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This study aims to examine the role of mathematics education in building numerical literacy in elementary schools, as well as strategies that can be implemented to enhance students' numerical skills. Numerical literacy is a fundamental skill needed by students to understand, interpret, and use numerical information in daily life. The research method used is library research, reviewing various related literature, including books and recent scholarly journals in the field of mathematics education. The results show that the integration of technology, the use of contextual approaches, and collaborative learning are effective strategies in improving students' numerical literacy. Technology helps simplify the understanding of abstract concepts, while contextual and collaborative approaches make mathematics more relevant and applicable. The implications of these findings are the need for further development in teacher training to integrate technology in teaching and the importance of involving students in more interactive and contextual learning processes. This study also suggests further evaluation of the implementation of these strategies in various educational settings.

This study aims to analyze the effect of implementing the Realistic Mathematics Education (RME) learning model on improving students' mathematical literacy, particularly in social arithmetic material at SMP Negeri 2 Wonorejo. The research used a quantitative method with a quasi-experimental design in the form of a non-equivalent control group design. The population consisted of seventh-grade students from three classes, samples selected through purposive sampling based on preliminary test results: class VII B as the control group and class VII C as the experimental group. Research instruments included a validated observation sheet on student activities and an essay-type mathematical literacy test. Data analysis was conducted using normality tests, homogeneity tests, independent t-tests, and effect size calculation. The results indicated that student activities in the RME learning model were categorized as excellent. Hypothesis testing with an independent t-test yielded tcalculated = 2.81 > ttable = 1.56. The average post-test score of the experimental group (73.00) was higher than that of the control group (50.41). The effect size calculation resulted in d = 1.75, which falls into the large effect category. Thus, it can be concluded that the RME learning model has a positive and significant influence on improving students' mathematical literacy.

Teaching plane geometry often faces challenges due to the abstract nature of geometric concepts, which are often detached from students’ real-life contexts. This study is a development research (Research and Development) using a modified 4D model reduced to 3D (Define, Design, Develop) aimed at producing and testing the validity of a Student Worksheet based on ethnomathematics with Batik Sekundang motifs on plane geometry material oriented toward Contextual Teaching and Learning (CTL). Validation was conducted by two mathematics education experts who assessed the feasibility of content/material, media, and language/readability using a Likert scale instrument. The data were analyzed quantitatively in a descriptive manner using percentage formulas to determine the level of validity. The results showed that the student worksheet obtained a validity percentage of 87.50% in content feasibility (very valid), 80.76% in media (valid), and 87.50% in language (very valid), with an overall average of 85.25%, which falls into the very valid category. Based on these results, the ethnomathematics-based student worksheet with Batik Sekundang motifs is declared suitable to be used as a supporting teaching material for contextual and meaningful plane geometry learning for students in South Bengkulu.

Learning geometric transformations requires a strong conceptual understanding due to their abstract nature. One effort to enhance students’ conceptual understanding of mathematics is through the development of contextual and meaningful instructional materials that incorporate local culture. This study is a research and development (R&D) study employing the 4D model (Define, Design, Develop, and Disseminate) aimed at examining the validity of the developed Student Worksheets. The validation of the Student Worksheets was conducted by two experts in mathematics education who evaluated the aspects of content feasibility, media, and language and readability. The data were analyzed using descriptive quantitative methods with percentage scores to determine the level of validity of the Student Worksheets. The results showed that the developed Student Worksheets obtained a validity percentage of 93.75% for the content feasibility aspect (very valid), 80.77% for the media aspect (valid), and 87.50% for the language and readability aspect (very valid), with an overall average of 87.34%, which falls into the very valid category. Based on these results, the ethnomathematics-based Student Worksheets using the Kepahiang Traditional House context are considered feasible for use as supporting instructional materials in learning geometric transformations.

