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This study aims to analyze the difficulties experienced by students in understanding abstract concepts in Islamic creed (akidah) and to evaluate the effectiveness of Islamic-based animation learning media as an innovative and interactive solution. The research employs a qualitative Classroom Action Research (CAR) approach, conducted in two learning cycles using observation, interviews, documentation, and questionnaires as data collection techniques. The implementation of Islamic animation learning media demonstrated a significant improvement in students’ conceptual comprehension. The results indicate that the average understanding score increased from 35.25% in the preliminary stage to 89.25% after the final cycle, showing a substantial rise in students’ achievement levels. In addition, students’ enthusiasm, motivation, and active participation in classroom activities increased markedly when learning materials were presented through animated visualization rather than conventional lecture-based instruction. Expert validation confirmed that the developed instructional media meets pedagogical, didactic, and visual quality standards, and responses from teachers and students revealed positive perceptions regarding the relevance and attractiveness of animation-based learning. The findings highlight that Islamic-based animation learning media serves as an effective educational tool capable of simplifying and concretizing abstract theological concepts, enabling learners to construct deeper understanding through visual and contextual illustration.Therefore,the study recommends the broader application of animation-based Islamic instructional media in akidah education to enhance comprehension, engagement, and learning outcomes in schools.

The ambiguity of the concept of state economic loss in Article 2 paragraph (1) and Article 3 of the Corruption Crime Law (Tipikor Law) has yet to be defined normatively or by an official institution with the authority to do so. This uncertainty has given rise to legal problems in law enforcement, especially after Constitutional Court Decision No. 25/PUU-XIV/2016, which changed the qualification of corruption offenses to material offenses, so that the proof of economic loss to the state must be actual loss. However, in practice, as in the Surya Darmadi corruption case, law enforcement officials still face difficulties in determining the measure and method of proving economic loss to the state in a lawful manner. The issues in this study are the basis for the judge's consideration of the element of economic loss to the state in the Central Jakarta District Court Decision No. 62/Pid.Sus-TPK/2022/PN.Jkt.Pst and the obstacles and constraints in proving the element of economic loss to the state in criminal acts of corruption.This study uses a normative legal method with a statute approach, a case approach, and a conceptual approach. The results of the study show that the first-level panel of judges assessed that environmental damage and the loss of potential state revenue due to the illegal conversion of forest areas were part of the actual economic loss to the state, while the Supreme Court emphasized the importance of limiting this element to actual loss in accordance with Constitutional Court Decision No. 25/PUU-XIV/2016. The obstacles and constraints in proving the element of state economic loss in corruption crimes stem from internal and external factors that are interrelated and affect the effectiveness of law enforcement.

This study aims to analyze students' understanding and difficulties in probability in grade XII of SMA Negeri 1 Tanjung Morawa and identify the contributing factors. The research method used is descriptive with quantitative and qualitative approaches. Quantitative data were obtained from the results of the problems given to students, then analyzed to determine the level of understanding, types of errors, and the percentage of difficulties experienced. Meanwhile, qualitative data were obtained through interviews with subject teachers to deepen information regarding the obstacles faced by students and the learning strategies implemented. The results showed that most students experienced difficulties in determining the sample space, applying probability formulas, and interpreting calculation results. Contributing factors include limited understanding of basic concepts, a lack of variety in practice questions, and learning that still focuses on procedures. Based on these findings, the researcher offers solutions in the form of contextual learning, conceptual reinforcement through class discussions, and the provision of step-by-step practice questions with teacher guidance. This research is expected to contribute to teachers in improving the effectiveness of probability learning in schools.

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 study is a literature review aimed at examining in depth the concepts, characteristics, learning difficulties, and applications of quadratic functions in secondary mathematics education. The research employs a qualitative approach by analyzing ten articles published between 2019 and 2025 from both national and international journals. The findings indicate that the quadratic function is a fundamental topic in the mathematics curriculum, playing a crucial role in developing higher-order mathematical thinking skills such as analysis, synthesis, and problem-solving. It also serves as a foundation for understanding more advanced topics such as calculus, analytic geometry, and optimization. However, various studies have found that students continue to face significant learning difficulties, including misconceptions related to the shape of the parabola graph, understanding the discriminant value, and connecting algebraic forms to real-world contexts. To address these issues, research suggests that technology-assisted learning—particularly through interactive software such as GeoGebra—has proven effective in enhancing conceptual understanding, motivation, and student engagement. Therefore, this review highlights the importance of strengthening conceptual understanding, applying contextual learning approaches, and integrating digital technology as innovative strategies for teaching quadratic functions at the secondary education level.

