THE DIFFERENCE OF EFFECT OF PROBLEM BASED LEARNING AND NUMBERED HEADS TOGETHER TOWARD STUDENTS PROBLEM SOLVING ABILITY ON THE TOPIC OF STATISTICS IN GRADE XI SMA NEGERI 2 BALIGE.
THE DIFFERENCE OF EFFECT OF PROBLEM – BASED LEARNING
AND NUMBERED HEADS TOGETHER TOWARD STUDENTS’
PROBLEM SOLVING ABILITY ON THE TOPIC OF
STATISTICS IN GRADE XI SMA NEGERI 2 BALIGE
By:
Debby Masteriana
ID. 4113312003
Bilingual Mathematics Education
A THESIS
Submitted to Qualify for Academic Title of
Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
..
iv
PREFACE
Praise and great thanks to God The Almighty for His amazing grace, love,
strength, and health which have been given such that the author could finish this
thesis well. This thesis which entitled “The Difference of Effect of Problem–
Based Learning and Numbered Heads Together toward Students’ Problem
Solving Ability on The Topic of Statistics in Grade XI SMA Negeri 2 Balige” is
submitted in order to get the academic title of Sarjana Pendidikan from
Mathematics Department, FMIPA Unimed.
In this part, the author would like to thank for all supports which gained
for completion of this thesis. Special thanks to Mr. Drs. Syafari, M.Pd as thesis
supervisor who has provided guidance, direction and advice from the beginning
until the finishing part of this thesis. Great thanks are also due to Prof. Dr. Sahat
Saragih, M.Pd, Dr. KMS. Amin Fauzi, M.Pd, and Dr. W. Rajagukguk, M.Pd as
thesis examiners who have provided builded suggestion and revision in the
completion of this thesis. Thanks also extended for Prof. Dr. Bornok Sinaga,
M.Pd as academic supervisor and also for all lecturers in FMIPA Unimed.
The author also expressed sincerely thanks for Prof. Dr. Syawal Gultom,
M.Si as rector of Unimed, Prof. Drs.Motlan, M.Sc, Ph.D as Dean of Mathematics
and Natural Sciences Faculty, Prof. Dr. rer.nat Binari Manurung, M.Si as
Coordinator of Bilingual Program, Dr. Edy Surya, M.Si as Head of Mathematics
Department, Drs. Zul Amry, M.Si, Ph.D as Head of Mathematics Education Study
Program, Drs. Yasifati Hia, M.Si as Secretary of Mathematics Education, and all
staff employess which supported in helping author.
The author expressed thanks so much for Mr. Aldon Samosir, S.Pd as
principal of SMA Negeri 2 Balige, Mrs. Hanita Simangunsong, S.Si as
mathematics teacher, all teachers and staff employess who have helped author
conductiong the research well. Another thanks expressed by the author to all
students in SMA Negeri 2 Balige, especially Grade XI which consisted of
Invictusion and others, also Grade X which consisted of Argentium and others, for
every supports, love, and laugh during the research.
v
Most special thanks especially author would like to express for beloved
father Ir. Saut Tambunan and mother Dra. Anna Juniar, M.Si, who always give
spirit, motivation, and prayers for the success and completion of this thesis. The
author also says thanks for author’s big brother Pravil Mistryanto, M.Si for giving
support both of morale and materials such that this thesis has completed. For all of
author’s family, thanks to be a part of author’s inspiration.
The author also thanks for author’s best friends Nelly, Widi, and Yohannes
for every motivation and spirit for finishing well this “skripsweet”. Thanks for all
my friends in The Fourth Generation of Bilingual Mathematics Education, PPLT
Unimed in SMA Negeri 2 Balige especially Trendsetter Room, seniors and juniors
especially Danki in math department for every support, love, and oversight. For
Jesica, Natasya, Stella, and Vania, thanks to be one of author’s motivation and
friends to be “pacu and more pacu”. Thanks for every one who cannot be
mentioned one by one who support and motivate the author.
At last, the author has finished this thesis in maximum level but author
realized there are some imperfections. For that, the author asks for building
comments and suggestions in order to reach the perfection of this thesis. The
author wishes that this thesis would be useful to improve the knowledge,
understanding, and enrich the science education.
Medan, June
2015
Author,
Debby Masteriana
ID. 4113312003
iii
THE DIFFERENCE OF EFFECT OF PROBLEM – BASED LEARNING
AND NUMBERED HEADS TOGETHER TOWARD STUDENTS’
PROBLEM SOLVING ABILITY ON THE TOPIC OF
STATISTICS IN GRADE XI SMA NEGERI 2 BALIGE
Debby Masteriana (ID. 4113312003)
ABSTRACT
The type of this research is quasi – experiment. The objective of this research was
to determine whether students’ problem solving ability of mathematics which
taught by PBL is higher than NHT. Population of this research was 217 students
of grade eleventh science in SMA Negeri 2 Balige. Applying cluster-randomsampling, XI MIA 2 was taken as Experiment Class I and taught by using PBL,
meanwhile XI MIA 1 as Experiment Class II and taught by using NHT. Each of
class consist of 30 students. Technique of analzying data is consisted of normality,
homogeneity, and hypothesis test. Based on normality and homogeneity test, the
data was taken from normal distribution and homogeneous population. Hypothesis
test is done by using analysis of co-variance and coefficient of determination
index. The result of ANCOVA show that Fstatistics = 9.430 and F(0.5)(2, 58) = 3.160.
Consequently Fstatistics > Ftable, then H0 is rejected. It means there is significant
effect of learning model toward students’ problem solving ability. The coefficient
of determination index in PBL class is 0.5738 or 57.38% meanwhile in NHT class
is 0.4810 or 48.10%. It means students’ problem solving ability of mathematics
which taught by PBL is higher than NHT. Furthermore, the difference of both
effect is equal to 11.18%. The result of this research contributes to suggest the
using of PBL model to increase students’ problem solving ability of mathematics.
