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This study aimed to analyze the level of understanding of fraction concepts among fourth-grade students at SDIT Al Hidayah Pekanbaru and to identify effective learning strategies. Mathematics, particularly the concept of fractions, often poses a significant challenge at the primary education level. The research employed a descriptive quantitative approach, with primary data collected through the distribution of a questionnaire to 30 students. This questionnaire was designed to measure the students' mastery level of basic concepts, operations, and application of fractions.The findings indicate that the students' level of understanding of fraction concepts is in the very good category. This is evidenced by the questionnaire data, where 63.33% of respondents selected the "Strongly Agree" category and 25.71% selected "Agree," resulting in a cumulative total of 89.04% positive responses. This strong positive dominance suggests that the majority of students have mastered the fundamental concepts and can apply them. The results support the idea that contextual, interactive teaching methods, coupled with the use of manipulative media (as also suggested by relevant studies), are highly effective in facilitating students' deep conceptual understanding. The main conclusion is that implementing learning approaches oriented toward real-world contexts, combined with the use of instructional media, significantly improves student comprehension of fraction material. These findings are expected to serve as a valuable reference for teachers and stakeholders in developing more innovative and effective teaching methods in Primary Schools.

Service activities in this educational unit are carried out with the aim of fulfilling the teaching assistance program, in which one of the programs is the work program for developing mathematics teaching media in the form of snakes and ladders, the application of the educational game Snakes and Ladders (snakes and ladders) as a mathematics learning innovation in class II MIS NWDI Selong. This game is used as a medium to help students understand the concept of plane shapes and simple addition operations in a fun way. Service activities are carried out through four main stages, namely planning, implementation of learning, and evaluation of activities. The results of the activity show that the application of the Snakes and Ladders game is able to increase students' enthusiasm for learning, strengthen understanding of basic mathematical concepts, and foster teacher enthusiasm in developing creative learning. Educational game media has been proven to be able to create a more active, communicative, fun and meaningful learning atmosphere for elementary school students.

The use of virtual classrooms in the learning process is a strategic step to create a flexible learning experience, accessible anytime and anywhere. Schoology's "Plasma" as a virtual classroom platform offers various digital learning features that enable students to develop Self-Regulated Learning (SRL). Through access to materials, discussions, and other digital learning resources, students are encouraged to be more active, independent, and able to plan, monitor, and evaluate their own learning process. SRL is an important internal factor that plays a role in learning success, because it encourages students to realize their learning needs without relying on direct direction from the teacher. This study is a classroom action research conducted by mathematics teachers at SMA Negeri 1 Gedongtataan, Pesawaran, Lampung, with 30 students of grade XII IPA 1 in the 2022/2023 academic year. Data were collected through questionnaires, observations, and interviews, then analyzed using descriptive statistics. The results showed that the use of Schoology's virtual classroom significantly improved students' SRL. The comparison of the average SRL scores in Cycle I and Cycle II, 2.7 and 3.2, respectively, indicates a consistent increase. This finding confirms that the integration of Schoology's virtual classroom is effective in enhancing students' learning independence at the secondary education level.

This research is motivated by challenges in biology learning, including the lack of digital literacy assessment in schools and the use of conventional learning methods that tend to make students bored. Impractical printed teaching materials cannot be integrated into the form of videos. This research aims to develop an e-module based on Science, Technology, Engineering, and Mathematics (STEM) to analyze the feasibility, practicality, and effectiveness of e-modules in improving students' understanding of concepts and digital literacy on human respiratory system materials. This research uses the Development Research (R&D) method with the ADDIE (Analysis, Design, Development, Implementation, Evaluation) development model.  The research was carried out at SMAN 1 Malinau. The implementation stage used a non-equivalent control group  design involving 34 students in the experimental class and the control class. Data collection instruments include validation sheets for media and material experts, practicality questionnaires for teachers and students, and pretest-posttest  tests to measure concept understanding and digital literacy.  Analysis of effectiveness data using N-gain test and hypothesis test (independent sample t-test for concept understanding and Mann-Whitney for digital literacy). The results of the research based on the validation of media experts and subject matter experts show that the STEM-based e-module is declared "Excellent". The e-module is also rated "Very Practical" by biology teachers and students. The e-module was shown to be effective in improving conceptual understanding, where the average N-gain value of the experimental class (58.63; Quite Effective category) was significantly higher (p=0.017) than that of the control class (40.62).