Many students still face difficulties in understanding statistics because inaccurate preconceptions often develop into misconceptions. This condition is important to study since misconceptions can hinder the mathematics learning process and reduce the quality of students’ conceptual understanding. This study aims to analyze in depth how preconceptions affect the emergence of misconceptions among senior high school students in learning statistics. The research employed a qualitative descriptive method with a case study approach, involving three tenth-grade students from State Senior High School 1 Purwosari who were selected through purposive sampling based on high, medium, and low achievement categories. Data were collected through diagnostic tests in the form of essay questions to reveal students’ preconceptions and in-depth interviews to explore their reasoning, then analyzed descriptively. The findings show that students with accurate preconceptions did not experience misconceptions, students with partially correct preconceptions developed classificational, theoretical, and correlational misconceptions, while students with incorrect preconceptions experienced more complex misconceptions, such as considering the median as the largest value and failing to relate changes in data to the properties of the mean, median, and mode. The study concludes that inaccurate preconceptions directly contribute to the emergence of various forms of misconceptions. The implication is that teachers need to detect, identify, and correct students’ preconceptions from the beginning of the learning process so that misconceptions can be minimized and students’ understanding of statistics can develop more comprehensively.

Mathematics is a core subject that develops critical thinking skills; however, many third to fifth-grade elementary school students face difficulties with conventional teaching methods that tend to be uniform and less adaptive. This study aims to develop and implement a mobile-based educational game, "Ethno Run," which integrates the Bayesian Knowledge Tracing (BKT) algorithm to provide an adaptive learning experience. The method used is Research and Development (R&D) with the Multimedia Development Life Cycle (MDLC) framework. The system uses BKT to track students' mastery in real-time by analyzing their responses to pre-tests and exercises within the game, which then adjusts the difficulty level and focuses the post-test on areas identified as weak, such as arithmetic operations and geometry. The findings show that this adaptive approach significantly improves learning outcomes, with the average score increasing from 44.33 on the pre-test to 85.33 on the post-test among 30 students. This study concludes that the integration of Artificial Intelligence through BKT effectively personalizes learning, enhances student motivation, and provides data-driven insights for teachers regarding students' progress. The implication of this research is that adaptive game-based learning serves as a feasible interactive solution to bridge the gap in conventional basic mathematics education.

Graph theory as a branch of discrete mathematics has experienced significant development in its application to modern complex network systems, particularly in digital social networks and transportation systems. This research aims to analyze fundamental concepts of graph theory, examine characteristics of cycle detection algorithms along with their computational complexity, investigate their application in digital social network analysis, and explore their implementation in digital transportation system optimization. The research method employs a qualitative approach with library research focusing on scientific literature from 2020-2025 period from accredited academic databases such as Scopus, Web of Science, and IEEE Xplore, utilizing thematic analysis techniques to identify meaningful patterns from the examined literature. Research findings indicate that fundamental graph theory concepts including vertices, edges, and graph classifications form the foundation for relational structure modeling. Cycle detection algorithms such as Depth-First Search, Union-Find, and Tarjan demonstrate effectiveness with O(V+E) complexity for large-scale graphs. Applications in digital social networks facilitate community identification through Multi-View Clustering, centrality analysis for influencer detection, and understanding viral information dissemination patterns. Implementation in digital transportation systems demonstrates route planning optimization using Dijkstra and Bellman-Ford algorithms, vulnerability analysis through articulation point and bridge identification, and bottleneck detection with betweenness centrality. The research concludes that integration of graph theory in discrete mathematics education enhances critical thinking skills and real-world application understanding, with recommendations for algorithm development for massive dynamic graphs and machine learning integration in graph algorithm optimization.

This study investigates the impact of GeoGebra-assisted collaborative learning on students' understanding of function graphs. Function graphs are fundamental in mathematics education, yet many students struggle to grasp the relationships between variables, primarily due to traditional teaching methods that focus on procedural skills rather than conceptual understanding. To address this challenge, the study incorporates GeoGebra, a dynamic mathematics software, alongside collaborative learning strategies. The research utilizes a quasi-experimental design involving high school students who had previously struggled with function graphs. The results demonstrate that the experimental group, which engaged in GeoGebra-assisted collaborative learning, showed a significant improvement of 27% in their post-test scores, compared to just a 6% improvement in the control group using traditional methods. The study highlights the effectiveness of GeoGebra in fostering a deeper conceptual understanding of mathematical functions by enabling students to visualize and manipulate graphs interactively. Additionally, collaborative learning encouraged peer interaction, reinforcing the learning process and promoting better problem-solving skills. The findings suggest that combining interactive tools like GeoGebra with collaborative learning techniques can enhance students’ mathematical comprehension, leading to improved engagement and performance in mathematics education.

