

B. Problems Identification

Based on above rationale, the matter that considered as problem identification are :

1. Students consider that mathematics is the difficult subject

2. Students have low degree of understanding of mathematical concept, so they hard to solve mathematics problem by their own way especially in linear equation of two variables system.

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3. Teacher-centered learning makes students tend to be passive in teaching and learning process.

4. Students afraid to ask the teacher about their problem, they feel more enjoy when they share with their friends.

5. Teaching and learning process still dominated by traditional learning strategy.

C. Problem Restriction

Based on above problem identification, the problem must be restricted so that it will be more focus on the restricted problem. The restriction of problems in this research proposal are:

1. Students in class VIII5 SMP Negeri 5 Percut Sei Tuan has low conceptual understanding especially in linear equation of two variables system.

2. Teacher-centered learning makes student’s activity along learning process tend to be passive

D. Problems Formulation

According to above problem restriction, the researcher conclude the problem formulation are:

1. Whether the implementation of Numbered Head Together model able to improve the student’s understanding of mathematical concept in linear equation system of twoa variables class VIII at academic year 2013/2014 2. How is the level of students activity by implementation of cooperative

learning strategy Numbered Head Together Model?

E. Research Goals

The goal of this researh which want to be achieved are:

1. Knowing Whether the implementation of Numbered Head Together model able to improve the student’s understanding of mathematical concept in linear equation system of twoa variables class VIII at academic year 2013/2014

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2. Describing the level of student’s activity in implementation of cooperative learning strategy Numbered Head Together model

F. Research Benefits

The findings which obtained from this class action research about learning strategy of Numbered Head Together model give some benefits as below: 1. For teacher

a. As consideration for teacher about the implementation of cooperative learning strategy Numbered Head Together model

b. Helping to choose and determine the alternative learning model which proper to use in learning process so that the objective of implementation of conceptual understanding in mathematics will be exact and effective 2. For Student

a. Helping and facilitating students in class VIII-5SMP Negeri 5 Percut Sei Tuan to understand the mathematics concept.

b. Helping and training students to familiarizing with group discussion, by discussion students are able to critically thinking, sharing the idea and opinions to solve the problems.

3. For Researcher

a. Increasing the knowledge about educational condition in Indonesia, especially in SMP Negeri 5 Percut Sei Tuan. So that, all associated elements try to improve the quality of education proper to subject matter and learning strategy

b. Knowing what is the proper learning model to be implemented in learning process as prospective teacher

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G. Operational Definition

To avoid misinterpretation, there are some special term used in this research, they are:

1. Cooperative learning strategy:

Method of instruction that has students working together in groups, usually with the goal of completing a specific task. This method can help students develop leadership and the ability to work with others as a team. However gifted students are often placed in groups with non-gifted children, sometimes with the goal of having the gifted student help the others, either directly or by example. In these instances, the gifted students is not likely to learn anything new, while the non-gifted students are not likely to develop any leadership skills.

2. Numbered Head Together

Cooperative learning strategy that holds each student accountable for learning the material. Students are placed in groups and each person is given number (from one to the maximum number in each group). The teacher poses a question and students “put their heads together” to figure out the answer. The teacher calls a specific number to respond as spokesperson for the group. By having students work together in a group, this strategy ensures that each member knows the answer to problems or questions asked by teacher. Because no one knows which number will be called, all team members must be prepared.

3. Mathematical Concept

One thing that represent any object in mathematic which has the same characteristic.

4. Student’s Understanding Concept

His or her collection of privately held beliefs about the concept. It satisfies three indicators able define the concepts by own words, able to give the example and counter example of concepts, able to apply the concept to solve the problems.

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5. Level of student’s activity

All activities which conducted by students along learning process, observed by observer and measured based on ideal time attainment which are: (1) listening, watching the teacher’s explanation, (2) reading/comprehending the problem in worksheet, (3) solving the problem/discovering the way and solution of the problem, (4) writing the problem solution, summarizing and concluding the procedure/concept, (5) presenting the result, (6) discussing/asking to friend/asking to the teacher, (7) writing the relevant things to the learning process, (9) all irrelevant things to the learning process

