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This study was conducted to analyze the relationship between students’ critical thinking skills and mathematical problem-solving abilities through a literature review approach. The study is based on the importance of mastering higher-order thinking skills in the mathematics learning process, particularly when students are faced with complex problems related to real-life situations. The method used in this research was a literature review by examining various relevant scientific journals and academic books published between 2021 and 2026. The data analysis process was carried out through stages of identification, classification, evaluation, and synthesis of the collected sources. The findings revealed a significant and positive relationship between critical thinking skills and students’ mathematical problem-solving abilities. Critical thinking skills play an important role in helping students understand problems, process and analyze information, select appropriate solution strategies, and systematically review the results obtained. Students with strong critical thinking skills generally demonstrate more optimal mathematical problem-solving abilities. In addition, the implementation of learning models such as Problem-Based Learning and contextual approaches has been considered effective in improving both abilities. Therefore, critical thinking skills are regarded as an essential aspect that needs to be developed in mathematics learning in order to enhance students’ mathematical problem-solving abilities.

This study aims to analyze various research results related to the application of context-based mathematics learning in improving students' mathematical literacy. Mathematical literacy is an important skill that enables students to understand, use, and apply mathematical concepts and reasoning in solving various problems related to real life. This study uses a qualitative approach with a literature review method. Research data was obtained through a review of various scientific articles relevant to the research topic. The analysis process was carried out in several stages, namely identification of literature sources, selection of articles based on topic suitability, and synthesis of published research findings. The results of the study show that integrating everyday contexts into mathematics learning can improve students' conceptual understanding, mathematical reasoning abilities, and problem-solving skills. Learning that links mathematical material to real-life situations can also help students understand concepts more meaningfully and encourage active engagement in the learning process. The findings of this study provide an overview that the application of mathematics learning based on everyday life contexts can be an effective strategy in improving students' mathematical literacy. Therefore, teachers need to design learning that links mathematical concepts to real-life situations so that students' mathematical literacy skills can develop optimally.

This study aims to analyze in depth the effectiveness of Realistic Mathematics Education (RME) and ethnomathematics in improving students’ mathematical abilities through a Systematic Literature Review (SLR) approach. This study is motivated by the low level of students’ conceptual understanding, mathematical literacy, and mathematical communication skills, which are still dominated by conventional teaching approaches. Data were collected from ten research articles relevant to the topics of RME and ethnomathematics. The analyzed articles employed various research methods, including experimental research, classroom action research, and research and development (R&D). The results of the review indicate that the implementation of RME is consistently effective in enhancing students’ mathematical abilities, such as critical thinking, problem-solving, mathematical communication, and mathematical literacy. The RME approach, which is based on real-life contexts, helps students understand mathematical concepts more deeply and meaningfully. In addition, the integration of culture through ethnomathematics strengthens the effectiveness of learning by providing contexts that are closely related to students’ daily lives, thereby increasing motivation, engagement, and active participation in the learning process.Furthermore, the findings reveal that the success of culture-based RME is influenced by instructional design, the selection of appropriate contexts, and the teacher’s role in managing the learning process. Therefore, culture-based RME can be considered an effective and relevant approach to improving the quality of mathematics education.

This study aims to analyze students’ mathematical reasoning abilities in quadratic function material through the use of Desmos. The research employed a qualitative descriptive approach using a case study and usability testing method. Data were collected through post-tests and interviews involving students’ responses in solving quadratic function problems. The analysis focused on several indicators of mathematical reasoning, including procedural skills, conceptual understanding, and analytical ability. The results show that students generally demonstrate adequate procedural reasoning, particularly in substitution and computation tasks. They are also able to relate algebraic representations to geometric interpretations, such as determining intercept points and analyzing the direction of parabolas. However, limitations were found in conceptual understanding, especially in identifying graph characteristics without relying on procedural steps. The use of Desmos significantly supports the development of students’ mathematical reasoning by providing real-time visualization, facilitating exploration of function parameters, and enabling verification of results. Overall, Desmos contributes to enhancing procedural, conceptual, and analytical dimensions of mathematical reasoning, although its effectiveness depends on proper instructional design.

