ANALYSIS OF STUDENT ERRORS IN SOLVING PROBLEMS OF ALGEBRA OPERATIONS IN CLASS VIII MEDAN JUNIOR HIGH SCHOOL ACADEMIC YEAR 2012/2013.
ANALYSIS OF STUDENT ERRORS IN SOLVING PROBLEMS
OF ALGEBRA OPERATIONS IN CLASS VIII
MEDAN JUNIOR HIGH SCHOOL
ACADEMIC YEAR
2012/2013
By :
Christina Gultom
ID Number 408111037
Study Program Mathematics Education
THESIS
Submitted to Fulfill Requirement for the Degree of
Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
2013
i
iv
PREFACE
Praise and gratitude author say for the blessing and grace of God, her
Lord, her Savior so she can finish this thesis. The title of the thesis "Analysis Of
Students Errors In Solving Problems Of Algebra Operation In Class VIII Medan
Junior High School Academic Year 2012/2013" thesis is structured as one
requirements for a degree of Sarjana Pendidikan at Mathematics Department,
Faculty of Mathematics and Natural Science, State University Of Medan.
In writing this paper the author a lot of assistance from various parties
either directly or indirectly. With all humility author express gratitude and special
thanks to :
Prof. Dian Armanto, M.Pd, MA, M.Sc, Ph.D as Thesis Supervisor for
guidace, directions, advices, comments, suggestions and his precious time that he
spent on supervising this thesis so this thesis can be done well.
DR. E. Elvis Napitupulu, MS, Mulyono, S.Si, M.Si, and Prof. DR. S.
Saragih, M.Pd as her Examiner Lecturer for their advices, corrections, comments,
and suggestions for this thesis and Dra. Nerli Khairani, M.Si as Academic
Supervisor has been always give advice, Prof. DR. Ibnu Hajar,M.Si as her Rector
in State University Of Medan, Prof. Drs. Motlan, M.Sc, Ph.D as Dean of Faculty
of Mathematics And Natural Science in State University of Medan, Prof. Dr.
Mukhtar, M.Pd as Department Chairman, Drs. Yasifati Hia, M.Si as Department
Secretary, Drs. Syafari, M.Pd as Head of Mathematics Education Study Program
and all lecturers and employees of Mathematics Department who have taught,
advices, and guided her throughout her academic year at the university.
Drs. Murgap, M.Sc as Secretary in Ministry Of Education, Nursyam
Syamsuar Guci, B.Sc as Headmaster of SMP Budi Satrya, Indra Suardi, MA as
Headmaster of SMP Shafiyyatul Amaliyyah, Drs. Hasbullah as Vice Headmaster
of SMP Negeri 14 Medan have given permission to do the research in those
schools.
Her beloved mother and father for their endless love, pray, advices and
financial support that have enable her to finish her study, her beloved brothers(
Benhur Gultom,Rio Gultom, Rimba Gultom and Makmur Gultom) and her
beloved sisters (Yunita gultom, Berliana Gultom, and Evalina Gultom) and also
her nephews for love, pray, and advices.
Her friends in The Ruth small group and its former(Marni, Natalia, Dewi
Rotua, Sabtriana, Donna) and her older sister in The Ruth small group (K’ Murni
and K’Ika D) for pray, love and motivation. Her friends in Class B Mathematics
education (Tina m, Ervides, Otto, and others that can not be mentioned one by
one) for pray, love and motivation.
Hopefully the good of all parties avenged doubled from God.
iv
Author recognize that the preparation of the thesis is still far from perfect,
therefore suggestions and constructive criticism authors expect. Hopefully, this
paper can be useful for the purposes of education.
Medan, Februari 2013
Christina Gultom
ID Numb. 408111037
iii
ANALYSIS OF STUDENT ERRORS IN SOLVING PROBLEMS OF
ALGEBRA OPERATIONS IN CLASS VIII
MEDAN JUNIOR HIGH SCHOOL
ACADEMIC YEAR
2012/2013
By:
Christina Gultom
408111037
ABSTRACT
The purposes of this research is (1) Knowing kinds of students errors in solve
problems of algebra operations in class VIII(2) Knowing the level of students
errors in solve problems of algebra operation in class VIII (3) Knowing the factors
that causes students errors in solve problems of algebra operations in class VIII.
Population in this research was Medan Junior High School and the sample was
Class VIIID SMP Shafiyyatul Amaliyah,Class VIIIA SMP Budi Satrya and Class
VIIIC SMP Negeri 14 Medan taken of the data of Ministry Education in Medan.
All of subject in that 3 school is 98 students. Data collected by test, interview and
observation. Test used for knowing kinds of error and level error by student,
interview used for knowing the factors of students error when answer the question
and observation for knowing the factors of students errors from teacher. Analysis
method used is qualitative and quantitave description.
The result of research showed that : (1) kinds of errors which many done by
students were transformation error, skill process error and encoding error. (2) The
level of students error in solving problems of algebra operation in class VIII
Medan junior high school could be concluded that still very high error. (3) The
factors that causes students error in solving problems of algebra operation divided
into 2 factors: a. Internal factors (Lack of master concept,principle and skill in
algebra operation, Lack of master prerequisites material, Lack of exercise solving
mathematics problems, Students were careless) and b. External factors(Teacher
was not as good demonstrator, Teacher was not good controller class, and Teacher
was not good mediator).