x
LIST OF TABLES
Table 2.1. Differences Between PBL and NHT
18
Table 3.1. Rubric Scoring of Problem Solving Ability
29
Table 3.2. Criterion of Student’s Problem Solving Ability
30
Table 3.3. The Research Planning
32
Table 3.4. Analysis of Variance for Simple Linear Regression
36
Table 3.5. Analysis of Variance for Linearity of Regression Model
37
Table 3.6. Summary Table for ANCOVA
39
Table 3.7. Classification of Determination Index Value
40
Table 4.1. Descriptive Statistics of Pre-Test in Experiment Class I and
41
Experiment Class II
Table 4.2. Descriptive Statistics of Post-Test in Experiment Class I and
42
Experiment Class II
Table 4.3. Result of Normality Test in Experiment Class I
43
Table 4.4. Result of Normality Test in Experiment Class II
43
Table 4.5. Result of Homogeneity Test of Pre-Test in Experiment Class I and 44
Experiment Class II
Table 4.6. Result of Homogeneity Test of Post-Test in Experiment Class I and 45
Experiment Class II
Table 4.7. Coefficient of Regression Model in Experiment Class I
45
Table 4.8. Coefficient of Regression Model in Experiment Class II
46
Table 4.9. Result of Coefficient Significance Test in Experiment Class I
47
Table 4.10. Result of Coefficient Significance Test in Experiment Class II
47
Table 4.11. Result of Analysis of Variance in Experiment Class I
48
Table 4.12. Result of Analysis of Variance in Experiment Class II
48
Table 4.13. Result of Homogeneity Test of Regression Model
49
Table 4.14. Result of ANCOVA
50
ix
LIST OF FIGURES
Figure 1.1. Sample of Students’ Alternative Solution
3
Figure 1.2. Sample of Students’ Opinion
3
Figure 2.1. Design of Problem Solving Steps by Polya
8
Figure 2.2. Harvest of Chili
19
Figure 2.3. Mode
20
Figure 2.4. Example of Group Table
23
Figure 2.5. Histogram with Normal Curve
24
Figure 3.1. The Chart of Procedural Research
33
Figure 4.1. Regression Model of Experiment Class I
46
Figure 4.2. Regression Model of Experiment Class II
46
Figure 4.3. Regression Model of Experiment Classes
53
xi
LIST OF APPENDICES
Appendix 1.
Score List of Mid – Odd Semester Examination of Math
59
Grade XI SMA Negeri 2 Balige Y.A. 2014/2015
Appendix 2.
Lesson Plan (Experiment Class I)
60
Appendix 3.
Lesson Plan (Experiment Class II)
79
Appendix 4.
Student Activity Sheet (SAS) 1
94
Appendix 5.
Student Activity Sheet (SAS) 2
97
Appendix 6.
Blue Print of Pre – Test
106
Appendix 7.
Instrument Test of Problem Solving Ability: Pre – Test
107
Appendix 8.
Answer Sheet of Pre – Test
109
Appendix 9.
Alternative Solution of Pre – Test
113
Appendix 10.
Blue Print of Post – Test
118
Appendix 11.
Instrument Test of Problem Solving Ability: Post – Test
119
Appendix 12.
Answer Sheet of Post – Test
121
Appendix 13.
Alternative Solution of Post – Test
126
Appendix 14.
Validator Evaluation Scale
131
Appendix 15.
Validator Evaluation Sheet
132
Appendix 16.
Observation Sheet of Learning Process Experiment Class I
135
Appendix 17.
Observation Sheet of Learning Process Experiment Class II
139
Appendix 18.
Procedure to Execute Validity Test in SPSS
143
Appendix 19A. Result of Validity Test: Pre – Test
145
Appendix 19B. Result of Validity Test: Post – Test
147
Appendix 20.
149
Procedure to Execute Reliability Test in SPSS
Appendix 21A. Result of Reliability Test: Pre – Test
151
Appendix 21B. Result of Reliability Test: Post – Test
152
Appendix 22.
153
Result of Initial Students’ Problem Solving Ability
(Data of Pre – Test)
Appendix 23.
Result of Final Students’ Problem Solving Ability
157
(Data of Post – Test)
Appendix 24.
Procedure to Execute Normality Test in SPSS
161
xii
Appendix 25.
Result of Normality Test
163
Appendix 26.
Procedure to Execute Homogeneity Test in SPSS
164
Appendix 27.
Result of Homogeneity Test
166
Appendix 28.
Procedure to Execute Hypothesis Test in SPSS
168
Appendix 29.
Result of Hypothesis Test
175
Appendix 30.
Students’ Pattern Way to Answer
182
Appendix 31.
Table of t – Distribution
192
Appendix 32.
Table of F Distribution
193
Appendix 33.
Documentation of Research
194
Appendix 34.
Letter
199
1
CHAPTER I
INTRODUCTION
1.1.
Background of Research
Mathematics is one of the most important subjects that provide several
vital skills to the learners. Most of jobs needs ability and understanding of
mathematics. That is why mathematics is basic science that have a main action in
developmental of science and technology. Technology nowadays made and
dominated by mastery mathematics early. It also the reason why mathematics is
one of subject matters that should be given to students since in kindergaten up to
higher education.
According to NCTM (in Walle, 2007: 1), in this changing world, those
who understand and can do mathematics will have significantly enhanced
opportunites and options for shaping their futures. Mathematical competence
opens doors to productive futures. A lack of mathematical competence keeps
those doors closed. NCTM challenges the assumption that mathematics is only for
the select few. On the contrary, everyone needs to understand mathematics. All
students should have the opportunity and the support necessary to learn significant
mathematics with depth and understanding.
The purpose of learning mathematics was explained well on the
Regulation of National Education Minister (Permendiknas) number 81A of 2013
about Concept and Learning Strategies. It stated that the learning process is
needed using some principles which contained of: (1) students center,
(2) developing the creativity of students, (3) creating fun and challenging
condition, (4) contains the value of ethics, aesthetics, logic and kinesthetic,
(5) provides a diverse learning experience through the implementation of various
strategies and joyful learning methods, contextual, effective, efficient, and
meaningful.
Two international researches conducted to demonstrate the ability of
mastery in mathematics learning showed that Indonesian student capability still in
2
the low level. Based on data of Education for All (EFA) Global Monitoring
Report that released by United Nations Educational, Scientific, and Cultural
Organization (UNESCO) in 2012, the Education Development Index (EDI)
position of Indonesia was in level 64th from 120 countries in the world.
Meanwhile the survey of Program for International Study Assesment (PISA) in
2012 showed that from 65 survey countries for mathematics, reading and science
skills, Indonesia was in 64thlevel with the mean score of mathematics skill was
375 while the average of OECD (Organization for Economic Co-Operation and
Development) was 494.
EFA 2012 provides the real condition of education in countries respected
to six goals of education which was arranged in global meeting in Senegal, 2000.
While PISA 2012 provides the most comprehensive picture of the mathematics
skills developed in schools that has ever been available, looking not just at what
students know in the different domains of mathematics, but also at what they can
do with what they know. Both of
the survey suggest that improvement of
mathematics education in schools need to be considered by various parties,
including government, education observers and by teachers as the perpetrator of
education itself.
Although the government has released Curriculum of 2013 and expected
the teachers to develop their teaching way and do their function in the classroom
as a facilitator of learning, the real fact that researcher found when doing
Integrated Field Experience Program (PPLT) in SMA Negeri 2 Balige was
different. The learning process mostly happened in conventional way. Teachers
directly provide mathematical formulas to the students and the students only see,
memorize, and apply the formulas. Then mathematics was presented as very bored
lesson and most of them sleeping in the class. As a result, the math test scores of
students are still low.
The statement above is evident based on the data which researcher found
when doing Integrated Field Experience Program (PPLT), all of students in grade
XI of Science (XI MIA1 – XI MIA6) passed the mid – odd semester examination
with the average value 75.04. While the minimum standar criteria (KKM) was 75.
