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This study aims to describe students’ mathematical problem-solving abilities on the topic of Systems of Linear Equations in Two Variables (SPLDV) based on Polya’s problem-solving stages in relation to their levels of self-efficacy. The research employed a descriptive qualitative approach with three ninth-grade students from SMP Negeri 5 Gresik in the 2024/2025 academic year, selected through purposive sampling to represent high, medium, and low levels of self-efficacy. Data were collected using a self-efficacy questionnaire, problem-solving tests consisting of two contextual essay items on SPLDV, and semi-structured interviews. Data analysis followed the interactive model of Miles, Huberman, and Saldana, encompassing data reduction, display, and conclusion drawing, referring to Polya’s four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. The results revealed that students with high self-efficacy were able to complete all four stages comprehensively and reflectively, demonstrating systematic and accurate reasoning. Students with medium self-efficacy successfully performed the first three stages but failed to verify their final results, while students with low self-efficacy only reached the stage of understanding the problem and struggled to plan or execute solutions. In conclusion, the level of self-efficacy influences students’ mathematical problem-solving performance, particularly in terms of strategic accuracy, procedural precision, and reflective evaluation.

This study aims to analyze junior high school students’ mathematical reasoning abilities in terms of their levels of learning independence. The research employed a descriptive qualitative approach involving three ninth-grade students from UPT SMP Negeri 5 Gresik, each representing high, medium, and low levels of learning independence. Data were collected through a self-regulated learning questionnaire, a mathematical reasoning test based on the topic of Systems of Linear Equations in Two Variables (SPLDV), and semi-structured interviews. Data analysis followed Miles and Huberman’s interactive model, consisting of data reduction, data display, and conclusion drawing. The results revealed that students with high learning independence demonstrated strong reasoning skills across all seven indicators of mathematical reasoning (representing statements, making conjectures, performing manipulations, constructing proofs, drawing conclusions, verifying arguments, and identifying patterns). Students with medium learning independence fulfilled only some indicators, while those with low learning independence could only make simple conjectures without systematic reasoning. These findings highlight that learning independence plays a crucial role in developing mathematical reasoning, as it enables students to regulate their thinking processes, evaluate solutions, and correct errors. Teachers are encouraged to integrate learning strategies that foster self-regulation—such as the CORE and Flipped Classroom models—to enhance students’ mathematical reasoning skills.

The study examines the effects of implementing the Creative Problem Solving (cps) instructional model integrated with Wordwall gamification on the mathematical problem solving abilities of eighth-grade Students at MTs. L-Bashriyah. The purpose of this research is to avaluate the impact of  CPS combined with Wordwall on students’ Performance in Two-Variable Linear Equation Systems (SPLDV) compared to conventional methods. This research employs a Quasi-Experimental design with a non-equivalent pretest-posttest control group. Using a quantitave approach. The sample consists of 40 eighth-grade students of MTs. AL-Bashriyah as the experimental group and 32 students of MTs. Nurul Huda as the control group. Selected through purposive sampling. Data analysis utilizes normalized gain scores and descriptive statistics with a 5% significance threshold. Results indicate a statistically significant improvement : the experimental group’s average postest score (81.16) markedly increased from the pretest (33.99). The control group showed moderate growth (66.45 from 32.91). Normalized gain analysis classifies the experimental group’s progress as high and the control group’s as medium. The findings demonstrate that CPS-Wordwall integration significantly enhances mathematical problem-solving skills. Thus, this model presents a viable innovative strategy for SPLDV instruction.

The purpose of this study is to find out the difficulties experienced by students in solving mathematical problems, especially in working on or solving problems in the two-variable linear equation system material and to find out the causes of difficulties in the two-variable linear equation system material that has been carried out by grade VIII students. This type of research is qualitative research, namely by making observations, then the researcher gives several questions given to the research subject to work on. The test instrument used in this study is in the form of 2 questions, namely about the material of the two-variable linear equation system that has been validated. The subjects in this study were 19 students in class VIII A who participated in the research process, then the researcher selected 6 students as representatives of the research subjects. The instrument of this study is a written test by giving questions, then interviews. In the results of the research that have been observed along with the results of interviews used to determine the type of difficulty students in solving problems of the two-variable linear equation system, the test results show that students experience difficulties shown by making mistakes in working on the problem. The causes of students' difficulties that often occur are usually lack of concentration when working, difficulties when faced with different forms of problems, forgetting the material that has been taught.

