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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.

This study explores the influence of locus of control on junior high school students’ creative mathematical thinking and its implications for instructional strategies. Using a quantitative approach with a descriptive correlational method, 16 eighth-grade students from various Jakarta schools participated. The research instruments consisted of a questionnaire and a creative thinking test. The Shapiro-Wilk normality test indicated that the data were not normally distributed, prompting the use of the Wilcoxon non-parametric test. The findings revealed a significant relationship between locus of control and students’ creative thinking abilities (p = 0.013 < 0.05). These results highlight the importance of strengthening internal control beliefs to foster creativity in mathematical problem-solving.

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 aims to improve students' mathematical problem solving abilities by using a learning model Think Aloud Pair Problem Solving (TAPPS) with the help of animated videos. The research was conducted at SMA Negeri 1 Sumbul involving 36 class X-G students as research subjects. The type of research used is classroom action research (PTK) with steps, namely, providing an initial test to measure students' mathematical problem solving abilities before taking action, identifying problems in the classroom, planning action, implementing action, namely applying the TAPPS learning model (Think Aloud Pair Problem Solving) With the help of animated videos as a medium for conveying summaries of learning material, observation, giving post tests, data analysis and data reflection.  The research was carried out in 2 cycles where each cycle included two meetings, while observation activities were carried out simultaneously with the implementation of actions with the aim of observing the activities of researchers and students during learning activities. The research results showed that after the first cycle of research was carried out, the average student score from the pretest results to the first cycle posttest results increased from 52.56 to 72.94 with the average observation of student and researcher activities being 2.38 and 2.38. In the second cycle, students' mathematical problem solving abilities increased based on the average student score on posttest II, namely 84.62, the results of observations in the second cycle also improved better to 3.23 for student activities and 3.44 for researchers' ability to manage class, apart from that 34 out of 36 students (94%) obtained scores above the KKM (70). These results show that students' mathematical problem solving abilities increased after implementing the TAPPS learning model (Think Aloud Pair Problem Solving) Assisted by animated videos.

Math Card is a card-based board game that contains questions for mathematics learning media. The purpose of the Math Card is to make it easier and more interesting for students in math lessons to make it more fun. This research uses the ADDIE method, namely analysis, design, development, implementation, and evaluation.  At the analysis stage, analysis is carried out related to material needs by following per under the syllabus/curriculum and design needs to get design results that attract the attention of students. At the design stage, the design is carried out according to the needs of the Math Card, namely by designing cards, packaging, guidebooks, and game boards. The development stage is to develop the results of the material and design, namely compiling questions according to the syllabus and printing products. The implementation stage is to conduct trials for grade 10 SMK students in the classroom. The last is the evaluation stage, namely by improving and perfecting the Math Card learning method to be more effective and efficient.    

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 study aims to determine whether applying the Problem Based Learning model can improve the mathematical problem solving ability of students of class VIII-A SMP Negeri 1 Stabat on SPLDV. This research is a class action research conducted in two cycles. Each cycle consists of 2 meetings. The subjects in this study were students of class VIII-A SMP Negeri 1 Stabat totalling 30 students. The object of this research is the improvement of students' mathematical problem solving ability through the application of the Problem Based Learning learning model on SPLDV material at SMP Negeri 1 Stabat in the 2023/2024 school year. Based on the results of data analysis, the average initial test score was 47.11 with the number of students who reached mastery as many as 4 students (13.33%) and students who had not reached mastery as many as 26 students (86.67%). Then learning was carried out with the Problem Based Learning learning model in cycle I and there was an increase in the problem solving ability test with an average value of 63.44 with 19 students or as many as (63.33%). Then students who have not reached completeness are 11 students or as many as (36.67%). Then in cycle II there was an increase with the average value of the student problem solving ability test being 84.11, with a total completeness of 26 students or as many as (86.67%) and the number of students who had not reached completeness was 4 students or as many as (13.33%). The level of student completeness of the problem solving ability test given in cycle II reached the good category, therefore it can be said that learning has been achieved. Thus it can be said that the class has reached more than 85% of students who have been completed to solve problems. So it can be concluded that using the Problem Based Learning model can improve students' mathematical problem solving skills.

