Polya's Problem Research Articles

Students' Difficulties In Solve Trigonometry Problem Solving According To Step Polya's

This study aims to describe students' difficulties in solve trigonometry problem solving according Polya's steps. Determining research subjects by giving students difficulty test questions using Polya steps to 36 students of class X MIPA 8 SMAN 1 Indramayu. From these results, 6 subjects were selected purposively as a sample with subjects falling into the high, medium and low score categories. The instruments used were diagnostic tests of students' difficulties in solving trigonometric problems using Polya's problem solving and interviews. The data analyzing technic in the research started with collecting information in the fields, interviews, and documentations which are collected by coding. By considering into account the results obtained from this study, the difficulty of students in handling problem solving of trigonometry problems according to Polya's steps owned by students of class X MIPA 8 SMA Negeri 1 Indramayu is able to solve a problem using Polya's steps. When students who have high test scores will have little difficulty learning because the subject can explain and solve problems well and there are no difficulties. While it is different when students who have low scores feel confused, difficult, wrong in solving a problem. In fact, in this study, the highest score and the lowest score both answered the questions correctly, the only difference was the student's accuracy and overestimation, causing the student to get a low score. The research results show that the students with high score category had less difficulty than students with low score categories. Therefore, teachers must be more careful in paying attention to students and teachers must also explain Polya's stages gradually without rushing. It is expected that students can understand Polya's stages as a whole so as to reduce student learning difficulties.

ANALISIS PENGARUH PEMAHAMAN KONSEP TERHADAP KEMAMPUAN PEMECAHAN MASALAH PADA MATERI TEOREMA PYTHAGORAS

This study aims to describe how the influence of conceptual understanding on the problem solving abilities of class VIII students at MTs Negeri 6 Pasuruan, on the Pythagorean theorem material. This study used a descriptive qualitative method with 3 research sample, which were selected using a purposive sampling technique. The research instrument used was a conceptual understanding questionnaire which contained 5 descriptive questions and 5 statements with correct, doubtful and false answer choices to determine the research sample. Then a problem solving test according to the Polya problem solving steps as many as 2 description questions. The results of the study showed that students with high conceptual understanding had good problem solving abilities and did not experience difficulties and did problem solving according to Polya’s steps. Students with moderate understanding of concepts have good abilities but experience difficulties in solving problems and according to Polya steps. Whereas students with low conceptual understanding have poor problem-solving abilities, so they experience difficulties and do not solve problems according to Polya’s steps.

THE EFFECTS OF POLYA'S PROBLEM SOLVING WITH DIGITAL BAR MODEL ON THE ALGEBRAIC THINKING SKILLS OF SEVENTH GRADERS

There is a dearth of empirical data to support the positive effects of problem solving (PS) combined with digital technology in the classroom, despite claims that these activities improve students' algebraic thinking abilities. Therefore, the purpose of this study was to evaluate how the teaching method known as Polya's problem solving with digital bar model (PSDMB) affected the seventh graders' ability to think algebraically. Ralston's framework, which covers Generalised Arithmetic, Function, and Modelling within the topic of Linear Equation, served as the foundation for the evaluation of algebraic thinking abilities. A quasi-experimental pre-test and post-test control group design was employed. A total of 90 seventh graders, aged twelve- to thirteen-year-olds, from a secondary school in Tambunan, Sabah, Malaysia, made up the sample. Three teaching groups were formed out of these randomly chosen students: PSDMB (n = 30), Bar Model (MB) (n = 30), and Conventional Problem Solving (CPS) (n = 30). Both the pre- and post-algebraic thinking tests were taken by students. The post-test results were analysed using MANCOVA with the students' pre-test results acting as covariates. The results indicated that students in the PSDMB group performed notably better in Generalised Arithmetic, Function, and Modelling than those in the MB group, who, in turn, outperformed those in the CPS group. These results imply that incorporating digital bar model into problem-based learning is a successful strategy for improving seventh graders' algebraic thinking abilities. Keywords: algebraic thinking skills, digital bar model, Polya's problem solving, seventh graders

Mathematical Problem-Solving Ability of Junior High School Students Based on Polya

