IMPROVEMENT THE CONCEPTUAL UNDERSTANDING ABILITY OF STUDENT THROUGH PROBLEM BASED
LEARNING (PBL) MODEL ON TOPIC POLYHEDRAL (CUBE AND RECTANGULAR PRISM) IN
MTS. AL-WASHLIYAH TEMBUNG ACADEMIC YEAR 2012/2013
By:
QORIYANTI Reg. Number: 409312022 Mathematics Education Bilingual
THESIS
Submitted to Fulfill the Requirement for Getting the Sarjana Pendidikan Degree
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
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PREFACE
Give thank’s to Allah Subhanallahu Wata’ala give me more spirit to finish my thesis. The title of thesis is Improvement the Conceptual Understanding Ability of Student through Problem Based Learning (PBL) Model on Topic Polyhedral (Cube and Rectangular Prism) in Mts. Al-Washliyah Tembung Academic Year 2012/2013. This thesis was arranged to satisfy the law to get the sarjana pendidikan of Mathematics and Science Faculty in State University of
Medan.
For this chance I want to say thank you for the rector of State University of Medan, Mr. Prof. Dr. Ibnu hajar, M.S and his staff, Mr. Prof. Drs. Motlan, M.Sc., Ph.D for dean of FMIPA UNIMED and his college assistant of Dean I, II, II in UNIMED, Mr. Prof. Dr. Mukhtar, M.Pd as Leader of Mathematics Department, Mr. Drs. Syafari, M.Pd as Leader of Mathematics Education program study program and then Mr. Drs. Yasifati Hia, M.Si as secretary of Mathematics Department.
Big Thank’s for Mr. Prof. Dr. Mukhtar, M.Pd as supervisor who guide to prepare this thesis. And the thanks a lot for Mr. Dr. E. Elvis Napitupulu, M.S., Drs. Syafari, M.Pd, and Dr. KMS. M. Amin Fauzi, M.Pd who’s the persons responsible for my thesis from the beginning until end. Thanks to Mr. Prof. Drs. Dian Armanto, M.Pd., M.A., M.Sc., Ph.D as my academic supervisor and then thank you so much for all my lecturer and staff in FMIPA.
Special thanks to my lovely father Mr. Sharial, S.H., and my lovely mother Maimunah Lubis for giving motivation, pray and all I need in finishing this thesis. And then thanks for love to my brother and sister kak Hafsah Purwasih S.Hut., Reza Nachsybandi, Liliana and Chairiyah Aldha.
And then, thank you so much for helping Mr. M. Zubir Nasution S.Ag as headmaster of Mts Al-Washliyah Tembung, Mr. M. Yunus, S.PdI, Mr. Wahyudi,
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Also thanks to big family in Bilingual Mathematics Education 2009 for sadness and happiness in class. Iwan ‘kochu’, Enny, Rini, Rizki ‘Kiki’, Kak Evi, Iin, Siska, Epril, Joy, Bibah, Widi, Dilla, Dini, Siti, Kak Noya, Retni. Special thank’s to murabbi and murabbiyah in Unimed. My close friend Rida, Rika, Ismi, Husna, Arlina, Ari, Aan, Titin, Arisqa, Yessi, Sri Rukmana, Kak Rina, Tuti, Erna, Ayu and others. All big brothers and sisters are in UKMI Ar-Rahman Unimed and Ummat Unimed. Thank to special friend there, Aisyah Fitri Tambunan, Nurmalita and you, AQ.
The writer should give a big effort to prepare this thesis, and the writer know that this thesis have so m any weakness. So that, the writer needs some suggestions to make it this be better. And big wishes, it can be improve our knowledge.
Medan, Juli 2013 Writer
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IMPROVEMENT THE CONCEPTUAL UNDERSTANDING ABILITY OF STUDENT THROUGH PROBLEM BASED LEARNING (PBL) MODEL
ON TOPIC POLYHEDRAL (CUBE AND RECTANGULAR PRISM) IN MTS. AL-WASHLIYAH TEMBUNG ACADEMIC YEAR 2012/2013
Qoriyanti (409312022)
ABSTRACT
The aim of this research is to improve the conceptual understanding ability of student through problem based learning model was done in Mts. Al-Washliyah Tembung. The type of this research is Classroom Action Research. The research has done respect to the student of VIII-1 in number 40 students.
Instrument used to collect the data is conceptual understanding mathematics test and observation sheet. These researches consist of two cycles and the end of every cycle given conceptual understanding mathematics test. Before given, at the first test must be validity. Validity test done is contents validity where expert as validator.
