ENHANCING STUDENTS MATHEMATICAL PROBLEM SOLVING ABILITY THROUGH CONTEXTUAL TEACHING AND LEARNING (CTL) APPROACH.
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
MEDAN
2015
iv
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
and all teacher, staffs and also the students in grade VIII-A SMP N 1 Parbuluan
who have helped writer conducting the research.
v
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,
Natalita Siahaan
ID. 4113312011
iii
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.
From the results of this research can be concluded that the implementation
of Contextual Teaching and Learning (CTL) approach can improve student’s
problem solving ability. The suggestion that given for teachers is to be able to
implement Contextual Teaching and Learning (CTL) approach as an alternative in
the learning process that can improve problem soving ability.
vi
CONTENTS
Sheet of Agreement
Biography
Abstract
Preface
Contents
List of Figure
List of Table
List of Appendix
Page
i
ii
iii
iv
vi
ix
xi
xiii
CHAPTER I INTRODUCTION
1.1. Background
1.2. Problem Identification
1.3. Problem Limitation
1.4. Problem Formulation
1.5. Research Objectives
1.6. Research Benefits
1
1
8
8
9
9
10
CHAPTER II LITERATURE REVIEW
2.1. Theoretical Framework
2.1.1. Mathematical Problem
2.1.2. Mathematical Problem Solving
2.1.3. Mathematical Problem Solving Ability
2.2. Learning Approach
2.3. Contextual Teaching and Learning Approach
2.3.1. Main Components in CTL Approach
2.3.2. The Strength and Weaknesses of CTL Approach
2.4. Learning Teory
2.5. Content Materials
2.6. Virtual Manipulative
2.7. Relevant Research
2.8. Conceptual Framework
2.9. Action Hypothesis
11
11
11
12
16
16
17
19
22
23
24
29
30
31
34
CHAPTER III RESEARCH METHODOLOGY
3.1. Type of Research
3.2. Location and Time of Research
3.3. Subject and Object of Research
35
35
35
36
vii
3.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.3.1. Subject of Research
3.3.2. Object of Research
Operational Defenition
Design of Research
Procedure
Cycle I
a. Problem I
b. Action Plan I
c. Implementation I
d. Observation I
e. Data Analysis I
f. Reflection I
Cycle II
a. Problem I
b. Action Plan II
c. Implementation II
d. Observation II
e. Data Analysis II
f. Reflection II
Instrument of Research
Data Analysis Technique
Indicators of Succeed
CHAPTER IV RESEARCH RESULTS AND DISCUSSIONS
4.1 The Result of Research
4.1.1 Research Cycle I
A. Problem
B. Action Plan
C. Implementation
D. Data Analysis I
E. Observation
F. Reflection I
4.1.2 Research Cycle II
A. Problem
B. Action Plan
C. Implementation
D. Data Analysis II
E. Observation
F. Reflection II
36
36
36
37
38
38
38
38
39
40
40
40
41
41
41
41
42
43
43
46
52
57
58
58
60
60
61
65
65
75
78
81
81
82
82
84
93
95
viii
4.2
4.3
4.4
Discussion of Result
Discussion of Observation
The Restrictiveness of Research
CHAPTER V
4.5
5.2
CONCLUSION AND SUGGESTION
Conclusion
Recommendation
97
101
103
105
105
105
REFERENCE
107
APPENDIX
110
DOCUMENTATION OF RESEARCH
213
xi
LIST OF TABLE
Page
Table 1.1
The Table of Preliminary Diagnostic Test
6
Table 3.1
Description of every cycle in this research
43
Table 3.2
Lattice of Initial Test of Problem Solving Ability
47
Table 3.3
Lattice of Problem Solving Test I
47
Table 3.4
Lattice of Test Problem Solving II
48
Table 3.5
Table of Guidelines Scoring of Test
48
Table 3.6
Scoring Criteria of the Process of Students’ Answer
50
Table 3.7
Interval Score Problem Solving Ability
53
Table 3.8
Criteria of the Process of Students’ Answer
55
Table 3.9
Interpretation of Observation
56
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
66
Level of Student’s ability of Carrying out the plan in
Problem Solving Diagnostic Tests I
Table 4.5
65
Level of Student’s ability of Devising a plan Problem
Solving In Diagnostic Tests I
Table 4.4
59
67
Level of Student’s ability of Looking Back in Problem
Solving Diagnostic Tests I
68
Table 4.6