Mathematical problem-solving ability is the ability to identify known information, ask questions, adequacy of the information needed, skill in creating or compiling mathematical models, being able to find the right solution strategy, and being able to explain and check the correctness of the solution obtained. This research aims to analyze students' mathematical problem-solving abilities in the topic on mixed integer arithmetic operations based on Polya's problem-solving steps. This research uses a qualitative approach with a narrative research type. The research subjects consisted of 32 junior high school students. Data collection was carried out using mathematical problem-solving ability test instruments and interviews with several selected participants. Data was analyzed based on Polya's problem solving steps. Based on the results of data analysis, students' problem-solving abilities obtained based on these four steps are in the form of students who can determine important information in the problem and can plan solutions resulting in them being able to solve problems more regularly, namely by executing the plans they have planned. After that, students who understand the problem well can also check the correctness of the answers they have obtained. Therefore, it is hoped that this research can help teachers to implement a learning process that can develop problem solving abilities.

Miskonsepsi Pemahaman Materi Bangun Datar dengan Penerapan Teori Polya di PGMI 3

This research aims to 1) analyze students' problem solving abilities in solving story problems based on polya stages in plane material in the PGMI 3 class at UIN North Sumatra, 2) find out how to improve students' problem solving abilities in solving story problems based on polya stages. This research uses a qualitative descriptive research type. Data collection in this research was carried out by means of written tests, interviews and documentation. Subjects were taken in this research using purposive sampling technique. Interviews were conducted with research subjects and class teachers. The research results obtained were that students with low abilities were quite capable of goingthrough the stages of understanding the problem and preparing a solution plan. Students with moderate abilities are able to go through the stages of understanding the problem, preparing a solution plan, and implementing the solution plan. Meanwhile, students with high abilities are able to go through all stages of Polya problem solving.

Pengembangan Mathematics Olympiad Digital Book (MODiB) Berdasarkan Strategi Pemecahan Masalah Polya untuk Meningkatkan Kreativitas dan Hasil Belajar Matematika Siswa Sekolah Dasar

Mathematics Olympiad is a prestigious competition that is growing and has many enthusiasts in Indonesia. Thus the need for math olympiad teaching media is getting higher. The purpose of this research is to develop a digital book that is 1) valid, 2) practical and 3) effective for improving learning outcomes and mathematical creativity of elementary school students, which is named MODiB (Mathematics Olympiad Digital Book). MODiB contains Elementary Mathematics Olympiad material according to the OSN syllabus and in solving problems using the Polya Problem Solving Strategy. MODiB development applies the 5 steps of ADDIE (Analysis, Design, Development, Implementation, Evaluation). The subjects of this study were SD DCS Semarang students who had passed the selection for OSN guidance. Starting with analyzing the condition of coaching mathematics Olympiads at SD DCS Semarang and recording the needs needed to foster the OSN team, designing and developing MODiB accompanied by validators who are material experts and media experts, and then implementing MODiB at SD DCS Semarang. Evaluation is carried out at each stage and after implementation is complete. From the research results, data were obtained: 1) the feasibility results of the material on MODiB were 89.09% which were included in the feasible category to be tested on students, and the feasibility results of learning media were 88.57% in the feasible category to be tested on students, 2) practical results MODiB according to students is 80.48% which is included in the practical category, 3) the results of the analysis of increasing learning outcomes with the gain test obtained a score 0,244 that is included in the low category based on the Gain score category according to Hake, and 4) the value of mathematical creativity of 16 respondents (53.3 %) increased, 4 respondents (13.3%) remained and 10 respondents (33.3%) decreased. Overall, the average increase in the value of mathematical.

