ENHANCING STUDENT’S MATHEMATICAL PROBLEM SOLVING ABILITY THROUGH CONTEXTUAL TEACHNG
AND LEARNING (CTL) APPROACH
By:
Natalita Siahaan ID 4113312011
Mathematics Education Study Program
THESIS
Submittedto Fulfill the Requirement for Getting the Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
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PREFACE
Give thankfulness to God that gives the God’s mercy and spirit so that writer can finish this thesis. The title of this thesis is “Enhancing Student’s Mathematical Problem Solving Ability through Contextual Teaching and Learning (CTL) approach”. This thesis was arranged to satisfy the requirement to obtain the Degree of Sarjana Pendidikan from Faculty of Mathematics and Natural Science in State University of Medan.
In the completion of this thesis, the writer received support from various parts, therefore it was appropriate writer big thanks to Mrs. Dra. Ida Karnasih, M.Sc,Ed, Ph.D as my thesis supervisor who has provided guidance, direction, and advice to the perfection of this thesis. Thanks are also due to Dr. Edy Surya, M.Si, Dr.W. Rajagukguk, M.Pd and Prof. Dr. Sahat Saragih,M.Pd. as my examiners who have provided input and suggestion from the planning to the completion of the preparation of the research of this thesis. Thanks are also extended to Mr. Mulyono. M.Si as academic supervisor and then thank you so much for all my lecturers in FMIPA.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Pd, as rector of State University of Medan and employee staff in office of university head, Prof. Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural Sciences and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy Surya, M. Si. as Chief of Mathematics Department, Zul Amry, M. Si. as Chief of Mathematics Education Study Program, Drs. Yasifati Hia, M. Si as Secretary of Mathematics Education, and all of employee staff who have helped the author.
Thanks to Mr. Sinarta as principle of SMP N 1 Parbuluan who has given permission to writer do research, Mr. Torang Siburian S.Pd as mathematics teacher
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Especially the writer would like to express my gratitude to my dear father Marihot Siahaan S.Pd (+) and my dear mother Mrs. Denny Silitonga that always be my hero and continues to provide motivation and prayers for the success of the writer completed this thesis. Special big thanks to my beloved brother Frans R.W Siahaan, Amd.Far my sister F. Nelsa Siahaan S.Farm,Apt, Natalia Siahaan S.Pd and Anna M. Siahaan, my brother Andreas Siahaan that always give me support even moril or material and all my family for all pray, motivation, and support until the end of writer’s study.
Writer wants to say thanks to my special friends Anggi Zefri S.Si for your support and helping me. My best friends in Bilingual Mathematics Class 2011 especially for Dewi, Yerni, Anna, Aprita, Kristiani, Lestari, Samantha, Rony, Vera, Nelly, Widy, Joe, Debby also Time for the valuable support and motivation. Thanks also for permanen inna (Nova, Erni, Dita), and my adventure friends (Aam, Marihot, Marcel, Renata, Marixon, Royman, Fitri, Nanda). Big thanks for church server GPdI Kasih Bapa Medan, my familiy in IKBKM and PELMAP UNIMED and also for my friends in PPL SMA N 1 Sidikalang for motivation and your support that have give me the best experience.
The writer should give a big effort to prepare this thesis, and the writer know that this thesis have so many weakness. So that, the writer needs some suggestions to make it be better. And big wishes, it can be improve our knowledge.
Medan, Juni 2015 Author,
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ENHANCING STUDENT’S MATHEMATICAL PROBLEM SOLVING ABILITY THROUGH CONTEXTUAL TEACHING
AND LEARNING (CTL) APPROACH
Natalita Siahaan (4113312011)
ABSTRACT
The purpose of this research was to know how enhancing student’s mathematical problem solving ability by implementing Contextual Teaching and Learning (CTL) approach was conducted in SMP Negeri 1 Parbuluan. The type of this research was Classroom Action Research.
The subjects of this research were students of VIII-A class in academic year 2014/2015 that have total of 34 students. The object of this research was student’s problem solving ability and Contextual Teaching and Learning (CTL) approach.
This research was implemented by 2 cycle. Every cycle was consist 2 meetings. Test of student’s mathematical problem solving ability was done in the end of cycle. Instrument used to collect the data in this research is test and observation sheet.