This research aims to determine the influence of students' learning activities on the ability to understanding mathematical concepts through the STEAM Learning Approach Makerspace model based on PBL on SPLDV materials. As for the type of research Quasi-Experiments. The population in this study was 90 students who were distributed into 3 classes with 2 classes that sampled grades VIII A and VIII C. The sampling techniques in this study used randomized classes and data collection techniques in this study were tests and observations, while the research instruments used preliminary tests and final tests to measure the ability to understand mathematical concepts and observation sheets to see students' learning activities. Data analysis techniques using a two-way ANOVA test. The research showed that there is an influence of the PBL-based Makerspace STEAM Learning Approach model on the ability to understand mathematical concepts, there is no influence on students' learning activities on mathematical concept comprehension capabilities, and there is no interaction between the PBL-based Stem Learning Approach Makerspace model and student learning activities on the ability to understand mathematical concepts. Conclusion, there is a positive direct effect of cognitive structures on the ability to understanding mathematical concepts.

Kemampuan penalaran matematis adalah kemampuan yang dinilai penting dimiliki siswa dalam mempelajari matematika. Tujuan penelitian ini adalah untuk mendeskripsikan kemampuan penalaran matematis siswa dalam menyelesaikan soal cerita SPLDV. Jenis penelitian ini adalah penelitian kualitatif. Metode yang digunakan adalah metode tes dan wawancara. Berdasarkan hasil pekerjaan siswa terhadap soal tes, siswa dibagi menjadi tiga kelompok kemampuan kognitif yaitu tinggi, sedang, dan rendah, masing-masing kelompok dipilih satu orang untuk dijadikan subjek penelitian. Dengan demikian subjek penelitian ini ada tiga orang yaitu siswa dengan kemampuan kognitif tinggi (T), sedang (S), dan rendah (R). Indikator pertama penalaran matematis yaitu mengajukan dugaan mampu dipenuhi oleh subjek T, S, dan R. Indikator kedua penalaran matematis yaitu manipulasi matematika mampu dipenuhi oleh subjek T dan subjek S. Indikator ketiga penalaran matematis yaitu memberikan bukti dan alasan terhadap solusi yang dioeroleh hanya mampu dipenuhi oleh subjek T. Indikator keempat penalaran matematis yaitu menarik kesimpulan tidak dapat dipenuhi oleh ketiga subjek.

Rendahnya kemampuan pemecahan masalah matematis siswa khususnya pada materi SPLDV disebabkan karena kurangnya perhatian dan keterlibatan siswa dalam proses pembelajaran, kesulitan siswa dalam memahami soal-soal SPLDV yang berbentuk cerita, pembelajaran yang kurang inovatif serta siswa yang kurang aktif dan kreatif dalam mengkonstruksi ide-ide pemecahan masalah. Oleh karena itu, dibutuhkan suatu model pembelajaran yang dapat meningkatkan kemampuan pemecahan masalah matematis siswa yaitu melalui model pembelajaran berbasis masalah. Penelitian ini bertujuan untuk menganalisis peningkatan kemampuan pemecahan masalah matematis siswa setelah diterapkan model pembelajaran berbasis masalah dan meningkatkan kemampuan pemecahan masalah matematis siswa minimal tuntas klasikal melalui model pembelajaran berbasis masalah. Penelitian ini adalah penelitian tindakan kelas. Data dikumpulkan melalui tes, observasi dan angket. Teknik analisis data menggunakan statistik deskriptif. Berdasarkan hasil penelitian ini di peroleh bahwa: (1) Menunjukkan adanya peningkatan kemampuan siswa dalam pemecahan masalah matematis dilihat dari hasil tes siswa meningkat secara individual, pada siklus I dan siklus II mengalami peningkatan yaitu dari nilai rata-rata 58,33 menjadi 84,91 setelah penerapan model pembelajaran berbasis masalah. (2) Menunjukkan adanya peningkatan kemampuan pemecahan masalah matematis siswa secara klasikal, pada siklus I dan siklus II mengalami peningkatan yaitu dari 43,33% menjadi 93,33% setelah penerapan model pembelajaran berbasis masalah. Jadi dapat disimpulkan bahwa untuk meningatkan kemampuan pemecahan masalah matematis siswa sebaiknya menggunakan model pembelajaran berbasis masalah.

