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The study aims to analyze the relationship between learning discipline and students' critical thinking abilities in math learning. A quantitative approach with correlational survey methods is used in this study. Sample of 44 junior high school students selected through simple random sampling technique. Instruments used as lamps to measure learning discipline and tests to measure critical thinking ability. Data analysis was performed through Liliefors normality testing, Pearson correlation testing, and simple linear regression. The normality test results show that discipline learning data is normally distributed (Lo = 0.0995 < Ltable = 0.133), whereas critical thinking data is not normally distributed (Lo = 0.2266 > Ltable = 0.133). The correlation test results show the value of r = 0.211 and thitung = 1.423 < ttable = 1.683, meaning there is no significant relationship between learning discipline and critical thinking ability. The regression results also show the value of Fhitung = 2.15 < Ftabel = 4.08, which means there is no significant influence between learning discipline on critical thinking ability. Thus, that learning discipline does not affect significantly on students' critical thinking ability in math learning. This results in a more comprehensive learning approach to develop critical thinking skills.

This study aims to: (1) produce e-LKPD based on problem-based learning oriented to mathematical problem-solving ability and self-confidence of high school students on the material of equations and quadratic functions and (2) describe the feasibility of PBL-based e-LKPD oriented to mathematical problem- solving ability and self-confidence of high school students on the material of equations and quadratic functions seen from the aspects of validity,  practicality, and effectiveness. This type of research is research and development using the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The research was conducted at SMA Negeri 1 Malinau with the research subject of class X-3 students totaling 35 students. Data collection was carried out using interview techniques, observation, e-LKPD validation sheets, pretest-posttest, and questionnaires. To determine the validity, the e-LKPD assessment sheet of material and media experts was used, practicality used student and teacher response questionnaires, and effectiveness used mathematics problem solving ability test questions and student self-confidence questionnaires. Data analysis consisted of qualitative data analysis and quantitative data analysis. Qualitative data analysis was conducted by analyzing the results of interviews, observations, and comments or suggestions given to make improvements to the e-LKPD products developed. Quantitative data analysis was conducted by converting quantitative data into qualitative data in the form of certain categories, normality test using shapiro-wilk, t-test with paired samples test, and N-Gain score. The results showed: (1) PBL-based e-LKPDs oriented towards mathematical problem solving skills and self-confidence of high school students on the material of quadratic equations and functions have been produced, (2) PBL-based e-LKPDs developed meet product feasibility, namely valid with excellent categories based on material and media experts; practical with very practical categories based on teacher responses and practical based on student responses; effective on math problem solving skills with classical completeness of 77%, the t-test results obtained a significance value of 0.000 <0.05 which means that there is a difference in the average ability to solve mathematical problems before and after learning using e-LKPD, the N-Gain result is 0.65 with moderate criteria, and effective on student self-confidence with an increase in the average score of each indicator before and after learning,  the N-Gain result is 0.49 with moderate criteria, and the t-test results with a significance value of 0.000 < 0.05.

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 analyze the influence of learning interest, learning discipline, and critical thinking skills on student learning outcomes in the Simple Financial Processing subject for class XI MPLB at SMK PGRI 2 Sidoarjo. Learning outcomes are understood as skills or abilities acquired by students after participating in the learning process, the success of which is measured through scores in the form of numbers, symbols, or letters. Three factors selected in this study as independent variables are learning interest, learning discipline, and critical thinking skills. This type of research is quantitative research with an explanatory approach, which aims to explain the cause-and-effect relationship between these variables. The population in this study were all 102 class XI MPLB students. The sampling technique used non-probability sampling with a total sampling type, so that the entire population was sampled. Data collection was carried out by distributing questionnaires to students. The data obtained were then analyzed using SPSS version 27 software. Before conducting multiple linear regression analysis, validity and reliability tests were first conducted to ensure that the instruments used were appropriate and consistent in measuring the variables studied. The analysis results show that the three independent variables—learning interest, learning discipline, and critical thinking skills—have a significant influence on student learning outcomes. Therefore, it can be concluded that improvements in these three aspects will positively impact student learning outcomes in the subjects studied.

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.