This study aims to identify various aspects that pose obstacles or difficulties for students in learning Mechanics. This study uses a qualitative descriptive approach that focuses on describing the types of difficulties students encounter in solving mechanics problems. The research subjects were first-semester students of the Science Education Study Program at KH. Mukhtar Syafaat University (UIMSYA) Blokagung Banyuwangi who were taking Basic Physics courses on Mechanics material. Data collection was carried out through diagnostic tests and interviews with students. The instruments used were diagnostic tests and interview guidelines. The location of students' learning difficultdiies was analyzed based on the errors that appeared in the completion of the diagnostic test. The results showed that the main difficulty students had in learning mechanics was in mastering basic mathematical skills, particularly in differential and integral material. Therefore, lecturers or teachers need to design and develop more appropriate learning strategies so that students' problem-solving skills can improve.

This article examines the conceot of knowledge (ilmu) within the Islamic perspective, which holds a highliy privileged position, ranking second only to the word Tauhid (Monotheism) in Islamic teachings. his paper employs a Library Research methodology (kajian pustaka). his approach involves the assimilation, study, and in-depth analysis of various readings utilized by the author. he presence of knowledge and education profoundly influences the development of human life concepts. In the Qur'an, the word "ilmu" (knowledge/science), in its various forms, in Quran, testifying to the distinctiveness of humans as caliphs on earth. Literally, "ilmu" is defined as knowing or to know, while technically it means understanding the reality of something or the rule governing it. The ultimate source of knowledge is Allah SWT. The process of teaching knowledge from Allah can be direct (revelation/inspiration or wahyu/ilham) or indirect (through the medium of natural phenomena He created). Knowledge acquisition can be achieved through several approaches, including: practice (pengamalan), experience (pengalaman), rational (rasional using intellect/reason), emotional, and habituation (pembiasaan). Islamic scholars have classified knowledge based on its object of study and source. For instance, Ibn Sina categorized knowledge into three types: al-‘ilm al-ilahi (divine and metaphysical knowledge), al-ilm al-riyahi (mathematics), and il-‘ilm tabi’I (natural sciences). Al-Ghazali classified it into ilmu shariah and ilmu gayr al-shari’ah, which aligns with Ibn Khaldun’s division of ilmu naql (transmitted knowledge) and ilmu aqal (intellectual knowledge). This division is based on the object of study, not meant to be contradictory.

This study aims to analyze the role and strategies of introducing mathematical proofs appropriately for students, as well as to describe their contribution to enhancing logical, critical thinking, and understanding of mathematical concepts. The method used is library research with a descriptive qualitative approach through the analysis of various current scientific literature relevant to mathematics learning and education. The results of the study indicate that mathematical proofs not only function as a tool for verifying the truth of a statement but also as an epistemological process that develops deductive, argumentative, and reflective reasoning skills in understanding the structure and relationships of mathematical logic. Effective introduction strategies include the use of visual representations, collaborative learning, linguistic scaffolding, and the application of a gradual approach from informal argumentation to formal deduction. The approach has been proven to enhance students conceptual understanding, argumentative skills, and logical awareness. The implication is that proofs need to be systematically integrated into mathematics learning in secondary schools to strengthen Higher Order Thinking Skills (HOTS) and develop a scientific mindset in accordance with the principles of the Merdeka Curriculum

