High Mathematical Ability Research Articles

PROFIL KOMUNIKASI MATEMATIKA TULIS SISWA SMP DALAM MEMECAHKAN MASALAH MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA SISWA

One factor in learning mathematics is the need for communication skills. Carpenter & Gorg (2000: 60) states "Communication is an essential part of mathematics and mathematics education", which means that communication is an important part of mathematics and mathematics education. Mathematical communication is related to problem solving, because with the existence of mathematical communication students will understand better in solving mathematical problems. This qualitative descriptive study aims to describe the written mathematics communication of junior high school students in solving mathematical problems in terms of students' mathematical abilities. The data obtained came from three subjects, namely VIII grade junior high school students who had received the material system of two-variable linear equations (SPLDV). The three subjects consisted of students with high mathematical abilities, students with moderate mathematical abilities, and students with low mathematical abilities. The results of this study are the accuracy of writing mathematics for high ability and medium ability students is declared accurate, but low abilities is not declared accurate. In the completeness aspect, high ability and medium ability students written mathematics communication is complete for any information that has been submitted. But, student with low abilities is not complete. In the aspect of fluency, students with high abilities are able to communicate fluently in mathematics, but students with moderate and low abilities cannot fluently.
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 Keywords: Mathematical Communication, Problem Solving, Mathematical Ability.

Analisis Pemecahan Masalah Berdasarkan Teori Pemrosesan Informasi

The purpose of this study is to describe students' thought processes in solving mathematical problems based on information processing theory. This research is a descriptive study with a qualitative approach that uses data collection techniques using the method of think aloud and interviews. The instrument in this study used written test questions and interview guidelines. The subjects in this study consisted of one high ability person, one moderate ability student and one low ability student. The results showed that information or stimulus in the form of questions received by students with high, medium, and low mathematical abilities entered the sensory register through the sense of sight and sense of hearing. Then attention occurs after reading the problem and perception arises. Next, students realize perception by retrieval the concepts needed from long term memory to solve problems. When conducting a retrieval of students with moderate mathematical abilities, there is a student who experiences a retrieval failure in explaining the concept. Then for students who have low mathematical ability, the concepts needed for short term memory are not stored well by long term memory, so students often experience errors and forget.

The Effect of the Jigsaw Cooperative Learning Model and the Student’s Initial Mathematical Abilities and Its Effect on the Mathematical Representation Ability and Learning Motivation of Students in the PAB 10 Sampali Private Elementary School

The Influence of Jigsaw Cooperative Learning Model on Mathematical Representation Ability and Student Learning Motivation at PAB 10 Sampali Private Elementary School. Thesis. Medan: UNIMED Postgraduate Program, 2020. This study aims to determine 1) the magnitude of the influence of the learning model on students' mathematical representation abilities and learning motivation; 2) the magnitude of the influence of early mathematical abilities on the ability of mathematical representation and student learning motivation; and 3) the interaction between the learning model and the initial mathematical ability of the mathematical representation ability and student learning motivation. The research was conducted in private SD PAB 10 Sampali with a sample of 2 classes with each class totaling 35 students. This research is a type of experimental research all with a 2 × 2 factorial design. The results showed that there is an effect of the learning model on the students 'mathematical representation ability, where the jigsaw cooperative learning model has a 9.1% higher effect on students' mathematical representation abilities than the expository learning model, there is an effect of initial mathematical ability on students 'mathematical representation abilities, where the high initial mathematical ability of students has an 11.5% higher effect on students' mathematical representation abilities compared to low initial mathematical abilities, there is no interaction between the learning model and the students 'mathematical initial ability to the students' mathematical representation ability.

ANALISIS KEMAMPUAN BERPIKIR KRITIS DALAM PEMECAHAN MASALAH MATEMATIKA

Critical thinking ability is essential for the future of students, bearing in mind that it used to prepare students for the many challenges that will arise in their lives, careers, and at the level of their obligations and responsibilities. Critical thinking ability is crucial for students to master so that students are more skilled in preparing an argument, checking the credibility of a source, or making a decision. Critical thinking ability is an essential component that students must-have, especially in the process of learning mathematics. That student can create or formulate, identify, interpret, and plan problem-solving. Critical thinking is a high-level ability to think in terms of analyzing, managing strategies, evaluating, building a logical and clear argument, and drawing conclusions in solving a problem. This research is qualitative research with a phenomenological approach. The purpose of this study is to describe the students' critical thinking skills in solving mathematical problems in the material of the Two-Variable Linear Equation System (SPLDV). The subjects of this study were students of class VIII (eight) who had high mathematical abilities at one of the public Junior High Schools in Purworejo. Based on the results of research and discussion, students' critical thinking ability in solving mathematics problems of junior high school students who have top mathematical skills have been able to achieve all the indicators of critical thinking.