Exploring The Student’s Problem-Solving Skills In Missouri Mathematic Project Learning From The Self-Regulated Learning In Statistics Material

Education is the heart of the world. Exploration activities demonstrate students' mathematical problem-solving skills. Research purposes; The first, Identification learning outcomes by describing high, medium, and low Self-Regulated Learning (SRL) problem-solving abilities through the Missouri Mathematics Project (MMP). The second is to find out if the MMP model has a role in achieving classical mastery in its ability to solve mathematical problems the average value is it purpose achieved ≥ 80 in 75% of all samples. Mixed method, concurrent embedded design. A total of 75 students of the 8th grade of the SMP Pesantren Attaqwa Bogor in 2022-2023. Data from Problem-solving skills tests, SRL questionnaires, and interviews. Include 6 subjects; two high SRL students, two medium SRL students, and two low SRL students are picked from the 75 SRL-enrolled students. The teacher of the topic to be questioned in this study choose which students to interview. The research results show that: First, Students with high SRL are able to master the 4 components of Polya problem solving; medium SRL students are still able to understand the problem, make a settlement plan, carry out the settlement plan but are less able to re-examine the work; low SRL students are able to understand the problem but are less able to make a settlement plan, carry out the completion plan and re-check the work. Secondly, the KPM of statistical material students in the MMP model exceeded the mastery learning average score of ≥ 80 in 75% of class VIII students.

The process of solving skill-based problems about multipliers and multiples by advanced learners in math and gifted students

Globalization has also been reflected in mathematics education, and as a result, international exams, in which Turkey also participate, have become widespread since the 20th century. After participating in international exams in Turkey, it started to make changes in the questions in the exams it held throughout the country. The most striking of these changes is the preparation of skill-based questions that measure metacognitive skills in the High School Entrance System exam. In order to solve such questions effectively, as emphasized in the mathematics curriculum, the problem solving process must be managed well and correctly. In this research, it is aimed to examine the processes of solving skill-based questions about multipliers and multiples. The difficulties experienced by the students in the process of solving skill-based questions and the points they missed were determined. In this study, case study, one of the qualitative research methods, was used. The study group consists of 8 students, 4 of whom are highly successful in mathematics and 4 of whom are gifted, studying in the 8th grade. The Factors and Multiples Achievement Test consisting of 10 open-ended questions was developed in order to measure the students' skills on the subject of multipliers and multiples. While applying the Multipliers and Multiples Achievement Test, we conducted a clinical interview with each student and enabled the students to solve the questions by thinking aloud. We made the descriptive analysis of the obtained data according to the Polya’ problem solving steps. While presenting the findings, we made use of the tables and interpreted them according to each question and step. As a result of the research, we determined that the students who successfully realized the step of understanding the problem were able to perform the other steps and solve the questions correctly. We also found that students who are successful in mathematics try to apply Polya's problem solving steps more and are more successful than gifted students. According to these results, we recommend that students use Polya's problem-solving steps effectively while solving problems and that the research results should be investigated in more detail

HIGH SCHOOL STUDENTS’ CRITICAL THINKING ABILITY

Problem solving is an important skill, and making decisions about the basis of critical thinking skills. This study is a descriptive qualitative study to describe the critical thinking of 8th grade public junior high school students in the suburbs of Surabaya, East Java in solving TVLS problems. Fifteen junior high school students contributed to the study and were given questionnaires to get three subjects with different critical thinking abilities. Furthermore, each subject was requested to solve TVLS word problems and then interviewed. The instruments used in this study were a critical thinking questionnaire (CTAT), TVLS word problems, semi-structured interview guidelines. The data was analyzed based on indicators that combined the stages of Polya's problem solving and critical thinking. The data were analyzed using critical thinking indicators that have been determined by the authors and the results obtained showed that (1) uncritical and low critical subjects were unable to complete the critical thinking indicators at each stage of problem solving; (2) medium critical, critical, and highly critical subjects were able to complete the critical thinking indicators at each stage of problem solving. For this reason, it is advised that teachers teach their students to think critically in solving problems in every learning process

Analisis Kemampuan Pemecahan Masalah Word Problem PLSV

Problem-solving ability is a primary skill students should acquire in learning mathematics and is often connected to Adversity Quotient (AQ). This qualitative descriptive study describes the ability to solve PLSV problems regarding AQ (climbers, campers, and quitters) in 7th-grade students of SMP Negeri 21 Surabaya. Data were collected through questionnaires, tests, and interviews using instruments such as the AQ questionnaire sheet, Word Problem Solving Test (TPWP), questionnaires, and interview guidelines. The problem-solving ability in this study refers to the four stages of Polya's problem-solving ability including understanding the problem, planning, implementing, and evaluating. The results of this study showed that (1) the climbers subject was able to accomplish all of Polya's stages, (2) the campers subject, was able to accomplish three stages of Polya's problem solving, which were able to understand the problem, plan the problem solving, and carry out the problem-solving. Whereas, (3) the quitters subject, was unable to complete Polya's problem-solving stages as it showed that the subject was poorly understanding the problem, planning to solve the problem, implementing the solution plan, and incapable of looking back at problems that had been solved.