4
Interview was also conducted with mathematics’ teacher in SMA Negeri 2
Balige, Mrs. Hanita Friska Simangunsong, S.Si. Researcher found that most of the
teachers have received continuous training about various learning methods. But,
in the implementation, most of them still using conventional way because of
limitation of time and the content of material which sould be given to students.
Actually there is a lot of learning methods that have been used in learning
process of mathematics. Whether Curriculum of KTSP or Curriculum 2013 which
is used in the school, problem – based learning is one of suitable model. PBL
makes students work with classmates to solve complex and authentic problems
that help develop content knowledge as well as problem – solving, reasoning,
communication, and self-assessment skills. These problems also help to maintain
student interest in course material because students realize that they are learning
the skills needed to be successful in the field (White, 2011: 1).
In another side, Larson and Timothy (2013: 204) said that cooperative
learning involves quickly formed groups that may work together for a few
minutes or a whole class period. Slavin (2005: 8) also stated that in cooperative
learning method, students work together in four member teams to master material
initially presented by the teacher. Numbered Heads Together (NHT) is one of the
cooperative learning model that requires student works together and cooperatives
so that the problem can be solved well. Spancer Kagen as the developer of this
learning model designed the learning such that the students can check and look at
their insight about the content of material.
Millis (2010: 11) recognize the close kinship between cooperative learning
and problem – based learning – both on highly structured group work. PBL and
cooperative learning are ideally suited for each other. PBL fits into the
cooperative learning framework like a hand in a glove. Well, the characteristics of
Problem – Based Learning (PBL) and Numbered Heads Together (NHT) refers to
student centered learning which improve the conceptual understanding in
mathematics. Furthermore, Tokuhama – Espinosa (2014: 204) explain process of
finding solution at the group level considering PBL as a type of cooperative
learning, and vice versa. It means PBL and cooperative learning is similar.
5
Based on those descriptions above, researcher comes with any doubts
whether both of learning models in this case are: PBL and cooperative learning
type of NHT, have different effect toward students’ learning outcomes,
particularly to the students’ problem solving ability. Therefore, the researcher has
interested to do research entitled “The Difference of Effect of Problem – Based
Learning and Numbered Heads Together toward Students’ Problem Solving
Ability on The Topic of Statistics in Grade XI SMA Negeri 2 Balige.”
1.2.
Problem Identification
Based on the background above can be identified the problem as follows:
1. The conventional way is often used in SMA Negeri 2 Balige while respected to
Curriculum of KTSP or Curriculum 2013, student centered learning has not
been applied fully in the teaching and learning process of mathematics.
2. The result of mid – odd semester examination in SMA Negeri 2 Balige shows
45.95% students of grade XI got score under the KKM score.
3. Most of students in SMA Negeri 2 Balige had low problem solving ability of
mathematics and ignoring steps which sould be passed when solving problems.
1.3.
Limitation of Problem
Based on the limitation scope of research location, research time and the
research variable causes this study is limited in the scope as follows:
1. Students’ problem solving ability on the topic of Statistics for Class XI in SMA
Negeri 2 Balige for Even Semester 2014/2015.
2. The learning activities for this study are given by using problem – based
learning and numbered heads together.
1.4.
Problem of Research
Based on the background above, the problems are formulated as:
“Is students’ problem solving ability of mathematics which taught by using
Problem – Based Learning (PBL) higher than students’ problem solving ability of
mathematics which taught by using Numbered Heads Together (NHT)?”.
6
1.5.
Objectives of Research
The objectives of the research are as follows:
1. To know whether there are differences of effect of students’ problem solving
ability of mathematics that taught by problem – based learning and numbered
heads together on the topic of statistics in grade XI SMA Negeri 2 Balige.
2. To determine whether students’ problem solving ability of mathematics which
taught by Problem – Based Learning (PBL) is higher than taught by Numbered
Heads Together (NHT) in grade XI SMA Negeri 2 Balige.
1.6.
Benefits of Research
This research is expected will give the benefits as follows:
1. For students, helping them to increase their problem solving ability of math.
2. For teachers, opening their insight about developing the learning process well.
3. For school, increasing the quality of school caused by the increasing of
students’ learning outcomes and teacher activities.
4. For researcher or advanced researcher, improving the insight, ability,
information and experience in increasing the competency as teacher student.
1.7.
Operational Definition
The operational definition of this study is described as follows:
1. Problem – based learning model is learning model which use the real problem as a
keyword of the learning process such that they can learn actively by think,
communicate, find and process data, and finally make conclusion of essential
concept of the subject.
2. Numbered heads together is learning model which holds each student accountable
for learning the material by having students work together in a group, giving the
numbers and put their heads together to develop a complete answer to the given
question.
3. Problem solving ability is the ability which gained by students to understand and
complete the problems which are faced by using their skills and abilities to
determine the concept they should use to be applied in solving the problem.
55
CHAPTER V
CONCLUSION AND SUGGESTION
5.1.
Conclusion
Based on the result and discussion of research in the previous chapter, can
be concluded that:
1. Students’ problem solving ability of mathematics which taught by problem–
based learning is higher than numbered heads together on the topic of statistics
in grade XI SMA Negeri 2 Balige. The effect size of PBL is 0.5738 or 57.38%
meanwhile the effect size of NHT is 0.4810 or 48.10%.
2. There is a difference of effect of students’ problem solving ability of
mathematics that using problem–based learning and numbered heads together
on the topic of statistics in grade XI SMA Negeri 2 Balige. It is 11.18%.
3. Problem – based learning model has more significant effect to improve the
students’ common pattern to answer mathematics question which related to
problem solving ability rather than numbered heads together.
5.2.
Suggestion
Based on the conclusion and relevant study of this research, there are some
suggestions as follows:
1. For mathematics teacher, to implement problem – based learning model in the
learning activity such that students’ problem solving ability can be increased
significantly.
2. For students, to cooperate with teachers by following the steps of learning
process and don’t ignore the steps of problem solving ability.
3. For next researcher, to observe another students’ ability of mathematics which
can be affected by problem based learning model and another choices of
learning model.
4. Because in this research the learning models are implemented to the topic of
statistics, it is suggested to try another topic of mathematics and relate it to
others factor which may influent students’ learning outcomes.
56
REFERENCES
Ahsanullah, Mohammad., (2008), Applied Statistics Research Progress, Nova
Science Publishers, New York.
Arends, Richard., (2010), Teaching for Student Learning: Becoming an
Accomplished Teacher, Routledge, New York.
Arikunto, Suharsimi., (2010), Prosedur Penelitian, Rineka Cipta, Jakarta.
Asmin., (2012), Pengukuran dan Penilaian Hasil Belajar dengan Analisis Klasik
dan Modern, LARISPA, Medan.
Asra, Abuzar and Rudiansyah., (2013), Statistika Terapan: Untuk Pembuat
Kebijakan dan Pembuat Keputusan, IN MEDIA, Jakarta.
Belvel, Patricia Sequeira., (2010), Rethinking Classroom Management: Strategies
for Prevention, Intervention, and Problem Solving Second Edition, Corwin
A SAGE Company, California.