The results of this study shown that: (1) The results of student’s problem solving ability test in the first cycle known the students can understanding the problem is 100% (very good), can devising a plan is 76.46% (enough), can carrying out the plan is 58.87% (less), can looking back is 48.83% (bad), the classical mastery was 38.23%. (2) The results of student’s problem solving ability test in the second cycle known the students can understanding the problem is 100% (very good), can devising a plan is 86.3% (good), can carrying out the plan is 85.2% (good), can looking back is 82.4% (good), the classical mastery was 85.30%. (3) The process of student’s answer were reached good category. (4) Learning by using Contextual Teaching and Learning (CTL) approach can make student’s activity and teacher’s activity were good categorized in learning.
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CONTENTS
Page
Sheet of Agreement i
Biography ii
Abstract iii
Preface iv
Contents vi
List of Figure ix
List of Table xi
List of Appendix xiii
CHAPTER I INTRODUCTION 1
1.1. Background 1
1.2. Problem Identification 8
1.3. Problem Limitation 8
1.4. Problem Formulation 9
1.5. Research Objectives 9
1.6. Research Benefits 10
CHAPTER II LITERATURE REVIEW 11
2.1. Theoretical Framework 11
2.1.1. Mathematical Problem 11
2.1.2. Mathematical Problem Solving 12
2.1.3. Mathematical Problem Solving Ability 16
2.2. Learning Approach 16
2.3. Contextual Teaching and Learning Approach 17
2.3.1. Main Components in CTL Approach 19
2.3.2. The Strength and Weaknesses of CTL Approach 22
2.4. Learning Teory 23
2.5. Content Materials 24
2.6. Virtual Manipulative 29
2.7. Relevant Research 30
2.8. Conceptual Framework 31
2.9. Action Hypothesis 34
CHAPTER III RESEARCH METHODOLOGY 35
3.1. Type of Research 35
3.2. Location and Time of Research 35
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3.3.1. Subject of Research 36
3.3.2. Object of Research 36
3.4. Operational Defenition 36
3.5. Design of Research 37
3.6. Procedure 38
Cycle I 38
a. Problem I 38
b. Action Plan I 38
c. Implementation I 39
d. Observation I 40
e. Data Analysis I 40
f. Reflection I 40
Cycle II 41
a. Problem I 41
b. Action Plan II 41
c. Implementation II 41
d. Observation II 42
e. Data Analysis II 43
f. Reflection II 43
3.7. Instrument of Research 46
3.8. Data Analysis Technique 52
3.9. Indicators of Succeed 57
CHAPTER IV RESEARCH RESULTS AND DISCUSSIONS 58
4.1 The Result of Research 58
4.1.1 Research Cycle I 60
A. Problem 60
B. Action Plan 61
C. Implementation 65
D. Data Analysis I 65
E. Observation 75
F. Reflection I 78
4.1.2 Research Cycle II 81
A. Problem 81
B. Action Plan 82
C. Implementation 82
D. Data Analysis II 84
E. Observation 93
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4.2 Discussion of Result 97
4.3 Discussion of Observation 101
4.4 The Restrictiveness of Research 103
CHAPTER V CONCLUSION AND SUGGESTION 105
4.5 Conclusion 105
5.2 Recommendation 105
REFERENCE 107
APPENDIX 110
DOCUMENTATION OF RESEARCH 213
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LIST OF TABLE
Page Table 1.1 The Table of Preliminary Diagnostic Test
Table 3.1 Description of every cycle in this research
Table 3.2 Lattice of Initial Test of Problem Solving Ability Table 3.3 Lattice of Problem Solving Test I
Table 3.4 Lattice of Test Problem Solving II Table 3.5 Table of Guidelines Scoring of Test
6 43 47 47 48 48 Table 3.6 Scoring Criteria of the Process of Students’ Answer
Table 3.7 Interval Score Problem Solving Ability
50 53 Table 3.8 Criteria of the Process of Students’ Answer
Table 3.9 Interpretation of Observation
Table 4.1 Description of Student’s Problem Solving Ability Level Based on the Initial Diagnostic Test Results
Table 4.2 Level of Students Ability Understanding the Problem In the Diagnostic Tests Problem Solving Test I Table 4.3 Level of Student’s ability of Devising a plan Problem
Solving In Diagnostic Tests I
55 56 59 65 66 Table 4.4 Level of Student’s ability of Carrying out the plan in
Problem Solving Diagnostic Tests I
Table 4.5 Level of Student’s ability of Looking Back in Problem Solving Diagnostic Tests I
Table 4.6 The Classical Learning Mastery Cycle I
Table 4.7 Results of Analysis The Process of Student’s Answer Cycle I
Table 4.8 Result of Teacher’s Activity Observation Cycle I Table 4.9 Result of Students’ Activities Observation Cycle I
67 68 69 70 76 77 Table 4.10 Level of Capability Students Understanding the Problem
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Table 4.11 Level of Student’s ability of Devising a plan Problem Solving In Diagnostic Tests II
Table 4.12 Level of Student’s ability of Carrying out the plan in Problem Solving Diagnostic Tests II
Table 4.13 Level of Student’s ability of Looking Back in Problem Solving Diagnostic Tests II