vi
TABLE OF CONTENTS
Authentication sheet
Curriculum Vitae
Abstract
Preface
Table Of Contents
List Of Figure
List Of Table
List Of Appendices
CHAPTER I INTRODUCTION
Page
i
ii
iii
iv
vi
viii
ix
x
1.1. Background
1
1.2. Identification of the Problem
4
1.3. Boundary Problems
5
1.4. Problem Formulation
5
1.5. Research Purposes
5
1.6. Benefits of the Research
6
1.7. Operational Definition
6
CHAPTER II REVIEW OF LITERATUR
2.1. Mathematics Achievement
7
2.2. Errors in Mathematics Instruction
8
2.3. Errors In Solve Math Problems
10
2.4. The Level of Student errors
14
2.5. The factors that Cause Student Errors
14
2.6. Algebra Operation
17
2.6.1. Meaning of Algebra
17
2.6.2. Meaning of Multiplication, powers, and division it the
Algebra of singular tribe
2.6.3. Substitute Numbers in The Algebra
18
18
2.6.4. Addition and Substraction in Similar Tribe and Unsimilar
Tribes
18
2.6.5. Power of Fractions on Algebra
19
2.6.6. Algebra Fraction
19
2.6.7. Special Multiplication of Algebra
20
vi
2.7. Conceptual Framework
21
CHAPTER III RESEARCH METHODOLY
3.1. Research Sites
23
3.2. Time of Research
23
3.3. Popolation and Sample
23
3.4. Type of Research
24
3.5. Method of Data Collection
24
3.4.1 Test
24
3.4.2 Obsevation
27
3.4.3 Interview
27
3.5. Data Analysis
29
3.6. Procedural of Research
32
CHAPTER IV RESULT OF RESEARCH AND DISCUSSION
4.1. Result of research
34
4.1.1. Description of test
34
4.1.2. Description of test and interview
38
4.1.3. Description of observation
47
4.2. Discussion
48
CHAPTER V CONCLUSSIONS AND SUGGESTIONS
5.1. Conclussions
55
5.2. Suggestions
56
REFERENCES
57
ix
LIST OF TABLE
Table 2.1.
Table 2.2.
Table 3.1.
Table 3.2.
Table 3.3.
Table 4.1.
Table 4.2.
The Level of student mastery
The Level of student errors
Schedule of research in three school
Blueprint of diagnostic test problem of algebra operation subject
The guidelines of checking students errors
The percentage of kinds of errors
The Level Of Students Errors In Solving Problems Of Algebra
Operation in Class VIII Medan Junior High School
14
14
23
25
29
36
38
viii
LIST OF FIGURE
Figure 1.1. Student Answer 1
Figure 2.1. Factors that Influence mathematics teaching and learning
Process
Figure 3.1. Procedural of Research
Figure 4.1. The Chart Of Student Errors In Each Kinds Of Errors
Page
3
9
33
37
x
LIST OF APPENDICES
Appendix 1. Diagnostics Test Problems
Appendix 2. The answer of diagnostic test
Appendix 3. Kinds of students error SMP Budi Satrya
Appendix 4. Kinds of students error SMP Negeri 14 Medan
Appendix 5. Kinds of students error SMP Shafiyyatul Amaliyyah
Appendix 6. The Number Of Students Who Answered Correctly And
Incorrectly In SMP Budi Satrya
Appendix 7. The Number Of Students Who Answered Correctly And
Incorrectly In SMP Negeri 14 Medan
Appendix 8. The Number Of Students Who Answered Correctly And
Incorrectly In SMP Shafiyyatul Amaliyyah
Appendix 9. Analysis data SMP Budi Satrya
Appendix 10. Analysis data SMP Negeri 14 Medan
Appendix 11. Analysis data SMP Shafiyyatul Amaliyyah
Appendix 12. Observation sheet in Budi Satrya
Appendix 13. Observation sheet in SMP Negeri 14 Medan
Appendix 14. Observation sheet in SMP Shafiyyatul Amaliyyah
Appendix 15. Indikator penilaian observasi guru mengajar
Appendix 16. Validation sheet
Appendix 17. Research Documentation
Appendix 18. teachers’ lesson plan
59
65
70
83
97
105
107
109
111
116
121
124
126
128
130
133
139
143
CHAPTER I
INTRODUCTION
1.1.
Background
Education is a process of changing a person's behavior and ability toward
progress and improvement. Education can change a person's mindset to always
make innovations and improvements in all aspects of life in the direction of self
improvement as develop knowledge insight, able to adjust the daily problems they
face, positive attitude and behavior towards the social and natural environment.
Mathematics education has important role because the mathematics is
basic science that used in various fields of life. Through the learning of
mathematics students are expected to develop critical thinking abilities, logical,
systematic, thorough, effective, and efficient in solving problems. Like Cornelius
expressed (in Abdurrahman 1999:253) that:
“Five reasons for studying mathematics because mathematics is:means to
think clear and logical, means to solve daily problems, means to know
the patterns of relationships and generalization of experience, means to
develop creativity, and means to raise awareness towards cultural
development.”
No doubt anymore that every student must get mathematics subject in
school. As the purposes of mathematics have been given in the school, we can see
that school mathematics held important role. Generally the purposes of
mathematics
in
the
school
can
be
classified
become(in
http://p4tkmatematika.org/2011/10/peran-fungsi-tujuan-dan-karakteristikmatematika-sekolah/) : 1)formally purpose is emphasize to organize reasoning
and form the students personality ,2) material purpose is emphasize to problem
solving and apply mathematics. So, it is important to realize benefits of
mathematics as a subject that is very important in human civilization, especially in
education system in the world.
However, in reality, nowadays Indonesian student’s mathematics
achievment is still low. The low mathematics achievement is demonstrated by the
low value of daily tests, semester, or UN (National Examination) in mathematics.
Moreover according to data from the Trends in Mathematics and Science Study
(TIMSS),
“the average score of Indonesian students' mathematics achievement in
1999, 2003, and 2007 in a row were 435, 420, and 433. By the score the
1
2
Indonesian students got rank 34th out of 38 countries in 1999, ranked 35th
of 46 countries in 2003, and ranked 36 th of 49 countries in 2007. The
average score of Indonesian students in the TIMSS 2007 substandard of
500, and only reached Low International Benchmark. By these
achievements, the average of Indonesian students are only able to
recognize a number of basic facts but haven’t been able to communicate
and relate various topics of science,moreover apply complex and abstract
concepts.”(Http://litbang.kemdikbud.go.id/detail.php?id=214)
The low student mathematics ability can be seen from the students'
mastery towards material. One of way is giving test or a problems about the
material to the students. Students errors in solving problems can be one of clues to
know how far students master the materials. Therefore, the presence of these
errors need to be analyzed and searched by any factors that influence. Thus,
informations about errors in solving mathematics problems can be used to
improve the quality of teaching and learning activities and ultimately improve
student mathematics achievement.
