THE DIFFERENCES LEARNING BY USING M-APOS AND EXPOSITORY TO IMPROVE STUDENT PROBLEM
SOLVI NG ABILIT Y I N GRADE VII AT S MP-IT KHAI RUL IMAM
By:
Noya Yukari Siregar ID. Number 409312011
Bilingual Mathematics Education Program
THESIS
Submitted to Eligible Requirement for Sarjana Pendidikan Degree
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES STATE UNIVERSITY OF MEDAN
The Differences of Learning By Using M-APOS And Expository To Improve Student
Problem Solving Ability In Grade VII At SMP-IT Khairul Imam.
Noya Yukari Siregar (409312011)
ABSTRACT
This research is an experimental research using a experimental design pretest-posttest with two classes, one class as an experimental class and one as a control class that have been based on the ability of the student. The population of this research is the entire junior class VII at SMP-IT Khairul Imam, and the sample are all students of the class VIIC given learning experiment using M-APOS and all students of the class VIIB given control learning by using Expository. The method of hypothesis testing used is the independent sample t-test.
This research aims to determine the differences in improvement of problem solving ability among the student that learn by using M-APOS and student learn by using Expository method.
There is the difference of student problem solving ability that learn by M-APOS and learn by expository method at grade VII at SMP-IT Khairul Imam. Then form the research found that students that learn by using M-APOS is better than learn by expository method.
PREFACE
Give thanks to God should give me more spirit to finish my thesis. The title of this thesis is “The Differences Learning by Using M-APOS and Expository to Improve Student Problem Solving Ability in Grade VII at SMP-IT Khairul Imam.” This thesis was arranged to satisfy the requirement to get the Sarjana Pendidikan of Mathematics and Science Faculty in State University of Medan.
For this chance I want to say thank you to Rector of State University of Medan, Prof. Dr. Ibnu Hajar, M.Si and his staff, Dean of Mathematics and Science faculty Prof. Drs. Motlan, M.Sc., P.hd, Header of Mathematics Department Drs. Syafari, M.Pd, Header of Mathematics Education Study Program Drs. Zul Amry, M.Si and then Drs. Yasifati Hia, M.Si as secretary of Mathematics Department and special thanks to Coordinator of Bilingual Program Prof. Dr. rer. nat. Binari Manurung, M.si.
Special thanks to Dr. KMS. M. Amin Fauzi, M.Pd because he always guide me preparing, doing, and finishing this thesis, and then thanks a lot for Drs. Syafari, M.Pd, Dr. Edy Surya M.Si and Drs. Zul Amry, M.Si, being proper for my thesis.
Special thanks to my parent who give me some motivation, prays until I can finish my thesis. And then, thank you so much also to my beloved sibling, Asro, Ami, and Nova.
Writer say thank to Sir Ridwan, S.Pd as the headmaster of SMP-IT Khairul Imam and Ms. Siti Rahma, S.Pd as Mathematics teacher who help the writer in the research activities.
