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
ii
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
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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
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.
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
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 4.15 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
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
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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
1
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,
2
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
3
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
or 11% have high deg
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
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
6
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
7
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
8
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
9
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
10
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
11
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
1011 1
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
1021 1
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.
101
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