ANALYSIS OF STUDENTS' MATHEMATICAL ABILITY IN SOLVING FRACTION PROBLEMS AT ELEMENTARY SCHOOL LEVEL

Abstract
 This research is qualitative research with a case study approach. This study aims to describe the level of students' problem-solving in fraction operations. The subjects of this study were three students of SDN 70 Manjalling who had low, moderate, and high abilities in solving fractions. Data were collected through written tests and individual interviews to obtain valid information. The results showed that students with high problem-solving abilities were able to apply all of Polya's problem-solving steps. Students with moderate problem-solving abilities could not do all of Polya's problem-solving steps. They only applied steps of understanding the problem and making a solution plan. Students with low abilities found it challenging to use fractions and were unable to use each step to solve the Polya's problem. Those students could only apply steps of understanding the problem and making a solution plan, but they did not understand the problem and could not convert it into mathematical forms.

PERSEPSI PELAJAR DIPLOMA BERPENCAPAIAN RENDAH TERHADAP KAEDAH PEMBELAJARAN KOPERATIF JIGSAW DAN MODEL PENYELESAIAN MASALAH POLYA DALAM PEMBELAJARAN PENGENALAN KEPADA TEKNIK KUANTITATIF

This qualitative study was carried out to explore the challenges faced by low-achieving diploma students in the subject of Introduction to Quantitative Techniques. In addition, this study explored how the Jigsaw cooperative learning method and the Polya Problem Solving Model can help low-achieving students and their perception on this alternative method in learning. This study was conducted at a private college in Sabah involving five low-achieving second semester Management Diploma students. Data was collected through interviews, field notes, and document analysis. The findings of the study show that low-achieving students faced difficulties in understanding the requirements of the question and cannot identify the correct formula in the solution. Polya's Problem Solving Model helped students to better understand the requirements of the questions and solve long sentence problems step by step. Help from classmates who act as facilitators improved the skills of low-achieving students in understanding concepts and formulas and solving long sentence problems, at the same time obtaining better grades. The results of the study provide positive implications for low-achieving Management Diploma students to improve problem-solving skills in the subject of Introduction to Quantitative Techniques.

The Development of Computational Thinking and Mathematics Problem Solving Skills Through Mathematics Modelling Activities

The latest TIMSS report highlighted that secondary school students from Malaysia did not perform well in this global assessment on mathematics achievement. Some studies have pointed out that students’ mathematics achievement can be improved by equipping them with computational thinking. Therefore, this study examined the development of computational thinking skill and mathematics problem-solving skills via mathematics modelling activities among secondary students in Malaysia. The research instrument used for the assessment of computational thinking was adapted from UK Berbras Challenges and CAS Barefoot Team from United Kingdom. In addition, rubrics for development of mathematics problem solving skill was adapted from Polya problem solving model. This study adopted qualitative approach and the modelling activities were conducted for six weeks. The activities were introduction of modelling, individual modelling task and group modelling task. Data were also collected based on results of computational thinking test and mathematics test. Data from observation and interviews were analyzed, and the scores obtained from both tests were compared and analyzed as well. Based on the findings of the study, it could be concluded that the students progressed at different levels during the development of their computational thinking skill and mathematics problem-solving competency via mathematics modelling activities. These results indicated that mathematics modelling activities can be conducted at schools to improve students’ performance in Mathematics.