This study aims to analyze the errors made by eleventh-grade students of SMA Swasta Eria in solving word problems related to quadratic equations and quadratic function graphs using Newman’s error taxonomy. The research employed a descriptive qualitative method involving 25 students who were given essay-type tests to measure both conceptual understanding and problem-solving skills. Data were collected from students’ written answers and analyzed according to Newman’s stages, which include reading, comprehension, transformation, process skills, and encoding. The findings reveal that errors occurred across all stages, with transformation errors and encoding errors being the most dominant. These mistakes generally stemmed from students’ inability to extract key information into correct mathematical models, inaccuracies in arithmetic operations, and insufficient understanding of fundamental quadratic concepts and their graphical representations. The results highlight the importance of instructional approaches that emphasize conceptual understanding, varied practice problems, and proper mathematical notation. Regular application of Newman’s error analysis is expected to help teachers provide more targeted feedback and improve students’ problem-solving abilities.

This study aims to analyze the effectiveness of the question-and-answer method in mathematics learning. The research method employed is a literature review using a descriptive qualitative approach. Findings from several relevant studies indicate that the question-and-answer method enhances students' learning outcomes, fosters active participation, and strengthens critical thinking and communication skills. Variations in its implementation, such as multi-directional questioning, chain questioning, and experiment-based questioning, enrich classroom interaction and help students grasp abstract mathematical concepts. Furthermore, the method promotes an interactive learning environment where students are encouraged to think critically, reflect on their understanding, and actively engage with their peers. The collaborative nature of the question-and-answer technique supports the development of social skills, making it an effective tool for both cognitive and social learning. Therefore, the question-and-answer method can be considered an effective instructional strategy to improve the quality of mathematics learning, particularly in enhancing problem-solving abilities, fostering a deeper understanding of mathematical concepts, and improving student-teacher interactions.

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.

Real analysis is one of the main branches of mathematics that serves as a fundamental foundation for the development of science and technology. This study emphasizes the understanding of basic concepts such as real numbers, limits, continuity, the principle of mathematical induction, as well as deductive and axiomatic approaches as a strong framework for mathematical proofs. This research employs the Systematic Literature Review (SLR) method by examining articles and journals related to both the theoretical aspects and the implementation of real analysis in solving mathematical problems. The findings indicate that the application of Polya’s method, visualization through demonstration, and the use of modern technology such as augmented reality (AR) can enhance the effectiveness of real analysis learning. These approaches help students connect abstract concepts with real applications, thereby strengthening logical, systematic, critical, and rigorous thinking skills. However, several learning difficulties are also identified, including the complexity of the material, weak learning habits, social influences, and inappropriate teaching strategies. Therefore, more applicative, interactive, and contextual learning strategies are needed to support the achievement of learning objectives. The conclusion of this review highlights that the integration of theoretical understanding, problem-solving methods, and innovative technology is a strategic step to improve students’ thinking quality in real analysis courses. Thus, real analysis is not only positioned as a theoretical subject but also as a medium for developing problem-solving abilities and higher-order thinking skills that are relevant to both academic needs and real-world applications.

This study aims to improve the mathematics achievement of third-grade elementary school students through the implementation of the Problem-Based Learning (PBL) model within the framework of Classroom Action Research (CAR). The research was conducted at UPT SD Negeri Kutorejo 1 Tuban and involved 27 students over two instructional meetings. The study was carried out in two cycles, each comprising the stages of planning, implementation, observation, and reflection. Data collection techniques included learning outcome tests, interviews, and documentation. The data were analyzed using both quantitative and qualitative descriptive approaches. The findings indicate a notable improvement in students’ average mathematics scores, increasing from 79.47 in the first cycle to 83.91 in the second cycle. This improvement reflects the positive impact of the PBL model on students' conceptual understanding, problem-solving abilities, and active participation during the learning process. Throughout the intervention, students demonstrated increased engagement in group discussions, greater confidence in expressing ideas, and enhanced independence in addressing given problems. The PBL model proved effective in fostering active, collaborative, and meaningful learning. By presenting real-world contextual problems, the model not only enhanced students’ academic performance but also promoted the development of critical thinking, communication, and social skills. These outcomes align with 21st-century educational goals, which emphasize the cultivation of higher-order thinking skills. Theoretically, this study reinforces the effectiveness of PBL as an innovative pedagogical approach for mathematics instruction at the elementary level. It is recommended that educators systematically and consistently implement the PBL model in classroom practice. Future research is encouraged to explore the interaction between individual student characteristics and instructional models, in order to further optimize learning outcomes across various subject areas.