Learning mathematics not only focuses on mastering concepts and calculation skills, but also requires creating a conducive learning environment so that students can think critically, logically, and creatively. A conducive learning environment plays a crucial role in fostering student motivation and active engagement, making the success of the learning process highly dependent on the strategies implemented by the teacher. This research aims to describe mathematics teachers' strategies in creating a conducive learning environment thru the application of active and contextual learning strategies. The method used is library research, which involves collecting and reviewing various scientific sources such as books, journals, and academic articles relevant to the research topic. The research results indicate that active learning strategies are able to increase student participation, strengthen reasoning abilities, and foster learning motivation. Teachers play an important role as facilitators, motivators, mediators, and evaluators, directly influencing the learning climate in the classroom. Contextual learning strategies like REACT (Relating, Experiencing, Applying, Cooperating, Transferring) have proven effective in connecting mathematical concepts with students' real-life experiences and creating a fun and meaningful learning environment. In addition, humanistic classroom management, the use of technology, and adapting learning to students' different abilities are supporting factors in achieving a conducive learning environment. The implications of this research indicate that the success of mathematics learning is not solely determined by the methods used, but also by the teacher's ability to build positive relationships with students and create an interactive, adaptive learning environment that optimally fosters students' potential development.

The rapid development of information and communication technology has transformed the way people access information, interact, and live their daily lives. In this regard, students from the Mathematics Education Study Program at the State Islamic University of North Sumatra conducted "Smart Socialization" during a community service activity in Jaharun A Village, Galang District. The main objective of this community service activity was to increase awareness and understanding among residents of Jaharun A Village, Galang District, regarding the importance of digital literacy in facing the challenges of AI-based disinformation on social media. The implementation methods included initial observation, outreach, and interviews. The results of this activity indicated high community enthusiasm, active participation, and a better understanding of how to use social media wisely and responsibly. This activity successfully built critical public awareness of the importance of verifying information before sharing it and increased local community preparedness for the complex digital information era. This activity is expected to become a model for applicable and sustainable digital literacy education in rural areas.

Mathematics learning demands optimal student activity, concentration, and participation. However, many students still exhibit a passive attitude during the learning process, resulting in learning outcomes that have not reached the expected level. This article aims to analyze various effective classroom management strategies for fostering enthusiasm for learning and increasing student participation in mathematics learning. This study uses a library research method by reviewing various scientific sources, such as journals, academic books, and relevant research reports. The results of the study indicate that effective classroom management plays a crucial role in creating a conducive, interactive, and student-centered learning environment. Teachers function not only as transmitters of material but also as facilitators and administrators capable of building positive social relationships and motivating students to actively think and participate. Preventive, curative, and repressive classroom management strategies have been proven to improve student focus, motivation, and learning outcomes, especially when integrated with learning approaches such as discovery learning, teacher-centered learning, and the use of creative methods like squad games and block systems. Thus, adaptive and innovative classroom management is key to realizing participatory, enjoyable, and meaningful mathematics learning for the development of students' overall potential.

This study aims to analyze the role of the Selected Topics in Mathematics course in developing Higher Order Thinking Skills (HOTS) among prospective mathematics teachers through a systematic literature review. The review covered 21 articles published between 2020 and 2025, sourced from nationally accredited Sinta-indexed journals and reputable international journals. The research employed the Systematic Literature Review (SLR) method, following the stages of data reduction, data display, and verification and interpretation based on the model by Miles, Huberman, and Saldaña (2014). The analysis revealed that the implementation of problem-based learning and inquiry-based learning strategies is effective in enhancing students’ abilities in analysis, evaluation, and creation. The use of authentic assessments such as projects and reflective rubrics proved to be more comprehensive in measuring higher-order thinking processes compared to conventional tests. Key challenges identified include limited lecturer training, lack of contextual teaching materials, and insufficient technological support. This study confirms the strategic potential of the Selected Topics in Mathematics course in fostering HOTS among prospective teachers and offers recommendations for strengthening the curriculum and developing HOTS-based assessments in higher education.