Proses Berpikir Aljabar Siswa SMP Ditinjau Dari Kemampuan Akademik Matematika Dan Gender

The purpose of this research is to know algebra thinking process of students in rectangular material reviewed from Mathematics ability and gender. The method of this research was qualitative descriptive. The research subjects were 9 female students and 9 male students of grade IX with high, medium, and low Mathematics ability. The research instruments were test and interview. The research results show that female students with high ability have algebra thinking. Male students with high ability have algebra thinking but indicator of concluding and rechecking was not fulfilled yet. Female students with medium ability have algebra thinking but there was carelessness in the calculation. Male students with medium ability have started to thought algebra but at indicator of interpreting and applying Mathematics findings was not fulfilled yet. Female and male students with low ability do not think algebra yet because all indicators were not fulfilled. This occurred because they still did not understand algebra concept until they could not solve Mathematics problem. Female and male students with high and medium ability who already thought algebra can solve Mathematics problem. However, female and male students with low ability still do not think algebra until they cannot solve the problem.

Adaptive Reasoning of Students in Solving Beam Problems in Elementary School

This study aims to describe the adaptive reasoning of students in solving beam mathematical problems with high, medium, and low mathematical solving abilities. The research location is at Siti Aminah Surabaya elementary school, with 24 students in grades VI-A and will take 3 students as research subjects. This study uses qualitative research, by conducting several stages, namely, preparation, implementation, and analysis. Data analysis techniques used observation methods, tests of ability to solve mathematical problems (TPMM), and interviews. The results showed students with high mathematical abilities students were able to collect data then identify the components of the building blocks, be able to provide evidence and explanations and verify what he had obtained. Students with mathematical abilities while students are able to understand the problem by reading repeatedly to be able to explain and verify their findings. Students with low mathematical abilities are able to understand after doing trial and error, understanding from many data sources. From the experience and data sources obtained by students, they are only able to understand the problems, construct and connect with objects around them, gather information, so they can provide an explanation of the concept and verify it.

KESULITAN BELAJAR MATEMATIK SISWA SEKOLAH DASAR PADA OPERASI HITUNG BILANGAN BULAT

One of the goals of teaching mathematics in elementary schools is students are able to understand mathematical concepts, explain the interrelationships of the concepts and apply algorithmic concepts in a flexible, accurate, efficient and precisely in solving their daily problems. The elementary schools nowadays show that there are still found many students who have difficulty in solving problems related to the subject matter, especially on arithmetic operations of integers. This research is a qualitative descriptive study. Students in first grade are given a worksheet to solve individually by writing out the work steps clearly. Six students were chosen as research subjects to be analyzed. The sixth research subject consists of 2 subjects who have high mathematical abilities, 2 medium, and 2 low mathematical abilities. The difficulty of the subject was observed by examining the worksheet's answer and giving clinical interviews related to the results of his work. Based on the results of data analysis, the difficulty of learning mathematics of elementary school students in integer operations is: 1) students have difficulty understanding the purpose of the question so that it incorrectly translated into mathematical sentences; 2) students have difficulty operating numbers that contain negative signs; 3) 95% of students have difficulty understanding the meaning of equal sign (=); 4) students have difficulty carrying out the division operations.