This study aims to describe the mathematical literacy skills of vocational high school students in solving statistics problems with the help of Microsoft Excel based on digital literacy levels, which are grouped into high, medium, and low. The background of this study is based on the importance of mathematical literacy in dealing with everyday problems and the demands of the world of work, as well as the increasing need for digital literacy mastery in the information technology era. Both are essential competencies that support each other, especially in technology-based mathematics learning. The research approach used is descriptive qualitative with a purposive sampling technique, where the selection of subjects is based on the results of the digital literacy questionnaire, equivalence of mathematics scores, and adequate communication skills to support the interview process. The research instruments include a digital literacy questionnaire, a mathematical literacy test in the form of descriptive questions completed using Microsoft Excel, and interview guidelines that have been validated by experts. The data collection procedure was carried out through tests and in-depth interviews, while data analysis included the stages of data reduction, data presentation, and drawing conclusions. The results of the study indicate differences in students' mathematical literacy skills based on their digital literacy levels. Students with high digital literacy are able to master mathematical literacy indicators well, including communication, mathematization, problem-solving strategies, and reasoning and argumentation. They can optimally utilize Microsoft Excel features to present data, perform calculations, and draw logical conclusions. Students with moderate digital literacy demonstrate fairly good mastery, but still experience difficulties in aspects of problem-solving strategies and in-depth reasoning. Based on these findings, it can be concluded that digital literacy plays a crucial role in supporting students' mathematical literacy abilities.  

This research started from the difference in understanding of mathematical concepts found in students in grades XI-1 of SMA Kanjeng Sepuh Sidayu. The main purpose of this study is to analyze students' understanding of mathematical concepts based on extroverted and introverted personalities, with an ethnomathematical approach on the building of the Kanjeng Sepuh Sidayu Mosque. The research subjects consisted of four students who were selected with two personality categories, namely two students with introverted personalities and two students with extroverted personalities, which were determined through a personality questionnaire. Data collection techniques were carried out using questionnaires to find out personality types, mathematical concept understanding tests, and in-depth interviews to further explore students' understanding. The results showed that there were significant differences in the understanding of mathematical concepts between students with introverted and extroverted personalities. Students with introverted personalities show good ability to meet indicators 1, 3, and 5. This indicator includes the ability to restate a concept, provide examples and non-examples of a concept, and apply concepts or logarithms in problem solving. Students with extroverted personalities, on the other hand, excel in indicators 1, 2, and 4. This indicator includes the ability to restate a concept, classify objects according to the concept, and use and choose certain procedures or operations in solving problems. This study provides insight that the understanding of mathematical concepts is not only influenced by cognitive abilities alone, but also by students' personality factors. Introverted and extroverted personalities affect the way they absorb and apply mathematical concepts. Therefore, it is important for educators to pay attention to these differences in designing teaching approaches that suit the characteristics of the students.

This study aims to develop a contextual learning-based mathematics test instrument focused on Statistics and intended for eighth-grade junior high school (SMP) students. The instrument developed consists of essay questions designed by integrating real-life situations to make them more relevant and meaningful for students. This contextual approach is expected to help students understand statistical concepts more deeply and improve their ability to solve mathematical problems related to everyday life. In the instrument development process, a series of analyses were conducted to test the quality of the test items, including validity, reliability, discriminating power, and difficulty level. The validity of the test items was tested using the correlation between item scores and total scores, with the results showing that all test items had a correlation coefficient greater than the r value of the table, thus being declared valid. Meanwhile, the reliability coefficient obtained was 0.84, indicating that this instrument has a high level of consistency and is suitable for use in measurement. Analysis of the discriminating power showed that each test item had excellent ability to differentiate students with high and low abilities. The analysis of the difficulty level showed balanced variations, namely from easy, medium, to difficult categories. This variation is important to accommodate differences in student ability levels and reflect the diversity in the context of the problems presented. Overall, the results of this study indicate that the developed test instrument is of excellent quality and can be used as an evaluation tool to measure students' mathematical problem-solving abilities. Furthermore, this instrument supports more contextual, interactive, and meaningful statistics learning.