Analysis of Mathematics Problem Solving Ability Based on Polya Problem Solving Steps

This research is a descriptive study with a qualitative approach that aims to describe the ability of students' mathematical problem-solving classes. The instruments in this study were a logical-mathematical intelligence test, a problem-solving ability test, and an interview guide. Data collection in this study was carried out using test, interview, and observation techniques. Checking the validity of the data carried out in this study was a technical triangulation. The results of this study indicate students' ability to solve mathematical problems based on Polya's problem-solving steps: (1) Understanding the problem, subjects who are able to correctly determine what is known and asked about the problem are subjects with high and moderate logical-mathematical intelligence, whereas subjects with low logical-mathematical intelligence are only able to determine things that are known in the problem and have not been able to determine what is being asked in the problem; (2) Develop a problem-solving plan, subjects who are able to develop relevant problem-solving plans to solve problems appropriately and find relationships between things that are known to find things needed in solving problems are subjects with high logical-mathematical intelligence, then for subjects with moderate logical-mathematical intelligence are only able to find connections between things that are known, whereas subjects with low logical-mathematical intelligence are not yet able to devise relevant problem-solving plans and find relationships between things that are known; (3) Carry out the plan, subjects who are able to carry out the steps of the problem solving plan correctly, are skilled in performing arithmetic operations, and find the right solution to the problem are subjects with high logical-mathematical intelligence, while subjects with moderate logical-mathematical intelligence and low ability to carry out a solution plan that is made even though it is not relevant to solving problems and less skilled in performing arithmetic operations, so that the right solution to the problem cannot be found; and (4) Re-checking, subjects who are able to interpret the solutions to the problems that have been obtained and re-examine the steps and calculation results are subjects with high, medium, and low logical-mathematical intelligence.

ANALISIS KEMAMPUAN PEMECAHAN MASALAH MATEMATIS SISWA BERDASARKAN SELF EFFICACY

This study aims to determine the type of self-efficacy is the most at the level of low, medium and high ability to solve math problems and to describe the problem-solving ability of students in solving math problems in the material PLSV and PTLSV based on three dimensions of self-efficacy. This type of research is descriptive research using a qualitative approach. The subjects of this study were 9 students from grade VIIC Junior High School in Parongpong. Data collection in the form of written tests and interviews. The results showed that the most self-efficacy dimension for each mathematical ability is magnitude. At a high level of mathematical ability, most of the dimensions of self-efficacy students are able to perform each step of solving the Polya problem well. At the level of moderate mathematical ability, each dimension of self-efficacy students can partially understand the problem well and completely. At the stage of designing solutions some students have not been able to make a complete problem-solving plan and some do not make plans. At the stage of implementing the plan on each dimension of self-efficacy some students can work according to plan but not yet complete and visible from the results obtained less thorough. At the last stage of the Polya step, some students did not recheck and some did recheck. At the level of low mathematical ability, students from each dimension of self efficacy have not been able to desig n solutions and implement problem solving properly and completely according to plan, at the stage of re-examining students (dimension of self efficacy generality) re-examining their work and students (dimension of self efficacy magnitude and strength) do not re-examine their work.

Analysis Of Mathematical Problem-Solving Ability In View Of Mathematical Disposition

Problem solving is one-skills most importantly no could separated adri learning math. In the process of solving problems, students will not be separated from their positive attitude towards mathematics (mathematical disposition). On the other hand, the results of tests and observations during the pandemic show that the mathematical problem-solving ability of class X students of Gondang Vocational School is relatively low. Moment solve-problem math, students not enough motivated for solve it. Besides that, students feel less confident and unable to solve math problems. Goal writing article is to describe the mathematical problem-solving abilities of class X students of SMK Gondang in terms of mathematical dispositions. The research method used in article this is qualitative method. Class X TKR 4 has 26 students. Subjects are selected using purposive sample technique based on the results questionnaire categorization, taking into account learning activities students in learning mathematics. Data collection techniques include questionnaires, tests, and interviews. The data analysis techniques include data reduction, data presentation, and withdrawal conclusions referring to data processing Milles and Huberman. The research results show that position students dominant have a moderate level of disposition, and students who have the same level of disposition have different problem-solving abilities. This is because students have their own difficulties and mistakes in solving mathematics. Skills problem solving is based on the level of deep mathematical disposition post-pandemic learning, namely: students with a high disposition can fulfill four indicators of Polya problem solving, students with a moderate disposition are able to fulfill three indicators without re-examining the results and students with a low disposition can only fulfill one indicator that is understanding the problem