Mathematics consist of four broad insight is algebra, arithmetic,
geometry, and analysis. Algebra is one part of mathematics that includes variety
of material learned in junior high school. Learning algebra is very useful for
students in learning (understanding) and other mathematical material and algebra
concepts in higher education. For example, mastery of algebra concepts is helpful
to learn the concepts of geometry built flat in search of an angle. For example, the
angle of triangle.
According to Walle(2008:1) “Thinking algebra or algebra logic is one of
them is to generalize from experience with numbers and calculation, formulate
ideas by using a symbol system that are useful, and explore the concept of
patterns and function.” Thus, through studying algebra well, someone will have
analytical abilities. This abilities have an important role in the study of
mathematics is relatively complex. Thus, understanding the concepts of algebra
operation is essential as a basis for understanding other concepts of mathematical
material.
In Medan especially, students’ algebra operation abilities is still weak, it
is known based on the observations of researcher at three junior high schools in
3
Medan. The schools were selected by the category of high quality, medium, and
low based on the UN in Academic Year 2010/2011. The three schools were SMP
Shafiyyatul Amaliyyah with high quality category based on the UN 2010/2011
had an average of mathematics was 9.01; SMP Budisatrya with medium quality
category based on the UN 2010/2011 had an average mathematics was 8.90; SMP
Negeri14 Medan with low quality category based on the UN 2010/2011had an
average mathematics was 7.13. However, after researcher had given tests at the
time of observation it appears that the average value of the students in solving
problems of algebra operation in SMP Syaffiyatul Amaliyyah only 2.75 from 10;
SMP Budisatrya only 1.15 from 10; SMP Negeri 14 Medan only 2.75 from 10 .
This is very apprehensive, these schools are still very weak in algebra because
many students made errors in algebra operation. The example of students errors
in algebra operation is like this:
Problems:
Determine the multiplication of (3x-2)(x-1)
Student answer:
Figure 1.1. Student answer 1
From the student answer, concluded that student made error in transformation
errors because student disable identify the sequence of operation, skills process
errors because student didn’t know the procedure and encoding errors because
student error in solution. This could be caused because students have not
understanding
the concept and principle yet and poorly practise in solving
mathematics problem so that made error in skill in algebra operation. If this issues
aren’t overcomed so the students will dislike mathematics because they feel
mathematics is difficult. So that, the student errors must be analyzed and searched
what factors that cause it. Detailed error analysis is very needed so that students
errors and its factors can be seen further to help overcome these problems.
4
Many factors cause the low students’ mathematics ability. As Slameto
(2010:54-72) classified factors of learning, that is internal factor and external
factor. Internal factors are physical(health and handicap), physicological
(intelligent, careful, interest, talent, motive, maturity, readiness) and weariness
factor. While external factors are family ( manner of parents educate, relation
among member of family, house condition, family economics, parents
understanding, background of culture), school (teaching method, curriculum,
relation between teacher and student, relation among students, discipline of
school, instrument instruction, time of school, standard of subject over measure,
facilities, method learning, and homework), and community factor
(students
activities in community, media mass, friends and life condition of community). In
this research the factors will be seen from students and teacher. The factor from
student will be analyzed by work result in algebra operation, and the factor from
teacher will be analyzed by teacher role in teaching and learning process.
Based on this background, the researcher try to analyze students errors in
solving problems of algebra operations. For that, researchers chose the title
"Analysis Of Students Errors in Solving Problems of Algebra Operations in Class
VIII Medan Junior High School Academic Year 2012/2013". Analysis students
errors made by searching errors and factors that cause it. Thus, errors in solving
problems of algebra operations can be minimized so that mathematics
achievement can be improved.
1.2.
Identification of the Problem
Based on the background, can be identified some of issues that
arise in algebra learning are:
1. Students were poorly understand mathematics
2. Almost students made errors in algebra operations
3. Students made errors in transformation, skills process and encoding
errors in solving problems of algebra operations.
5
1.3.
Boundary Problems
In order to focus the research, this research only reveals the
errors and factors that cause students errors in solving problems of
algebra operations in class VIII Medan Junior High School Academic
Year 2012/2013.
1.4.
Problem Formulation
Based on the boundary problems above, the formulation of the
problem is:
1.
What kinds of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013?
2.
What is the level of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013?
3.
What are the factors that cause the students’ errors in solving
problems of algebra operations in class VIII Medan junior high school
Academic Year 2012/2013?
1.5.
Research Purposes
The purposes of this research is:
1.
Knowing kinds of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013.
2.
Knowing the level of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013?
3.
Knowing the factors that causes students errors in solving problems
of algebra operations in class VIII Medan junior high school
Academic Year 2012/2013.
6
1.6.
Benefits of the research
The benefits of this research are as follows:
1.
For teachers
a. Provide information about kinds of students errors in solving
problems of algebra operations.
b. Provide information about the factors that causes students errors in
solving problems of algebra operations.
c. Provide information about teacher shortage that causes students
errors in solving problems of algebra operations so that can give
the best solution.
2.
For students
Provide information about students errors so that they can learn
more to improve their achievement in mathematics especially in
algebra operation.
3.
For Headmaster
a. As a consideration to prepare the school curriculum.
b. Command every teacher make analysis of students errors for each
of held material.
4.
For next researchers
As a consideration and input for similar research.
1.7.
Operational Definition
a. Error
The error is defined as the deviation from the right and its systematic,
consistent and incidental to the particular section. Thus, the error is a
mistake of the student in solving problems.
b. Students Error
Students Errors are mistake of the student in solving problems.
