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
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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.
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,
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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
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
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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
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. Procedure to Execute Reliability Test in SPSS 149 Appendix 21A. Result of Reliability Test: Pre – Test 151 Appendix 21B. Result of Reliability Test: Post – Test 152 Appendix 22. Result of Initial Students’ Problem Solving Ability 153 (Data of Pre – Test)
Appendix 23. Result of Final Students’ Problem Solving Ability 157 (Data of Post – Test)
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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
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.
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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.
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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.
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
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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.
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.
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