Brown, Tom and John Eagles., (2011), Teaching Psychiatry to Undergraduates,
The Royal College of Psychiatrists, UK.
EFA Global Monitoring Report., (2014), Teaching and Learning: Achieving
Quality for All, UNESCO, France.
FMIPA, (2013), Pedoman Penulisan Proposal dan Skripsi, FMIPA Unimed,
Medan.
Foote, Chandra J., Paul Vermette, and Chaterine Battaglia., (2001), Constructivist
Strategies: Meeting Standards and Engaging Adolescent Minds, Eye On
Education Inc, New York.
Horn, Robert A., (2011), Understanding Ancova, Northern Arizona University,
http://oak.ucc.nau.edu/rh232/courses/eps625/handouts/ancova/understandi
ng%20ancova.pdf
Joyce, Bruce and Marsha Weill., (1973), Models of Teaching: School Review,
Journal of Education JSTOR, 82: 147 – 154. http://www.jstor.org/
stable/1084132
57
Keenan, Thomas and Subhadra Evans., (2009), An Introduction to Child
Development Second Edition, SAGE Publications Ltd, London.
Kennedy, Leonard M., (2008) Guiding Children’s Learning of Mathematics
Eleventh Edition, Thomson Wadsworth, USA.
Kothari, C. R., (2008), Research Methodology: Methods and Techniques Second
Revised Edition, New Age International Ltd Publishers, New Delhi.
Larson, Bruce E. and Timothy A. Keiper., (2013), Instructional Strategies for
Middle and High School Second Edition, Routledge, UK.
Luzet, Gael., (2013), Collaborative Learning Pocketbook, Teachers’ Pocketbooks
Ltd, UK.
Maher, Angela., (2004), Learning Outcomes in Higher Education: Implications
for Curriculum Design and Student Learning, Journal of Hospitality,
Leisure, Sport, and Tourism Education 3: 46 – 54.
Marshall, Stewart., (2006), Encyclopedia of Developing Regional Communities
with Information and Communication Technology, Idea Group Reference,
USA.
Mayer, Dan., (2004), Essential: Evidence – Based Medicine, Cambridge
University Press, UK.
Millis, Barbara J., (2010), Cooperative Learning in Higher Education: Across The
Disciplines, Across The Academy, Stylus Publishing LLC, Virginia.
Murdoch, Kath and Jeni Wilson., (2007), How to Succeed with Cooperative
Learning, Curriculum Corporation, Australia.
Netter, J. And Wasserman W., (1974), Applied Linear Statistical Models, Illinoi:
Richard D. Erwin, Inc
Noor, Juliansyah., (2011), Metodologi Penelitian: Skripsi, Tesis, Disertasi, dan
Karya Ilmiah, Kencana Prenada Media Group, Jakarta.
PISA., (2014), PISA 2012 Results in Focus: What 15-years-olds Know and What
They Can Do with What They Know, OECD, USA.
Rani, T. Swarupa., (2008), Teaching of Mathematics, S.B.Nangia APH Publishing
Corporation, New Delhi.
58
Richardson, Judy S., et all., (2009), Reading to Learn in The Content Areas
Seventh Edition, Wadsworth Cengage Learning, USA.
Rideout, Elizabeth., (2001), Transforming Nursing Education Through Problem –
Based Learning, Jones and Bartlett Publishers Inc, UK.
Ryan, Norma and Jennifer Murphy., (2009), The Bologna Process and Learning
Outcomes, NAIRTL Bologna Series: Qualification Recognition and Staff
Mobility, Proceedings of Symposia, 123 – 142.
Sari, Fitria Maya., (2011), Perbedaan Hasil dan Aktivitas Belajar Siswa yang
Diajar dengan Menggunakan Model Pembelajaran Kooperatif Tipe NHT
dan Tipe TGT pada Pokok Bahasan Logaritma di Kelas X MAN 3 Medan
T.P. 2010/2011, Skripsi, FMIPA – Unimed, Medan.
Savin-Baden, Maggie and Wilkie Kay., (2006), Problem – Based Learning
Online, Open University Press, New York.
Seel, Norbert M., (2012), Encyclopedia of The Sciences of Learning, Springer
Sciences, New York.
Shaffer, David. (2009), Social and Personality Development Sixth Edition,
Wadsworth, USA.
Sharp, Conni., (2000), Increasing Mathematical Problem Solving Performance
Through Relaxation Training, Mathematics Education Research Journal,
http://link.springer.com/article/10.1007/BF03217074
Sianipar, Hot Tiarma., (2013), The Influence of Problem Based Learning Method
toward Students Sequence and Series Problem Solving Ability in The
Twelfth Grade of SMA Negeri 2 Balige 2012/2013, Skripsi, FMIPA –
Unimed, Medan.
Silver, Edward A., (2013), Teaching and Learning Mathematical Problem
Solving: Multiple Research Perspectives, Lawrence Erlbaum Associates
Publishers, New Jersey.
Slavin, Robert., (2005), Cooperative Learning: Theory, Research and Practice,
Allymand Bacon, London.
Spiegel, Murray R., (2000), Schaum’s Easy Outline: Theory and Problems of
Statistics, McGraw – Hill Companies, USA.
59
Sudjana., (2009), Metoda Statistika, Tarsito, Bandung.
Sudjana, Nana., (2005), Penilaian Hasil Proses Belajar Mengajar, Rosda, Jakarta.
Sujarweni, V. Wiratna., (2014), SPSS untuk Penelitian, Pustaka Baru Press,
Yogyakarta.
Tan, Ai-Girl., (2012), Creativity, Tallent, and Excellent, Springer Sciences,
Singapore.
Tokuhama – Espinosa, Tracey., (2014), Making Classrooms Better: 50 Practical
Applications of Mind, Brain, and Education Science, W.W. Norton and
Company, New York.
Trianto.,
(2009),
Model-model
Pembelajaran
Inovatif
Berorientasi
Konstruktivistik, Prestasi Pustaka Publisher, Jakarta.
Trisna, Benny N., (2005), Pembelajaran Matematika Realistik di Kelas VIII
(Topik Persamaan Garis Lurus), Thesis, Post–graduates, Unimed, Medan.
Uden, Lorna., (2006), Technology and Problem – Based Learning, Information
Science Publishing, USA.
Udvari – Solner, Alice., (2008), Joyful Learning: Active and Collaborative
Learning in Inclusive Classrooms, Corwin Press, USA.
Walle, John A Van de., (2007), Elementary and Middle School Mathematics Sixth
Edition, Pearson Prentice Hall, USA.
White, Hal., (2011), Speaking of Teaching: Problem – Based Learning, Journal of
Winter 11: 1 – 7.
Williams, P. John., (2012), Technology Education for Teachers, Sense Publishers,
The Netherlands.
Whitmeyer, Steven J., et all., (2009), Field Geology Education: Historical
Perspectives and Modern Approaches, Geological Society of America
(GSA), USA.
Wonnacot, Thomas H., (1977), Introductory Statistics Third Edition, John Willey
and Son, Canada.