This preliminary study was conducted as the foundation for developing an animated video-based learning media using Canva. The main objective of this research is to present the initial data collected during the early investigation phase, which will serve as the basis for creating innovative, research-based learning media in the future. The development model applied in this research is the Plomp model, and the study has currently reached the preliminary investigation stage. Data were collected using several instruments, including interviews, classroom observations, and student needs assessment questionnaires. The results of the needs assessment revealed that the learning media currently used in schools is considered less effective, leading to difficulties for students in understanding the subject matter. Furthermore, 91.33% of students agreed that the development of an animated video-based learning media using Canva would be beneficial and support the learning process. These findings indicate a strong need for engaging, interactive, and technology-integrated learning media. The selected topic for development is “Food and the Digestive System,” which is part of the curriculum for grade XI students in senior high schools (SMA/MA), as this topic is often perceived as challenging. By utilizing Canva to create animated videos, it is expected that students’ learning motivation, conceptual understanding, and classroom engagement will significantly improve. The results of this preliminary study serve as an essential foundation for the next stages of development, ensuring that the final product will provide an effective and enjoyable learning experience tailored to students’ needs.

The topics of morphology, anatomy, and physiology are integral to biology learning, yet they often present challenges for students due to their abstract and complex nature. Difficulties in understanding body structures and invisible biological processes lead to low student interest and engagement. This study aims to identify innovative learning approaches through an analysis of national scientific literature over the past decade. The results show that the integration of digital technology and student-centered learning methods can improve conceptual understanding and learning motivation. The most prominent innovations include the use of VR and AR-based media to clarify visualizations, the use of interactive videos and simulations to explain biological functions, and the application of contextual learning models such as Problem-Based Learning (PBL) and Project-Based Learning (PjBL). These approaches have proven effective in creating a more immersive learning experience that is relevant to students' needs.

This study aims to analyze the forms of learning difficulties experienced by students in understanding the path independence theorem in the Vector Calculus course. The focus of the research is a group of students who had previously presented this material in class. Data were collected through a questionnaire containing both open- and close-ended questions to explore conceptual understanding, difficulties in distinguishing between conservative and non-conservative fields, and challenges in solving application problems. The analysis revealed that although students reported having a fair grasp of the basic concepts, they still expressed uncertainty in understanding the relationship between path independence and the conditions for conservative fields. Difficulties were also found in spatial visualization and in connecting concepts with the fundamental theorem of calculus. In addition, students showed a preference for worked example problem sets and visual learning media as the most effective learning supports. These findings indicate the need for an interactive, contextual, and visually supported instructional approach to enhance students’ conceptual understanding and application skills related to this topic.

This study aims to analyze students’ conceptual understanding of hydrocarbons through a literature review utilizing the Three-Tier Multiple Choice Diagnostic Instrument. Hydrocarbons are a fundamental topic in chemistry education that often leads to student misconceptions. The three-tier diagnostic instrument is designed not only to assess students’ cognitive knowledge through correct or incorrect answers but also to explore the reasoning behind their choices, enabling more accurate identification of misconceptions and conceptual understanding. The methodology employed is a literature review examining various scientific sources on the application of this diagnostic tool in teaching hydrocarbon concepts. The findings indicate that the Three-Tier Multiple Choice Diagnostic Instrument is effective in systematically detecting and classifying students’ difficulties and misconceptions. Furthermore, the use of this instrument contributes significantly to developing targeted and data-driven instructional strategies to enhance students’ conceptual mastery in chemistry. The implications of this study highlight the necessity of integrating three-tier diagnostic instruments in the assessment process to support optimal learning outcomes in hydrocarbon material.

Understanding chemical equilibrium concepts poses significant challenges for high school students due to the topic’s abstract and complex nature. This literature review identifies key factors contributing to these difficulties, including widespread misconceptions, cognitive and pedagogical barriers, and environmental influences such as family support and learning resources. The review highlights the importance of constructivist and cognitive learning theories in designing effective instructional strategies that actively engage students and facilitate deeper conceptual understanding. Furthermore, the integration of educational technologies—such as interactive simulations and virtual laboratories—provides enriched learning experiences that help overcome conceptual misunderstandings. An integrated approach combining innovative teaching methods and technology use is recommended to enhance students’ comprehension of chemical equilibrium. Future research should focus on practical applications of these models and evaluate their effectiveness across diverse educational settings.