Developing Mathematics Module Based on Literacy and Higher Order Thinking Skills (HOTS) Questions to Train Critical Thinking Ability of High School Students in Mojokerto

This research aims to describe the process and results of the developing mathematical module based on literacy and higher order thinking skills (HOTS) to train the critical thinking ability of high school students in Mojokerto that are valid, practical and effective. This research is a development research that uses an adopted Tessmer development model. The subjects of this research were 11th grade students at SMAN 1 Puri Mojokerto. Three students with high, medium and low mathematical ability for the One to One stage. In the Small Group stage, nine students, with the provisions of three students with high mathematical ability, three students with middle mathematical ability, and three students with low mathematical ability. While the field test stage, the research subjects were 30 students with heterogeneous mathematical ability. The students’ mathematical abilities were seen from the first semester of academic year report scores and in each stage. The development process starts from the preliminary stage, which is conducting literature studies about mathematics module based on literacy and HOTS questions, this process then followed by contacting the headmaster and teachers regarding the research schedule. The next stage is the self-evaluation, this stage consists of the analysis and design stages that analyze the students as the subject of this research and material used in the research. The materials used are Mathematical Induction, Linear Program, Matrix and Geometry Transformation, and designing a prototype. The third stage is prototyping, this stage consists of experts review, one to one, small group and field test. In the expert review, a prototype II was produced which were said to be valid. Whereas in the one to one, three students were tested and III prototypes were produced. The small group, a trial was conducted and a prototype IV was produced. Then the field test, testing and produced mathematical modules that met the valid, practical and effective. The results of this study are mathematics module based literacy and HOTS questions to train critical thinking ability that meet the validity criteria with valid categories, fulfill practical criteria with a very practical level. As well as meeting the module’s effectiveness criteria by having students’ critical thinking ability either high or high.

PROFILE OF OPEN-ENDED PROBLEM SOLVING BASED ON POLYA’S STEPS VIEWED FROM MATHEMATICAL ABILITY LEVEL OF JUNIOR HIGH SCHOOL STUDENTS

Problem solving is one of several important abilities a student must have. Problem solving is a planned process that mustbe done in order to get a certain solution of a problem that is not obtained immediately. One type of problem studentsmust solve is an open-ended problem. Open-ended problem solving for every student is certainly different from oneanother. The level of mathematical ability of students is one of the factors that influence these differences. This type ofresearch is a qualitative descriptive with the purpose to describe the profile of open-ended problem solving based onPolya’s steps viewed from mathematical ability level of junior high school students. Three students from grade VII arethe subjects in this research (one student having high mathematical ability, one student having moderate mathematicalability, and one student having low mathematical ability). This research uses instruments mathematical ability test, openended problem solving test, and interview guidelines. The results showed there were differences in the open-endedproblem solving profile on students with high, moderate, and low mathematical ability. Student with high mathematicalability can carry out all the steps of Polya’s problem solving. Student with moderate mathematical ability are able to carryout the step of understanding the problem, devising a plan, carrying out the plan, however there are indicators that are notfulfilled at looking back’s step they are using the other way to solve the problem and make conclusion. Student with lowmathematical ability can not show the adequacy of the data at understanding the problem’s step and can not carry out thesteps of devising a plan, carrying out the plan and looking back.

PROSES BERPIKIR REFLEKTIF SISWA SMA DALAM MENYELESAIKAN SOAL CERITA MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA

Being someone literate by statistics is very important for each individual to be able to interpret statisticalmessages in various contexts. This research is a descriptive-qualitative study to describe the statisticalliteracy profile of high school students in solving statistical problems based on mathematical ability. Thedata collection method uses written tests and interviews. The research subjects were one student with ahigh mathematical ability category and one student with a moderate mathematical ability category. Theresults showed that: (1) students with high mathematical abilities can understand data, interpret data, andevaluate data well. Students with a high mathematical ability to communicate data by presenting data inthe form of diagrams or graphs, but without considering the characteristics of the data in the presentation;(2) while students with moderate mathematical ability can understand data well. The results of datainterpretation of moderate mathematical students' ability experience errors in terms of determiningaverages and data distribution and communicating data by presenting data in the form of diagrams orgraphs that experience misconceptions related to the presentation of bar charts and histograms.