Table 4.14 The Students Learning Completeness at Problem Solving Ability Test II
Table 4.15 Results of Analysis The Process of Student’s Answer
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86
87
88
90 Table 4.16 The Result of Teacher’s Activity Observation Cycle II
Table 4.17 The Result of Student’s Activities Observation Cycle II Table 4.18 The Comparison Between Cycle I and Cycle II
Table 4.19 Diagnostic Test Results Problem solving Ability I Table 4.20 Diagnostic Test Results Problem Solving II
Table 4.21 Teacher’s Activity Observation Cycle I and Cycle II
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LIST OF FIGURE
Page Figure 1.1 Sample of Student’s Sheet Answer Number 1
Figure 1.2 Sample of Student’s Sheet Answer Number 2
Figure 2.1 The Example of Object Shaped Cube and Rectangular Prism 4 5 24
Figure 2.2 Cube 24
Figure 2.3 The Nets of Cube 25
Figure 2.4 Cube Unit 26
Figure 2.5 Rectangular Prism 26
Figure 2.6 Nets of Rectangular Prism 28
Figure 2.7 Rectangular Prism Unit 29
Figure 3.1 Classroom Action Research Process of Kemmis Model Figure 4.1 Teacher Activity Guiding Students Meeting 1 Cycle I
37 61 Figure 4.2 Process of Students’ Answer in SAW 1 Question 1
Figure 4.3 Student Presenting Results of Discussion Cycle I Figure 4.4 Activity of Students in Meeting 2 Cycle I
Figure 4.5 Process of Students’ Answer in SAW 2 Question 2
62 62 63 64 Figure 4.6 Percentage of Classical Learning Mastery Cycle I 69 Figure 4.7 The Process of Student’s Answer in Problem 1 71 Figure 4.8 The process of student’s answer in Problem 2 71 Figure 4.9 The process of student’s answer in Problem 3
Figure 4.10 The process of student’s answer in Problem 4
72 72 Figure 4.11 The Student’s Activity Worksheet Cycle I Meeting I
Figure 4.12 The Process of Student’s Answer Cycle I MeetingI Figure 4.13 The student’s activity worksheet cycle I Meeting II Figure 4.14 Process of Students’ Answer in SAW
73 74 74 75
Figure 4.15 Students Activity in cycle II 82
Figure 4.16 Students Presenting the Results of Discussion Cycle II Figure 4.17 Process of Student’s Answer SAS 4 Question 4
83 84 Figure 4.18 Percentage of Classical Learning Completeness Cycle II
Figure 4.19 The Process of Student’s Answer in Problem 1
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Figure 4.20 The Process of Student’s Answer in Problem 2 Figure 4.21 The Process of Student’s Answer in Problem 3
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LIST OF APPENDIX
Page
Appendix 1 Lesson Plan I 110
Appendix 2 Lesson Plan II 116
Appendix 3 Lesson Plan III 124
Appendix 4 Lesson Plan IV 129
Appendix 5 Student Worksheet I 135
Appendix 6 Student Worksheet II 140
Appendix 7 Student Worksheet III 145
Appendix 8 Student Worksheet IV 150
Appendix 9 Validation Sheet of Problem Solving Ability Initial Test 154 Appendix 10 Validation Sheet of Problem Solving Ability Test I 157 Appendix 11 Validation Sheet of Problem Solving Ability Test II 160 Appendix 12 Initial Test of Problem Solving Ability 163
Appendix 13 Problem Solving Ability Test I 165
Appendix 14 Problem Solving Ability Test II 168
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Appendix 29 List of Value Classical Learning Mastery Test II 198 Appendix 30 List of Value The Process of Student’s Answer Test II 199 Appendix 31 Observation Sheet of Teacher’s Activity Cycle I 201 Appendix 32 Observation Sheet of Student’s Activity Cycle I 203 Appendix 33 Observation Sheet of Teacher’s Activity Cycle II 205 Appendix 34 Observation Sheet of Student’s Activity Cycle II 207 Appendix 35 The Observation Result Of Teacher’s Activity Cycle I 209 Appendix 36 The Observation Result Of Student’s Activity Cycle I 210
Appendix 37 The Observation Result Of Teacher’s Activity Cycle II 211 Appendix 38 The Observation Result Of Student’s Activity Cycle II 212
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CHAPTER I
INTRODUCTION
1.1Background
Education is very important for humans, because education is an investment in human resources in the long term. Education is also a vehicle to improve and develop the quality of human resources. Education is not only seen as an attempt to provide information and skill formation, but expanded to include efforts to realize the desires, needs and abilities of individuals to achieve personal and social lifestyle satisfactory. Education not merely as a means of preparation for the next life, but for the life of children today who are experiencing growth towards maturity level. Efforts to improve the quality of education has been done by the government including curriculum renewal, improvement of educational facilities, the use of methods of teaching, doing research, and improving the quality and quantity of learning outcomes. Teaching and learning process is a core activity in an effort to improve the quality of education. The good and bad of a learning process is one of the dominant factors in determining the quality of education.