The Classical Learning Mastery Cycle I
69
Table 4.7
Results of Analysis The Process of Student’s Answer
Cycle I
70
Table 4.8
Result of Teacher’s Activity Observation Cycle I
76
Table 4.9
Result of Students’ Activities Observation Cycle I
77
Table 4.10
Level of Capability Students Understanding the Problem
In the Diagnostic Tests Problem Solving Test II
85
xii
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
86
Level of Student’s ability of Looking Back in Problem
Solving Diagnostic Tests II
Table 4.14
86
87
The Students Learning Completeness at Problem
Solving Ability Test II
88
Table 4.15
Results of Analysis The Process of Student’s Answer
90
Table 4.16
The Result of Teacher’s Activity Observation Cycle II
93
Table 4.17
The Result of Student’s Activities Observation Cycle II
94
Table 4.18
The Comparison Between Cycle I and Cycle II
97
Table 4.19
Diagnostic Test Results Problem solving Ability I
97
Table 4.20
Diagnostic Test Results Problem Solving II
98
Table 4.21
Teacher’s Activity Observation Cycle I and Cycle II
101
Table 4.22
Student’s Activity Observation Cycle I and Cycle II
102
ix
LIST OF FIGURE
Page
Figure 1.1
Sample of Student’s Sheet Answer Number 1
4
Figure 1.2
Sample of Student’s Sheet Answer Number 2
5
Figure 2.1
The Example of Object Shaped Cube and Rectangular Prism
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
37
Figure 4.1
Teacher Activity Guiding Students Meeting 1 Cycle I
61
Figure 4.2
Process of Students’ Answer in SAW 1 Question 1
62
Figure 4.3
Student Presenting Results of Discussion Cycle I
62
Figure 4.4
Activity of Students in Meeting 2 Cycle I
63
Figure 4.5
Process of Students’ Answer in SAW 2 Question 2
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
72
Figure 4.10 The process of student’s answer in Problem 4
72
Figure 4.11 The Student’s Activity Worksheet Cycle I Meeting I
73
Figure 4.12 The Process of Student’s Answer Cycle I MeetingI
74
Figure 4.13 The student’s activity worksheet cycle I Meeting II
74
Figure 4.14 Process of Students’ Answer in SAW
75
Figure 4.15 Students Activity in cycle II
82
Figure 4.16
83
Students Presenting the Results of Discussion Cycle II
Figure 4.17 Process of Student’s Answer SAS 4 Question 4
84
Figure 4.18 Percentage of Classical Learning Completeness Cycle II
89
Figure 4.19 The Process of Student’s Answer in Problem 1
90
x
Figure 4.20 The Process of Student’s Answer in Problem 2
91
Figure 4.21 The Process of Student’s Answer in Problem 3
91
Figure 4.22 The Process of Student’s Answer in Problem 4
92
xiii
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
Appendix 15 Alternative Solution of Initial Test of Problem Solving Ability 171
Appendix 16 Alternative Solution of Problem Solving Ability Test I
175
Appendix 17 Alternative Solution of Problem Solving Ability Test II
180
Appendix 18 The Result of Diagnostic Initial Test
184
Appendix 19 List of Value for Understanding the Problem Test I
186
Appendix 20 List of Value for Devising a Plan Test I
187
Appendix 21 List of Value for Carrying Out the Plan Test I
188
Appendix 22 List of Value for Looking Back Test I
189
Appendix 23 List of Value Classical Learning Mastery Test I
190
Appendix 24 List of Value The Process of Student’s Answer Test I
191
Appendix 25 List of Value for Understanding the Problem Test II
193
Appendix 26 List of Value for Devising a Plan Test II
194
Appendix 27 List of Value for Carrying Out the Plan Test II
196
Appendix 28 List of Value for Looking Back Test II
197
xiv
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
Appendix 39 Research Documentation
213
1
CHAPTER I
INTRODUCTION
1.1 Background
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
mathematics then come to school with an understanding of mathematical concepts
and problem solving strategies that they have discovered through explorations of
the world around them. Many problems that found in of mathematics learning.