Analysis of Errors is a description of mistakes made by students in
solving problems.
CHAPTER V
CONCLUSIONS AND SUGGESTIONS
5.1. CONCLUSIONS
1) Kinds of errors in solving problems of algebra operation in Class VIII
Medan Junior High School were: transformation error, skill process
error and encoding error.
2) The level of students error in solving problems of algebra operation in
Class VIII of sample can be concluded that still very high error.
3) The factors that causes students error in solving problems of algebra
operation divided into 2 factors:
1. Internal factors
a. Lack of master concept,principle and skill in algebra operation
b. Lack of master prerequisites material
c. Lack of exercise solving mathematics problems
d. Students were careless
2.
External factors
a. Teacher was not as good demonstrator
b.
Teacher was not as good controller class
c.
Teacher was not as good mediator
55
56
5.2. SUGGESTIONS
The suggestions can be given so that students mathematics achievement
can be improve,especially in algebra operations :
1.
For teachers
a. Teacher must repair the teacher role in teaching as demonstrator,
controller class and mediator especially.
b. Teacher must analyze students errors in solving mathematics
problems so that teacher know what is the causes of students error
and can give the best solution.
c. Teacher create instruction method that can stimulate students
respond in learning mathemtics.
2.
For students
Students must be often exercise mathematics problems especially
algebra operation so that can improve students mastery in
mathematics.
3.
For Headmaster
Command every teacher make analysis of students errors for each
of held material.
4.
For next researchers
a. This research can be made the similar research in another
material.
b. Specify kinds of error before doing this research.
REFERENCES
Abdurrahman, Mulyono. 2009. Pendidikan Bagi Anak Berkesulitan Belajar.
Jakarta: PT. Rineka Cipta
Arikunto, suharsimi. 2010. Prosedur Penelitian suatu pendekatan praktik. Jakarta:
PT. Rineka Cipta
_______, ________. 2011. Dasar-Dasar Evaluasi Belajar. Jakarta: Bumi Aksara
Direktorat Pembinaan SMP. 2007. Pedoman Pengembangan Tes Diagnostik Mata
Pelajaran IPA SMP/MTs. Jakarta: Direktorat Jenderal Manajemen
Pendidikan
Dasar
Dan
Menengah.
(http://www.google.co.id/url?sa=t&rct=j&q=tes%20diagnostik&source=
web&cd=2&cad=rja&ved accessed on September 19,2012)
Ekawati, estina. 2011. Peran, Fungsi, Tujuan, dan Karakteristik Matematika
Sekolah.
Jakarta:
Kementrian
Depdikbud
RI.
(http://p4tkmatematika.org/2011/10/peran-fungsi-tujuan-dankarakteristik-matematika-sekolah/ accessed on Mey 17,2012 )
Junaidi, wawan.2010. Pembelajaran Matematika. Semarang:Universitas Negeri
Semarang.(http://wawan-junaidi.blogspot.com/2010/06/pembelajaranmatematika.html accessed on September 4,2012)
Moleong, Lexy. 2010. Metodologi Penelitian Kualitatif edisi revisi. Bandung: PT.
Remaja Rosdakarya Offset
Nasution, s. 2010. Kurikulum dan Pengajaran. Jakarta: PT. Bumi Aksara
Purwanto. 2011. Evaluasi Hasil Belajar. Yogyakarta: Pustaka Pelajar
Rihdawati, santi.2011. Analisis Kesalahan Siswa Dalam Menyelesaikan Soal-Soal
Pada Pokok Bahasan Persamaan Kuadrat Siswa Kelas I(Bab II).
Yogyakarta:
UNY.(http://skripsiplus.blogspot.com/2011/05/analisiskesalahan-siswa-dalam.html accessed on September 3,2012.
Sabri, achmad. 2007. Strategi Belajar Mengajar Micro Teaching. Padang: Ciputat
press group
Samosir, ernawati.2012. Penerapan Genius Learning Strategy Untuk
Meningkatkan motivasi dan Hasil Belajar Siswa Pada Pokok Bahasan
Bilangan Bulat Di Kelas VII SMP Negeri 10 Medan T.A. 2011/2012.
Medan: UNIMED
58
59
Setiyawati, indra.2011. Identifikasi Kesalahan Dalam Menyelesaikan Soal Cerita
Materi Pelajaran Segitiga Dan Segi Empat Siswa Kelas Vii Smp N 5
Depok Sleman Yogyakarta Tahun Ajaran 2010/2011. Yogyakarta: UNY.
(http://eprints.uny.ac.id/1892/1/Skripsi_Indra_Setiyawati.pdf accessed on
September 4,2012)
Slameto. 2010. Belajar dan faktor-faktor yang mempengaruhinya. Jakarta: PT.
Rineka Cipta
Sukardi. 2009. Metodologi Penelitian Pendidikan kompetensi dan praktiknya.
Jakarta: PT. Bumi Aksara
Syah, Muhibbin. 2010. Psikologi Pendidikan dengan Pendekatan Baru. Bandung:
PT. Remaja Rosdakarya
Walle, Jhon. 2006. Matematika Sekolah Dasar dan Menengah Pengembangan
Pengajaran (authorized translation from Elementary and middle school
mathematics sixth edition). Jakarta: Erlangga
Widoyoko, E.Putro. 2012. Teknik Penyusunan Instrumen Penelitian. Yogyakarta:
Pustaka Pelajar
www.downloads.ziddu.com/downloadfile/16751212/siKemampuanSiswadalamM
enyelesaikanSoal-soalAljabar.doc.html (accessed on September 4,2012)
www.fadjarp3g.files.wordpress.com/2008/12/download_08_gagne_median_1.pdf
(accessed on September 4,2012)
www.litbang.kemdikbud.go.id/detail.php?id=214( accessed on September 4,2012)
www.tips-belajar-internet.blogspot.com/2009/08/hasil-belajar-matematika.html
(accessed on September 16,2012)
www.uns.ac.id/data/0019a.pdf (accessed on January 20, 2012)
OF ALGEBRA OPERATIONS IN CLASS VIII
MEDAN JUNIOR HIGH SCHOOL
ACADEMIC YEAR
2012/2013
By :
Christina Gultom
ID Number 408111037
Study Program Mathematics Education
THESIS
Submitted to Fulfill Requirement for the Degree of
Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
2013
i
iv
PREFACE
Praise and gratitude author say for the blessing and grace of God, her
Lord, her Savior so she can finish this thesis. The title of the thesis "Analysis Of
Students Errors In Solving Problems Of Algebra Operation In Class VIII Medan
Junior High School Academic Year 2012/2013" thesis is structured as one
requirements for a degree of Sarjana Pendidikan at Mathematics Department,
Faculty of Mathematics and Natural Science, State University Of Medan.