CONTENT
Page
Attestation Sheet i
Biography ii
Abstract iii
Preface iv
Content vi
Table List viii
Figure List ix
Appendix x
CHAPTER I INTRODUCTION
1.1 Background 1
1.2 Problem Indication 6
1.3 Problem Limitation 6
1.4 Problem Formulation 7
1.5 Purpose of Research 7
1.6 Benefits of Research 7
1.7 Operational Definition 8
CHAPTER II LITERATURE
2.1 Definition of Learn 10
2.2 Learning Mathematic 11
2.3 Mathematics Difficulty Learning 13
2.4 Definition of Problem and Problem Solving 14
2.5 APOS Theory and Learning model M-APOS 17
2.6 Social Arithmetic 21
2.6.2. Rabat, Gross, Tara, Neto, and Interest 22
2.7 Research Hypothesis 23
CHAPTER III METHODOLOGY
3.1 Research Method 24
3.2 Population and Sample 24
3.3 Research Design 24
3.4 Research Instrument 25
3.5 Research Procedure 27
3.6 Technique Data Collection 29
3.7 Procedure of Processing Data Analysis 29
CHAPTER IV
RESEARCH RESULT AND DISCUSSION
4.1 Research Result in Problem Solving 36
4.1.1. The Difference of Problem Solving Ability in Experiment
Class and Control Class 36
4.1.2. Normality Test in Problem Solving Ability 37
4.1.3. Homogeneity Test Problem Solving 37
4.1.4. Hypothesis Testing Problem Solving Ability 39
4.2 Discussion of Research Result 39
CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion 45
5.2 Suggestion 46
REFERENCES 47
TABLE LIST
Page
3.1 The guidance of test scoring 26
3.2 Category of Questioner Score 34
4.1 Data of Score Difference in Problem Solving Ability at Experiment
Class and Control Class 36
4.2 Result of Normality Test Difference Data Problem Solving Ability 37
4.3 Result of Data Homogeneity in Problem Solving 37
4.4 Data Difference Average Pretest – Posttest in Problem Solving Ability
Both Classes 38
FIGURE LIST
Page
Figure 2.1 ACE Cycles 19
Figure 3.1 Diagram of Research Procedure 28
Figure 4.1 Diagram of Difference average posttest - pretest in Problem Solving Ability Both Classes 38
Figure 4.2 Student Error Form in Understanding 43
Figure 4.3 Student Error Form to Change in Mathematic Model 43
Figure 4.4 Student Errors in Calculation 43
APPENDIX LIST
Appendix 11: Lesson Plan Expository 101
Appendix 12: Students Worksheet 3 105
Appendix 13: Problem Solving Test 3 108
Appendix 14: Posttest 114
Appendix 15: Pretest Blueprint 119
Appendix 16: Validity Sheet 120
Appendix 17: Posttest Blueprint 124
Appendix 18: Validity Sheet 125
Appendix 19: Data of Student Problem Solving Ability in Experiment Class
And Control Class 128
Appendix 20: Differences Data of Student Problem Solving Ability in
Experiment Class and Control Class 129
Appendix 21: Calculation of Means, Variance, and Standard Deviation 130
Appendix 22: Calculation of Data Normality Test Student Problem Solving
Ability in Experiment Class and Control Class 131
Appendix 22: Calculation of Homogeneity Test of Student Problem Solving
Appendix 22: Calculation of Hypothesis Test of Problem Solving Ability 134
CHAPTER I INTRODUCTION 1.1 Background
Mathematics is one subject that includes concepts, rules, principles, and
theories are useful in problems solving in almost all the subjects taught in school.
Mathematics is also a compulsory subject in formal education and has an
important role in education. Mastering math becomes important capital to study
other subjects, such as physics, chemistry, biology, and social sciences.
Even so, it's not unusual if still there are students who think of
mathematics as a subject that is very difficult resulting in less favored
mathematics. Learning Mathematics for this is still regarded as a difficult lesson
for the use of symbols and emblems interpreted as memorizing formulas.
Learning mathematics is also very influenced by the view that mathematics is a
tool that ready to use. This view encourages teachers are likely to tell the concept /
properties / theorems and how to use it.
Understanding the theories of how people learn and the ability to apply
them in the teaching of mathematics is an essential requirement for creating
effective teaching process. One theory is used to learn the dominant flow of
developmental psychology and constructivism. In practice, the teacher is not
giving the final answer to the question of students, but rather directs them to form
(construct) knowledge of mathematics in order to obtain the structure of
mathematics. In addition, teachers must also consider the diversity of skills among
the students so that the teacher created certain conditions, the potential of each
student to develop optimally.