Mathematics is often referred to as a field of knowledge developed through logical reasoning and is considered essential in everyday life, particularly in problem-solving. One effective way to apply problem-solving skills in mathematics education is through the use of word problems. This study aims to explore and analyze the various obstacles students encounter when solving mathematical word problems. The research employs a descriptive qualitative approach, with data collection methods including tests, interviews, and a project involving the construction of a staircase using standard units of length. The subjects of the study were four third-grade elementary school students in Batusangkar who had previously studied standard units of length. The findings reveal that students faced a range of difficulties, such as challenges in understanding the problems, failure to organize solution steps systematically, and limited comprehension of the concept of standard measurement units. Additionally, a lack of interest in learning was found to negatively impact students’ ability to solve word problems. Therefore, conceptual understanding and increased motivation to learn are crucial factors in enhancing students’ mathematical problem-solving abilities.

Mathematics is often referred to as a field of knowledge developed through logical reasoning and is considered essential in everyday life, particularly in problem-solving. One effective way to apply problem-solving skills in mathematics education is through the use of word problems. This study aims to explore and analyze the various obstacles students encounter when solving mathematical word problems. The research employs a descriptive qualitative approach, with data collection methods including tests, interviews, and a project involving the construction of a staircase using standard units of length. The subjects of the study were four third-grade elementary school students in Batusangkar who had previously studied standard units of length. The findings reveal that students faced a range of difficulties, such as challenges in understanding the problems, failure to organize solution steps systematically, and limited comprehension of the concept of standard measurement units. Additionally, a lack of interest in learning was found to negatively impact students’ ability to solve word problems. Therefore, conceptual understanding and increased motivation to learn are crucial factors in enhancing students’ mathematical problem-solving abilities.

Early reading is an important foundation in mastering language skills, especially for first grade elementary school students. Problems that often arise at this stage include difficulty in recognizing letters, arranging letters into words, and pronunciation and understanding simple reading. This study aims to analyze the early reading skills of first grade students in terms of cognitive and psychomotor aspects, and to identify factors that hinder their achievement. This study uses a descriptive quantitative approach with test instruments to assess cognitive abilities and observations to assess psychomotor skills. The subjects of the study consisted of five first grade students. The results showed that most students had very good cognitive abilities in early reading, but their psychomotor abilities tended to be low. A gap was found between theoretical understanding and practical skills of students. This finding emphasizes the importance of a balanced and holistic learning strategy so that students not only understand conceptually, but are also able to apply reading skills in real life.

This article explores the significance of gaining a clear understanding of the topic concept addition as the main foundation in mathematical literacy. This study examines various pedagogical approaches in introducing the concept of addition to students, emphasizing the importance of conceptual understanding compared to procedural learning. Analysis of several learning methods shows that the use of manipulative objects, visual representations, and the application of real contexts significantly improve students' understanding of the idea behind addition. The results of the research also indicate that difficulties in understanding the concept of addition at the early stage of Learning may affect the progress of advanced mathematical abilities. This article concludes that a learning approach that emphasizes conceptual understanding of addition as a quantity combination operation will establish a strong basis for the advancement of students' mathematical abilities in the future.

Understanding geometric concepts is an essential part of the mathematics learning process in elementary school. However, many fifth-grade students face challenges in grasping these concepts due to monotonous and less interactive learning media. These difficulties contribute to students' low comprehension of geometric concepts. The purpose of this study is to analyze the contribution of interactive media in strengthening students' understanding of geometric concepts in elementary school. The research employs a qualitative approach, with data collected through observations, interviews with teachers and students, and documentation. The findings reveal that less interactive teaching methods, the lack of concrete learning media, and an unconducive learning environment are the main factors hindering students' understanding. Increasing student participation and facilitating their comprehension of geometric concepts can be achieved by implementing interactive media such as digital simulations, animated videos, and educational games. Thus, interactive media can enhance students' learning motivation and create a more enjoyable learning atmosphere. By integrating interactive media into the mathematics learning process, students are expected to become more actively engaged, focused, and able to understand geometric concepts more effectively.