Students’ difficulties in solving geometry problems

This study is based on research findings that examines students' difficulties utilizing Polya's problem to solve geometry problems -solving stages. Thirty-one students were assigned to work on questions about the material in order to calculate the distance in space. Researchers examined each student’s work to determine which stage of Polya they struggled with. In-depth interviews were also conducted to clarify answers and investigate students' difficulties in solving math problems. The results showed that students who were able to answer completely and correctly, based on Polya’s stages in understanding the problem, compiling or thinking about a solution plan, solving the problem according to the plan and re- examining the procedure and the results of solving the answer, had a very low success rate. Scaffolding is given to students who have difficulty and recognition of the accuracy of correct answers for those who are successful. Keywords: Geometry, Polya’s problem-solving stages, students difficulties.

Problem-solving ability in solving linear program story problems based on Polya procedures

This study aims to describe problem solving skills in solving linear programming story problems based on the Polya procedure at level II cadets of SMKN 1 Kapuas Kuala majoring in multimedia. This research is descriptive qualitative research. Data collection techniques using tests, interviews, and documentation. Data analysis techniques used are data reduction, data presentation, and drawing conclusions. The results of this study indicate that: (1) The problem-solving ability of cadets with high abilities can carry out the four Polya problem solving steps very well, namely understanding the problem, planning the solution, implementing the solution plan, and re-examining the solution. (2) Troubleshooting abilities of cadets with moderate abilities have started to solve problems based on Polya's procedures by taking steps to understand the problem, plan problem solving, carry out problem solving plans, and re-examine solutions. (3) The problem-solving ability of cadets who have low abilities have been able to carry out the stage of understanding the problem and planning problem solving, but the subject is still lacking in implementing the solution plan and has not been able to re-examine the solution.

Problem-solving ability in solving linear program story problems based on polya procedures

This study aims to describe problem solving skills in solving linear programming story problems based on the Polya procedure at level II cadets of SMKN 1 Kapuas Kuala majoring in multimedia. This research is descriptive qualitative research. Data collection techniques using tests, interviews, and documentation. Data analysis techniques used are data reduction, data presentation, and drawing conclusions. The results of this study indicate that: (1) The problem-solving ability of cadets with high abilities can carry out the four Polya problem solving steps very well, namely understanding the problem, planning the solution, implementing the solution plan, and re-examining the solution. (2) Troubleshooting abilities of cadets with moderate abilities have started to solve problems based on Polya's procedures by taking steps to understand the problem, plan problem solving, carry out problem solving plans, and re-examine solutions. (3) The problem-solving ability of cadets who have low abilities have been able to carry out the stage of understanding the problem and planning problem solving, but the subject is still lacking in implementing the solution plan and has not been able to re-examine the solution.

Kemampuan Pemecahan Masalah dalam Menyelesaikan Soal Cerita Program Linear Berdasarkan Prosedur Polya

One of the goals of learning mathematics is so that students have problem-solving abilities which include the ability to understand problems, plan solutions, carry out solving plans, and re-examine solutions. Problem solving skills in the form of story questions need to get serious attention because story questions are questions related to everyday life that provide a real picture of real life problems using mathematical sentences. This study aims to describe problem solving skills in solving linear programming story problems based on the Polya procedure at level II cadets of SMKN 1 Kapuas Kuala majoring in multimedia. Jens This research is a descriptive qualitative research. Data collection techniques using tests, interviews, and documentation. Data analysis techniques used are data reduction, data presentation, and drawing conclusions. The results of this study indicate that: (1) The problem solving ability of cadets with high abilities can carry out the four polya problem solving steps very well, namely understanding the problem, planning the solution, implementing the solution plan, and re-examining the solution. (2) Troubleshooting abilities of cadets with moderate abilities have started to solve problems based on Polya's procedures by taking steps to understand the problem, plan problem solving, carry out problem solving plans, and re-examine solutions. (3) The problem-solving ability of cadets who have low abilities have been able to carry out the stage of understanding the problem and planning problem solving, but the subject is still lacking in implementing the solution plan and has not been able to re-examine the solution..