One of the factors that because the low quality of education is a model of
learning that teachers use less varied. Many teachers are still using the
conventional method of teacher-centered learning (teacher-oriented) that does not
involve students actively. In fact, the active involvement of children in a learning
2
eventually be able to increase children's understanding of the material. According
to Cawley in Suherman (2003: 146) identify the types of learning errors, that is:
1. Teaching is not proper, incorrect or always limiting,
2. Students should switch to another topic, while topics previously not
mastered,
3. Establishing learning objectives excessive.
To obtain a good learning outcomes, the learning process should be
planned systematically and involves students participate in the learning process.
The selection of methods and models appropriate learning will help smooth the
learning process.
According to Sudjana (2002: 158) that: “Participation that needed to be a
strategy in learning to make collaborate of students as active in planning, implementation, and evaluation of program activity of learn.”
One of the goals of learning mathematics is that students have the ability
to solve problems that include the ability to understand the problem, devised a
mathematical model, solve the model and interpret the obtained solution (BSNP,
2006: 346).
The goal put the problem into part of the mathematics curriculum is
important. In the process of learning and problem solving, students can gain
experience using the knowledge and skills already possessed. Experience is then
train the students to think logically, analytical, systematic, critical, and creative in
dealing with problems.
Based on the results of the tests was conducted the percentage of students
of class VII which has a value equal to or above the KKM only reached 60%. The
school set a value of 70 for the KKM mathematics courses. This means that
students who pass the study around half of it, while others have the ability to solve
problems below average. The teacher also stated that: “The students just
memorizing the formula. By memorizing the formula without understanding well
and less practice is difficult to try the problem related in daily life. The material is
3
the understanding the concept still lack in primary school, automatically students
have difficulty to learn again this topic in junior high school.
Based on classroom observations, many student still hard to received the
lesson, it caused they think that teacher not too good to teach the matter. Teacher
only explained at the beginning of learning as an introduction to the material to be
studied. After that, teacher gives student worksheet to student and asks them to do
and discuss it.
During the discussion, most visible group members work on individual
worksheets. So that in one group there has been no communication in group. In
addition, discussions on several groups have also involves every
member. Discussion was dominated by just a few students. The other student
passive in expressed opinion. Then see that students are still not up to using focus
groups as a learning medium. As a result, when faced with math problems
students are less able to solve it.
Students are active in restoring the feedback provided by the teacher
though often wrong in giving an answer. During the Teaching and Learning
Activities (KBM), the teacher can control the way the learning process well, but
still student learning outcomes are lacking. Thus it is necessary to study other
models to increase student learning outcomes especially in problem-solving
abilities.
Low ability students in solving this problem are related to the possibility
of learning approaches used by teachers. Results of the assessment carried out
Slameto (2003: 13) suggest that in general the process of mathematics learning is
still done conventionally encountered, drill, and lectures. Learning process like
this only emphasizes on achieving the demands of the curriculum than students'
learning abilities. Therefore, it is necessary to find the model and learning
approach that is able to improve the learning ability of students principally in
mathematical problem solving.
The view that problem-solving skills in the learning of mathematics
teaching is a general purpose, contains an understanding that mathematics can
4
this problem solving capabilities become a general purpose learning mathematics.
While the view of problem solving as a core process and major in mathematics
curriculum, the mathematics learning processes and strategies prioritize the
student to solve it rather than just the results, so that the skills and strategies in
solving the problem into learning basic skills in mathematics.
The lacks of students’ mathematics understanding have direct impact on the ability of problems solving in mathematical and the quality of education in
Indonesia. The facts is an indicator that the teacher should choose and use the
model varies with the material that will be taught so as to increase interest in
learning mathematics and improve students' creative thinking.
The low ability students in this problem solving likely has something to do
with the learning approach used by the teacher. The results of the assessment
In teaching of mathematics, many teachers complain less optimal student
ability in problem solving. It looks from the mistakes students in solving
problems, and low potential for student learning (value) in both the daily tests and
final exams. Therefore, to improve the quality of education and increasing skills
in problem solving the need for reform in education, namely the renewal method
or increasing relevance of teaching methods. The method of teaching is said to be
able to deliver relevant if students achieve educational goals through teaching.