In writing this paper the author a lot of assistance from various parties
either directly or indirectly. With all humility author express gratitude and special
thanks to :
Prof. Dian Armanto, M.Pd, MA, M.Sc, Ph.D as Thesis Supervisor for
guidace, directions, advices, comments, suggestions and his precious time that he
spent on supervising this thesis so this thesis can be done well.
DR. E. Elvis Napitupulu, MS, Mulyono, S.Si, M.Si, and Prof. DR. S.
Saragih, M.Pd as her Examiner Lecturer for their advices, corrections, comments,
and suggestions for this thesis and Dra. Nerli Khairani, M.Si as Academic
Supervisor has been always give advice, Prof. DR. Ibnu Hajar,M.Si as her Rector
in State University Of Medan, Prof. Drs. Motlan, M.Sc, Ph.D as Dean of Faculty
of Mathematics And Natural Science in State University of Medan, Prof. Dr.
Mukhtar, M.Pd as Department Chairman, Drs. Yasifati Hia, M.Si as Department
Secretary, Drs. Syafari, M.Pd as Head of Mathematics Education Study Program
and all lecturers and employees of Mathematics Department who have taught,
advices, and guided her throughout her academic year at the university.
Drs. Murgap, M.Sc as Secretary in Ministry Of Education, Nursyam
Syamsuar Guci, B.Sc as Headmaster of SMP Budi Satrya, Indra Suardi, MA as
Headmaster of SMP Shafiyyatul Amaliyyah, Drs. Hasbullah as Vice Headmaster
of SMP Negeri 14 Medan have given permission to do the research in those
schools.
Her beloved mother and father for their endless love, pray, advices and
financial support that have enable her to finish her study, her beloved brothers(
Benhur Gultom,Rio Gultom, Rimba Gultom and Makmur Gultom) and her
beloved sisters (Yunita gultom, Berliana Gultom, and Evalina Gultom) and also
her nephews for love, pray, and advices.
Her friends in The Ruth small group and its former(Marni, Natalia, Dewi
Rotua, Sabtriana, Donna) and her older sister in The Ruth small group (K’ Murni
and K’Ika D) for pray, love and motivation. Her friends in Class B Mathematics
education (Tina m, Ervides, Otto, and others that can not be mentioned one by
one) for pray, love and motivation.
Hopefully the good of all parties avenged doubled from God.
iv
Author recognize that the preparation of the thesis is still far from perfect,
therefore suggestions and constructive criticism authors expect. Hopefully, this
paper can be useful for the purposes of education.
Medan, Februari 2013
Christina Gultom
ID Numb. 408111037
iii
ANALYSIS OF STUDENT ERRORS IN SOLVING PROBLEMS OF
ALGEBRA OPERATIONS IN CLASS VIII
MEDAN JUNIOR HIGH SCHOOL
ACADEMIC YEAR
2012/2013
By:
Christina Gultom
408111037
ABSTRACT
The purposes of this research is (1) Knowing kinds of students errors in solve
problems of algebra operations in class VIII(2) Knowing the level of students
errors in solve problems of algebra operation in class VIII (3) Knowing the factors
that causes students errors in solve problems of algebra operations in class VIII.
Population in this research was Medan Junior High School and the sample was
Class VIIID SMP Shafiyyatul Amaliyah,Class VIIIA SMP Budi Satrya and Class
VIIIC SMP Negeri 14 Medan taken of the data of Ministry Education in Medan.
All of subject in that 3 school is 98 students. Data collected by test, interview and
observation. Test used for knowing kinds of error and level error by student,
interview used for knowing the factors of students error when answer the question
and observation for knowing the factors of students errors from teacher. Analysis
method used is qualitative and quantitave description.
The result of research showed that : (1) kinds of errors which many done by
students were transformation error, skill process error and encoding error. (2) The
level of students error in solving problems of algebra operation in class VIII
Medan junior high school could be concluded that still very high error. (3) The
factors that causes students error in solving problems of algebra operation divided
into 2 factors: a. Internal factors (Lack of master concept,principle and skill in
algebra operation, Lack of master prerequisites material, Lack of exercise solving
mathematics problems, Students were careless) and b. External factors(Teacher
was not as good demonstrator, Teacher was not good controller class, and Teacher
was not good mediator).