Indonesia is a country rich in culture, one of which is batik, recognized by UNESCO as an intangible cultural heritage of Indonesia. Batik is not only a visual art form but also holds significant potential as a context for teaching mathematics. Unfortunately, the integration of local culture into mathematics education has not been widely implemented. Therefore, this community service activity aims to train teachers and assist students in applying Realistic Mathematics Education (RME) based on batik culture at MTs Nurul Ummah Kotagede, Yogyakarta. The activity was carried out in three stages: preparation, implementation, and evaluation. In the preparation stage, teachers were provided with training on the theory and practice of RME, which was then applied in the classroom. The lesson focused on geometric transformations, using batik patterns as a real-world context. By linking mathematical concepts to the familiar cultural context of batik, it was hoped that students would more easily understand abstract mathematical ideas and find them more meaningful. The results of the activity showed high enthusiasm from the students and positive appreciation from the teachers toward the RME model based on culture. Students demonstrated a better understanding of mathematical concepts, as the learning process connected theoretical knowledge to real-world contexts they recognized. Additionally, teachers acknowledged that using batik culture in mathematics education made the learning experience more enjoyable and meaningful. This activity proves that integrating local culture, such as batik, into RME can increase students' interest in mathematics and help them understand abstract concepts by relating them to real-life experiences.

This research aims to develop a mathematics teaching module based on differentiated learning integrated with the Project-Based Learning (PjBL) method, specifically for the topic of spatial structures ("get up room") for students at Nanasi 1 Elementary School. The development process follows the 4D model, which includes the stages of Define, Design, Develop, and Disseminate. In the Define stage, analysis revealed the absence of instructional modules that align with students' learning styles and needs. Consequently, learning objectives were formulated based on geometric elements and problem-solving criteria. During the Design stage, a prototype module and validation instruments were produced. Validation was conducted by two experts, yielding high scores for both content and visual presentation—each achieving 90% validity. Practicality assessments also showed strong results, with content rated at 90.8% and visual aspects at 90%, categorizing the module as “very valid” and “very practical.” The integration of the PjBL method was implemented to enhance active student participation, encouraging collaborative exploration and real-world application of mathematical concepts. The developed module is considered suitable for supporting differentiated mathematics instruction in elementary schools. It accommodates diverse learning styles and promotes student engagement through project-based tasks. The findings suggest that combining differentiated learning with PjBL fosters a more inclusive and effective learning environment, particularly in geometry-related topics. This module not only meets pedagogical standards but also contributes to the advancement of innovative teaching practices in primary education.

Limited access to learning resources appropriate to the local context presents a challenge in the mathematics learning process in indigenous communities such as the Baduy Tribe. Conventional mathematics learning is often considered too abstract and less relevant to the daily lives of Baduy children, especially in the Outer Baduy region. To address this challenge, this community service activity aims to introduce contextual mathematics learning media based on the surrounding environment and local culture. The media developed is designed to be easily accessible, affordable, and environmentally friendly, while still respecting prevailing traditional values. The method used in this activity is Participatory Action Research (PAR), with a collaborative approach between a team of lecturers and the Outer Baduy community. The activity implementation process includes six stages, namely: identification of local problems and potential, planning, designing learning media, implementation, evaluation, and documentation of activity results. The results of the activity show an increase in interest and understanding of basic mathematics concepts among Outer Baduy children. Children appear more active, enthusiastic, and confident in participating in the learning process through educational games and concrete activities. The media used utilizes natural objects and local cultural elements, such as woodcuts, ancient angklungs, traditional hats, and distinctive Baduy woven motifs. The community responded positively because these media do not conflict with traditional values. This activity has had positive cognitive and social impacts and strengthened awareness of the importance of a contextual and culturally based educational approach as a relevant and inclusive learning strategy.  

The Abbasid dynasty was one of the most influential Islamic caliphates and left a long legacy in the development of world civilization. Established in 750 AD and ending in 1258 AD, the Abbasid period is known as the Golden Age of Islam due to its extraordinary progress in various fields, including politics, economics, and science. This study aims to examine how the Abbasid political and economic policies and the development of science that took place during that period were able to contribute significantly to the progress of global civilization. This study uses a qualitative method with a descriptive-historical approach through the study of relevant literature in the last five years. The results of the study indicate that political stability and a structured bureaucratic system provided a strong foundation for economic growth and intellectual progress. The Abbasid government established a center of knowledge in Baghdad known as Baitul Hikmah (House of Wisdom). Here, scientists from various religious and cultural backgrounds gathered to translate, develop, and disseminate knowledge from Greek, Persian, Indian, and other scientific traditions into the Islamic world. Some of the great figures who emerged during this period included Al-Khwarizmi (mathematics), Ibn Sina (medicine and philosophy), and Jabir Ibn Hayyan (chemistry). Their discoveries and work became the foundation for modern science. However, the glory of the Abbasids slowly declined due to internal conflicts, power struggles, and the weakening of the caliph's authority. The peak of the fall occurred when Baghdad was attacked and destroyed by the Mongols in 1258 AD. However, the intellectual and cultural heritage of the Abbasid dynasty continues to have an important influence on the development of world science and civilization to this day.