Mathematics is one of principle fundamental human activity– a way of making sense of the world. Children have natural curiosity and interest in
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mathematics is one subject that difficult to learn. There no attractive that teacher can do to make they feel comfort when learning mathematics. Teacher just explaining formula to the other formula. There is no something concept understanding. Student also difficult to share what they know to teacher directly. When student is asked to make their answer about some problem in front of the class, student still look afraid and doubt about the information that their know. Then observation of learning process was also held to know what is actually happen in the learning process when learning mathematics is ongoing.
Based on observations made, teachers still use direct instruction that by teacher centered method. Students as an object which receive all the material that teacher’s said. Association of learning with of daily life has been done but the students still feel bored and less active in learning. It was seen when the teacher asks students still mostly silent and did not want to participate. Students just fall silent and wait for the teacher to explain in detail about the given question. It is happen because the teacher is only charging a little explanation was followed by various formulas. The formula was a mainstay of teachers in answering all questions. Not understanding the concept of precedence so that students are not interested in active learning. Mathematics problem that teacher given to students is also a factor of student disinterest towards solving the problem. Problems associated with of daily life will encourage students to work on the problems. An interest will arise when we give a real problem. With the real problem, automatically the students will feel that math is important in of daily life.
Interview with teachers was also conducted to find out the any problems faced by students in learning mathematics. Based on an interview with teacher, students have a lot of problems especially in problem-solving abilities. They are hard working on the form of word problems.The method that teacher use still
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Then one of the difficulties mathematics factor in the school is solving the problem.
Solving a problem is a basic human activity. Reality shows that most of life is faced with problems. To face the problem, individuals are required to have the ability to solve problems. Education is one of the effort to develop problem-solving skills for students is through the study of mathematics (Hudojo, 2005). Learning mathematics trains students to think logically and skillfully solve problems in everyday life. Learning mathematics is also work to develop the
ability to communicate ideas and language through a mathematical model in the form of sentences and mathematical equations, diagrams, graphs, and tables.
Problem solving is an important component of mathematics education because of its practical role to the individual and society. By learning problem solving in Mathematics, students should acquire the ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that will serve them well outside the mathematics classroom. (NCTM, 2000).
Problem solving is a very important ability in mathematics as in problem solving, the ability of solving concepts students should master. During the learning process, students can follow the lessons well but by the time students are working on or given question, the students have not been able to think for themselves how to solve a given problem. Although it has been given direction by the teacher, students are still not able to apply the concepts they have learned in solving the problem. So as to improve students' independence in thinking towards which seem to be more difficult to achieve high. From the description above, it can be concluded that the mathematical skills of students in solving problems still have to be increased again.
According to Polya (in Hudojo, 2005) problem solving ability can be
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found when we give a problem to the students. That is one factor that causes low ability student’s mathematical problem solving. This is supported by the observation has been made. The diagnostic test also given to students when the observation is doing. The test is word problem form to know the initial mathematical problem solving ability of students. Giving diagnostic tests carried out on the third day that is dated 21 January. There are 34 students answer the diagnostic test in class VIII-A.