This study explores the integration of financial numeracy with local wisdom in mathematics education in Indonesia. By incorporating real-life financial scenarios, such as budgeting, saving, and investment calculations, into mathematics lessons, the research aims to enhance students' understanding of mathematical concepts while simultaneously improving their financial literacy. The study also emphasizes the importance of using local cultural and economic knowledge as a context for learning, making abstract mathematical concepts more relevant and accessible. The findings suggest that contextualizing mathematics education through local wisdom significantly improves student engagement, understanding, and practical application of mathematical knowledge. The integration of financial numeracy helps students make informed financial decisions and prepares them for future financial challenges. This research contributes to the development of a mathematics curriculum that combines financial literacy with local context, offering a more inclusive, relevant, and practical approach to education. The study’s findings contribute to the ongoing development of more inclusive, relevant, and practical educational frameworks that incorporate financial literacy into the mathematics curriculum.

Measurement learning is a fundamental and applicable mathematical topic in everyday life, but it often causes learning difficulties for students, especially in understanding the meaning of units, relationships between quantities, and the conceptual measurement process. These difficulties are not only caused by students' limited cognitive abilities, but also by learning designs that do not fully facilitate social interaction and student learning development. This study aims to reconstruct the contextual didactic design in measurement learning by reviewing the role of social interaction and the Zone of Proximal Development (ZPD) in the student learning process. This study uses a qualitative approach with the type of Didactic Design Research (DDR). The research stages include analysis of the initial didactic situation to identify student learning barriers, implementation of contextual didactic design in measurement learning, and retrospective analysis of student responses as a basis for reconstructing the didactic design. Data were collected through learning observations, analysis of student work results, interviews, and learning documentation. Data analysis was carried out qualitatively by examining social interaction patterns, forms of scaffolding, and student movements in the Zone of Proximal Development. The results of this study indicate that understanding of measurement concepts develops through social interactions between students and between students and teachers within a meaningful learning context. Social interactions and scaffolding provided gradually can encourage students to move from actual abilities to potential abilities within the Zone of Proximal Development. Retrospective analysis indicates that reconstruction of the didactic design is necessary to refine the learning context, activity sequence, and scaffolding strategies to better align with students' learning characteristics. The reconstruction of the didactic design can reduce learning barriers and improve the quality of students' conceptual understanding in measurement learning. This research provides theoretical contributions to the study of social constructivism-based mathematics education and provides practical implications for teachers in designing measurement learning that is more responsive to social interactions and student learning development.

This study aims to explore the integration of financial literacy into context-based mathematics education at the elementary school level by emphasizing the use of local knowledge in learning activities. Employing a qualitative descriptive approach, this research investigates the experiences and perceptions of students and teachers involved in mathematics learning that connects mathematical concepts with real-life financial situations, such as budgeting, saving, and personal financial management. Data were collected through interviews, classroom observations, and documentation analysis to obtain a comprehensive understanding of the learning process and its outcomes. The findings indicate that integrating financial literacy into context-based mathematics learning enhances the relevance of mathematical content and facilitates students’ conceptual understanding. Students reported increased interest and engagement in mathematics lessons, as well as greater confidence in applying mathematical skills to manage personal finances. The use of familiar financial contexts enabled students to perceive mathematics as meaningful and applicable to their daily lives. Teachers identified limited instructional time and difficulties in explaining abstract concepts as key obstacles in the implementation process. Overall, the results suggest that context-based mathematics learning integrated with financial literacy has strong potential to improve students’ mathematical understanding and financial awareness while fostering practical life skills. Nevertheless, effective implementation requires careful instructional planning, adequate time allocation, and appropriate pedagogical strategies to address complex financial concepts. This study contributes to the growing body of research on contextualized mathematics education by highlighting the importance of integrating local context and financial literacy to enhance the quality and relevance of elementary mathematics education.

