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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 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 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.

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%.

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.

This study aims to describe students' learning barriers in solving SPLDV questions based on problem solving abilities. This research uses descriptive qualitative research, and the sampling technique uses purposive sampling technique. This research was conducted at Sungai Kakap 1 Public Middle School, the data used were the results of researchers to clarify students' obstacles in answering questions based on problem-solving abilities with data sources, namely class VIII students of SMP 1 Sungai Kakap. Data collection techniques used measurement techniques, direct communication techniques and indirect communication techniques with data collection tools in the form of test questions, interview guides and documentation. The data analysis techniques used are data reduction, data presentation, and drawing conclusions. In this study it was concluded that the students' barriers in the high group were wrong in determining the formula and wrong in the concept of completion, the students' barriers in the medium group were wrong in determining the formula, discrepancies in using the formula to answer a problem and did not re-examine the answers, and student barriers in the low group were unable to determine the formula and solve the problem on the question then also did not re-check the answer after completing the given question.    

. Penelitian ini menggunakan penelitian metode deskriptif. Dengan bentuk penelitian studi kasus. Subjek penelitian adalah siswa kelas VIII berjumlah 23 siswa. tempat penelitian di SMPN 2 Sebangki Kecamatan Sebangki, Dusun Senunuk, Desa Agak. Dalam penelitian ini hanya mengambil tiga kelompok peserta didik kelompok tinggi, sedang dan rendah. Tujuan penelitian ini untuk mengetahui proses berpikir kritis siswa dalam pemecahan masalah matematika ditinjau dari Motivasi Belajar Siswa. Alat pengumpul data yang digunakan adalah tes kemampuan berpikir kritis, angket, dan wawancara. Berdasarkan perhitungan angket didapatkan hasil kelompok tinggi dengan kriteria X ≥ 77,49 yaitu ada 2 siswa, kelompok sedang dengan kriteria 67,29 ≤ X < 77,49 yaitu ada 16 siswa, dan kelompok rendah dengan kriteria X < 67,29 yaitu ada 5 siswa. Sedangkan pada perhitungan hasil tes, kelompok tinggi dengan kriteria X ≥ 11,64 yaitu ada 9 siswa, kelompok sedang dengan kriteria 9,56  ≤ X < 11,64 yaitu ada 5 siswa, dan kelompok rendah dengan kriteria X < 9,56 yaitu ada 9 siswa. berdasarkan hasil wawancara, responden siswa yang memiliki proses berpikir kritis siswa motivasi tingkat tinggi lebih baik dalam menyelesaikan soal dibandingkan siswa yang memiliki proses berpikir kritis motivasi tingkat sedang dan rendah.    

Tujuan penelitian ini untuk mengembangkan media pembelajaran E-Flip Builder berdasarkan Pedagogic Knowledge  yang valid, praktis dan efektif terhadap hasil belajar siswa pada materi SPLDV kelas X SMA Negeri 1 Marau. Metode yang digunakan adalah metode penelitian ADDIE. Subjek dalam penelitian ini yaitu siswa kelas X SMA Negeri 1 Marau sebanyak 16 orang, 4 orang ahli sebagai validator istrumen penelitian. Instrumen yang digunakan dalam penelitian ini adalah lembar validasi ahli media, lembar validasi ahli materi, lembar validasi ahli pedagogic knowledge, pedoman wawancara dan observasi, angket respon guru dan respon siswa. Hasil penelitian validasi E-Flip Builder berdasarkan Pedagogic Knowledge yaitu validasi media dengan nilai rata-rata dari ketiga ahli sebesar 93,89% dengan kriteria sangat valid. Yang kedua adalah hasil uji coba produk, dilihat dari nilai angket yang diisi guru dan seluruh siswa yang diakumulasikan sehingga diperoleh persentase sebesar  91,19%  dengan kriteria sangat praktis. Selanjutnya dari nilai hasil pengerjaan posttest siswa dengan jumlah siswa yang tuntas sebanyak 12 orang dari 16 orang dengan persentase 75,00%  dengan kriteria sangat efektif.        