Xiang, Yun Du and Mads Jakob Kirkebaek., (2012), Exploring Task –Based PBL
in Chinese Teaching and Learning, Cambridge Scholars Publishing, UK.
AND NUMBERED HEADS TOGETHER TOWARD STUDENTS’
PROBLEM SOLVING ABILITY ON THE TOPIC OF
STATISTICS IN GRADE XI SMA NEGERI 2 BALIGE
By:
Debby Masteriana
ID. 4113312003
Bilingual Mathematics Education
A THESIS
Submitted to Qualify for Academic Title of
Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
..
iv
PREFACE
Praise and great thanks to God The Almighty for His amazing grace, love,
strength, and health which have been given such that the author could finish this
thesis well. This thesis which entitled “The Difference of Effect of Problem–
Based Learning and Numbered Heads Together toward Students’ Problem
Solving Ability on The Topic of Statistics in Grade XI SMA Negeri 2 Balige” is
submitted in order to get the academic title of Sarjana Pendidikan from
Mathematics Department, FMIPA Unimed.
In this part, the author would like to thank for all supports which gained
for completion of this thesis. Special thanks to Mr. Drs. Syafari, M.Pd as thesis
supervisor who has provided guidance, direction and advice from the beginning
until the finishing part of this thesis. Great thanks are also due to Prof. Dr. Sahat
Saragih, M.Pd, Dr. KMS. Amin Fauzi, M.Pd, and Dr. W. Rajagukguk, M.Pd as
thesis examiners who have provided builded suggestion and revision in the
completion of this thesis. Thanks also extended for Prof. Dr. Bornok Sinaga,
M.Pd as academic supervisor and also for all lecturers in FMIPA Unimed.
The author also expressed sincerely thanks for Prof. Dr. Syawal Gultom,
M.Si as rector of Unimed, Prof. Drs.Motlan, M.Sc, Ph.D as Dean of Mathematics
and Natural Sciences Faculty, Prof. Dr. rer.nat Binari Manurung, M.Si as
Coordinator of Bilingual Program, Dr. Edy Surya, M.Si as Head of Mathematics
Department, Drs. Zul Amry, M.Si, Ph.D as Head of Mathematics Education Study
Program, Drs. Yasifati Hia, M.Si as Secretary of Mathematics Education, and all
staff employess which supported in helping author.
The author expressed thanks so much for Mr. Aldon Samosir, S.Pd as
principal of SMA Negeri 2 Balige, Mrs. Hanita Simangunsong, S.Si as
mathematics teacher, all teachers and staff employess who have helped author
conductiong the research well. Another thanks expressed by the author to all
students in SMA Negeri 2 Balige, especially Grade XI which consisted of
Invictusion and others, also Grade X which consisted of Argentium and others, for
every supports, love, and laugh during the research.
v
Most special thanks especially author would like to express for beloved
father Ir. Saut Tambunan and mother Dra. Anna Juniar, M.Si, who always give
spirit, motivation, and prayers for the success and completion of this thesis. The
author also says thanks for author’s big brother Pravil Mistryanto, M.Si for giving
support both of morale and materials such that this thesis has completed. For all of
author’s family, thanks to be a part of author’s inspiration.
The author also thanks for author’s best friends Nelly, Widi, and Yohannes
for every motivation and spirit for finishing well this “skripsweet”. Thanks for all
my friends in The Fourth Generation of Bilingual Mathematics Education, PPLT
Unimed in SMA Negeri 2 Balige especially Trendsetter Room, seniors and juniors
especially Danki in math department for every support, love, and oversight. For
Jesica, Natasya, Stella, and Vania, thanks to be one of author’s motivation and
friends to be “pacu and more pacu”. Thanks for every one who cannot be
mentioned one by one who support and motivate the author.
At last, the author has finished this thesis in maximum level but author
realized there are some imperfections. For that, the author asks for building
comments and suggestions in order to reach the perfection of this thesis. The
author wishes that this thesis would be useful to improve the knowledge,
understanding, and enrich the science education.
Medan, June
2015
Author,
Debby Masteriana
ID. 4113312003
iii
THE DIFFERENCE OF EFFECT OF PROBLEM – BASED LEARNING
AND NUMBERED HEADS TOGETHER TOWARD STUDENTS’
PROBLEM SOLVING ABILITY ON THE TOPIC OF
STATISTICS IN GRADE XI SMA NEGERI 2 BALIGE
Debby Masteriana (ID. 4113312003)
ABSTRACT
The type of this research is quasi – experiment. The objective of this research was
to determine whether students’ problem solving ability of mathematics which
taught by PBL is higher than NHT. Population of this research was 217 students
of grade eleventh science in SMA Negeri 2 Balige. Applying cluster-randomsampling, XI MIA 2 was taken as Experiment Class I and taught by using PBL,
meanwhile XI MIA 1 as Experiment Class II and taught by using NHT. Each of
class consist of 30 students. Technique of analzying data is consisted of normality,
homogeneity, and hypothesis test. Based on normality and homogeneity test, the
data was taken from normal distribution and homogeneous population. Hypothesis
test is done by using analysis of co-variance and coefficient of determination
index. The result of ANCOVA show that Fstatistics = 9.430 and F(0.5)(2, 58) = 3.160.
Consequently Fstatistics > Ftable, then H0 is rejected. It means there is significant
effect of learning model toward students’ problem solving ability. The coefficient
of determination index in PBL class is 0.5738 or 57.38% meanwhile in NHT class
is 0.4810 or 48.10%. It means students’ problem solving ability of mathematics
which taught by PBL is higher than NHT. Furthermore, the difference of both
effect is equal to 11.18%. The result of this research contributes to suggest the
using of PBL model to increase students’ problem solving ability of mathematics.
x
LIST OF TABLES
Table 2.1. Differences Between PBL and NHT
18
Table 3.1. Rubric Scoring of Problem Solving Ability
29
Table 3.2. Criterion of Student’s Problem Solving Ability
30
Table 3.3. The Research Planning
32
Table 3.4. Analysis of Variance for Simple Linear Regression
36
Table 3.5. Analysis of Variance for Linearity of Regression Model
37
Table 3.6. Summary Table for ANCOVA
39
Table 3.7. Classification of Determination Index Value
40
Table 4.1. Descriptive Statistics of Pre-Test in Experiment Class I and
41
Experiment Class II
Table 4.2. Descriptive Statistics of Post-Test in Experiment Class I and
42
Experiment Class II
Table 4.3. Result of Normality Test in Experiment Class I
43
Table 4.4. Result of Normality Test in Experiment Class II
43
Table 4.5. Result of Homogeneity Test of Pre-Test in Experiment Class I and 44
Experiment Class II
Table 4.6. Result of Homogeneity Test of Post-Test in Experiment Class I and 45
Experiment Class II
Table 4.7. Coefficient of Regression Model in Experiment Class I
45
Table 4.8. Coefficient of Regression Model in Experiment Class II
46
Table 4.9. Result of Coefficient Significance Test in Experiment Class I
47
Table 4.10. Result of Coefficient Significance Test in Experiment Class II
47
Table 4.11. Result of Analysis of Variance in Experiment Class I
48
Table 4.12. Result of Analysis of Variance in Experiment Class II
48
Table 4.13. Result of Homogeneity Test of Regression Model
49
Table 4.14. Result of ANCOVA
50
ix
LIST OF FIGURES
Figure 1.1. Sample of Students’ Alternative Solution
3
Figure 1.2. Sample of Students’ Opinion
3
Figure 2.1. Design of Problem Solving Steps by Polya
8
Figure 2.2. Harvest of Chili
19
Figure 2.3. Mode
20
Figure 2.4. Example of Group Table
23
Figure 2.5. Histogram with Normal Curve
24
Figure 3.1. The Chart of Procedural Research
33
Figure 4.1. Regression Model of Experiment Class I
46
Figure 4.2. Regression Model of Experiment Class II
46
Figure 4.3. Regression Model of Experiment Classes
53
xi
LIST OF APPENDICES
Appendix 1.