Thus mathematics learning, now and in the future should not stop at
achieving basic skills, but instead should be designed to achieve a high level of
mathematical competence (high order skill) as mathematical problem solving
ability.
One approach that has the characteristics of constructivist learning based
5
encourage the formation of knowledge and are predicted to increase students'
mathematical problem solving is a modification of APOS.
The process of formation of new knowledge (especially in mathematics) is
believed to be result of a series of processes introduced by Dubinsky as the
Action-Process-Object-Schema (APOS). Objects that have been stored in one's
memory as knowledge will be processed when the action occurs due to some
particular stimulus.
The terms of action, process, object, and the scheme is essentially a mental
construction in an attempt to understand a mathematical idea. According to APOS
theory, if one is trying to understand a mathematical idea then the process will
start from the idea of mathematical mental action, and will eventually get anyway
construction schemes of certain mathematical concepts covered in the given
problem.
In the process of thought, an idea can’t suddenly appear in your mind. The
ideas came after a wide range of symbols processed so that it can be said that the
thought process going through the construction of stage miraculous mental as
mentioned Asiala, et al in Nurlaelah and Usdiyana (2009: 10), that is:
1. Action, at this stage of the transformation objects that individuals perceived as necessary and the instructions step by step how to perform the operation.
2. The process, which is a mental construction that occurs internally when someone is able to do the level of action repeatedly.
3. Object, can be interpreted as resulting from the construction of the mental
that has been done at this stage of the process.
4. The scheme, which is a collection of actions, processes, and objects that are summarized into a scheme.
Relating with the foregoing, we need a mathematical learning model that
6
Based on the issues that have been raised, the authors feel compelled to conduct research entitled “The Differences Learning by using M-APOS and Expository to Improve Student Problem Solving Ability in Grade VII at SMP-IT KHAIRUL IMAM”.
1.2
Problem IdentificationBased on the background of the issues outlined above, it can be identified
the problems posed are:
1. Problem solving ability in mathematics of students still low.
2. Learning is not meaningful; it means that the students can’t relate the material into daily life.
3. The students have difficulty in problem solving mathematical, because the
understanding of the concept still lack.
4. The students have problems in learning the Arithmetic Social which are
already entered on a higher level, namely its application in daily life.
1.3Problem Limitation
The limit problems in this study are:
1. This study is limited simply to measure the problem-solving ability on
subject of Social Arithmetic using learning model of M-APOS.
2. Population in this research is student at SMP-IT Khairul Imam grade VII in
odd semester of academic year 2013/2014.
3. Indicator of mathematical problem-solving ability that is identifies the
problem, formulates a mathematical model, determines the completion of
7
1.4Problem Formula
Based on limitation problem above, then that becomes the focus of the
problem in this study can be formulated as follows:
1. Is there difference of improving student problem solving ability that learn by
using M-APOS and expository in grade VII at SMP-IT Khairul Imam.
2. How the students' response to learning by using a model M-APOS?
3. Is there any differences students’ activity that is learning using M-APOS and
expository method?
1.5 Purpose of Research
Based formulation of the problem that has been described above, the
purpose of this study is as follows.
1. Knowing the differences of students’ problem solving ability that learning using M-APOS is better than the students' problem-solving skills through the
use of conventional teaching expository method.
2. Knowing the students' response to learning of mathematics by using learning
model of APOS modification.
3. Knowing the students' activities that are learning using model of APOS
modification and expository.
1.6 Benefits of Research
This study is expected to be providing the following benefits:
1. Theoretical benefits
In general, the results of this study is expected to be provide benefits to
learning of mathematics, especially to improving mathematical problem-solving
ability of students in follow the learning of mathematics by using learning model
of APOS modification.