The first problem tested to students are as follows: “A wire with length size 1.5 m
will be used to create two models of rectangular prism frame with a size of 7 cm x
3 cm x 5 cm. What is the remaining length of the wire?”
This following figure 1.1 is one sample of student’s answer sheet:
Figure 1.1 Sample of Student’s Answer Sheet Number 1
Based on Figure 1.1 students could not understand what the plan to solve the problem. Students only wrote what is known and what is asked. In the process, students also could not find the exact answer to figure out remains wire after used to make rectangular prism frame.
On the third problem also contained the following errors in understanding the problem and using the formula were not correctly. “Classrooms VIII will be renovated. The room is square with an area of 9 m2. The floor will be covered with a square-shaped ceramic with a size of 30 cm x 30 cm for the ceramic pieces.
Price 1 ceramic box is 100.000, -. And 1 box contains 5 pieces of ceramic tile.
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Figure 1.2 Sample of Student’s Sheet Answer Number 2
Based on figure 1.2 students did not understand the problems mentioned
above, she/he didn’t write what the question is. Student also had not been able to write a formula that can solve these problems so as a result students could not do the calculations right and got the right answer.
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Tabel 1.1 The Table of Preliminary Diagnostic Test
Aspect Categorized Not Categorized
1. Understanding the
problem 82.35% 17.65%
2. Devising a plan
52.94% 47.06 %
3. Carrying out the
plan 20.59% 79.41%
4. Looking back
8.82% 91.18%
This is shown with still low entirely student answer sheet. In this aspect of the students are not able to substitute the results obtained into equation and cannot prove the results obtained.
The other problem that found in this research is also seen from the student’s answers. From the results of the initial diagnostic test is given, the student written answers are less varied. The process of students' answers also not fulfilled the criteria a good completion process. There are still many students who solve the problem but did not get the correct results. There are incorrect estimates when answering the questions.
Low ability students' problems can be improved in various ways. One of which is to improve the delivery of a material. Delivering material by linking
learning materials for everyday life is how. So that students feel that mathematics is a very important science is applied in everyday life. Other factors that have
contributed very important in determining the success of learning mathematics is learning model selection. The use of appropriate learning models will overcome saturation students receive lessons in mathematics so that not only focused on teachers.
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learning (student-oriented). As a manager of student learning, teachers are obliged to improve attention, and truly efforts, in providing school mathematics learning, so the lesson material can be understood by students. Students are required to be better, to use the ability of thinking to be skilled in problem solving in dailylife related to mathematics.
Problem solving ability will be improved if the teacher can use the innovative and contextual learning approach. Through contextual approach, the concept of thinking and understanding of the students will be more open to
mathematics, not only focused on a specific topic being studied, so will lead to a positive attitude towards mathematics itself. The need for capabilities and skills to be able to solve the problem the development of thinking that the study would be more meaningful if the students directly experience for themselves what is learned, this research is done by using the learning which is considered to be relevant to be applied in mathematics learning is contextual learning approach.
Because we expect students actively in learning, the learning students must construct their own knowledge, that knowledge can be gained from their own experience or from others by social interaction. Contextual Teacthing and Learning (CTL) Approach is one of a learning approach that can construct their knowledge by giving a contextual situation. CTL approach is the concept of learning that help teachers find connections between the material being taught by real-world situations and may encourage making the relationship between knowledge and its application in everyday life, so that students will understand the concept to solve a problem. Sanjaya (2008) mentions that the CTL is a learning approach that emphasizes the involvement of students in the full process to be able to locate the material studied and relate it to real life situations that encourage students to be able to apply them in everyday life.
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1.2Problem Identifications
Based on the description in the background, some of the problems that can be identified are as follows:
a. Students still consider that mathematics is the difficult subject.
b. Students is still doubt and not self confidence to answer question to teacher directly.
c. The most activities in learning activities are still dominated by teacher
d. Students still give a low participation on solve a mathematical problem. e. Teacher explains the material is only targeting on learning outcomes rather
than on learning process.
f. Students’ mathematical problem solving ability are generally low.
g. The process of student’s answer in solving the problem are still less varied, yet follow a good completion
1.3Problem Limitation
Based on several problems identified, the problems is focused on:
Low ability student’s mathematical problem solving in learning and
teaching.
Lack of teacher’s knowledge of teahers in implementing the learning model thus inhibiting the ability of student’s mathematical problem solving in learning and teaching.