Score List of Mid – Odd Semester Examination of Math
59
Grade XI SMA Negeri 2 Balige Y.A. 2014/2015
Appendix 2.
Lesson Plan (Experiment Class I)
60
Appendix 3.
Lesson Plan (Experiment Class II)
79
Appendix 4.
Student Activity Sheet (SAS) 1
94
Appendix 5.
Student Activity Sheet (SAS) 2
97
Appendix 6.
Blue Print of Pre – Test
106
Appendix 7.
Instrument Test of Problem Solving Ability: Pre – Test
107
Appendix 8.
Answer Sheet of Pre – Test
109
Appendix 9.
Alternative Solution of Pre – Test
113
Appendix 10.
Blue Print of Post – Test
118
Appendix 11.
Instrument Test of Problem Solving Ability: Post – Test
119
Appendix 12.
Answer Sheet of Post – Test
121
Appendix 13.
Alternative Solution of Post – Test
126
Appendix 14.
Validator Evaluation Scale
131
Appendix 15.
Validator Evaluation Sheet
132
Appendix 16.
Observation Sheet of Learning Process Experiment Class I
135
Appendix 17.
Observation Sheet of Learning Process Experiment Class II
139
Appendix 18.
Procedure to Execute Validity Test in SPSS
143
Appendix 19A. Result of Validity Test: Pre – Test
145
Appendix 19B. Result of Validity Test: Post – Test
147
Appendix 20.
149
Procedure to Execute Reliability Test in SPSS
Appendix 21A. Result of Reliability Test: Pre – Test
151
Appendix 21B. Result of Reliability Test: Post – Test
152
Appendix 22.
153
Result of Initial Students’ Problem Solving Ability
(Data of Pre – Test)
Appendix 23.
Result of Final Students’ Problem Solving Ability
157
(Data of Post – Test)
Appendix 24.
Procedure to Execute Normality Test in SPSS
161
xii
Appendix 25.
Result of Normality Test
163
Appendix 26.
Procedure to Execute Homogeneity Test in SPSS
164
Appendix 27.
Result of Homogeneity Test
166
Appendix 28.
Procedure to Execute Hypothesis Test in SPSS
168
Appendix 29.
Result of Hypothesis Test
175
Appendix 30.
Students’ Pattern Way to Answer
182
Appendix 31.
Table of t – Distribution
192
Appendix 32.
Table of F Distribution
193
Appendix 33.
Documentation of Research
194
Appendix 34.
Letter
199
1
CHAPTER I
INTRODUCTION
1.1.
Background of Research
Mathematics is one of the most important subjects that provide several
vital skills to the learners. Most of jobs needs ability and understanding of
mathematics. That is why mathematics is basic science that have a main action in
developmental of science and technology. Technology nowadays made and
dominated by mastery mathematics early. It also the reason why mathematics is
one of subject matters that should be given to students since in kindergaten up to
higher education.
According to NCTM (in Walle, 2007: 1), in this changing world, those
who understand and can do mathematics will have significantly enhanced
opportunites and options for shaping their futures. Mathematical competence
opens doors to productive futures. A lack of mathematical competence keeps
those doors closed. NCTM challenges the assumption that mathematics is only for
the select few. On the contrary, everyone needs to understand mathematics. All
students should have the opportunity and the support necessary to learn significant
mathematics with depth and understanding.
The purpose of learning mathematics was explained well on the
Regulation of National Education Minister (Permendiknas) number 81A of 2013
about Concept and Learning Strategies. It stated that the learning process is
needed using some principles which contained of: (1) students center,
(2) developing the creativity of students, (3) creating fun and challenging
condition, (4) contains the value of ethics, aesthetics, logic and kinesthetic,
(5) provides a diverse learning experience through the implementation of various
strategies and joyful learning methods, contextual, effective, efficient, and
meaningful.
Two international researches conducted to demonstrate the ability of
mastery in mathematics learning showed that Indonesian student capability still in
2
the low level. Based on data of Education for All (EFA) Global Monitoring
Report that released by United Nations Educational, Scientific, and Cultural
Organization (UNESCO) in 2012, the Education Development Index (EDI)
position of Indonesia was in level 64th from 120 countries in the world.
Meanwhile the survey of Program for International Study Assesment (PISA) in
2012 showed that from 65 survey countries for mathematics, reading and science
skills, Indonesia was in 64thlevel with the mean score of mathematics skill was
375 while the average of OECD (Organization for Economic Co-Operation and
Development) was 494.
EFA 2012 provides the real condition of education in countries respected
to six goals of education which was arranged in global meeting in Senegal, 2000.
While PISA 2012 provides the most comprehensive picture of the mathematics
skills developed in schools that has ever been available, looking not just at what
students know in the different domains of mathematics, but also at what they can
do with what they know. Both of
the survey suggest that improvement of
mathematics education in schools need to be considered by various parties,
including government, education observers and by teachers as the perpetrator of
education itself.
Although the government has released Curriculum of 2013 and expected
the teachers to develop their teaching way and do their function in the classroom
as a facilitator of learning, the real fact that researcher found when doing
Integrated Field Experience Program (PPLT) in SMA Negeri 2 Balige was
different. The learning process mostly happened in conventional way. Teachers
directly provide mathematical formulas to the students and the students only see,
memorize, and apply the formulas. Then mathematics was presented as very bored
lesson and most of them sleeping in the class. As a result, the math test scores of
students are still low.
The statement above is evident based on the data which researcher found
when doing Integrated Field Experience Program (PPLT), all of students in grade
XI of Science (XI MIA1 – XI MIA6) passed the mid – odd semester examination
with the average value 75.04. While the minimum standar criteria (KKM) was 75.
4
Interview was also conducted with mathematics’ teacher in SMA Negeri 2
Balige, Mrs. Hanita Friska Simangunsong, S.Si. Researcher found that most of the
teachers have received continuous training about various learning methods. But,
in the implementation, most of them still using conventional way because of
limitation of time and the content of material which sould be given to students.
