ANALYSIS OF STUDENT ERRORS IN SOLVING PROBLEMS OF ALGEBRA OPERATIONS IN CLASS VIII MEDAN JUNIOR HIGH SCHOOL ACADEMIC YEAR 2012/2013.

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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

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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.

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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

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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.

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LIST OF TABLE

Table 2.1. The Level of student mastery 14

Table 2.2. The Level of student errors 14

Table 3.1. Schedule of research in three school 23

Table 3.2. Blueprint of diagnostic test problem of algebra operation subject 25

Table 3.3. The guidelines of checking students errors 29

Table 4.1. The percentage of kinds of errors 36

Table 4.2. The Level Of Students Errors In Solving Problems Of Algebra

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LIST OF FIGURE

Page

Figure 1.1. Student Answer 1 3

Figure 2.1. Factors that Influence mathematics teaching and learning

Process 9

Figure 3.1. Procedural of Research 33

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LIST OF APPENDICES

Appendix 1. Diagnostics Test Problems 59

Appendix 2. The answer of diagnostic test 65

Appendix 3. Kinds of students error SMP Budi Satrya 70

Appendix 4. Kinds of students error SMP Negeri 14 Medan 83

Appendix 5. Kinds of students error SMP Shafiyyatul Amaliyyah 97

Appendix 6. The Number Of Students Who Answered Correctly And

Incorrectly In SMP Budi Satrya 105

Incorrectly In SMP Negeri 14 Medan 107

Incorrectly In SMP Shafiyyatul Amaliyyah 109

Appendix 9. Analysis data SMP Budi Satrya 111

Appendix 10. Analysis data SMP Negeri 14 Medan 116

Appendix 11. Analysis data SMP Shafiyyatul Amaliyyah 121

Appendix 12. Observation sheet in Budi Satrya 124

Appendix 13. Observation sheet in SMP Negeri 14 Medan 126

Appendix 14. Observation sheet in SMP Shafiyyatul Amaliyyah 128

Appendix 15. Indikator penilaian observasi guru mengajar 130

Appendix 16. Validation sheet 133

Appendix 17. Research Documentation 139

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1 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-karakteristik-matematika-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),

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Indonesian students got rank 34th out of 38 countries in 1999, ranked 35th of 46 countries in 2003, and ranked 36th 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.

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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

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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

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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

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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

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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

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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.

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