This research explores the effectiveness of heuristic techniques for solving combinatorial optimization problems, with a particular focus on the Traveling Salesman Problem (TSP). Combinatorial optimization is a critical area of study, especially in fields like computer science, engineering, and economics, where finding optimal solutions from a finite set of possibilities is crucial. However, the NP-hard nature of many combinatorial problems, such as the TSP, makes traditional exact methods like Branch-and-Bound and Dynamic Programming computationally expensive and inefficient for larger problem sizes. The primary objective of this research is to evaluate the performance of heuristic methods, including Simulated Annealing (SA), Genetic Algorithms (GA), and Iterative Computation techniques, such as Tabu Search (TS) and Particle Swarm Optimization (PSO). These methods are tested for their ability to provide approximate solutions efficiently. The findings reveal that while ACO provided the best solution quality, it had the longest runtime. TS was the fastest, though with slightly lower solution quality. SA and GA demonstrated a balance between solution quality and computational efficiency, but their performance heavily depended on parameter tuning. The hybridization of SA and GA showed potential for improving solution quality but introduced additional complexity. The research concludes that heuristic methods, especially when combined, offer viable solutions for large-scale combinatorial optimization problems, though the trade-off between solution quality and computational time must be considered when selecting an algorithm.

Integral equations are essential tools in applied mathematics, with wide-ranging applications in fields such as physics, engineering, and finance. However, solving these equations presents significant challenges, particularly when dealing with complex, high-dimensional, or singular problems. Traditional methods, such as manual analytical techniques or direct numerical approaches, often struggle with computational efficiency, especially for large-scale systems, and may not be suitable for handling ill-conditioned problems. This study aims to develop an efficient numerical method for solving integral equations by combining adaptive quadrature techniques with Python-based iterative solvers. The adaptive quadrature method adjusts the step size dynamically based on error estimates, ensuring high accuracy even in the presence of singularities or near-singularities, which are common in many real-world problems. The iterative solver, based on Krylov subspace methods, enhances computational efficiency by reducing memory usage and improving the convergence speed of the solution. By using these techniques together, the proposed method significantly improves the computational time required to solve large-scale and complex systems of integral equations, while maintaining satisfactory accuracy. The results demonstrate that the adaptive quadrature technique, when combined with the Python-based iterative solver, offers a substantial advantage in both speed and precision compared to traditional methods. The proposed method is especially effective in handling complex, high-dimensional systems and ill-conditioned problems, making it a powerful tool for applied mathematics, physics, and engineering applications. In conclusion, this study presents a robust and efficient approach for solving integral equations, with potential for future research in solving non-linear and multi-dimensional integral equations.

The Faculty of Mathematics and Natural Sciences (FMIPA) of the University of East Kalimantan (Unikaltar) consistently conducts satisfaction surveys to improve the quality of services provided to students. This survey aims to evaluate the performance of each work unit, including lecturers, with the hope that the results obtained can identify aspects that are still hampering or suboptimal. The survey results serve as the basis for formulating steps to improve and enhance the quality of educational services within the faculty. This study specifically highlights the level of student satisfaction with the performance of lecturers in the Islamic Religious Education course. The survey implementation process includes several stages, starting from data collection using a survey instrument, the data input process, and testing the validity and reliability of the instrument to ensure data reliability. Next, the collected data is processed and analyzed to obtain an objective picture of student perceptions. Based on the analysis, the student satisfaction index value obtained is 3.16. This figure is in the "Good" or "Satisfied" category, indicating that students are generally satisfied with the service and learning process carried out by lecturers in the course. These findings provide important input for the institution in maintaining and improving the quality of learning, particularly in the field of religious studies. In the future, it is hoped that similar surveys can continue to be carried out periodically so that the service improvement process can run continuously.

Relations in mathematics are a fundamental concept that describe the connection between two sets. This concept is crucial because it forms the foundation for understanding functions and various other mathematical topics. In everyday life, relations can be found in numerous real-world situations, such as the relationship between teachers and their students, sellers and buyers, or students and their exam scores. By understanding relations, students can see how elements from one set are linked to elements in another set based on specific rules. Unfortunately, many students still find it difficult to grasp the concept of relations because it is often taught in an abstract way, filled with mathematical symbols that are not connected to their real-life experiences. As a result, students may feel that the topic is irrelevant to their lives, leading to a lack of interest and poor comprehension. In fact, if taught contextually and practically, the concept of relations can serve as a key bridge to help students understand functions and their relevance in the real world. This article aims to explain the concept of relations through a more practical and relatable approach. For example, it can be illustrated by connecting students' names with their attendance numbers, or linking foods with their nutritional contents. Through these examples, students can see that relations are not just rigid parts of a math lesson but also reflect meaningful connections in everyday life. In this way, it is expected that students will gain a more comprehensive understanding of relations—not only mathematically but also in terms of practical application and functionality. A solid understanding of relations will make it easier for students to learn advanced concepts such as functions, mappings, and mathematical logic. Therefore, a learning approach that emphasizes contextual understanding is essential, so that students are not merely memorizing formulas but are also capable of applying the concept of relations in real-world situations.