This study aims to describe students' critical thinking skills in solving numeracy literacy problems by considering their mathematical dispositions. Critical thinking skills are an important competency in 21st-century learning because they play a significant role in understanding concepts, analyzing information, and solving problems with a logical and systematic approach. Numeracy literacy, as part of basic mathematical competencies, requires students not only to be able to calculate but also to understand the context and apply mathematical concepts in real life. In this context, mathematical disposition—which includes self-confidence in mathematics, persistence in solving problems, and curiosity—is seen as a factor that influences students' critical thinking skills. This study used a descriptive qualitative approach with student subjects selected based on high, medium, and low mathematical disposition categories. The instruments used consisted of a numeracy literacy test and a semi-structured interview guide. Data were collected through completing a mathematical disposition questionnaire, working on numeracy literacy problems, and in-depth interviews with selected subjects. Data analysis techniques included data reduction, data presentation, and inductive conclusion drawing. The results of the study indicate that students with a high mathematical disposition tend to have more developed critical thinking skills. They are able to analyze problems in depth, evaluate relevant information, and draw logical and structured conclusions. Conversely, students with medium and low dispositions tend to have limited critical thinking skills, particularly in the aspects of evaluation and conclusion drawing. This finding emphasizes the importance of strengthening mathematical dispositions as an integral part of learning strategies to improve students' critical thinking skills in the context of numeracy literacy.

This study aims to compare the effectiveness of the Deep Learning and Differentiated Instruction models in improving junior high school students’ mathematical problem-solving and reasoning abilities. The background of this research stems from the low level of mathematical literacy among Indonesian students, which demands innovative and reflective learning approaches. A quasi-experimental method was used with a Nonequivalent Control Group Design. The sample consisted of two eighth-grade classes at SMP Negeri Satu Atap 01 Ciseeng, each receiving different instructional treatments: one class was taught using the Deep Learning approach, and the other using the Differentiated Instruction approach. The instruments employed included mathematical problem-solving tests, observation sheets, and student perception questionnaires. The data analysis results indicated that the class taught with the Deep Learning model experienced a more significant improvement in mathematical reasoning ability compared to the class using Differentiated Instruction. These findings suggest that Deep Learning-based instruction is more effective in promoting students’ higher-order thinking skills. It encourages deeper engagement with mathematical concepts, fosters critical and analytical thinking, and allows students to construct knowledge through meaningful learning experiences. However, Differentiated Instruction remains relevant in providing learning comfort and addressing diverse student needs, making it beneficial in inclusive classroom settings. The theoretical and practical implications of this research highlight the importance of integrating both depth of thinking (Deep Learning) and flexibility in learning (Differentiation) within mathematics instruction. Such integration could offer a balanced learning environment that supports both cognitive development and emotional engagement, leading to more effective and equitable mathematics education. In conclusion, this study recommends educators and curriculum developers to consider incorporating Deep Learning strategies to enhance students’ mathematical reasoning while maintaining the adaptive and student-centered principles of Differentiated Instruction. Future research could explore hybrid learning models that combine the strengths of both approaches to maximize student outcomes in mathematics learning.

This study aims to improve the critical thinking skills of fourth-grade elementary school students in understanding the concept of fractions through the application of the Problem Based Learning (PBL) model. The background of this study focuses on students' still low abilities in: (1) analyzing mathematical problems; (2) planning solution strategies; (3) drawing logical conclusions when working on fraction problems. This study uses the Classroom Action Research (CAR) design model Kemmis & McTaggart which was implemented at SD Negeri 2 Tahunan during the even semester of the 2024/2025 academic year. The research subjects consisted of 23 fourth-grade students who were selected purposively based on the results of the initial diagnosis. Data collection techniques were carried out by triangulation through: (1) formative evaluation tests; (2) participatory observation sheets; (3) learning video documentation; and (4) field notes. Data were analyzed quantitatively and qualitatively with a comparative descriptive approach. The results showed that the application of the PBL model was proven to be effective in improving: (1) students' critical thinking skills on average from 39.13 (low category) to 92.61 (very good category); (2) classical completeness from 8.7% to 91.3%; and (3) learning activities became more meaningful. Statistical analysis of paired sample t-test showed a significant difference (t=19.09; p<0.05) between before and after treatment. Other important findings include: (1) an increase in students' questioning skills by 78%; (2) an increase in the ability to provide arguments by 82%; (3) an increase in problem-solving skills by 85%. In addition, there was an increase in the following aspects: (1) group cooperation; (2) self-confidence; and (3) active involvement in class discussions.