Actually there is a lot of learning methods that have been used in learning
process of mathematics. Whether Curriculum of KTSP or Curriculum 2013 which
is used in the school, problem – based learning is one of suitable model. PBL
makes students work with classmates to solve complex and authentic problems
that help develop content knowledge as well as problem – solving, reasoning,
communication, and self-assessment skills. These problems also help to maintain
student interest in course material because students realize that they are learning
the skills needed to be successful in the field (White, 2011: 1).
In another side, Larson and Timothy (2013: 204) said that cooperative
learning involves quickly formed groups that may work together for a few
minutes or a whole class period. Slavin (2005: 8) also stated that in cooperative
learning method, students work together in four member teams to master material
initially presented by the teacher. Numbered Heads Together (NHT) is one of the
cooperative learning model that requires student works together and cooperatives
so that the problem can be solved well. Spancer Kagen as the developer of this
learning model designed the learning such that the students can check and look at
their insight about the content of material.
Millis (2010: 11) recognize the close kinship between cooperative learning
and problem – based learning – both on highly structured group work. PBL and
cooperative learning are ideally suited for each other. PBL fits into the
cooperative learning framework like a hand in a glove. Well, the characteristics of
Problem – Based Learning (PBL) and Numbered Heads Together (NHT) refers to
student centered learning which improve the conceptual understanding in
mathematics. Furthermore, Tokuhama – Espinosa (2014: 204) explain process of
finding solution at the group level considering PBL as a type of cooperative
learning, and vice versa. It means PBL and cooperative learning is similar.
5
Based on those descriptions above, researcher comes with any doubts
whether both of learning models in this case are: PBL and cooperative learning
type of NHT, have different effect toward students’ learning outcomes,
particularly to the students’ problem solving ability. Therefore, the researcher has
interested to do research entitled “The Difference of Effect of Problem – Based
Learning and Numbered Heads Together toward Students’ Problem Solving
Ability on The Topic of Statistics in Grade XI SMA Negeri 2 Balige.”
1.2.
Problem Identification
Based on the background above can be identified the problem as follows:
1. The conventional way is often used in SMA Negeri 2 Balige while respected to
Curriculum of KTSP or Curriculum 2013, student centered learning has not
been applied fully in the teaching and learning process of mathematics.
2. The result of mid – odd semester examination in SMA Negeri 2 Balige shows
45.95% students of grade XI got score under the KKM score.
3. Most of students in SMA Negeri 2 Balige had low problem solving ability of
mathematics and ignoring steps which sould be passed when solving problems.
1.3.
Limitation of Problem
Based on the limitation scope of research location, research time and the
research variable causes this study is limited in the scope as follows:
1. Students’ problem solving ability on the topic of Statistics for Class XI in SMA
Negeri 2 Balige for Even Semester 2014/2015.
2. The learning activities for this study are given by using problem – based
learning and numbered heads together.
1.4.
Problem of Research
Based on the background above, the problems are formulated as:
“Is students’ problem solving ability of mathematics which taught by using
Problem – Based Learning (PBL) higher than students’ problem solving ability of
mathematics which taught by using Numbered Heads Together (NHT)?”.
6
1.5.
Objectives of Research
The objectives of the research are as follows:
1. To know whether there are differences of effect of students’ problem solving
ability of mathematics that taught by problem – based learning and numbered
heads together on the topic of statistics in grade XI SMA Negeri 2 Balige.
2. To determine whether students’ problem solving ability of mathematics which
taught by Problem – Based Learning (PBL) is higher than taught by Numbered
Heads Together (NHT) in grade XI SMA Negeri 2 Balige.
1.6.
Benefits of Research
This research is expected will give the benefits as follows:
1. For students, helping them to increase their problem solving ability of math.
2. For teachers, opening their insight about developing the learning process well.
3. For school, increasing the quality of school caused by the increasing of
students’ learning outcomes and teacher activities.
4. For researcher or advanced researcher, improving the insight, ability,
information and experience in increasing the competency as teacher student.
1.7.
Operational Definition
The operational definition of this study is described as follows:
1. Problem – based learning model is learning model which use the real problem as a
keyword of the learning process such that they can learn actively by think,
communicate, find and process data, and finally make conclusion of essential
concept of the subject.
2. Numbered heads together is learning model which holds each student accountable
for learning the material by having students work together in a group, giving the
numbers and put their heads together to develop a complete answer to the given
question.
3. Problem solving ability is the ability which gained by students to understand and
complete the problems which are faced by using their skills and abilities to
determine the concept they should use to be applied in solving the problem.
55
CHAPTER V
CONCLUSION AND SUGGESTION
5.1.
Conclusion
Based on the result and discussion of research in the previous chapter, can
be concluded that:
1. Students’ problem solving ability of mathematics which taught by problem–
based learning is higher than numbered heads together on the topic of statistics
in grade XI SMA Negeri 2 Balige. The effect size of PBL is 0.5738 or 57.38%
meanwhile the effect size of NHT is 0.4810 or 48.10%.
2. There is a difference of effect of students’ problem solving ability of
mathematics that using problem–based learning and numbered heads together
on the topic of statistics in grade XI SMA Negeri 2 Balige. It is 11.18%.
3. Problem – based learning model has more significant effect to improve the
students’ common pattern to answer mathematics question which related to
problem solving ability rather than numbered heads together.
5.2.
Suggestion
Based on the conclusion and relevant study of this research, there are some
suggestions as follows:
1. For mathematics teacher, to implement problem – based learning model in the
learning activity such that students’ problem solving ability can be increased
significantly.
2. For students, to cooperate with teachers by following the steps of learning
process and don’t ignore the steps of problem solving ability.
3. For next researcher, to observe another students’ ability of mathematics which
can be affected by problem based learning model and another choices of
learning model.
4. Because in this research the learning models are implemented to the topic of
statistics, it is suggested to try another topic of mathematics and relate it to
others factor which may influent students’ learning outcomes.
56
REFERENCES
Ahsanullah, Mohammad., (2008), Applied Statistics Research Progress, Nova
Science Publishers, New York.
Arends, Richard., (2010), Teaching for Student Learning: Becoming an
Accomplished Teacher, Routledge, New York.
Arikunto, Suharsimi., (2010), Prosedur Penelitian, Rineka Cipta, Jakarta.
Asmin., (2012), Pengukuran dan Penilaian Hasil Belajar dengan Analisis Klasik
dan Modern, LARISPA, Medan.
Asra, Abuzar and Rudiansyah., (2013), Statistika Terapan: Untuk Pembuat
Kebijakan dan Pembuat Keputusan, IN MEDIA, Jakarta.
Belvel, Patricia Sequeira., (2010), Rethinking Classroom Management: Strategies
for Prevention, Intervention, and Problem Solving Second Edition, Corwin
A SAGE Company, California.
Brown, Tom and John Eagles., (2011), Teaching Psychiatry to Undergraduates,
The Royal College of Psychiatrists, UK.
EFA Global Monitoring Report., (2014), Teaching and Learning: Achieving
Quality for All, UNESCO, France.