STUDENTS’ STRATEGIC COMPETENCE PROFILES IN SOLVING MATHEMATICS PROBLEM BASED ON LEARNING STYLES

The purpose of this research was to describe the profiles of students' strategic competences that havevisual, auditory, and kinesthetic learning style in solving mathematics problem. There were three subjects,one visual student, one auditory student, one kinesthetic student, which were chosen from the eleventhgrade students of Science with high mathematical abilities, good communication skills, and the samegender. The instruments used were the VAK learning style test, the mathematics ability test, themathematics problem solving test, and the interview guidelines. The results obtained the description ofvisual student profile, auditory student profile, and kinesthetic student profile in selecting andimplementing strategies when formulating, representing, and solving problems, as follows: (1) visualstudent read silently, imagined, and drew to understand the problem; mentioned the known and unknowninformation verbally with the help of images; used images and symbols to represent problems; observed,analyzed and broke down images to find relevant concepts and formulas; solved the problem using thoseconcepts and formulas. (2) Auditory student read in a low voice and drew to understand the problem;mentioned the known and unknown information verbally and in writing; used images and symbols torepresent problems; observed images and recalled her knowledge to find relevant concepts and formulas;solved the problem using those concepts and formulas. (3) Kinesthetic student read silently while drawingto understand the problem; mentioned the known and unknown information verbally followed by her bodycues; used images and symbols to represent problems; observed, analyzed and broke down images to findrelevant concepts and formulas; solved problems using those concepts and formulas; random checked toexamine her solution. The results of this study are important as information for mathematics teachers aboutthe strategic competences of visual, auditory, and kinesthetic students in solving mathematics problems.From this information, mathematics teachers are expected to be able to design learning that can facilitateall students in developing their strategic competences.

PROSES BERPIKIR REFLEKTIF SISWA SMA DALAM MENYELESAIKAN SOAL CERITA MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA

Penelitian ini bertujuan untuk mendeskripsikan proses berpikir reflektif siswa SMA dalam menyelesaikansoal cerita matematika ditinjau dari kemampuan matematika. Jenis penelitian ini adalah penelitiankualitatif yang bersifat deskriptif. Subjek penelitian ini adalah siswa kelas X SMA yang terdiri dari siswadengan jenis kelamin laki-laki, komunikatif, berkemampuan matematika tinggi (ST), sedang (SS), danrendah (SR) masing-masing satu orang. Instrumen penelitian yang digunakan terdiri dari tes kemampuanmatematika (TKM), tes berpikir reflektif (TBR), dan pedoman wawancara. Hasil penelitian ini ketigasiswa menunjukkan proses berpikir reflektif pada tahap reacting dimulai dengan mendeskripsikan halyang diketahui dan hal yang ditanyakan, menjelaskan hubungan antara yang ditanya dengan yangdiketahui disertai dengan alasan. Pada tahap comparing, ST mengklarifikasi pernah mengahadapi soalyang serupa sebelumnya dengan menganalisis persamaan dan perbedaannya, menyatakan metodeeliminasi-substitusi adalah metode yang efektif, menjelaskan proses penyelesaian yang diperoleh danmeyakini penyelesaian yang diperoleh sudah benar. SS mengklarifikasi tidak pernah menghadapi soalyang serupa sebelumnya, menyatakan metode eliminasi-substitusi adalah metode yang efektif,menjelaskan proses penyelesaian yang diperoleh. Sedangkan SR, mengklarifikasi pernah mengahadapisoal yang serupa sebelumnya dengan menganalisis persamaan dan perbedaannya, menjelaskan prosespenyelesaian yang diperoleh walaupun siswa tidak menjawab apa yang ditanyakan pada soal cerita yangdiberikan. Pada tahap contemplating, ST memeriksa kembali penyelesaian yang diperoleh, membuat danmeyakini kesimpulan yang diperoleh. Sedangkan SS dan SR, tidak memeriksa kembali penyelesaian yangtelah diperoleh. Namun, saat diminta untuk memperbaiki kesalahan dari jawaban yang diperoleh, SSmemperbaikinya serta membuat kesimpulan sedangkan SR tidak memperbaiki dan tidak membuatkesimpulan.

The Mathematical Critical Thinking of MTs Students in Solving Math Problems

The purpose of this descriptive qualitative research was to provide a description of the mathematical critical thinking skills of MTs students in solving mathematical problems, more precisely in the context of a flat side room shape. The research subjects were selected based on the UTS Math score. Subjects who were Grade VIII students of the Riau Technology Islamic Boarding School were grouped into high, medium, and low mathematical abilities. From each group, one student who has good communication skills is chosen as the research subject. After giving tests and interviews to the three subjects, the results obtained showed that the average test for each indicator of mathematical critical thinking skills at the inference stage reached 96.83, the analysis stage reached 88.33, the evaluation stage reached 79.33 and the inference stage reached 59.83. Each subject has different critical thinking skills according to the indicators of mathematical critical thinking skills