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CHAPTER V

CONCLUSSION AND SUGGESTION

A. CONCLUSSION

1. Based on above research result, it can be concluded that implementation of Numbered Head Together model in teaching learning process able to improve the degree of student’s conceptual understanding in the topic linear equation system of two variables. It has shown by the score of conceptual understanding test which has been improved in every cycle. In cycle I, the average score of conceptual understanding test is 58 while in cycle II, the average score of conceptual understanding test is improved becomes 72.57. In cycle I, the percentage of student in middle category is 12 student or 42.9% of total students, while in cycle II is 11 students or 39.3%. In cycle I, the student in high category is 6 students or 21.4%, while in cycle II increase to be 14 students or 50%. In cycle I, no one student in very high category while in cycle II, there are 3 students or 10.7% are in very high category. Regarding to indicator of conceptual understanding, in cycle I, the highest score was achieved on giving the example and counter example aspect is 65.71%, and the lowest score was achieved by applying the concept aspect is 55.68%. While in cycle II, the highest score was achieved by defining the concept is 82.14%, and the lowest score was achieved by applying the concept aspect is 63.57. In cycle I, student who’s already satisfy the minimal point criteria is 29% while in cycle II is being improved to be 86%.

2. The student’s activity in learning process with Numbered Head Together has high activity concentration. In cycle I, known that percentage of student’s learning activity to actively and independently learn is 86.1% while in cycle II is 88.05% of available time. It means that, Numbered Head Together model provides the students the opportunity to work independently, they use their time mostly to learn more by sharing with their friend and cooperate each other.

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B. SUGGESTION

Based on result of research and overall explanation of implementation of Numbered Head Together model which has been conducted, researcher gives some suggestions which are need to be considered by state alike as effort to improve the degree of student’s conceptual understanding for student in class VIII SMP Negeri 5 Percut Sei Tuan as below:

1. For school, expected that this research will be an alternative model which be used in SMP Negeri 5 Percut Sei Tuan, keep on turns with other learning model. Because, implementation of Numbered Head Together model was proven to improve the degree of student’s conceptual understanding.

2. For teacher, in conducting the mathematics learning by Numbered Head Together model, teacher as could as possible give ample opportunity to students to teach and refine their ideas, questions and approaches in the security of a small study team and also explain what they think they know to the else teammate.

3. For student, in order to actively build their new knowledge, student had better to read the book literature. Student should be actively engaged in learning process to create the better understanding. Because discussing the problems together assure that each member understands the information better.

4. For other researcher, mathematics learning by Numbered Head Together model can be used as alternative to improve the degree of student’s conceptual understanding. For the next research, can further examine about Numbered Head Together model with different aspects.

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Creswell, John W. (2008). Educational Research: Planning Conducting, And

Evaluating Quantitative and Qualitative Research. Perason Merrill Prentice Hall: Ohio, New Jersey.

Femini, Joan-Mundy. (2000). Principles and Standards for School Mathematics A

Guide for Mathematicians. National Council of Teachers of

Mathematics 47_{: 868 – 876.}

Kastberg, Signe E. (2002). Understanding Mathematical Concepts: The Case of

The Logarithmic Function. Dissertation. Mathematic and Sciences Faculty, University of Georgia, Athens, Georgia.

Kember, David. (2000). Action Learning and action Research. Routledge Falmer:

United Kingdom.

Klein, Stephen B. (1991). Learning: Principles and Applications 2nd ed.

McGraw-Hill International: Singapore

Loepp, Franzie L. (2000). Standards: Mathematics and Science Compared To

104

National Association for The Education of Young Children (2002). Early

Chilhood Mathematics: Promoting Good Beginning. Reston, VA: Author.

Slavin. (1989). Cooperative Learning and Student’s Achievement. In R. Slavin

(Ed.). School and Classroom Organization. Hillsdale, NJ: Lawrence,

Erlbaum.

Stipek, Debora. (2002). Motivating to Learn, Integrating Theory and Practice.

McGraw Hill International: USA.

Stylianides, Andreas J. and Stylianides, Gabriel J. (2007). Learning Mathematics With Understanding: A Critical Consideration of The Learning Principle in The Principles and Standards for School Mathematics.