Mathematics plays a crucial role in developing students' problem-solving abilities and independence. Educators need to consider the varying characteristics of students when it comes to solving problems, one of which is their adversity quotient (AQ) level. The adversity quotient relates to a student's ability to handle complex problems or to overcome challenging situations. This research aims to analyze the mathematical problem-solving abilities of Class X students in the context of Systems of Linear Equations in Two Variables (SPLDV) based on their Adversity Quotient (AQ). This qualitative, descriptive study involved selecting research subjects using an AQ questionnaire and was conducted in Class X. Data collection methods included testing, interviews, and documentation. Data analysis techniques included data reduction, data presentation, and conclusion drawing. The results indicate that subjects with the Climber type can understand problems, develop problem-solving plans, solve problems with accurate and appropriate steps, and use available information to re-check their answers. Subjects with the Camper type can understand problems, develop problem-solving plans, solve problems with accurate and appropriate steps, but often cannot use available information to re-check their answers. Subjects with the Quitter type can understand the problem and formulate a plan but struggle to solve the problem accurately and appropriately, and tend not to use available information to re-check their answers.

This research uses the Polya problem-solving procedure to describe students' difficulty in problem-solving in the material about systems of linear equations in two variables. The method in this research is descriptive research. The subjects in this research were three students in Class VIII of SMP Negeri 6 Tondano. The data analysis techniques used are data presentation, data reduction and conclusion. The results of this research show that of the four stages of Polya problem solving, students who have the highest scores can fulfil all stages of Polya problem solving, students who have medium scores can fulfil three stages of Polya problem solving, and students who have high scores can fulfil two stages of Polya problem-solving.

This research aims to analyze students' errors in solving mathematics problems on Systems of Linear Equations in Two Variables according to the Newman procedure. This research was conducted in class VIIIA of St. Catholic Middle School. Johanis Laikit. This type of research uses descriptive qualitative. The methods used in collecting data were written tests and interviews. The written test was given to class VIIIA students, totaling 18 students as subjects, the test questions consisted of 3 essay questions. Based on the test results, 5 students were selected based on different mistakes to be interviewed. The research results showed that from the 3 questions given, the majority of students made mistakes in answering SPLDV story questions using the Newman procedure as shown in the test results, namely errors in writing the final answer with a percentage of 74.07%, process skills errors with a percentage of 66.66%. , transformation errors with a percentage of 48.14%, understanding errors 35.18%, and reading errors 25.92%.

This study tries to identify the faults and circumstances that lead students to miscalculate when attempting to solve word problems involving a system of linear equations with two variables using Watson's criteria. This kind of study employs qualitative, descriptive research methods. Data was gathered using a variety of methods, including analysis, interviews, documentation, and a written test with five-item description questions. Class VIII students from SMP Negeri 5 Tondano 2022/2023 served as the study's sources and subjects. They were chosen after careful consideration. Data analysis techniques in this study through data reduction, data presentation, and conclusions. The results showed that the students' errors were incorrect data, inappropriate procedures, response level conflicts, and skills hierarchy problems. The causative factors are that students are not careful when writing answers, students think that conclusions do not need to be written down, students forget how to change the story form questions into the form of mathematical models or the principles used are still wrong, students forget to write examples, students are wrong in operating numbers either subtraction, addition, division and multiplication, students forgot to write conclusions, students were unable to write down existing data, students did not know how to answer questions, students forgot to find x and y values using the substitution method, students used wrong marks in mathematics, students ran out of time when solving problems.