Penerapan model pembelajaran yang tepat pada pembelajaran sangatlah berpengaruh dalam meningkatkan kualitas pembelajaran. Pada penelitian ini difokuskan pada peningkatan hasil belajar siswa dengan menerapkan model pembelajaran kooperatif tipe make a match pada materi SPLDV. Penelitian ini mengambil subjek kelas VIII SMP Negeri 2 Tatoareng yang terdiri dari 15 siswa sebagai kelas eksperimen. Kemudian data dikumpul berdasarkan hasil tes akhir setelah perlakuan diberikan pada subjek penelitian. Penelitian ini juga melakukan uji prasyarat yaitu uji normalitas dan homogenitas dimana didapatkan hasil yang data yang normal dan homogen, serta dilanjutkan dengan pengujian hipotesis menggunakan uji-t. Hasil diperoleh bahwa t-hitung = 1,941 dan t-tabel = 1,710 dengan taraf nyata yang digunakan adalah 0,05. Kesimpulan yang diperoleh adalah hasil belajar siswa yang menggunakan model kooperatif tipe make a match lebih tinggi dibandingkan dengan hasil belajar yang menggunakan model konvensional, sehingga model make a match cocok untuk digunakan dalam pembelajaran SPLDV

Penelitian ini berfokus pada ekperimentasi model blended learning pada materi sistem persamaan linear dua variabel. Penelitian ini membandingkan rata-rata hasil belajar siswa yang diajarkan dengan model blended learning dan model pembelajaran langsung. Populasi adalah seluruh kelas VIII SMP Negeri 2 Tondano, dan sampel yang menjadi subjek penelitian adalah kelas VIIIA (Kelas Eksperimen) dan kelas VIIIB (Kelas Kontrol). Metode yang digunakan adalah model eksperimen semu dengan desain Randomized Subjects Posttest Only Control Group Design. Hasil analisis Uji-t mendapatkan thitung = 2,67 > ttabel = 1,68 dengan taraf nyata α = 0.05. Hal ini berarti H1 diterima dan H0 ditolak. Kesimpulan nyang didapat adalah penggunaan model blended learning berpengaruh positif terhadap hasil belajar siswa.

Pendekatan penelitian ini adalah kuantitatif yang menggambarkan penerapan model pembelajaran problem based learning berbantuan edugame interaktif nearpod terhadap kemempuan pemecahan masalah matematis siswa. Penelitian ini menggunakan bentuk pre-Eksprimental Designs. Alasan peneliti menggunakan bentuk penelitian ini karena peneliti menggunakan satu kelas sampel, dimana satu kelas tersebut akan dijadikan sebagai kelas eksperimen. Pada kelas sampel pertama akan diberikan tes awal (pre-test) kemudian siswa diberi perlakuan dengan menerapkan model pembelajaran problem based learning berbantuan edugame interaktif nearpod pada materi SPLTV, setelah itu dilakukan pengukuran terhadap siswa dengan memberi tes akhir (pos-test). Penelitian ekperimen ini menggunakan rancangan One-Grup Pretest-Posttest Design. Pada rancangan ini terhadap Pretest sebelum diberikan perlakuan sehingga hasil perlakuan Posttest dapat diketahui lebih akurat, karena membandingkan dengan keadaan sebelum diberikan perlakuan. Berdasarkan hasil pengolahan data penelitian yang telah dilakukan oleh peneliti, secara umum dapat disimpulkan bahwa kemampuan pemecahan masalah matematis siswa melalui model pembelajaran problem based learning berbantuan edugame interaktif nearpod dalam materi SPLTV kelas X MAN Bengkayang berjalan dengan efektif sehingga meningkatkan kemampuan pemecahan masalah matematis siswa.