vi
TABLE OF CONTENTS
Authentication sheet
Curriculum Vitae
Abstract
Preface
Table Of Contents
List Of Figure
List Of Table
List Of Appendices
CHAPTER I INTRODUCTION
Page
i
ii
iii
iv
vi
viii
ix
x
1.1. Background
1
1.2. Identification of the Problem
4
1.3. Boundary Problems
5
1.4. Problem Formulation
5
1.5. Research Purposes
5
1.6. Benefits of the Research
6
1.7. Operational Definition
6
CHAPTER II REVIEW OF LITERATUR
2.1. Mathematics Achievement
7
2.2. Errors in Mathematics Instruction
8
2.3. Errors In Solve Math Problems
10
2.4. The Level of Student errors
14
2.5. The factors that Cause Student Errors
14
2.6. Algebra Operation
17
2.6.1. Meaning of Algebra
17
2.6.2. Meaning of Multiplication, powers, and division it the
Algebra of singular tribe
2.6.3. Substitute Numbers in The Algebra
18
18
2.6.4. Addition and Substraction in Similar Tribe and Unsimilar
Tribes
18
2.6.5. Power of Fractions on Algebra
19
2.6.6. Algebra Fraction
19
2.6.7. Special Multiplication of Algebra
20
vi
2.7. Conceptual Framework
21
CHAPTER III RESEARCH METHODOLY
3.1. Research Sites
23
3.2. Time of Research
23
3.3. Popolation and Sample
23
3.4. Type of Research
24
3.5. Method of Data Collection
24
3.4.1 Test
24
3.4.2 Obsevation
27
3.4.3 Interview
27
3.5. Data Analysis
29
3.6. Procedural of Research
32
CHAPTER IV RESULT OF RESEARCH AND DISCUSSION
4.1. Result of research
34
4.1.1. Description of test
34
4.1.2. Description of test and interview
38
4.1.3. Description of observation
47
4.2. Discussion
48
CHAPTER V CONCLUSSIONS AND SUGGESTIONS
5.1. Conclussions
55
5.2. Suggestions
56
REFERENCES
57
ix
LIST OF TABLE
Table 2.1.
Table 2.2.
Table 3.1.
Table 3.2.
Table 3.3.
Table 4.1.
Table 4.2.
The Level of student mastery
The Level of student errors
Schedule of research in three school
Blueprint of diagnostic test problem of algebra operation subject
The guidelines of checking students errors
The percentage of kinds of errors
The Level Of Students Errors In Solving Problems Of Algebra
Operation in Class VIII Medan Junior High School
14
14
23
25
29
36
38
viii
LIST OF FIGURE
Figure 1.1. Student Answer 1
Figure 2.1. Factors that Influence mathematics teaching and learning
Process
Figure 3.1. Procedural of Research
Figure 4.1. The Chart Of Student Errors In Each Kinds Of Errors
Page
3
9
33
37
x
LIST OF APPENDICES
Appendix 1. Diagnostics Test Problems
Appendix 2. The answer of diagnostic test
Appendix 3. Kinds of students error SMP Budi Satrya
Appendix 4. Kinds of students error SMP Negeri 14 Medan
Appendix 5. Kinds of students error SMP Shafiyyatul Amaliyyah
Appendix 6. The Number Of Students Who Answered Correctly And
Incorrectly In SMP Budi Satrya
Appendix 7. The Number Of Students Who Answered Correctly And
Incorrectly In SMP Negeri 14 Medan
Appendix 8. The Number Of Students Who Answered Correctly And
Incorrectly In SMP Shafiyyatul Amaliyyah
Appendix 9. Analysis data SMP Budi Satrya
Appendix 10. Analysis data SMP Negeri 14 Medan
Appendix 11. Analysis data SMP Shafiyyatul Amaliyyah
Appendix 12. Observation sheet in Budi Satrya
Appendix 13. Observation sheet in SMP Negeri 14 Medan
Appendix 14. Observation sheet in SMP Shafiyyatul Amaliyyah
Appendix 15. Indikator penilaian observasi guru mengajar
Appendix 16. Validation sheet
Appendix 17. Research Documentation
Appendix 18. teachers’ lesson plan
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CHAPTER I
INTRODUCTION
1.1.
Background
Education is a process of changing a person's behavior and ability toward
progress and improvement. Education can change a person's mindset to always
make innovations and improvements in all aspects of life in the direction of self
improvement as develop knowledge insight, able to adjust the daily problems they
face, positive attitude and behavior towards the social and natural environment.
Mathematics education has important role because the mathematics is
basic science that used in various fields of life. Through the learning of
mathematics students are expected to develop critical thinking abilities, logical,
systematic, thorough, effective, and efficient in solving problems. Like Cornelius
expressed (in Abdurrahman 1999:253) that:
“Five reasons for studying mathematics because mathematics is:means to
think clear and logical, means to solve daily problems, means to know
the patterns of relationships and generalization of experience, means to
develop creativity, and means to raise awareness towards cultural
development.”
No doubt anymore that every student must get mathematics subject in
school. As the purposes of mathematics have been given in the school, we can see
that school mathematics held important role. Generally the purposes of
mathematics
in
the
school
can
be
classified
become(in
http://p4tkmatematika.org/2011/10/peran-fungsi-tujuan-dan-karakteristikmatematika-sekolah/) : 1)formally purpose is emphasize to organize reasoning
and form the students personality ,2) material purpose is emphasize to problem
solving and apply mathematics. So, it is important to realize benefits of
mathematics as a subject that is very important in human civilization, especially in
education system in the world.
However, in reality, nowadays Indonesian student’s mathematics
achievment is still low. The low mathematics achievement is demonstrated by the
low value of daily tests, semester, or UN (National Examination) in mathematics.
Moreover according to data from the Trends in Mathematics and Science Study
(TIMSS),
“the average score of Indonesian students' mathematics achievement in
1999, 2003, and 2007 in a row were 435, 420, and 433. By the score the
1
2
Indonesian students got rank 34th out of 38 countries in 1999, ranked 35th
of 46 countries in 2003, and ranked 36 th of 49 countries in 2007. The
average score of Indonesian students in the TIMSS 2007 substandard of
500, and only reached Low International Benchmark. By these
achievements, the average of Indonesian students are only able to
recognize a number of basic facts but haven’t been able to communicate
and relate various topics of science,moreover apply complex and abstract
concepts.”(Http://litbang.kemdikbud.go.id/detail.php?id=214)
The low student mathematics ability can be seen from the students'
mastery towards material. One of way is giving test or a problems about the
material to the students. Students errors in solving problems can be one of clues to
know how far students master the materials. Therefore, the presence of these
errors need to be analyzed and searched by any factors that influence. Thus,
informations about errors in solving mathematics problems can be used to
improve the quality of teaching and learning activities and ultimately improve
student mathematics achievement.