2. Practical benefits
This research is expected to be providing a real solution in the form the
steps to improve the mathematical problem-solving ability through the learning
8
Results of this research are expected to provide benefits for teachers, students, and
other researchers.
a. For students, can assist the students in learning of mathematics concepts so
that it can improve students' mathematical problem solving ability.
b. For teachers, become input in order to apply the learning model of APOS
modification an effort to improve students' mathematical problem solving
ability toward improvements to the quality of teaching of mathematics in
schools.
c. For other researcher, the results of of this research are expected to provide
and broaden knowledge as well as a reference for conducting research
related to the learning model of APOS modification.
1.7 Operational Definition
To avoid misunderstandings and research efforts are consistent with the
objectives, the operational definition is given as follows:
1. Learning model of APOS modification is a learning model that based on the
theory of APOS (Action-Process-Object-Schema) are modified.
Modifications performed on the activity phase, where activity in the
computer lab learning model APOS replaced with recitation of assignment
given before learning implemented. Recitation assignments presented in the
form of a worksheet that guide and assist the students in reviewing of
person is able to perform the action level over and over again.
c. Object can be interpreted as resulting from the constructed something
9
d. Schemes, which are collections of actions, processes, and object that
summarized into a scheme.
2. A conventional learning model that uses the expository method of teaching
models commonly performed by mathematics teachers generally, where the
learning process is only centered on the teacher explains or convey the
material while the students only recording what has been submitted by
teachers.
3. Improvement problem solving of mathematical ability can be interpreted as
an increase in ability to identify problems, formulate mathematics models, to
determine the completion of the mathematical model and an interpretation of
the results obtained.
4. Mathematical problem-solving ability is a students ability to solve
mathematics problem by considering the following steps:
a. Understand the problem,
b. Planning the problems or choosing an appropriate resolution strategy,
c. Implement problem-solving plan or strategy planned settlement,
CHAPTER V
CONCLUSIONS AND SUGGESTIONS
5.1. CONCLUSION
Based on the analysis and discussion of research results on class VII at
SMP-IT Khairul Imam Academic Year 2013/2014 which has been described in
the previous chapter, it can be concluded as follows:
1. The application of M-APOS learning model can improve mathematical
problem solving ability than expository method. It seen from the data
difference posttest and pretest between both classes, those in experimental
class is 44,688 then in control class that is 29,589 so it can be concluded that
the experimental class higher than control class.
2. Improved problem solving ability of students learning mathematics using
M-APOS learning model is better than the students who are learning with
expository method. It is seen from the results of analysis the difference data
posttest-pretest between both classes that showed the improving the
mathematics problem solving ability experimental classes are better than the
control class.
3. Students that learn by M-APOS more active in the class than students learn by
expository it can be seen from the activity in class discussion. Then it make
there is a difference activity in the both classes. Students also make a
classroom being conducive. It is seen from the observation sheet that observe
by teacher in both classes.
4. Most students showed a positive attitude towards learning mathematics using
a model of the M-APOS. This is supported by the results of a questionnaire
data analysis has an average score above 3 and observer ratings in the
observation sheet which gives the range of values between 3 (enough) and 4
(good) and shows that the most students responded positively to the learning
45
5.2. SUGGESTION
Based on the research results and the conclusions obtained, and then some
suggestions can be thought are as follows:
1. Because implementing of this research only three meetings, then another
researcher or teacher are expected to continue this research to find more
significant result.
2. To mathematics teacher, especially to mathematics teacher of SMP-IT Khairul
Imam, implementation of M-APOS model can be one alternative to increase
mathematics problem solving ability of student, especially in topic of Social
Arithmetics.
3. To student, teacher and all school party in SMP-IT Khairul Imam, in order to
keep trying to develop and to find creative innovation of mathematics learning
especially that relates M-APOS Model.
4. To advance researcher, in order to make result and instrument in this research
as consideration material to implement learning by using M-APOS model in
topic of Social Arithmetics or another topic and can be developed for advance
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