FMIPA, (2013), Pedoman Penulisan Proposal dan Skripsi, FMIPA Unimed,
Medan.
Foote, Chandra J., Paul Vermette, and Chaterine Battaglia., (2001), Constructivist
Strategies: Meeting Standards and Engaging Adolescent Minds, Eye On
Education Inc, New York.
Horn, Robert A., (2011), Understanding Ancova, Northern Arizona University,
http://oak.ucc.nau.edu/rh232/courses/eps625/handouts/ancova/understandi
ng%20ancova.pdf
Joyce, Bruce and Marsha Weill., (1973), Models of Teaching: School Review,
Journal of Education JSTOR, 82: 147 – 154. http://www.jstor.org/
stable/1084132
57
Keenan, Thomas and Subhadra Evans., (2009), An Introduction to Child
Development Second Edition, SAGE Publications Ltd, London.
Kennedy, Leonard M., (2008) Guiding Children’s Learning of Mathematics
Eleventh Edition, Thomson Wadsworth, USA.
Kothari, C. R., (2008), Research Methodology: Methods and Techniques Second
Revised Edition, New Age International Ltd Publishers, New Delhi.
Larson, Bruce E. and Timothy A. Keiper., (2013), Instructional Strategies for
Middle and High School Second Edition, Routledge, UK.
Luzet, Gael., (2013), Collaborative Learning Pocketbook, Teachers’ Pocketbooks
Ltd, UK.
Maher, Angela., (2004), Learning Outcomes in Higher Education: Implications
for Curriculum Design and Student Learning, Journal of Hospitality,
Leisure, Sport, and Tourism Education 3: 46 – 54.
Marshall, Stewart., (2006), Encyclopedia of Developing Regional Communities
with Information and Communication Technology, Idea Group Reference,
USA.
Mayer, Dan., (2004), Essential: Evidence – Based Medicine, Cambridge
University Press, UK.
Millis, Barbara J., (2010), Cooperative Learning in Higher Education: Across The
Disciplines, Across The Academy, Stylus Publishing LLC, Virginia.
Murdoch, Kath and Jeni Wilson., (2007), How to Succeed with Cooperative
Learning, Curriculum Corporation, Australia.
Netter, J. And Wasserman W., (1974), Applied Linear Statistical Models, Illinoi:
Richard D. Erwin, Inc
Noor, Juliansyah., (2011), Metodologi Penelitian: Skripsi, Tesis, Disertasi, dan
Karya Ilmiah, Kencana Prenada Media Group, Jakarta.
PISA., (2014), PISA 2012 Results in Focus: What 15-years-olds Know and What
They Can Do with What They Know, OECD, USA.
Rani, T. Swarupa., (2008), Teaching of Mathematics, S.B.Nangia APH Publishing
Corporation, New Delhi.
58
Richardson, Judy S., et all., (2009), Reading to Learn in The Content Areas
Seventh Edition, Wadsworth Cengage Learning, USA.
Rideout, Elizabeth., (2001), Transforming Nursing Education Through Problem –
Based Learning, Jones and Bartlett Publishers Inc, UK.
Ryan, Norma and Jennifer Murphy., (2009), The Bologna Process and Learning
Outcomes, NAIRTL Bologna Series: Qualification Recognition and Staff
Mobility, Proceedings of Symposia, 123 – 142.
Sari, Fitria Maya., (2011), Perbedaan Hasil dan Aktivitas Belajar Siswa yang
Diajar dengan Menggunakan Model Pembelajaran Kooperatif Tipe NHT
dan Tipe TGT pada Pokok Bahasan Logaritma di Kelas X MAN 3 Medan
T.P. 2010/2011, Skripsi, FMIPA – Unimed, Medan.
Savin-Baden, Maggie and Wilkie Kay., (2006), Problem – Based Learning
Online, Open University Press, New York.
Seel, Norbert M., (2012), Encyclopedia of The Sciences of Learning, Springer
Sciences, New York.
Shaffer, David. (2009), Social and Personality Development Sixth Edition,
Wadsworth, USA.
Sharp, Conni., (2000), Increasing Mathematical Problem Solving Performance
Through Relaxation Training, Mathematics Education Research Journal,
http://link.springer.com/article/10.1007/BF03217074
Sianipar, Hot Tiarma., (2013), The Influence of Problem Based Learning Method
toward Students Sequence and Series Problem Solving Ability in The
Twelfth Grade of SMA Negeri 2 Balige 2012/2013, Skripsi, FMIPA –
Unimed, Medan.
Silver, Edward A., (2013), Teaching and Learning Mathematical Problem
Solving: Multiple Research Perspectives, Lawrence Erlbaum Associates
Publishers, New Jersey.
Slavin, Robert., (2005), Cooperative Learning: Theory, Research and Practice,
Allymand Bacon, London.
Spiegel, Murray R., (2000), Schaum’s Easy Outline: Theory and Problems of
Statistics, McGraw – Hill Companies, USA.
59
Sudjana., (2009), Metoda Statistika, Tarsito, Bandung.
Sudjana, Nana., (2005), Penilaian Hasil Proses Belajar Mengajar, Rosda, Jakarta.
Sujarweni, V. Wiratna., (2014), SPSS untuk Penelitian, Pustaka Baru Press,
Yogyakarta.
Tan, Ai-Girl., (2012), Creativity, Tallent, and Excellent, Springer Sciences,
Singapore.
Tokuhama – Espinosa, Tracey., (2014), Making Classrooms Better: 50 Practical
Applications of Mind, Brain, and Education Science, W.W. Norton and
Company, New York.
Trianto.,
(2009),
Model-model
Pembelajaran
Inovatif
Berorientasi
Konstruktivistik, Prestasi Pustaka Publisher, Jakarta.
Trisna, Benny N., (2005), Pembelajaran Matematika Realistik di Kelas VIII
(Topik Persamaan Garis Lurus), Thesis, Post–graduates, Unimed, Medan.
Uden, Lorna., (2006), Technology and Problem – Based Learning, Information
Science Publishing, USA.
Udvari – Solner, Alice., (2008), Joyful Learning: Active and Collaborative
Learning in Inclusive Classrooms, Corwin Press, USA.
Walle, John A Van de., (2007), Elementary and Middle School Mathematics Sixth
Edition, Pearson Prentice Hall, USA.
White, Hal., (2011), Speaking of Teaching: Problem – Based Learning, Journal of
Winter 11: 1 – 7.
Williams, P. John., (2012), Technology Education for Teachers, Sense Publishers,
The Netherlands.
Whitmeyer, Steven J., et all., (2009), Field Geology Education: Historical
Perspectives and Modern Approaches, Geological Society of America
(GSA), USA.
Wonnacot, Thomas H., (1977), Introductory Statistics Third Edition, John Willey
and Son, Canada.
Xiang, Yun Du and Mads Jakob Kirkebaek., (2012), Exploring Task –Based PBL
in Chinese Teaching and Learning, Cambridge Scholars Publishing, UK.