Students still give a low participation in learning process.
The process of student’s answer in solving the problem are still less
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1.4Problem Formulations
Based on problem limitation, the problem in this study is formulated as follows:
a. How does the enhancement of student’s mathematical problem solving ability by implementing Contextual Teaching and Learning (CTL) approach in learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
b. How does the learning management conducted teacher by implementing Contextual Teaching and Learning (CTL) approach in learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
c. How does the learning activity of students by implementing Contextual Teaching and Learning (CTL) approach in learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
d. How the process of student’s answer in solving the problem by implementing Contextual Teaching and Learning (CTL) approach in learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
1.5Research Objectives
In accordance with the problem formulation above, the objectives of this research are:
a. To know the enhancement of student’s mathematical problem solving
ability by implementing Contextual Teaching and Learning (CTL) approach in learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015. b. To know the learning management conducted teacher by implementing
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teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
c. To know the learning activities of students by implementing Contextual Teaching and Learning (CTL) approach in learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
d. To know the process of student’s answer in solving the problem by implementing Contextual Teaching and Learning (CTL) approach in
learning and teaching Cube and Rectangular Prism topic in Class VIII of SMP Negeri 1 Parbuluan in Academic Year 2014/2015.
1.6Research Benefits
After completion of this study are expected to be beneficial to all parties, including the:
1. For students. Giving students' learning experiences related to problem solving collaboratively through cooperative learning model Numbered Head Together.
2. For the teacher. The results of this study can be considered and input in developing a mathematical model of learning efforts to improve students' problem-solving abilities.
3. For schools. The results of the study can be used as input in making policy alternative implementation of innovative learning model in school.
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CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusion
Based on the results of research and discussion can be concluded that:
1. The level of student’s problem solving ability through implementation of Contextual Teaching and Learning (CTL) Approach on the subject of Cube and Rectangular Prism in class VIII SMPN 1 Parbuluan 2014/2015
academic year is in good categories.
2. Learning management conducted by teacher through implementation of Contextual Teaching and Learning (CTL) Approach on the subject of Cube and Rectangular Prism in class VIII SMPN 1 Parbuluan 2014/2015 academic year is in good categories.
3. Learning activities by students through implementation of Contextual Teaching and Learning (CTL) Approach on the subject of Cube and Rectangular Prism in class VIII SMPN 1 Parbuluan 2014/2015 academic year is in good categories.
4. The process of student’s answer in solving a problem through implementation of Contextual Teaching and Learning (CTL) Approach on the subject of Cube and Rectangular Prism in class VIII SMPN 1 Parbuluan 2014/2015 academic year is in good categories.
5.2 Recommendations
The recommendations in this research are as follows:
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student’s problem solving ability. For this case, the Contextual Teaching and Learning (CTL) approach can be one of learning alternative to improve student’s problem solving ability.
2. For the taking principle, properly can use the learning by implementation of Contextual Teaching and Learning (CTL) as one of learning approach which is need to be followed-up by training intensively about the learning approach.
3. For the further researcher is recommended to continue the research in more complex objectives. Because the students’ success in learning cannot be measured only with the written test.
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REFERENCES
Abdurrahman, M, (2009), Pendidikan Bagi Anak Berkesulitan Belajar, Rineka Cipta, Jakarta
Arrends, R., (2009), Learning to Teach Eight Eddition, McGraw-Hill, New York.
Baker, D,P., (1998), The Effects of Implementing The Cooperative Learning Structure, Numbered Head Together, In Chemistry Class At A Rural, Low Performing High School, B,S, Louisiana State University,p:1-3.
Bennet, A., Burton L, J., and Nelson T, L., (2010), Mathematics for Elementary Teachers: A Conceptual Approach, McGraw-Hill Higher Education, California
Departemen Pendidikan Nasional, (2003), Pendekatan Kontekstual, Jakarta, Departemen Pendidikan Nasional.
Hamalik, O., (2002), Proses Belajar Mengajar, Jakarta, PT Bumi Aksara.
Hudojo, H., (2005), Pengembangan Kurikulum dan Pembelajaran Matematika, Universitas Negeri Malang, Malang.
Hutajulu, D.W (2013), Upaya Meningkatkan Aktivitas dan Kemampuan Pemecahan Masalah Matematika Siswa dengan Model Pembelajaran Problem Based Learning pada Materi Pokok Aritmatika Sosial di Kelas VII SMP Negeri 1 Patumbak T.A 2012/2013, Skripsi, FMIPA UNIMED, Medan.