The result in this research has shown that learning by problem based learning model can improve the conceptual understanding mathematics. From initial test that given to student said that student has good ability in prerequisite material. It indicate from the average value of initial test of 40 student is 82.50. This case shown from the result before treatment, in first conceptual understanding test I of 40 students there are 18 students (45%) gained the score 70 with the average class is 48.25.
After given treatment so the students do the conceptual understanding test II of 40 students there are 35 students (87.5%) gained the score 70 with the average class is 82.25. The observation sheet get average score 2.735 in cycle 1, its in good category. In cycle 2 get average score 3.365, it indicate teacher is very good category in implement problem based learning in classroom.
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1.2. Problem Identification 5
1.3. Problem Limitation 6
1.4. Problem Formulation 6
1.5. Research Objectives 6
1.6. Research Benefits 7
CHAPTER II LITERATURE REVIEW 8
2.1. Theoretical Framework 8
2.1.1. Definition of Learning 8
2.1.2. Learning Mathematics 8
2.1.3. Concepts in Mathematics 9 2.1.4. Understanding Mathematical Concept 11 2.1.5. Conceptual Understanding in NCTM Principle 13
2.1.6. Learning Strategy 15
2.1.7. Problem Based Learning (PBL) Model 16 2.1.7.1. Definition of Problem Based Learning Model 16 2.1.7.2. Basic Concept and Characteristic PBL 16 2.1.7.3. The Nature of Problem in PBL 17
2.1.7.4. Phase of PBL 18
2.1.7.5. Strength and Weakness PBL 21 2.1.8. Polyhedral (Cube and Rectangular prism) 23
2.1.8.1. Cube 23
2.1.8.1.1. The Surface Area of Cube 23 2.1.8.1.2. Volume of Cube 24
2.1.8.2. Rectangular prism 25
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2.1.8.2.2. Volume of Rectangular prism 26
2.2. Conceptual Framework 27
2.3. Action Hypothesis 28
CHAPTER III RESEARCH METHODOLOGY 29
3.1. Location and Time of Research 29 3.2. Subject and Object of Research 29
3.2.1. Subject of Research 29
3.2.2. Object of Research 29
3.3. Type of Research 29
3.4. Operational Definition 29
3.5. Procedure and Research Design 30
3.5.1.Cycle I 30
3.5.1.1. Problem I 30
3.5.1.2. Action Plan of Phase I (Alternative Solution I) 30 3.5.1.3. Implementation Measures of Phase I 31
3.5.1.4. Observation I 32
3.5.1.5. Reflection Phase I 33
3.5.2. Cycle II 33
3.6. Data Collection Instruments 34
3.6.1. Test 34
3.6.2. Observation 35
3.6.2.1. Observation Sheet 35
3.7. Data Analysis 35
3.7.1 Data Reduction 35
3.7.2 Exposure Data 36
3.7.3 Deduce 36
3.8. Data Analysis Techniques 36
CHAPTER IV RESEACRH RESULTS AND DISCUSSIONS 39 4.1. Description of Research Results 39
4.1.1. Research Cycle I 39
4.1.1.1. Problems Cycle I 39
4.1.1.2. Action Planning Cycle I 42 4.1.1.3. Implementation of Measures I 43 4.1.1.4. Data Analysis Cycle I 43 4.1.1.5. Reflection Cycle I 55
4.1.2. Research Cycle II 56
4.1.2.1. Problems Cycle II 56
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4.1.2.3. Implementation Measures Cycle II 57 4.1.2.4. Data Analysis Cycle II 57 4.1.2.5. Reflection Cycle II 67 4.2. Discussion of Research Results 69
CHAPTER V CONCLUSIONS AND SUGGESTIONS 72
5.1.Conclusion 72
5.2. Suggestion 73
Reference 74
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LIST OF TABLE
Page Table 3.1. Interpretation of Level of Student Understanding…….………..