Measurement is a fundamental domain of mathematics that connects formal mathematical concepts with everyday experiences. Despite its practical relevance, students often experience persistent difficulties in understanding measurement conceptually, tending to approach it as a procedural activity rather than as a process of reasoning about quantities, units, and comparisons. These challenges indicate that learning measurement is influenced not only by individual cognitive factors but also by the social dynamics that shape classroom learning environments. This study aims to examine classroom social dynamics in learning measurement by providing empirical evidence from contextual learning situations. This study employed a qualitative research approach to explore how social interaction, scaffolding, and participation mediate students’ understanding of measurement in contextual learning environments. Data were collected through classroom observations, video recordings of learning activities, analysis of students’ written work, and interviews with selected students and the teacher. Contextual measurement tasks were designed to encourage collaboration, dialogue, and justification, enabling the examination of student–student and teacher–student interactions as they naturally occurred in the classroom. Data analysis was conducted iteratively to identify patterns of interaction, forms of scaffolding, and students’ learning progression within the Zone of Proximal Development. The findings reveal that students initially engaged with measurement tasks in a predominantly procedural manner, with limited conceptual understanding and minimal peer interaction. After the implementation of contextual learning situations, classroom social dynamics changed substantially. Students became more actively involved in discussion, collaborative problem-solving, and collective meaning-making. Peer interaction supported the articulation and refinement of students’ reasoning, while teacher scaffolding guided learning by extending students’ thinking without providing direct solutions. These social processes facilitated students’ movement from their actual level of understanding toward higher levels of conceptual competence within the Zone of Proximal Development. The study further shows that contextual learning tasks alone are insufficient to promote meaningful understanding unless they are supported by productive social interaction and adaptive scaffolding. Conceptual understanding of measurement emerged through socially mediated processes rather than through task completion alone. This study contributes to mathematics education research by emphasizing the central role of classroom social dynamics in contextual learning and by offering insights into how interaction and scaffolding can be orchestrated to support students’ conceptual understanding of measurement.

Mathematics learning plays an essential role in developing students’ logical, systematic, and analytical thinking skills. One of the higher-order thinking abilities that serves as a main focus in mathematics education is mathematical reasoning. This ability is closely related to the process of mathematical proof, which functions to justify the truth of a statement logically. This study aims to examine the relationship between the understanding of proof concepts and the development of mathematical reasoning among junior high school students through a library research approach. Data were obtained from various sources such as textbooks, journal articles, research findings, and relevant educational documents. The analysis was conducted using the content analysis method to review both conceptual and empirical findings from the literature. The results indicate that understanding the concept of proof not only helps students comprehend the logical structure of mathematics but also contributes to the development of deductive and reflective reasoning skills. Engaging in proof activities enables students to shift from merely imitative reasoning toward independent logical construction (creative reasoning). However, teaching proof at the junior high school level still faces several challenges, such as students’ limited understanding of basic logic, time constraints, and the lack of teacher training in teaching proof effectively. Therefore, learning strategies that emphasize students’ thought processes, provide opportunities for exploration, and integrate proof activities into meaningful learning contexts are needed.

This study aims to analyze the improvement of Higher Order Thinking Skills (HOTS) through mathematics learning on the Three-Dimensional Geometry topic in Grade XII of Yayasan Pendidikan Al-Fattah Medan. HOTS is a crucial aspect of 21st-century education because it helps students develop critical, creative, logical, and reflective thinking skills in addressing complex problems. In the context of mathematics learning, particularly in spatial geometry, mastering HOTS not only supports students in understanding abstract concepts but also in applying them to real-life situations. This study employed a descriptive qualitative method with instruments consisting of a pre-test, post-test, and an open-ended questionnaire to explore students’ understanding and learning experiences. The findings revealed a significant improvement, where the average pre-test score of 7 increased to 52.21 in the post-test. This result highlights that the implementation of HOTS-based learning strategies is effective in enhancing students’ comprehension of distance, angles, and point positions in space, while simultaneously strengthening their analytical, evaluative, and creative abilities. The study implies the importance of adopting innovative learning strategies oriented toward HOTS development to improve the quality of mathematics education and prepare students for global challenges.