This article describes the development of Dick & Carey's learning design model on the Carey on the material of Linear Equation System Two Variables (SPLDV) Class X Senior High School.The purpose of this research is to explain the stages of the development of the Dick & Carey development stages of Dick & Carey learning design in designing effective and structured learning in the context of mathematics learning on and structured in the context of mathematics learning on the material of the System of Linear Equations Two Variables (SPLDV) Class X SMA. Two Variable Linear Equation (SPLDV) material. As for the results of the development of learning design Dick & Carey's learning design development results provide a success in learning objectives. This learning model provides a systematic and structured stage process for teachers in making plans for structured for teachers in making plans or designs in the implementation of learning. implementation of learning. This learning model also emphasizes on achievement of specific learning objectives and evaluation of learning outcomes. learning outcomes. This article provides an overview of the importance of developing learning design model to achieve success in student learning process.

This study sought to examine and evaluate the average learning outcomes of students who received instruction in a system of two-variable linear equations using either the direct learning model or the blended learning model. The research employed the posttest-only control design. The participants in this study comprised of two groups: class VIII-A, an Experimental class consisting of 17 students, and class VIII-B, a control class consisting of 17 students at SMP Negeri 4 Touluaan. The data collected pertains to the posttest outcomes in both the Experiment and Control groups, indicating an average learning outcome of 85.29 for the Experiment group and 77.94 for the Control group. The normality test for the data is satisfied when the data follows a normal distribution. The study yielded results indicating a significant level of 0.05, with the obtained t-value of 1.89098 being greater than the critical t-value of 1.694. According to the findings of this study, students who engage in Blended Learning exhibit superior learning outcomes in the context of acquiring proficiency in solving systems of linear equations with two variables, as compared to students who rely solely on direct instruction.

This study aims to determine the ability of junior high school students in translating SPLDV word problems into mathematical models and their solutions. Especially in the matter of two-variable linear equation systems (SPLDV). This type of research is qualitative. The approach used is the phenomenological approach. Data collection using test techniques, interviews, field notes, and documentation. The research subjects took 2 students with high category classification from class VIII B of SMP Negeri 2 Puring which originated from the determination of high, medium and low group boundaries. The group limit is high if the Odd PAS value is > (x ̅ + SD), the group limit is medium if (x ̅ - SD) < Odd PAS value < (x ̅ + SD), while the group limit is low if the Odd PAS value < (x ̅ + SD). Data analysis techniques include data reduction, data presentation, and conclusions. Checking the validity of the data uses credibility and confirmability tests. The results of this study indicate that the subject has a high ability to translate because he is able to understand the problem (write down what is known and asked), is able to solve problems (make examples and mathematical models), is able to take steps to solve problems. But did not evaluate or check again. Students who have high translation skills experience a few mistakes, namely not carrying out the evaluation step or checking again.

The purpose of this study is to compare the learning outcomes of students who were taught a system of linear equations with two variables using the Contextual Teaching and Learning model versus those who were taught the same material using the Direct Instruction methodology. Class VIII-1, which used the Contextual Teaching and Learning approach, and class VIII-2, which used the Direct Instruction model, were the topics. This study used a Posttest Only Control Group Design and a Quasi-Experimental Method. The sample for this study was drawn from two classes, specifically classes VIII1 and VIII2, each of which included 25 pupils. Both classes were equal and uniform. This data analysis is tested using the t-test with the parameters tcount = 5.020 > ttable = 2.059. H1 is accepted because H0 is refused. For instance, the Contextual Teaching and Learning (CTL) methodology can help students learn more effectively utilizing social math tools.

Penelitian ini bertujuan untuk mengetahui pengaruh metode latihan terbimbing terhadap hasil belajar siswa materi sistem persamaan linier dua variabel. Penelitian ini menggunakan metode penelitian eksperimen semu terhadap siswa SMA Negeri 1 Tondano pada siswa kelas XI semester ganjil tahun ajar 2022-2023. Hasil penelitian mengungkapkan bahwa karena thitung> ttabel (8.441>1.694) maka Ho ditolak dan Ha diterima. Oleh karena itu, dapat disimpulkan bahwa hasil belajar siswa yang diajarkan menggunakan metode latihan terbimbing dalam pembelajaran matematika topik sistem persamaan linear dua variabel lebih tinggi dari hasil belajar siswa yang  diajarkan menggunakan pembelajaran konvensional.