This study aims to determine the effect of the application of PQ4R (Preview, Question, Read, Reflect, Recite, Review) learning strategies on the mathematical problem-solving ability and confidence of students at SMAN 1 Sembakung, Nunukan Regency. The background of this research is the low ability of students to solve mathematical problem-solving problems and their lack of confidence in facing academic challenges. The PQ4R strategy was chosen because it is considered to be able to encourage active student engagement, build deep understanding, and strengthen confidence through structured learning steps. This study uses a quantitative method with a quasi-experimental design of the pretest-posttest control group design. The research sample consisted of 73 students in grade XI who were divided into experimental and control groups at random. The research instruments include problem-solving ability tests and confidence questionnaires. The data analysis technique used t-test and MANOVA (Hotelling's Trace) after meeting the normality and homogeneity tests. The results showed that PQ4R learning strategies had a significant effect on students' mathematical problem-solving skills and confidence. The experimental group experienced a higher score increase than the control group. Thus, the PQ4R strategy can be an effective learning alternative to improve the quality of mathematics learning as well as students' affective aspects such as confidence.

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 investigates the algebraic reasoning processes of university students when expanding mathematical expressions in the context of nonroutine problem-solving. The research adopts a qualitative approach to explore how students interpret algebraic structures, apply symbolic transformations, and construct logical explanations while working through unfamiliar tasks. Data were collected through written tests, task-based interviews, and detailed analysis of students’ solution strategies. The findings reveal significant variation in students’ ability to generalize patterns, recognize structural relationships, and justify algebraic procedures. Students with strong conceptual understanding demonstrated flexible reasoning, coherent explanations, and appropriate use of algebraic properties. In contrast, students who relied heavily on procedural rules often struggled with symbolic manipulation, produced fragmented reasoning, and exhibited misconceptions related to variables and distributive operations. These results highlight the importance of fostering conceptual understanding, metacognitive awareness, and reasoning-oriented instruction in university mathematics. The study provides insights for educators seeking to design learning environments that promote deeper algebraic thinking and enhance students’ ability to solve complex, nonroutine problems.

This research is entitled “Implementation of Lumi H5P in Mathematics Learning Media at SDK PERO Using the MDLC Method.” The aim of this research is to create a digital-based interactive learning medium designed to enhance students’ understanding of the subject matter. media that can help students understand mathematics lessons, particularly on the topics of whole numbers and multiples, in an engaging and easy-to-understand way. The approach applied in this research is the MDLC method.. Each stage was carried out systematically to produce an interactive and high-quality learning media. The learning media application was developed using LUMI H5P, which provides various interactive features such as text, images, videos, and interactive exercises in the form of single choice sets and drag-and-drop activities. The results of the study show that the implementation of Lumi H5P-based learning media can increase students’ learning interest and facilitate their understanding of the material. Moreover, the simple interface design and user-friendly features make this application effective for both classroom learning and independent study. Therefore, the implementation of Lumi H5P in mathematics learning The media can act as an innovative solution to promote a learning process that is more engaging and effective.

This study aims to analyze the influence of the Problem-Based Learning (PBL) model assisted by e-LKPD on students’ problem-solving abilities and self-confidence in vocational high schools. Specifically, the objectives are: (1) to examine the simultaneous effect of the PBL model assisted by e-LKPD on both variables, (2) to determine its effect on problem-solving ability, and (3) to evaluate its effect on self-confidence. A quantitative approach with a quasi-experimental pretest–posttest control group design was applied. The population consisted of all 10th-grade students at SMK Negeri 1 Tarakan, while the sample was selected using purposive sampling, resulting in class X Marketing 1 (35 students) as the experimental group and class X Culinary 2 (34 students) as the control group. Research instruments included a problem-solving test and a self-confidence questionnaire. Hypothesis testing utilized Hotelling’s T² and independent sample t-tests. The findings showed that 97% of students in the experimental class met the Learning Objectives Mastery (KKTP), compared to only 18% in the control group. Improvement in the experimental group was categorized as high, whereas in the control group it was moderate. Self-confidence also increased significantly in the experimental group, with most students moving from low to high categories. Hotelling’s Trace (Fcount = 77.109, p < 0.001) and t-tests confirmed significant effects on both problem-solving (tcount = 11.657) and self-confidence (tcount = 8.140), proving that the PBL model assisted by e-LKPD effectively enhances students’ abilities and confidence.