One of which is the dislike of students in learning mathematics because
mathematics is a difficult subject. Mathematics is generally considered as the
most difficult subject. Mathematics is the dangerous subject for student. Just some
students like mathematics. This statement is supported by the results of
observations that have been made as direct interviews with students. The
observation is made on 19 to 21 January 2015 in SMP Negeri 1 Parbuluan. There
are 5 students of class VII - A were interviewed. Some students say that
2
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
conventional method. Teacher just explain directly what the objective material in
the used book. Teacher is not surely that student can build their knowledge
themself. Student is not active in learning process is does not matter because the
learning outcomes is more important than learning process on their targeting.
3
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 problemsolving 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
observed by 4 indicators, namely (1) understanding the problem by writing what
is known and asked; (2) devising a plan to write a formula that can find the
solution of the problem; (3) Carrying out the plan by doing a calculation; (4)
looking back, checking each step and whether the results are correct or not, is still
relatively low and needs improvement. Steps to solve a problems are still rarely
4
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.
What is the price that must be spent to renovate just the floor.”
5
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.
From the diagnostic test of problem solving ability, many students still
cannot understanding the problem, make the question into mathematics model and
formulate the problem. For the first indicators, namely understanding the problem,
82.35% of students have been understood the problem and 17.65% of students
have not been understood the problem. For the second indicators, deving a plan,
there are 52.94 % of student have been devised a plan and 47.04% of student
have not been devised a plan. For the third indicators, namely carrying out the
plan, there are 20.59% of student have been carried the plan and 79.41% of
student have not been carried the plan. And the last indicators, looking back,
8.82% of student have been looked back 91.18% of student have not been looked
back. The graphic will be shown as below:
6
Tabel 1.1 The Table of Preliminary Diagnostic Test
Aspect
1. Understanding the
problem
2. Devising a plan
3. Carrying out the
plan
4. Looking back
Categorized
Not Categorized
82.35%
17.65%
52.94%
47.06 %
20.59%
79.41%
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.
Recognizing the reality on the ground that the problem solving ability of
students is still low, we need a model of learning that makes the students become
active. It required a learning approach that can support successful learning. The
new paradigm in education today, to create meaningful learning process, the
learning process that takes place in schools let students actively involved in
7
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.
Based on the above description that the problem solving ability of
mathematics learning objectives are very important, and one of the learning
approach that can improve student’s problem-solving ability is Contextual
Teaching and Learning (CTL) approach. Therefore CTL approach is choosen in
doing this research.
8
1.2 Problem 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
1.3 Problem 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
varied, yet follow a good completion
9
1.4 Problem 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.
1.5 Research 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
Contextual Teaching and Learning (CTL) approach in learning and
10
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.
1.6 Research 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.
4. For researchers. The results of this study can be used as input in the
development of application of learning models to the students for a variety
of subject matter.
105
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:
1.
For teacher and school practitioner is equitable to change the learning
custom which is dominated by teacher and starting to involve students
more actively in the learning process, as well as give more attention to
106
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.
4.
For the further researcher is recommended to improve continuously the
learning scenario by implementation of Contextual Teaching and Learning
(CTL) especially in modelling and reflection as the low participation of
students.