Table 3.2. Criteria Tables of Average Rating Observation……….. 37 38
Table 4.1. Percentage of Restate Concept in Initial Test……….. 39
Table 4.2. Percentage of Present Concept in Initial Test ………. 40
Table 4.3. Percentage of Use Concept……….. 40
Table 4.4. Percentage of Conceptual Understanding in Initial Test………. 41
Table 4.5. Percentage of Restate Concept in CU Test I………... 43
Table 4.6. Percentage of Classify Object t in CU Test I……….. 44
Table 4.7. Percentage of Present Concept in CU Test I………... 44
Table 4.8. Percentage of Use Concept in CU Test I………. 45
Table 4.9. Percentage of Conceptual Understanding Test I………. 46
Table 4.10. Result of Observation in Learning Process Cycle I……… 52
Table 4.11. Result of Observation in Student Learning Process Cycle I…... 54
Table 4.12. Percentage of Restate Concept in CU Test II……….. 58
Table 4.13. Percentage of Present Concept in CU Test II……….. 58
Table 4.14. Percentage of Use Concept in CU Test II………... 59
Table 4.15. Percentage of Conceptual Understanding Test II……… 60
Table 4.16. Result of Observation in Learning Process Cycle II…………... 65
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LIST OF FIGURE
Page
Figure 2.1. Cube...………..…….. 23
Figure 2.2. Cube Net………. ……….………. 23
Figure 2.3. How to Find the Area of Cube ………. 24
Figure 2.4. Cube Filled Small Cube….……….... 24
Figure 2.5. How to Find Volume of Cube ………... 24
Figure 2.6. Rectangular prism.……….. 25
Figure 2.7. Rectangular prism Net ………... 25
Figure 2.8. How to find Area of Rectangular prism ………. 26
Figure 2.9. Rectangular prism Filled Small Cube ……… 27
Figure 2.10. How to Find Volume of Rectangular prism ……….. 27
Figure 3.1. Chronology of Events Classroom Action Research... 34
Figure 3.2. Taxonomy of Action Research Data Collection Tech 37 Figure 4.1. Result of Conceptual Understanding Test I………… 45
Figure 4.2. Result of Conceptual Understanding Test II……… 59
Figure 4.3. Improvement of Conceptual Understanding………... 68
Figure 4.4. Improvement Average Score of Each Indicator……. 69
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LIST OF APPENDIX
Page
Appendix 1 Lesson Plan I Cycle I ………. 77
Appendix 2 Lesson Plan II Cycle I ……… 82
Appendix 3 Student Worksheet I ………... 87
Appendix 4 Student Worksheet II ………... 91
Appendix 5 Alternative Solution of Student Worksheet I……….. 95
Appendix 6 Alternative Solution of Student Worksheet II…………...…. 98
Appendix 7 Blueprint of Initial Capability Test………. 101
Appendix 8 Initial Capability Test…………...……….. 102
Appendix 9 Alternative Solution of Initial Capability Test …………... 103
Appendix 10 Blueprint of Conceptual Understanding Test I………... 105
Appendix 11 Conceptual Understanding Test I……… 106
Appendix 12 Alternative Solution of Conceptual Understanding Test I….. 107
Appendix 13 Guidelines for Scoring of Conceptual Understanding Test I. 112 Appendix 14 Observation Sheet Implementation of Learning Cycle I…… 113
Appendix 15 Observation Sheet of Student Activity Cycle I………... 115
Appendix 16 Validation Sheet of Initial Capability Test………. 116
Appendix 17 Validation Sheet Of Conceptual Understanding Test I... 119
Appendix 18 Lesson Plan I Cycle II………. 122
Appendix 19 Lesson Plan II Cycle II………... 127
Appendix 20 Student Worksheet III………... 132
Appendix 21 Student Worksheet IV………... 135
Appendix 22 Alternative Solution of Student Worksheet III..………. 139
Appendix 23 Alternative Solution of Student Worksheet IV…………...… 141
Appendix 24 Blueprint of Conceptual Understanding Test II...…………... 144
Appendix 25 Conceptual Understanding Test II……….. 145
Appendix 26 Alternative Solution of Conceptual Understanding Test II.... 146
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CHAPTER I INTRODUCTION
1.1. Background
Education is a process to help people to develop themselves and to promote human dignity, so that people are able to cope with any changes that occur, heading in a better direction. As stated by John Dewey (in Sagala, 2009:3) that education is the process of forming the basis of the fundamental skills, both
related to intellectual, or emotional or feeling that power is directed to human nature and to one another. Learning is a process, in which students not only absorb the information submitted by teachers, but involves a variety of activities and actions that must be done to achieve better learning outcomes. Sagala (2009: 61) states learning is two-way communication, taught by the teachers as educators, while the study carried out by learners or students.