Mathematics anxiety is a psychological barrier that negatively affects students’ performance and self-confidence. A valid and reliable measurement tool is required to identify this condition accurately. This study aims to examine the construct validity of the Mathematics Anxiety Rating Scale 30 (MARS-30) using a Monte Carlo simulation approach. The research employed first-order confirmatory factor analysis (CFA) through R software with a simulated sample of 300 respondents. The findings revealed that the overall measurement model achieved excellent fit indices, as indicated by Normed χ², RMSEA, SRMR, and CFI, all within the optimal range. Nevertheless, only 8 out of 30 items (26.7%) met the validity criteria, while the remaining 22 items were found invalid. This result suggests that although the global model fit was adequate, most items of MARS-30 did not consistently represent the construct of mathematics anxiety. The implication of this study highlights the necessity of revising the instrument by refining item wording, adjusting indicators, and conducting further testing to ensure stronger construct validity. A more valid instrument will enable educators and researchers to design targeted pedagogical interventions for reducing mathematics anxiety and supporting students’ learning outcomes.

This study aims to develop a contextual-based mathematics learning module to improve mathematical numeracy literacy among fourth-grade elementary school students, particularly on arithmetic operations. This research employed a Research and Development (R&D) design using the ADDIE development model consisting of analysis, design, development, implementation, and evaluation stages. The research subjects were 22 fourth-grade students at SDN 2 Siryawangi. The instruments used included expert validation sheets, teacher and student response questionnaires, and numeracy literacy tests. Data were analyzed using a qualitative descriptive approach supported by the N-Gain test to measure students’ improvement after using the module. The findings indicate that the developed module meets the criteria of validity, practicality, and effectiveness. This is supported by the validation results from material and media experts, each obtaining an average score of 95%, which is categorized as highly valid. In addition, teacher responses of 75% and student responses of 88% show that the module is practical and feasible to be used in the learning process. Furthermore, the effectiveness test results, based on an N-Gain score of 84%, demonstrate a high-level improvement in numeracy literacy. Therefore, this module is feasible to be implemented as an alternative teaching material for contextual learning in elementary schools.

Rapid developments in information technology have made laptops an essential device for students, especially those in their final year of study. Choosing the right laptop plays an important role in supporting academic productivity, such as writing theses, analyzing data, and developing software. This study aims to classify the preferences of mathematics students at Gorontalo State University in choosing laptops based on usage characteristics and factors that influence purchasing decisions. The method used is Kernel Discriminant Analysis (KDA) with a Gaussian kernel function and an optimal bandwidth of 0.8. The research data involved 268 respondents divided into training and testing data. The analysis results show that the KDA model has an accuracy rate of 60% on the training data and 52% on the testing data, which indicates the model's ability to recognize student preference patterns despite a decrease in accuracy on new data. Based on the kernel density estimation results, Acer is the most widely used laptop brand, while Zyrex and Apple are rarely chosen. The most influential factor in purchasing decisions is processor specifications, with a contribution of 35.739%, followed by brand, warranty, and price. These findings indicate that hardware characteristics are the main consideration in laptop selection, with most students choosing laptops with Intel Core i5 processors, a minimum of 8GB of RAM, and SSD storage. The results of this study can also be used by universities to provide recommendations for selecting laptops that suit students' academic needs.  

Learning quadratic functions in high school still faces various challenges, primarily due to the abstract nature of the concepts, which require students to have strong analytical thinking skills. These difficulties often result in low student understanding of the relationship between quadratic equations and parabola graphs, as well as limitations in applying these concepts to mathematical problem-solving. GeoGebra, as a technology-based learning tool, offers interactive visualizations that allow students to observe the real-time changes in the shape of a parabola when the coefficients in a quadratic equation are modified. A literature review of recent studies reveals that the use of GeoGebra significantly enhances conceptual understanding, mathematical representation skills, and student motivation. Its effectiveness further increases when combined with appropriate teaching strategies, such as the 5E model (Engage, Explore, Explain, Elaborate, Evaluate), which encourages active involvement and concept exploration by students. However, several challenges remain, including limited access to devices, teachers’ readiness to utilize technology, and suboptimal infrastructure support. Therefore, the integration of GeoGebra into quadratic function learning requires careful planning, teacher training, and adequate facility support to maximize its benefits and improve the overall quality of mathematics education.