107
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ii
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
her study in State University of Medan as student in bilingual class for
Mathematics Education 2011.
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
MEDAN
2015
iv
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
and all teacher, staffs and also the students in grade VIII-A SMP N 1 Parbuluan
who have helped writer conducting the research.
v
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,
Natalita Siahaan
ID. 4113312011
iii
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.
From the results of this research can be concluded that the implementation
of Contextual Teaching and Learning (CTL) approach can improve student’s
problem solving ability. The suggestion that given for teachers is to be able to
implement Contextual Teaching and Learning (CTL) approach as an alternative in
the learning process that can improve problem soving ability.
vi
CONTENTS
Sheet of Agreement
Biography
Abstract
Preface
Contents
List of Figure
List of Table
List of Appendix
Page
i
ii
iii
iv
vi
ix
xi
xiii
CHAPTER I INTRODUCTION
1.1. Background
1.2. Problem Identification
1.3. Problem Limitation
1.4. Problem Formulation
1.5. Research Objectives
1.6. Research Benefits
1
1
8
8
9
9
10
CHAPTER II LITERATURE REVIEW
2.1. Theoretical Framework
2.1.1. Mathematical Problem
2.1.2. Mathematical Problem Solving
2.1.3. Mathematical Problem Solving Ability
2.2. Learning Approach
2.3. Contextual Teaching and Learning Approach
2.3.1. Main Components in CTL Approach
2.3.2. The Strength and Weaknesses of CTL Approach
2.4. Learning Teory
2.5. Content Materials
2.6. Virtual Manipulative
2.7. Relevant Research
2.8. Conceptual Framework
2.9. Action Hypothesis
11
11
11
12
16
16
17
19
22
23
24
29
30
31
34
CHAPTER III RESEARCH METHODOLOGY
3.1. Type of Research
3.2. Location and Time of Research
3.3. Subject and Object of Research
35
35
35
36
vii
3.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.3.1. Subject of Research
3.3.2. Object of Research
Operational Defenition
Design of Research
Procedure
Cycle I
a. Problem I
b. Action Plan I
c. Implementation I
d. Observation I
e. Data Analysis I
f. Reflection I
Cycle II
a. Problem I
b. Action Plan II
c. Implementation II
d. Observation II
e. Data Analysis II
f. Reflection II
Instrument of Research
Data Analysis Technique
Indicators of Succeed
CHAPTER IV RESEARCH RESULTS AND DISCUSSIONS
4.1 The Result of Research
4.1.1 Research Cycle I
A. Problem
B. Action Plan
C. Implementation
D. Data Analysis I
E. Observation
F. Reflection I
4.1.2 Research Cycle II
A. Problem
B. Action Plan
C. Implementation
D. Data Analysis II
E. Observation
F. Reflection II
36
36
36
37
38
38
38
38
39
40
40
40
41
41
41
41
42
43
43
46
52
57
58
58
60
60
61
65
65
75
78
81
81
82
82
84
93
95
viii
4.2
4.3
4.4
Discussion of Result
Discussion of Observation
The Restrictiveness of Research
CHAPTER V
4.5
5.2
CONCLUSION AND SUGGESTION
Conclusion
Recommendation
97
101
103
105
105
105
REFERENCE
107
APPENDIX
110
DOCUMENTATION OF RESEARCH
213
xi
LIST OF TABLE
Page
Table 1.1
The Table of Preliminary Diagnostic Test
6
Table 3.1
Description of every cycle in this research
43
Table 3.2
Lattice of Initial Test of Problem Solving Ability
47
Table 3.3
Lattice of Problem Solving Test I
47
Table 3.4
Lattice of Test Problem Solving II
48
Table 3.5
Table of Guidelines Scoring of Test
48
Table 3.6
Scoring Criteria of the Process of Students’ Answer
50
Table 3.7
Interval Score Problem Solving Ability
53
Table 3.8
Criteria of the Process of Students’ Answer
55
Table 3.9
Interpretation of Observation
56
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
66
Level of Student’s ability of Carrying out the plan in
Problem Solving Diagnostic Tests I
Table 4.5
65
Level of Student’s ability of Devising a plan Problem
Solving In Diagnostic Tests I
Table 4.4
59
67
Level of Student’s ability of Looking Back in Problem