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 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 was conducted to examine how well the use of augmented reality (AR) learning tools helps fifth-grade elementary school students understand mathematical concepts related to fractions.. The research was motivated by students' limited comprehension of the abstract nature of fractions and the lack of engaging educational tools capable of presenting the material in a meaningful and interactive way. Augmented reality is believed to improve student engagement and offer more appealing visual representations by integrating virtual elements into the real-world environment. A total of 30 students I participated in this study, which used a quasi-experimental design with a One Group Pretest-Posttest method. Information was collected through pre-tests, post-tests, written notes, and observations. We used SPSS software to analyze the data. The results showed that students' grades improved significantly, with the average increasing from 54.80 in the pretest to 91.83 in the posttest. The normality test indicated that while pretest scores were approximately normally distributed, the posttest scores followed a normal distribution. A one-sample t-test showed a statistically significant effect of AR media usage, with a p-value of 0.000 and t-values substantially higher than the critical value (pretest: 32.439; posttest: 112.071). These results suggest that AR-based instructional media are effective in supporting elementary students’ understanding of fraction concepts. Overall, the study confirms the positive impact of augmented reality in mathematics learning for fifth-grade students.

This article explores the concept of sets in mathematics, a fundamental foundation for various disciplines. The discussion includes the definition of a set as a well-defined collection of objects, as well as various methods of presenting them such as enumeration, description of properties, set-forming notation, and Venn diagrams. In addition, the article outlines the various types of sets (empty, universe, equal, part, disjoint, crossed, equivalent, power) and explains the fundamental properties of set operations (identity, dominance, complement, idempotent, absorption, commutative, associative, distributive, De Morgan). The primary objective is to provide a concise yet comprehensive understanding of sets as a foundational pillar of logical and mathematical thinking.

Penelitian ini bertujuan mendeskripsikan kemampuan berpikir kreatif matematis siswa kelas VII SMP Al Farabi pada materi geometri. Penelitian ini menggunakan pendekatan deskriptif kualitatif dengan melibatkan seluruh siswa kelas VII sebanyak 71 orang. Data diperoleh melalui tes tertulis berupa empat soal terbuka berbasis geometri yang dirancang untuk menggali empat indikator berpikir kreatif, yaitu kelancaran (fluency), keluwesan (flexibility), keaslian (originality), dan elaborasi. Hasil analisis menunjukkan kemampuan berpikir kreatif siswa tergolong “baik” pada setiap indikator, dengan skor tertinggi pada keluwesan (75,35%) dan terendah pada keaslian (61,27%). Temuan ini menunjukkan bahwa meskipun siswa telah memiliki kemampuan berpikir kreatif yang cukup baik, pengembangan ide-ide orisinal masih perlu ditingkatkan. Hasil penelitian ini diharapkan menjadi bahan masukan bagi guru untuk merancang strategi pembelajaran yang lebih relevan dan mendukung pengembangan kreativitas siswa

This thesis discusses efforts to increase students’ interest in learning Mathematics through the use of concrete media among third-grade students at SDN 110/1 Tenam. The purpose of the study is to improve students’ interest in learning Mathematics by using concrete media with these third-grade students. The results of the study show an increase in learning activities that indicate student interest during Cycle I and Cycle II. In Cycle I, all student learning activities were still at percentages below 70%, with ratings categorized as poor and adequate. Meanwhile, in Cycle II, the increase in student learning activities was shown by all activities reaching percentages above 74%, which means they exceeded the predetermined Learning Objectives Achievement Criteria (KKTP) and were rated good and very good. In addition, improved learning outcomes, as evidence of increased student interest, also showed a significant rise. In Cycle I, students’ learning outcomes did not meet the Learning Objectives Achievement Criteria (KKTP), with a class average of 68.9%, whereas in Cycle II, overall class mastery reached 82.3%. This improvement in learning outcomes indicates that students showed fairly good interest when learning with concrete media.