Real Analysis is a fundamental course in mathematics education characterized by its deductive and axiomatic structure, which requires logical, systematic, and conceptual understanding. However, many studies have shown that students often face difficulties in grasping abstract concepts and constructing mathematical proofs deductively. Lestari (2015) found that most students were only able to conduct proofs inductively, while their deductive proof skills remained low due to weak prerequisite knowledge and lack of formal reasoning practice. Meanwhile, Darmadi, Sanusi, and Rifai (2024) explained that students’ difficulties in understanding formal definitions and the structure of real numbers indicate the need for a learning approach that emphasizes conceptual comprehension. This article employs a literature review approach to analyze the application of conceptual approaches in helping beginners understand Real Analysis. The results show that a conceptual approach enhances students’ understanding of the meaning behind mathematical symbols and procedures, helps them build connections among concepts such as limits, continuity, and the real number system, and gradually develops their deductive reasoning skills. Therefore, applying a conceptual approach in Real Analysis learning is an essential strategy to help students achieve deep, logical, and meaningful understanding.

This paper seeks to analyze the impact of the Realistic Mathematics Education (RME) approach learning approach on the development of critical thinking and problem-solving skills in third-grade pupils at SDN 104202 Bandar Setia. This research employed a quantitative method with a nonrandomized pretest-posttest control group design, involving two groups: the control group (III A) without treatment and the experimental group (III B) that received the RME learning approach, with a total sample of 50 students. Both groups were administered pre-test and post-test instruments to measure problem-solving and critical thinking skills. The findings revealed that the application of the RME learning approach significantly improved both skills with p < 0.05. These results confirm that RME is effective in enhancing mathematics learning quality through real-life contexts and students’ direct experiences. The implication highlights the importance of integrating RME in elementary mathematics learning as an alternative strategy to foster critical thinking and problem-solving abilities, as well as providing a reference for future instructional innovations.

This research aims to: (1) produce mathematics learning media in the form of interactive e-modules with a learning approach.realistic mathematics education (RME) which is oriented towards numerical ability and mathematical growth mindset students and describe their characteristics; (2) describe the quality of the learning e-module which meets the criteria of being valid, practical and effective so that it is suitable for use by junior high school students using the approach realistic mathematics education (RME). The development model used in this development research is the ADDIE development model (Analysis, Design, Development, Implementation, and Evaluation). The research subjects consisted of one teacher and 32 seventh grade students of SMP Negeri 3 Pajangan in Bantul Regency, Yogyakarta, who participated in this research.The results of the study show that the developed e-module has the following main characteristics: (1) using the RME approach in learning strategies; (2) facilitating the improvement of numeracy through learning videos, LKPD, and quizzes; (3) fostering growth mindset through motivational videos, inspirational sentences, discussion spaces, as well as feedback and self-evaluation features; and (4) using test- and questionnaire-based evaluation instruments. Validity tests showed very good results with an average score of 96% from media experts and 98% from material experts. The practicality of the e-module was assessed as very good by teachers (96.19%) and good by students (80.47%), and the implementation of learning reached 96.8%. Effectiveness was proven through MANOVA and t-tests which showed a significant increase in numeracy and mathematical growth mindset after using the e-module. Thus, the RME-based interactive e-module is suitable for use as an innovative mathematics learning medium at the junior high school level.

This study aims to examine the potential of the Baduy traditional house as a realistic context in mathematics learning, particularly in the material of spatial geometry. The traditional houses of the Baduy people not only function as residences, but also hold cultural values, philosophies, and architectural structures rich in geometric elements. Using a systematic literature review (SLR) approach, this study explores various scientific sources, including journal articles, proceedings, and reference books, that discuss the relationship between spatial elements and the structure of traditional Baduy buildings. This approach was chosen so that the study obtained is comprehensive, directed, and able to illustrate the real contribution of ethnomathematics in learning. The results of the review indicate that the Baduy traditional house contains various forms of spatial geometry that can be clearly recognized, including cuboids, triangular prisms, pyramids, cubes, and cylinders. These elements are reflected in building components such as roofs, walls, floors, support pillars, and traditional household furniture. The visual and functional representation of these spatial geometry has the potential to be a contextual resource that can be utilized by teachers in the mathematics learning process, particularly through the Realistic Mathematics Education (RME) approach. By linking abstract mathematical concepts to local cultural phenomena, students not only gain a better conceptual understanding but also increase their active engagement, motivation to learn, and awareness of their own cultural identity. These findings emphasize the importance of utilizing local wisdom as an ethnomathematics approach that can provide meaningful, contextual learning rooted in the realities of students' daily lives. Through the integration of culture and education, mathematics learning can be more relevant, engaging, and support the preservation of national culture.

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 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.