KARAKTERISTIK INTUISI SISWA SMP DALAM MEMECAHKAN MASALAH MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA

The purpose of this study is to describe the intuition characteristics of junior high school students in solving mathematical problems viewed from mathematical abilities. This research based on qualitative descriptive study. The subjects of this study were taken from Lab School UNESA Junior High School, which consisted of three students from class VIII A, namely one student with high, moderate, and low mathematical ability. The method that used to collect data consists of the mathematical ability test, problem solving test and so of the interview method. Data analysis uses the intuitive characteristic indicators at each stage of the problem solving. The conclusion of this study indicate that student with high mathematical ability at the stage of understanding the problem using affirmatory intuition with the characteristics of extrapolativeness, intrinsic certainty and perseverance, at the stage of making plans using anticipatory intuition with the characteristics of global ideas, and at the stage of carrying out plans and checking again not using intuition. Student with moderate mathematical ability at the stage of understanding the problem using affirmatory intuition with the characteristics of extrapolativeness, intrinsic certainty and perseverance, at the stage of making plans using anticipatory intuition with the characteristics of global ideas, and at the stage of carrying out plans and checking again not using intuition. Student with low mathematical ability at the stage of understanding the problem using affirmatory intuition with the characteristics of perseverance and coerciveness, at the stage of making plans using anticipatory intuition with the characteristics of global ideas, and at the stage of carrying out plans and checking again not using intuition. Keywords: Intuition, Problem solving , Mathematics ability

The Decision Making Process of High School Students with High Mathematical Ability in Solving Social Arithmetic Problems

The decision making process is the individual steps in choosing an appropriate alternative choice from the various alternatives available to solve the problem. The purpose of this study is to describe the decision making process of high school students with high mathematical abilities in solving social arithmetic problems. The research approach used in this study is qualitative research. While the type of research is a qualitative descriptive study. The process of collecting data uses several instruments consisting of mathematics ability tests, social arithmetic problem solving tests, and interview guidelines. This research was conducted on 11th grade high school students in one of the state high schools in Sidoarjo. The subjects of this study consisted of one student with high mathematical abilities. The data collection method in this study began with the provision of mathematics ability tests for all students followed by selecting one subject with high mathematical ability through several considerations. The next step, the subject is given a problem solving test and interviewed to get the decision making process carried out by the subject. The results showed that students with high mathematical abilities carried out a series of activities in the stages of the decision making process, namely define the decision, understand the context, identify the options, prioritise the options, evaluate the consequences, review the decisions, and take actions.

The Pseudo Thinking Profile of Senior High School Students In Solving Mathematical Problems Reviewed from Mathematical Ability

In solving problems, students often experience thinking errors, one of which is pseudo thinking. Pseudo thinking is errors of thinking, wherein the individual process of solving a problem it is not the result of real thinking. Mistakes of thinking like this need attention and must be immediately addressed so as not to impact on students' understanding of the next mathematical concept. This study is a descriptive exploratory with a qualitative approach, aims to describe and explore the pseudo thinking profile of high school students with different mathematical abilities. The subjects in this study consisted of, one with high mathematical ability, one with moderate mathematical ability, and one with low mathematical ability. Data collection techniques were carry out by giving mathematics ability tests (TKM) and interviews. Data analysis was perform based on pseudo-thinking indicators (pseudo-right thinking and pseudo-wrong thinking). It was found that, subjects with high mathematical ability tend to be able to experience pseudo-right thinking and pseudo-wrong thinking. Subjects with moderate mathematical ability tend to be able to experience pseudo-right thinking, while subjects with low mathematical ability tend to be able to experience pseudo-wrong thinking.aKeywords: thinking mistakes, pseudo thinking, problem-solving, mathematical ability

Statistical Thinking Profile Of Field Independent And Field Dependent Senior High School Students In Problem Solving