Solving Diagnostic Tests I
68
Table 4.6
The Classical Learning Mastery Cycle I
69
Table 4.7
Results of Analysis The Process of Student’s Answer
Cycle I
70
Table 4.8
Result of Teacher’s Activity Observation Cycle I
76
Table 4.9
Result of Students’ Activities Observation Cycle I
77
Table 4.10
Level of Capability Students Understanding the Problem
In the Diagnostic Tests Problem Solving Test II
85
xii
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
86
Level of Student’s ability of Looking Back in Problem
Solving Diagnostic Tests II
Table 4.14
86
87
The Students Learning Completeness at Problem
Solving Ability Test II
88
Table 4.15
Results of Analysis The Process of Student’s Answer
90
Table 4.16
The Result of Teacher’s Activity Observation Cycle II
93
Table 4.17
The Result of Student’s Activities Observation Cycle II
94
Table 4.18
The Comparison Between Cycle I and Cycle II
97
Table 4.19
Diagnostic Test Results Problem solving Ability I
97
Table 4.20
Diagnostic Test Results Problem Solving II
98
Table 4.21
Teacher’s Activity Observation Cycle I and Cycle II
101
Table 4.22
Student’s Activity Observation Cycle I and Cycle II
102
ix
LIST OF FIGURE
Page
Figure 1.1
Sample of Student’s Sheet Answer Number 1
4
Figure 1.2
Sample of Student’s Sheet Answer Number 2
5
Figure 2.1
The Example of Object Shaped Cube and Rectangular Prism
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
37
Figure 4.1
Teacher Activity Guiding Students Meeting 1 Cycle I
61
Figure 4.2
Process of Students’ Answer in SAW 1 Question 1
62
Figure 4.3
Student Presenting Results of Discussion Cycle I
62
Figure 4.4
Activity of Students in Meeting 2 Cycle I
63
Figure 4.5
Process of Students’ Answer in SAW 2 Question 2
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
72
Figure 4.10 The process of student’s answer in Problem 4
72
Figure 4.11 The Student’s Activity Worksheet Cycle I Meeting I
73
Figure 4.12 The Process of Student’s Answer Cycle I MeetingI
74
Figure 4.13 The student’s activity worksheet cycle I Meeting II
74
Figure 4.14 Process of Students’ Answer in SAW
75
Figure 4.15 Students Activity in cycle II
82
Figure 4.16
83
Students Presenting the Results of Discussion Cycle II
Figure 4.17 Process of Student’s Answer SAS 4 Question 4
84
Figure 4.18 Percentage of Classical Learning Completeness Cycle II
89
Figure 4.19 The Process of Student’s Answer in Problem 1
90
x
Figure 4.20 The Process of Student’s Answer in Problem 2
91
Figure 4.21 The Process of Student’s Answer in Problem 3
91
Figure 4.22 The Process of Student’s Answer in Problem 4
92
xiii
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
Appendix 15 Alternative Solution of Initial Test of Problem Solving Ability 171
Appendix 16 Alternative Solution of Problem Solving Ability Test I
175
Appendix 17 Alternative Solution of Problem Solving Ability Test II
180
Appendix 18 The Result of Diagnostic Initial Test
184
Appendix 19 List of Value for Understanding the Problem Test I
186
Appendix 20 List of Value for Devising a Plan Test I
187
Appendix 21 List of Value for Carrying Out the Plan Test I
188
Appendix 22 List of Value for Looking Back Test I
189
Appendix 23 List of Value Classical Learning Mastery Test I
190
Appendix 24 List of Value The Process of Student’s Answer Test I
191
Appendix 25 List of Value for Understanding the Problem Test II
193
Appendix 26 List of Value for Devising a Plan Test II
194
Appendix 27 List of Value for Carrying Out the Plan Test II
196
Appendix 28 List of Value for Looking Back Test II
197
xiv
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
Appendix 39 Research Documentation
213
1
CHAPTER I
INTRODUCTION
1.1 Background
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
mathematics then come to school with an understanding of mathematical concepts
and problem solving strategies that they have discovered through explorations of
the world around them. Many problems that found in of mathematics learning.