The study looks at fiscal federalism, which is the distribution of resources between federating entities so that they can carry out their constitutional duties. The goal of this study was to identify the fundamental imperatives of fiscal federalism for the advancement of the country. In Nigeria's new democratic environment, the relative roles of the federal government, state governments, and local government authority (LGAs) in providing public services have become one of the most crucial subjects of candid and heated discussion. Federalism, fiscal federalism, and development were conceptually explained from the outset, and it became clear that the principles of fiscal autonomy and integrity are critical to the survival and ongoing existence of a properly federating form of government. In order to ascertain how the federal arrangements affect the provision of basic services in four crucial areas, the analysis will make use of fieldwork conducted in six states and twelve LGAs. primary health care, primary education, clean water and sanitation, and local roads that connect communities to marketplaces, schools, and medical facilities. The paper, which was based on Buchan Fiscal Residuum Theory, attempted to accomplish the study's goal by balancing the value of the public services returned to individuals with the payments paid. According to the article, the conflicting problems and difficulties of fiscal federalism may manifest as a misalignment between the functions of the different levels of government and the sources of money. According to the paper's conclusion and recommendations, it is important to make sure that revenue allocation encourages state and local governments to increase internal revenue generation rather than relying only on funding from In order to clearly define the duties to be carried out by each level of government, the federation account and intergovernmental relations issues should be examined and respected.

This study aims to analyze the difficulties faced by elementary school students in solving multiplication problems and the strategies implemented by teachers to address them. The background of this research lies in the importance of understanding multiplication as a foundational concept for mastering more advanced mathematical operations. This research employed a descriptive qualitative approach, using interviews as the primary data collection technique. The findings revealed that students struggle with understanding multiplication as repeated addition, applying problem-solving strategies, and maintaining accuracy due to over-reliance on rote memorization without conceptual understanding. To overcome these issues, teachers implemented various strategies such as the use of interactive learning media, concrete manipulatives, game-based learning, gradual practice, and individualized guidance in collaboration with parents. These strategies have proven effective in improving students’ conceptual understanding, accuracy, and confidence in solving multiplication problems.

This study aims to describe the difficulties of mathematics education students in solving mathematical induction problems in terms of concept understanding and calculation aspects. This type of research is descriptive using a qualitative approach. Based on the results of data processing, conclusions can be drawn, namely: (1) Concept errors, namely errors made by students because they do not understand the concept well. (2) Strategy error, which is an error that occurs because students choose the wrong way to work. (3) Calculation errors, namely errors in performing mathematical operations. Systematic errors, which are errors related to the wrong selection of extrapolation techniques. (4) Of the 10 mathematics education students, the data description of the research results shows an average in the normal category, namely 53%. Translated with DeepL.com (free version).

Many students find it difficult to connect abstract mathematical concepts with real-world applications, leading to limited problem-solving and modeling skills. This study aimed to develop a real-world problem-based mathematics module designed to enhance students’ mathematical modeling abilities. Using a Research and Development (R&D) approach with the 4D model Define, Design, Develop, and Disseminate the research involved secondary school students enrolled in mathematics classes. The Define stage identified learning difficulties and needs, while the Design and Develop stages focused on creating, validating, and refining a contextual mathematics module based on expert feedback. Quantitative data were collected through expert validation sheets, mathematical modeling tests, and student response questionnaires. The results demonstrated that the developed module achieved a high level of content and design validity, confirming its appropriateness for classroom use. Student responses indicated strong practicality and engagement during implementation. The effectiveness analysis showed a 28% improvement in mathematical modeling skills after the intervention, as evidenced by increased post-test scores and positive student feedback. Compared to traditional textbook-based instruction, the module proved more effective in fostering conceptual understanding, analytical reasoning, and real-world application of mathematics. In conclusion, the developed real-world problem-based module successfully bridges the gap between theoretical mathematics and authentic contexts, providing an innovative framework to cultivate modeling competence and critical thinking among students.

This study explores strategies to address students' difficulties in understanding and solving mathematical word problems involving long division in elementary schools. These difficulties can stem from internal factors, such as a lack of conceptual understanding, low motivation, and inaccuracy in solving problems, as well as external factors, such as ineffective teaching methods and minimal use of instructional media. Using the Systematic Literature Review (SLR) method, this research examines previous studies that discuss the causes of learning difficulties and possible solutions. The findings indicate that a contextual approach based on Realistic Mathematics Education (RME) and the use of concrete teaching aids can significantly enhance students' comprehension of long division. This approach helps students connect learning with real-life experiences and visualize mathematical concepts more clearly. Therefore, innovative instructional strategies are essential to improve elementary school students' understanding and numerical skills.