This study aims to produce interactive video learning media in mathematics learning to improve students' mathematical understanding that is valid, practical and effective. This research is a development research where the research procedure uses a 4D design, namely (Define, Design, Development, and Dissemination) but this research only reaches the Development stage due to limited time, costs and research subjects. The subjects in this study were 26 class X students of SMAN 1 Nanga Tayap. The instrument used by the researcher was a validation sheet to see the validity of interactive video media, a response questionnaire was used to see the practicality of interactive video media and a pilot test was used to see the practicality of interactive video media in improving students' mathematical understanding abilities. Based on the validation of the three validators on learning interactive video media, it can be declared valid with an average index percentage of 79.69% with valid criteria. Material expert validation was declared valid with an average index percentage of 78.88% with valid criteria. Meanwhile, media expert validation was declared valid with an average percentage index of 79.28% with valid criteria. The level of practicality with an average percentage of teacher responses is 80%, with very valid criteria and an average percentage of student responses is 82.66% with very practical criteria. From the results of completing the teacher and student response questionnaire, interactive video learning media for students' mathematical understanding can be stated to be very practical for students. The level of effectiveness of students after using interactive video learning media on mathematical understanding abilities is 80.76% with very effective criteria.    

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.

This study aims to determine the effect of the Realistic Mathematical Education (RME) approach on the ability to understand mathematical concepts in class VIII students of SMP IT Al-Hijrah 2 Deli Serdang Private Middle School in the 2022/2023 academic year. The type of research used is Quasi Experimental with a Pretest-Posttest Control Group Design. The sample used was 35 students who were selected through a purposive sampling technique. Data collection techniques are carried out using test instruments. Data analysis technique is done by descriptive analysis. The results of the descriptive analysis show that the average value in the experimental class is 87.3935 and in the control class is 54.3639, which means that there is a difference in the posttest average scores in the experimental class and the control class. Based on the Independent Sample T-Test, the value of Sig. (2-tailed) of 0.000 < 0.05. The tcount value is 8.428 and the ttable value is 2.03452, which means that tcount > ttable then H0 is rejected and Ha is accepted. From the results of this study, it can be concluded that there is an influence of the Realistic Mathematical Education (RME) approach on the ability to understand mathematical concepts in class VIII students of Private Middle School IT Al-Hijrah 2 Deli Serdang.

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.

Penelitian ini dilatarbelakangi dari data observasi yang menunjukkan bahwa hasil belajar siswa terhadap materi SPLDV tergolong rendah. Oleh karena itu, tujuan penelitian ini adalah untuk mengetahui apakah hasil belajar siswa pada materi sistem persamaan linier dua variabel berbeda ketika diajar menggunakan model Problem Based Learning dan Direct Instruction. Penelitian ini dilaksanakan di SMP N 12 Dumoga. Subjek penelitiannya adalah seluruh siswa pada dua kelas, yang mana satu kelas eksperimen, dan kelas kedua adalah kelas kontrol. Pengumpulan data dilakukan dengan memberikan pre-test kepada kedua kelas sebelum diberikan perlakuan, selanjutnya diberikan post-test setalah diberikan perlakuan. Dalam penelitian ini teknik analisis data yang digunakan adalah Uji Perbedaan Rata-Rata Dua Kelompok yang Tidak Berpasangan (Uji-t) dengan hasil pengujian hipotesis diperoleh , maka tolak . Berdasarkan hasil penelitian, diperoleh kesimpulan bahwa siswa yang mengalami pembelajaran dengan model PBL lebih baik dari siswa yang mengalami pembelajaran dengan model DI pada materi SPLDV. Dapat disimpulkan bahwa rata-rata hasil belajar siswa siswa yang diajar menggunakan model Problem Based Learning lebih baik dari siswa yang diajar menggunakan model Direct Instruction.