One of which is the dislike of students in learning mathematics because
mathematics is a difficult subject. Mathematics is generally considered as the
most difficult subject. Mathematics is the dangerous subject for student. Just some
students like mathematics. This statement is supported by the results of
observations that have been made as direct interviews with students. The
observation is made on 19 to 21 January 2015 in SMP Negeri 1 Parbuluan. There
are 5 students of class VII - A were interviewed. Some students say that
2
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
conventional method. Teacher just explain directly what the objective material in
the used book. Teacher is not surely that student can build their knowledge
themself. Student is not active in learning process is does not matter because the
learning outcomes is more important than learning process on their targeting.
3
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 problemsolving 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
observed by 4 indicators, namely (1) understanding the problem by writing what
is known and asked; (2) devising a plan to write a formula that can find the
solution of the problem; (3) Carrying out the plan by doing a calculation; (4)
looking back, checking each step and whether the results are correct or not, is still
relatively low and needs improvement. Steps to solve a problems are still rarely
4
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.
What is the price that must be spent to renovate just the floor.”
5
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.
From the diagnostic test of problem solving ability, many students still
cannot understanding the problem, make the question into mathematics model and
formulate the problem. For the first indicators, namely understanding the problem,
82.35% of students have been understood the problem and 17.65% of students
have not been understood the problem. For the second indicators, deving a plan,
there are 52.94 % of student have been devised a plan and 47.04% of student
have not been devised a plan. For the third indicators, namely carrying out the
plan, there are 20.59% of student have been carried the plan and 79.41% of
student have not been carried the plan. And the last indicators, looking back,
8.82% of student have been looked back 91.18% of student have not been looked
back. The graphic will be shown as below:
6
Tabel 1.1 The Table of Preliminary Diagnostic Test
Aspect
1. Understanding the
problem
2. Devising a plan
3. Carrying out the
plan
4. Looking back
Categorized
Not Categorized
82.35%
17.65%
52.94%
47.06 %
20.59%
79.41%
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.
Recognizing the reality on the ground that the problem solving ability of
students is still low, we need a model of learning that makes the students become
active. It required a learning approach that can support successful learning. The
new paradigm in education today, to create meaningful learning process, the
learning process that takes place in schools let students actively involved in
7
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.
Based on the above description that the problem solving ability of
mathematics learning objectives are very important, and one of the learning
approach that can improve student’s problem-solving ability is Contextual
Teaching and Learning (CTL) approach. Therefore CTL approach is choosen in
doing this research.
8
1.2 Problem 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
1.3 Problem 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
varied, yet follow a good completion
9
1.4 Problem 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.
1.5 Research 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
Contextual Teaching and Learning (CTL) approach in learning and
10
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.
1.6 Research 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.
4. For researchers. The results of this study can be used as input in the
development of application of learning models to the students for a variety
of subject matter.
105
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:
1.
For teacher and school practitioner is equitable to change the learning
custom which is dominated by teacher and starting to involve students
more actively in the learning process, as well as give more attention to
106
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.
4.
For the further researcher is recommended to improve continuously the
learning scenario by implementation of Contextual Teaching and Learning
(CTL) especially in modelling and reflection as the low participation of
students.
107
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ii
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
her study in State University of Medan as student in bilingual class for
Mathematics Education 2011.