Mathematics is one of the basic sciences and scientific thinking means much needed students to develop the ability to think logically, systematically, communicatory ideas and solves problems in everyday life. Slameto (2003:72) states that mathematics is way of thinking towards a clear, precise, meticulous, which underlies all science and philosophy and even the success of a country depends on the progress of mathematics. Mathematics is a subject that always exists in the level of education, from the kindergarten, elementary, junior high, senior high school, and even through college.
In each level of education, one of the areas of study that have never missed to learn is math. Mathematics is a field of study that supports the development of science and technology. Therefore mathematics teaching compulsory and occupy an important role in education. It aims to equip the students to have the ability to think, logical, analytical, systematic, critical and creative. Nevertheless, there are still many students who have a negative view of
According to Cornelius (in Abdurrahman, 2009:253):
"Everyone has to learn math, because math is a means of clear and logical thinking to solve problems in everyday life, a means to know the patterns and generalizations relationship, means to develop activities and tools to increase awareness of cultural development".
However, the high demand for mastering mathematics is not directly proportional to the results of students' mathematics learning. Things that support the poor quality of students' mathematics learning researchers found when conducting interview of teacher of mathematics on February 2nd, 2012 in the Mts. Al-Washliyah Tembung. After discussion from mathematics teacher indicate that the teaching and learning process, teachers only rarely engage students and emphasize the students to memorize formulas only. There are many students who still cannot understanding math concepts well and have not been able to apply the formula of any given problem.
Many factors lead to low math learning outcomes of students, both internal factors and external factors, but the teacher is an important factor in the overall education system. Not a few teachers who still adhered to the paradigm of transfer of knowledge in learning mathematics. This paradigm assumes that the object or target student learning, so the learning process more efforts made by teachers, ranging from the search for, collect, solve, and communicate information is intended for learners acquire knowledge.
Ansari (2008:3) reveals that things like this will lead to two consequences. First, students are less active and less learning patterns establish the concept of making it less inviting critical attitude. Second, if students are given
about the different exercises, they are confused because they do not know where to begin their work."
That is why understanding the concept becomes important and the demands in the mathematics curriculum. As purpose of learning mathematics in
KTSP 2006 litbang.kemdikbud.go.id/.../Buku%20Standar%20Isi%20SMP(1).pdf) is:
1. Understanding mathematical concepts explains the relationship between concepts and applies concepts or algorithms, flexibly, accurately, efficiently, and appropriately, in solving the problem.
2. Using the pattern and nature of reasoning, mathematical manipulation in making generalizations, compiles evidence, or explains mathematical ideas and statements.
3. Solve problems that include the ability to understand the problem, devise a mathematical model, solve the model and interpret the obtained solution.
4. Communicate ideas with symbols, tables, diagrams, or other media to clarify the situation or problem.
5. Having respect for the usefulness of mathematics in life, the curious, attention, and interest in studying mathematics, as well as a tenacious attitude and confidence in problem solving.
Understanding required in math goals are relational understanding, i.e. understanding of the concepts contained in a schema or structure of complex knowledge that could be used on a broader problem-solving and complex.
studied the concept of B that is based on the concept of A, one first needs to understand the concept of A. Without understanding the concept of A, that person may not understand the concept of B. This means that learning mathematics should be gradual and sequential, and based on the past learning experience.
Based on that it would be a matter of understanding concepts in mathematics should be placed on a priority. With the understanding of a concept, the wide variety of questions and problems will be easily solved. With the trends emerging situation as above, then in this case the need for the application of learning approaches that are expected to enhance students' understanding of mathematical concepts.
Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which is it useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those
ideas to what they already know.
Life is synonymous with problem. Applied learning model must be able to train and develop the ability to solve an authentic problem-oriented than the actual lives of the students, to stimulate higher level thinking skills that can enhance students' conceptual understanding. So, learning strategy should be able to change students' learning styles of students studying passive to active with a cozy atmosphere, conducive, open and democratic society that makes learning math more meaningful, reasonable, challenging, fun and suitable for students. Appropriate learning model is to make math more meaningful, reasonable, challenging, fun and suitable for students. One alternative is to modify the learning process by using learning model is Problem Based Learning (PBL).
and then memorize the subject matter, but through PBL students active thinking, communicating, searching and processing the data, and finally conclude. Second, learning activities geared to resolve the problem. PBL puts the problem as keyword of the learning process. That is, no matter there can be no learning. Third, problem solving is done by using a scientific approach to thinking.