Mathematics consist of four broad insight is algebra, arithmetic,
geometry, and analysis. Algebra is one part of mathematics that includes variety
of material learned in junior high school. Learning algebra is very useful for
students in learning (understanding) and other mathematical material and algebra
concepts in higher education. For example, mastery of algebra concepts is helpful
to learn the concepts of geometry built flat in search of an angle. For example, the
angle of triangle.
According to Walle(2008:1) “Thinking algebra or algebra logic is one of
them is to generalize from experience with numbers and calculation, formulate
ideas by using a symbol system that are useful, and explore the concept of
patterns and function.” Thus, through studying algebra well, someone will have
analytical abilities. This abilities have an important role in the study of
mathematics is relatively complex. Thus, understanding the concepts of algebra
operation is essential as a basis for understanding other concepts of mathematical
material.
In Medan especially, students’ algebra operation abilities is still weak, it
is known based on the observations of researcher at three junior high schools in
3
Medan. The schools were selected by the category of high quality, medium, and
low based on the UN in Academic Year 2010/2011. The three schools were SMP
Shafiyyatul Amaliyyah with high quality category based on the UN 2010/2011
had an average of mathematics was 9.01; SMP Budisatrya with medium quality
category based on the UN 2010/2011 had an average mathematics was 8.90; SMP
Negeri14 Medan with low quality category based on the UN 2010/2011had an
average mathematics was 7.13. However, after researcher had given tests at the
time of observation it appears that the average value of the students in solving
problems of algebra operation in SMP Syaffiyatul Amaliyyah only 2.75 from 10;
SMP Budisatrya only 1.15 from 10; SMP Negeri 14 Medan only 2.75 from 10 .
This is very apprehensive, these schools are still very weak in algebra because
many students made errors in algebra operation. The example of students errors
in algebra operation is like this:
Problems:
Determine the multiplication of (3x-2)(x-1)
Student answer:
Figure 1.1. Student answer 1
From the student answer, concluded that student made error in transformation
errors because student disable identify the sequence of operation, skills process
errors because student didn’t know the procedure and encoding errors because
student error in solution. This could be caused because students have not
understanding
the concept and principle yet and poorly practise in solving
mathematics problem so that made error in skill in algebra operation. If this issues
aren’t overcomed so the students will dislike mathematics because they feel
mathematics is difficult. So that, the student errors must be analyzed and searched
what factors that cause it. Detailed error analysis is very needed so that students
errors and its factors can be seen further to help overcome these problems.
4
Many factors cause the low students’ mathematics ability. As Slameto
(2010:54-72) classified factors of learning, that is internal factor and external
factor. Internal factors are physical(health and handicap), physicological
(intelligent, careful, interest, talent, motive, maturity, readiness) and weariness
factor. While external factors are family ( manner of parents educate, relation
among member of family, house condition, family economics, parents
understanding, background of culture), school (teaching method, curriculum,
relation between teacher and student, relation among students, discipline of
school, instrument instruction, time of school, standard of subject over measure,
facilities, method learning, and homework), and community factor
(students
activities in community, media mass, friends and life condition of community). In
this research the factors will be seen from students and teacher. The factor from
student will be analyzed by work result in algebra operation, and the factor from
teacher will be analyzed by teacher role in teaching and learning process.
Based on this background, the researcher try to analyze students errors in
solving problems of algebra operations. For that, researchers chose the title
"Analysis Of Students Errors in Solving Problems of Algebra Operations in Class
VIII Medan Junior High School Academic Year 2012/2013". Analysis students
errors made by searching errors and factors that cause it. Thus, errors in solving
problems of algebra operations can be minimized so that mathematics
achievement can be improved.
1.2.
Identification of the Problem
Based on the background, can be identified some of issues that
arise in algebra learning are:
1. Students were poorly understand mathematics
2. Almost students made errors in algebra operations
3. Students made errors in transformation, skills process and encoding
errors in solving problems of algebra operations.
5
1.3.
Boundary Problems
In order to focus the research, this research only reveals the
errors and factors that cause students errors in solving problems of
algebra operations in class VIII Medan Junior High School Academic
Year 2012/2013.
1.4.
Problem Formulation
Based on the boundary problems above, the formulation of the
problem is:
1.
What kinds of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013?
2.
What is the level of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013?
3.
What are the factors that cause the students’ errors in solving
problems of algebra operations in class VIII Medan junior high school
Academic Year 2012/2013?
1.5.
Research Purposes
The purposes of this research is:
1.
Knowing kinds of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013.
2.
Knowing the level of students errors in solving problems of algebra
operations in class VIII Medan junior high school Academic Year
2012/2013?
3.
Knowing the factors that causes students errors in solving problems
of algebra operations in class VIII Medan junior high school
Academic Year 2012/2013.
6
1.6.
Benefits of the research
The benefits of this research are as follows:
1.
For teachers
a. Provide information about kinds of students errors in solving
problems of algebra operations.
b. Provide information about the factors that causes students errors in
solving problems of algebra operations.
c. Provide information about teacher shortage that causes students
errors in solving problems of algebra operations so that can give
the best solution.
2.
For students
Provide information about students errors so that they can learn
more to improve their achievement in mathematics especially in
algebra operation.
3.
For Headmaster
a. As a consideration to prepare the school curriculum.
b. Command every teacher make analysis of students errors for each
of held material.
4.
For next researchers
As a consideration and input for similar research.
1.7.
Operational Definition
a. Error
The error is defined as the deviation from the right and its systematic,
consistent and incidental to the particular section. Thus, the error is a
mistake of the student in solving problems.
b. Students Error
Students Errors are mistake of the student in solving problems.
Analysis of Errors is a description of mistakes made by students in
solving problems.