The Montana Mathematics Enthusiast4_{: 103 – 114.}

Whickers, Kristina M. and Nunnery, John A. (1997). Cooperative Learning in The

Secondary Mathematics Classroom. The Journal of Educational

G. Operational Definition

To avoid misinterpretation, there are some special term used in this research, they are:

1. Cooperative learning strategy:

Method of instruction that has students working together in groups, usually with the goal of completing a specific task. This method can help students develop leadership and the ability to work with others as a team. However gifted students are often placed in groups with non-gifted children, sometimes with the goal of having the gifted student help the others, either directly or by example. In these instances, the gifted students is not likely to learn anything new, while the non-gifted students are not likely to develop any leadership skills.

2. Numbered Head Together

Cooperative learning strategy that holds each student accountable for learning the material. Students are placed in groups and each person is given number (from one to the maximum number in each group). The teacher poses a question and students “put their heads together” to figure out the answer. The teacher calls a specific number to respond as spokesperson for the group. By having students work together in a group, this strategy ensures that each member knows the answer to problems or questions asked by teacher. Because no one knows which number will be called, all team members must be prepared.

3. Mathematical Concept

One thing that represent any object in mathematic which has the same characteristic.

4. Student’s Understanding Concept

His or her collection of privately held beliefs about the concept. It satisfies three indicators able define the concepts by own words, able to give the example and counter example of concepts, able to apply the concept to solve the problems.

5. Level of student’s activity

All activities which conducted by students along learning process, observed by observer and measured based on ideal time attainment which are: (1) listening, watching the teacher’s explanation, (2) reading/comprehending the problem in worksheet, (3) solving the problem/discovering the way and solution of the problem, (4) writing the problem solution, summarizing and concluding the procedure/concept, (5) presenting the result, (6) discussing/asking to friend/asking to the teacher, (7) writing the relevant things to the learning process, (9) all irrelevant things to the learning process

CHAPTER V

CONCLUSSION AND SUGGESTION

A. CONCLUSSION

1. Based on above research result, it can be concluded that implementation of Numbered Head Together model in teaching learning process able to improve the degree of student’s conceptual understanding in the topic linear equation system of two variables. It has shown by the score of conceptual understanding test which has been improved in every cycle. In cycle I, the average score of conceptual understanding test is 58 while in cycle II, the average score of conceptual understanding test is improved becomes 72.57. In cycle I, the percentage of student in middle category is 12 student or 42.9% of total students, while in cycle II is 11 students or 39.3%. In cycle I, the student in high category is 6 students or 21.4%, while in cycle II increase to be 14 students or 50%. In cycle I, no one student in very high category while in cycle II, there are 3 students or 10.7% are in very high category. Regarding to indicator of conceptual understanding, in cycle I, the highest score was achieved on giving the example and counter example aspect is 65.71%, and the lowest score was achieved by applying the concept aspect is 55.68%. While in cycle II, the highest score was achieved by defining the concept is 82.14%, and the lowest score was achieved by applying the concept aspect is 63.57. In cycle I, student who’s already satisfy the minimal point criteria is 29% while in cycle II is being improved to be 86%.

2. The student’s activity in learning process with Numbered Head Together has high activity concentration. In cycle I, known that percentage of student’s learning activity to actively and independently learn is 86.1% while in cycle II is 88.05% of available time. It means that, Numbered Head Together model provides the students the opportunity to work independently, they use their time mostly to learn more by sharing with their friend and cooperate each other.

B. SUGGESTION

Based on result of research and overall explanation of implementation of Numbered Head Together model which has been conducted, researcher gives some suggestions which are need to be considered by state alike as effort to improve the degree of student’s conceptual understanding for student in class VIII SMP Negeri 5 Percut Sei Tuan as below:

1. For school, expected that this research will be an alternative model which be used in SMP Negeri 5 Percut Sei Tuan, keep on turns with other learning model. Because, implementation of Numbered Head Together model was proven to improve the degree of student’s conceptual understanding.

2. For teacher, in conducting the mathematics learning by Numbered Head Together model, teacher as could as possible give ample opportunity to students to teach and refine their ideas, questions and approaches in the security of a small study team and also explain what they think they know to the else teammate.

3. For student, in order to actively build their new knowledge, student had better to read the book literature. Student should be actively engaged in learning process to create the better understanding. Because discussing the problems together assure that each member understands the information better.

4. For other researcher, mathematics learning by Numbered Head Together model can be used as alternative to improve the degree of student’s conceptual understanding. For the next research, can further examine about Numbered Head Together model with different aspects.

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