Then, to apply Problem Based Learning to support of the student mathematical conceptual understanding the teacher has to choose the material of subject properly. To implement PBL, teachers need to select learning materials
that have problems that can be solved. These problems can take from a textbook or from other sources such as from events occurring in the environment, from the events in the family or social events. According to Sanjaya (2011: 215) Problem Based Learning have five strategies, as follow as.
• When the teacher wants the students to remember not just the subject matter, but to master and understand it fully.
• If the teacher intends to develop students' skills of rational thinking, the ability to analyze the situation, to apply their knowledge in new situations, recognize the difference between fact and opinion, as well as develop the ability to make an objective judgment.
• When the teacher wants the students' ability to solve problems and create intellectual challenge students.
• If the teacher supports the student to take more responsibility in their learning.
• If teachers want the students to understand the relationship between what is learned and the reality of its life (the relationship between theory and reality).
In Hung (2011) said that working in groups, students identify what they already know, what they need to know, and how and where to access new information that may lead to resolution of the problem. The teacher must build students' confidence to take on the problem, and encourage the students, while also stretching their understanding. In Loague (2001) states PBL assessments should be authentic, which is to say that they should be structured so that students
can display their understanding of problems and their solutions in
Based on the above, the researcher is interested to carry out research entitled: “Improvement the Conceptual Understanding Ability of Student
through Problem Based Learning (PBL) Model on Topic Polyhedral (Cube and Rectangular prism) in Mts. Al-Washliyah Tembung A.Y. 2012/2013”.
1.2. Problem Identification
1. Student still low to understand of mathematics concepts.
2. The involvement of the students in the learning process is very less
3. The application of learning strategies used by teacher is less varied with the subject matter.
4. There are still applied paradigm transfers of knowledge in mathematics learning
1.3. Problem Limitation
Because problem of research are breadth and lack of expertise and time, then the researcher need to limit problem. The limit problem studied is improvement the conceptual understanding ability of student through Problem Based Learning (PBL) model on topic polyhedral (cube and rectangular prism) in Mts. Al-Washliyah Tembung.
1.4. Problem Formulation
1. Is Problem Based Learning (PBL) model can improve the conceptual understanding ability of mathematics on topic polyhedral (cube and rectangular prism)?
2. How is the implementation of mathematics learning process on topic polyhedral (cube and rectangular prism) by applying Problem Based Learning (PBL) model in Mts. Al Washliyah Tembung?
1.5. Research Objectives
1. To know whether the implementation of Problem Based Learning (PBL) model can improve the conceptual understanding ability of mathematics on topic polyhedral (cube and rectangular prism) in Mts. Al Washliyah Tembung.
2. To know the implementation of Problem Based Learning (PBL) model in mathematics learning process on topic polyhedral (cube and rectangular
prism) in Mts. Al Washliyah Tembung.
3. To know the process of Problem Based Learning (PBL) model in improving the conceptual understanding on topic (cube and rectangular prism) in Mts. Al-Washliyah Tembung.
1.6. Research Benefits
1. For teachers, for consideration and input so that students can choose one of the alternative learning models are appropriate, effective and efficient in engaging students in the learning process.
2. For students, the learning model can enhance students' understanding of mathematical concepts in solving mathematical problems.
3. For researchers, additional insight and experience as prospective teachers in the future and information and reference material for other researchers associated with this research.
CHAPTER V
CONCLUSION AND SUGGESTION
5.1. Conclusion
The conclusions to be drawn from this study are:
1. Learning by applying problem based learning (PBL) model on topic cube and rectangular prism can improve conceptual understanding of mathematics.
2. The implementation of mathematics learning process in cycle I that researcher do is good enough in organizing and managing learning and teaching activities. Researcher should give more motivation and apperception to students interested in learning and in guiding the study groups when they perform the task. This shows that researcher has not optimized herself as a facilitator for learning by observing the average rating obtained is 2.735. Whereas in cycle II, it appears that the implementation of mathematics learning process is very good, it can be
seen in observing average rating is 3.365. There is improvement from cycle I to cycle II. Researcher can motivate students interested in learning and in guiding the study group at the time they perform a task. This shows
that researchers already optimize herself as facilitator for learning.
5.2. Suggestion
As for suggestion that can be drawn from these findings, namely:
1. Students are advised to be brave in delivering the opinion or ideas, can exploit the full potential of the learning mathematics.
2. Mathematics teacher suggested involving students in the teaching-learning process and use problem based learning model as an alternative learning model.
3. Recommended to the headmaster of school and teachers can coordinate to implement problem based learning model as an alternative learning can enhance students' understanding of mathematical concepts.
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