Statistical thinking is a mental activity that occurs from the process of identifying statistical information to the process of making decisions or drawing conclusions that are interconnected. One that can effect individual statistical thinking profiles is cognitive style. The purpose of this research is to describe the statistical thinking profile of Field Independent and Field Dependent high school student in solving problems. This research is a descriptive study with a qualitative approach. The instruments of this research are the researcher as the main instrument and cognitive style test, mathematics ability test, and interview guidelines as the supporting instruments. Research subjects are one of FI student and one of FD student with an equivalent level of high mathematical ability. The results of this study indicate differences in the profile of FI student an FD student statistical thinking. In evaluating the effectiveness of the data display, FI student can provide analytical argument about the presentation of data display that more effectively used and FD student provide answers for the presentation of effective data displays based on what is seen from the question. In describing the results of the available problems and making conclusions from the results that have been obtained, FI student describes the solutions in more detail accompanied by the arguments also provide conclusions related to the existing problems and FD student briefly describes the solutions and provide general conclusions and have not been linked to the existing problems. Because of the statistical ability of two subjects is defferent, teacher should pay attention to the statistical concepts and train students on solving statistical problems by any solutions. Keywords : Statistical thinking profile, problem solving, Field Independent, Field Dependent

Students’ Mental Construction in Cube and Cuboid Concepts Based on Mathematical Ability Differences

Understanding of cube and cuboid concepts is one of the essential goals of solid geometry learning. Most studies of students’ understanding of these concepts have posited a gap between the students’ surface area and volume conceptions of its and students’ understanding. The study aims to describe the students’ mental constructions in APOS (Action, Process, Object, and Schema) theory framework. This study used analysis of students as subject to three junior high school students who have differences in mathematical abilities with a qualitative approach. Data were collected by the task sheet and interview. The result of this study evidences that subject who has high mathematical ability could solve problems about cube and cuboid concepts correctly in the action stage. In the process and object stage, subject could provide detailed explanations of how steps to assess the surface area and volume of cube and cuboid. She compared two shapes with different sizes of cube and cuboid. In the schema stage, she made systematic understanding related to the concepts of surface area and volume of cube and cuboid. The subject who has medium mathematical ability explained her mental construction in action and process stage well, despite the error in the process stage. Next stage, she had compared two different shapes of cube and cuboid to found their ratio. The last stage, she had not completed her explanation. The subject has low mathematical ability could solve the problems about cube and cuboid concepts. At the process, object, and schema stage, she had not completed its indicators to show cube and cuboid concepts.

The Application of the Accelerated Learning Cycle, Brain-based Learning Model, and Direct Instruction Model toward Mathematical Reasoning in Terms of Mathematical Communication

The students' mathematical reasoning and mathematical communication abilities are influenced by several factors such as the use of learning models used by teachers in learning. The use of appropriate learning models can increase students' mathematical communication abilities and reasoning. This study aims to determine the effect of the Accelerated Learning Cycle, Brain-based learning model and Direct Instruction learning models on students' mathematical reasoning abilities seen from their communication abilities. This is a quasi-experimental research. The data were analyzed using analysis of variance with unequal cells. This study concludes that, first, Accelerated Learning Cycle provides better mathematical reasoning abilities than the Brain-based learning model and the Direct Instruction learning model and Brain-based learning model provide better mathematical reasoning abilities than the Direct Instruction learning model. Second, students who have high mathematical communication abilities have better mathematical reasoning than students with moderate or low mathematical communication abilities, students who have medium communication abilities have better mathematical reasoning than students with low mathematical communication abilities

Multi-representation raised by prospective teachers in expressing algebra

This study investigates multi-representations raised by prospective teachers in expressing algebra. Through a case study approach, as many as 112 prospective mathematics education teachers from Universitas Negeri Malang of Indonesia participated in this research. researchers use test, interview and research sheet instruments as data collection tools. Then an analysis is carried out so that the following categories are obtained: subjects that symbolically express algebra, pictorial, and geometric. The results obtained that some subjects express symbolically algebra (83 of 112 subjects), while some subjects expressed pictorially (17 of 112 subjects), and geometrically (12 of 112 subjects). The research findings show that there are three forms of representation raised by the subject in expressing algebra, namely the representation of algebraic symbols, image representations, and geometric representations. Most of the participants produced algebraic symbolic representations and some of them experienced obstacles in producing pictorial representations and geometric representations, also researcher found similar patterns in producing geometric representation namely, perception, appearance, strategy, and re-examination. Researchers recommend geometric representations for further research because they tend to be done by subjects with high mathematical abilities and rarely found research that produces geometrical representations when solving algebraic problems.