Kantowski, M. G., (1980), Some thoughts on teaching for problem solving. In S. Krulik & R.Reys (Eds.), Problem solving in school mathematics: 1980 yearbook (pp. 195-203), Reston, VA, National Council of Teachers of Mathematics.
Klein, Stephen, B., (1991), Learning Principle and Applications, McGraw-Hill Book Co, Singapore.
Komalasari, K., (2010), Pembelajaran Kontekstual;Konsep dan Aplikasi, Bandung, Refika Aditama
Kunandar, (2009), Guru Profesional, Rajawali Pers, Jakarta.
108
Misu, L., (2014), Mathematical Problem Solving of Student by Approach Behavior Learning Theory, International Journal of Education and Research, p,182 : 1-2.
Muijs, D and Reynolds, D., (2008), Effective Teaching, Pustaka Pelajar, Yogyakarta.
Muslich, M., (2011), Pendidikan Berkarakter, Bumi aksara, Jakarta
National Council of Teacher of Mathematics (NCTM), (2000), Principles and Standards for School Mathematics, NCTM, Reston, Virginia.
National Council of Teacher of Mathematics (NCTM), (2010), Principles and Standards for School Mathematics, NCTM, Reston, Virginia.
Prautami, R., (2014), Implementation of React Strategy to Improve Student Activities in Grade VIII Of SMP Negeri 1 Binjai, Skripsi, FMIPA UNIMED, Medan Rohani, A, (2004), Pengelolaan Pengajaran, Rineka Cipta, Jakarta.
Polya, G., (1981), Mathematical Discovery on Understanding, Learning and Teaching Problem Solving, John Wiley & Sons, New York.
Posamentier, A. S and Krulik, S., (1998), Problem-Solving Strategies For Efficient and Elegant Solutions, Corwin Press, USA.
Ruseffendi, E,T, (2006), Pengantar Kepala Membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA, Bandung, Tarsito
Rusman., (2011). Model-Model Pembelajaran Mengembangkan Profesionalisme Guru, Jakarta, PT RAJAGRAFINDO PERSADA.
Schoenfeld, A., (1983), Problem solving in the mathematics curriculum: A report, recommendations, and an annotated bibliography, Washington, D,C, Mathematical Association of America.
Slameto., (2010), Belajar dan Faktor-Faktor yang Mempengaruhinya, Rineka Cipta, Jakarta.
109
Sinaga, B., (2008), Pengembangan Model Pembelajaran Matematika Berdasarkan Masalah Berbasis Budaya Batak (PBM-B3), Laporan Hasil Penelitian (Hibah Bersaing), Medan, UNIMED.
Sudjana., (2005), Metoda Statistika, Bandung, Tarsito.
Suherman, E.,Winataputra,. and Udin, S., (2001), Strategi Pembelajaran Matematika Kontemporer, UPI, Bandung.
Tao, T., (1991), Solving Mathematical Problems: A Personal Perspective, M.A. (Ken) Clements, Deakin University
Travers, M,W,R., (1977), Essentials of Learning, Macmillan Publishing Co,Inc, New York
Trianto., (2011), Mendesain Model Pembelajaran Inovatif-Progresif: Konsep, Landasan, dan Implementasinya Pada Kurukulum Tingkat Satuan Pendidikan (KTSP), Kencana, Jakarta
Wardhani, I,.Rohayati, K,. and Irianto B,. (2010), Pembelajaran Kemampuan Masalah Matematika di SMP, Yogyakarta, PPPPTK Matematika.
Wena, Made., (2011), Strategi Pembelajaran Inovatif Kontemporer, Bumi Aksara, Jakarta.
Widodo, R., (2009), “Pembelajaran dengan Pendekatan CTL” (online),
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BIOGRAPHY
Natalita Siahaan was born in Sigalingging on December, 28th 1992. Her
father’s name is Marihot Siahaan and her mother’s name is Denny Silitonga. She
is the fourth of her family. She was jointed in SDN 030294 Sigalingging on 1999 and graduated in 2005. In 2005, she continued the study to SMP N 1 Parbuluan and graduated in 2008. In 2008, she continued the study to SMA N 1 Sidikalang and graduated in 2011. After graduated from Senior High School, she continued