CHAPTER V
CONCLUSIONS AND SUGGESTIONS
5.1. CONCLUSIONS
1) Kinds of errors in solving problems of algebra operation in Class VIII
Medan Junior High School were: transformation error, skill process
error and encoding error.
2) The level of students error in solving problems of algebra operation in
Class VIII of sample can be concluded that still very high error.
3) The factors that causes students error in solving problems of algebra
operation divided into 2 factors:
1. Internal factors
a. Lack of master concept,principle and skill in algebra operation
b. Lack of master prerequisites material
c. Lack of exercise solving mathematics problems
d. Students were careless
2.
External factors
a. Teacher was not as good demonstrator
b.
Teacher was not as good controller class
c.
Teacher was not as good mediator
55
56
5.2. SUGGESTIONS
The suggestions can be given so that students mathematics achievement
can be improve,especially in algebra operations :
1.
For teachers
a. Teacher must repair the teacher role in teaching as demonstrator,
controller class and mediator especially.
b. Teacher must analyze students errors in solving mathematics
problems so that teacher know what is the causes of students error
and can give the best solution.
c. Teacher create instruction method that can stimulate students
respond in learning mathemtics.
2.
For students
Students must be often exercise mathematics problems especially
algebra operation so that can improve students mastery in
mathematics.
3.
For Headmaster
Command every teacher make analysis of students errors for each
of held material.
4.
For next researchers
a. This research can be made the similar research in another
material.
b. Specify kinds of error before doing this research.
REFERENCES
Abdurrahman, Mulyono. 2009. Pendidikan Bagi Anak Berkesulitan Belajar.
Jakarta: PT. Rineka Cipta
Arikunto, suharsimi. 2010. Prosedur Penelitian suatu pendekatan praktik. Jakarta:
PT. Rineka Cipta
_______, ________. 2011. Dasar-Dasar Evaluasi Belajar. Jakarta: Bumi Aksara
Direktorat Pembinaan SMP. 2007. Pedoman Pengembangan Tes Diagnostik Mata
Pelajaran IPA SMP/MTs. Jakarta: Direktorat Jenderal Manajemen
Pendidikan
Dasar
Dan
Menengah.
(http://www.google.co.id/url?sa=t&rct=j&q=tes%20diagnostik&source=
web&cd=2&cad=rja&ved accessed on September 19,2012)
Ekawati, estina. 2011. Peran, Fungsi, Tujuan, dan Karakteristik Matematika
Sekolah.
Jakarta:
Kementrian
Depdikbud
RI.
(http://p4tkmatematika.org/2011/10/peran-fungsi-tujuan-dankarakteristik-matematika-sekolah/ accessed on Mey 17,2012 )
Junaidi, wawan.2010. Pembelajaran Matematika. Semarang:Universitas Negeri
Semarang.(http://wawan-junaidi.blogspot.com/2010/06/pembelajaranmatematika.html accessed on September 4,2012)
Moleong, Lexy. 2010. Metodologi Penelitian Kualitatif edisi revisi. Bandung: PT.
Remaja Rosdakarya Offset
Nasution, s. 2010. Kurikulum dan Pengajaran. Jakarta: PT. Bumi Aksara
Purwanto. 2011. Evaluasi Hasil Belajar. Yogyakarta: Pustaka Pelajar
Rihdawati, santi.2011. Analisis Kesalahan Siswa Dalam Menyelesaikan Soal-Soal
Pada Pokok Bahasan Persamaan Kuadrat Siswa Kelas I(Bab II).
Yogyakarta:
UNY.(http://skripsiplus.blogspot.com/2011/05/analisiskesalahan-siswa-dalam.html accessed on September 3,2012.
Sabri, achmad. 2007. Strategi Belajar Mengajar Micro Teaching. Padang: Ciputat
press group
Samosir, ernawati.2012. Penerapan Genius Learning Strategy Untuk
Meningkatkan motivasi dan Hasil Belajar Siswa Pada Pokok Bahasan
Bilangan Bulat Di Kelas VII SMP Negeri 10 Medan T.A. 2011/2012.
Medan: UNIMED
58
59
Setiyawati, indra.2011. Identifikasi Kesalahan Dalam Menyelesaikan Soal Cerita
Materi Pelajaran Segitiga Dan Segi Empat Siswa Kelas Vii Smp N 5
Depok Sleman Yogyakarta Tahun Ajaran 2010/2011. Yogyakarta: UNY.
(http://eprints.uny.ac.id/1892/1/Skripsi_Indra_Setiyawati.pdf accessed on
September 4,2012)
Slameto. 2010. Belajar dan faktor-faktor yang mempengaruhinya. Jakarta: PT.
Rineka Cipta
Sukardi. 2009. Metodologi Penelitian Pendidikan kompetensi dan praktiknya.
Jakarta: PT. Bumi Aksara
Syah, Muhibbin. 2010. Psikologi Pendidikan dengan Pendekatan Baru. Bandung:
PT. Remaja Rosdakarya
Walle, Jhon. 2006. Matematika Sekolah Dasar dan Menengah Pengembangan
Pengajaran (authorized translation from Elementary and middle school
mathematics sixth edition). Jakarta: Erlangga
Widoyoko, E.Putro. 2012. Teknik Penyusunan Instrumen Penelitian. Yogyakarta:
Pustaka Pelajar
www.downloads.ziddu.com/downloadfile/16751212/siKemampuanSiswadalamM
enyelesaikanSoal-soalAljabar.doc.html (accessed on September 4,2012)
www.fadjarp3g.files.wordpress.com/2008/12/download_08_gagne_median_1.pdf
(accessed on September 4,2012)
www.litbang.kemdikbud.go.id/detail.php?id=214( accessed on September 4,2012)
www.tips-belajar-internet.blogspot.com/2009/08/hasil-belajar-matematika.html
(accessed on September 16,2012)
www.uns.ac.id/data/0019a.pdf (accessed on January 20, 2012)