This research focuses on exploring the mathematical reasoning abilities of Madrasah Aliyah students in solving problems that integrate mathematical concepts with the Islamic science of faraidh (inheritance law), specifically within the topic of fractions. The study employs a qualitative approach with a case study design and was conducted among 11th-grade students enrolled in the Religious Program at MA Raudlatul Ulum Putri. Data collection techniques included written tests, semi-structured interviews, and classroom observations, focusing on three selected students who represented high, moderate, and low levels of mathematical ability. The analysis centers on several key indicators of mathematical reasoning: identifying problems, formulating hypotheses, presenting logical arguments, and drawing conclusions. The results show that most students fall into the moderate reasoning category, while a smaller number are categorized as high or low. Students in the high category demonstrate a strong capacity to approach problems systematically and accurately, combining mathematical logic with a proper understanding of Sharia-based inheritance rules. In contrast, students in the low category struggle with interpreting problem contexts and executing fraction calculations correctly, which indicates gaps in both conceptual understanding and application skills. These findings underscore the importance of contextual and integrative learning, particularly the combination of mathematics with Islamic values, to enhance deeper comprehension. By embedding religious relevance into mathematical instruction—especially through real-life contexts such as inheritance laws—educators can support the development of more meaningful reasoning abilities. The study suggests that integrating mathematics and Islamic teachings can significantly benefit student learning outcomes and foster stronger conceptual foundations.

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.

Mathematics learning does not only focus on students' mastery of numbers, but also functions significantly in developing the ability to solve problems holistically. This skill is not something that is taught separately, but is integrated into the entire educational process, offering a real context so that mathematical concepts and abilities can be understood and applied. One approach that is highly recommended to achieve this is Problem Based Learning (PBL). This method has been proven effective in improving students' critical thinking skills through exploration and solving relevant problems, allowing students' knowledge to grow in a constructive way. The low achievement in problem-solving competency in Indonesia is a strong reason to apply PBL in mathematics teaching. This study aims to analyze the literature on the application of PBL to improve students' problem-solving abilities. Data were collected and analyzed from relevant journals, and testing and comparison of results were carried out to identify patterns and results from previous studies. In addition, this study also applies a bibliometric approach to explore publication trends, keywords, and the development of themes related to PBL in mathematics education. The analysis was carried out using VOSviewer software to map the relationship between topics and the progress of PBL research themes in the world of mathematics education.

The research conducted at MAS Daarul Uluum Lido Bogor Jl. Mayjen Hr Edi Sukma KM 22, Ciburuy Village, Cigombong District, Bogor Regency, aims to analyze the level of Mathematical Problem Solving Ability in the Sequence and Series Material of Class 11 at MA Daarul Uluum Lido through Google Form Media. The research method used is qualitative research with the sampling technique used is purposive sampling. The target population in this study were all class 11 students at MAS Daarul Uluum Lido. The accessible population in this study was only class 11 D MIA MAS Daarul Uluum Lido students. The research sample was 6 students, consisting of 2 students with low-level mathematical problem solving abilities, 2 students with medium-level mathematical problem solving abilities and 2 students with high-level mathematical problem solving abilities. The data analysis technique was carried out descriptively qualitatively before and during the field, namely data reduction analysis, data presentation and drawing conclusions and data verification. Based on the results of the study, it can be concluded that students in the low category are 2 students with a percentage of 5.55%, 28 students with a percentage of 77.77% are in the medium category and 6 students with a percentage of 16.6% are in the high category. So the dominant ability of solving mathematical problems in the material of Sequences and series at MAS Daarul Uluum Lido is in the medium category with a percentage of 77.77%.