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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.

Logic is an important foundation in mathematics learning because it shapes critical and systematic thinking skills. Introducing the concept of proof early on plays a strategic role in developing reasoning skills, identifying patterns, and providing simple arguments. This article aims to examine the role of logic in mathematics learning by emphasizing the importance of introducing the concept of proof from the outset. The methods used are a literature review of various relevant studies and descriptive analysis based on learning practices in early childhood education. The results of the study show that play, exploration, and concrete experience-based learning activities can improve children's ability to understand cause-and-effect relationships, make predictions, and convey logical reasons. In addition, social interaction and dialogue in the learning process have been proven to strengthen simple reasoning skills. In conclusion, the integration of logic and reasoning from an early age not only supports the development of mathematical abilities, but also builds the foundation for critical and analytical thinking needed for further education.

This study aims to determine the effect of the mathematical puzzle playing method on the subtraction calculation ability of first-grade students of SDN 104202 Bandar Setia. The type of research used is a quasi-experiment with a pretest-posttest control group design. The research subjects consisted of two classes, namely class IA as the control class (22 students) and class IC as the experimental class (22 students). The research instrument was a subtraction calculation ability test that has been tested for validity and reliability. The results showed that the average posttest score of both classes was 78.86 in the control class and 84.77 in the experimental class where there was a significant difference. The independent t-test of both classes showed a significance value of 0.000 < 0.05, so the hypothesis H0 was rejected and H1 was accepted. Thus, it can be concluded that the mathematical puzzle method significantly improved the arithmetic and subtraction skills of first-grade students at SDN 104202 Bandar Setia.

The problem addressed in this community service project is the low understanding of PKBM Permata Paket B students in applying mathematics to everyday life. The objective of this study is to improve students' understanding of mathematics through context-based learning, as well as to stimulate their interest and independence in solving problems involving numbers. The method used is a contextual teaching approach involving group discussions, problem-solving exercises, and real-life problem applications. The results show that context-based mathematics learning significantly improved students' understanding of budgeting, expenses, and personal finance management. Students also showed increased active participation in learning activities and a better ability to connect mathematical theory with practical problems in their daily lives. This program also had a positive impact on social empowerment, increasing students' independence in managing their daily lives. However, challenges related to understanding more complex concepts remain, and it is recommended to use more varied methods and extend the learning time in the future.

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.

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

This study aims to examine the application of behaviorism learning theory in enhancing student engagement in mathematics learning, particularly arithmetic sequences and series. The study was conducted at SMK Karya Serdang Lubuk Pakam with 24 tenth-grade students in a single meeting on September 17, 2025. The research team delivered the material, provided stimulus in the form of problems written on the board, and applied positive reinforcement by giving rewards to students who dared to and successfully answered. Data were collected through observation, field notes, and brief interviews. The results showed a significant increase in student engagement: more students volunteered to solve problems on the board, the classroom atmosphere became more lively, and participation in discussions improved. Although some students remained hesitant, the behaviorist strategy proved effective in enhancing motivation and engagement. These findings reinforce the theories of Thorndike, Pavlov, and Skinner, which emphasize the stimulus–response relationship and reinforcement as the basis of learning (Hamruni et al., 2021; Yusup, 2024).

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 aims to analyze junior high school students’ mathematical reasoning abilities in terms of their levels of learning independence. The research employed a descriptive qualitative approach involving three ninth-grade students from UPT SMP Negeri 5 Gresik, each representing high, medium, and low levels of learning independence. Data were collected through a self-regulated learning questionnaire, a mathematical reasoning test based on the topic of Systems of Linear Equations in Two Variables (SPLDV), and semi-structured interviews. Data analysis followed Miles and Huberman’s interactive model, consisting of data reduction, data display, and conclusion drawing. The results revealed that students with high learning independence demonstrated strong reasoning skills across all seven indicators of mathematical reasoning (representing statements, making conjectures, performing manipulations, constructing proofs, drawing conclusions, verifying arguments, and identifying patterns). Students with medium learning independence fulfilled only some indicators, while those with low learning independence could only make simple conjectures without systematic reasoning. These findings highlight that learning independence plays a crucial role in developing mathematical reasoning, as it enables students to regulate their thinking processes, evaluate solutions, and correct errors. Teachers are encouraged to integrate learning strategies that foster self-regulation—such as the CORE and Flipped Classroom models—to enhance students’ mathematical reasoning skills.

This study aims to describe students’ mathematical problem-solving abilities on the topic of Systems of Linear Equations in Two Variables (SPLDV) based on Polya’s problem-solving stages in relation to their levels of self-efficacy. The research employed a descriptive qualitative approach with three ninth-grade students from SMP Negeri 5 Gresik in the 2024/2025 academic year, selected through purposive sampling to represent high, medium, and low levels of self-efficacy. Data were collected using a self-efficacy questionnaire, problem-solving tests consisting of two contextual essay items on SPLDV, and semi-structured interviews. Data analysis followed the interactive model of Miles, Huberman, and Saldana, encompassing data reduction, display, and conclusion drawing, referring to Polya’s four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. The results revealed that students with high self-efficacy were able to complete all four stages comprehensively and reflectively, demonstrating systematic and accurate reasoning. Students with medium self-efficacy successfully performed the first three stages but failed to verify their final results, while students with low self-efficacy only reached the stage of understanding the problem and struggled to plan or execute solutions. In conclusion, the level of self-efficacy influences students’ mathematical problem-solving performance, particularly in terms of strategic accuracy, procedural precision, and reflective evaluation.

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.

The background of this research is the richness of Indonesian culture that is very diverse from Sabang to Merauke. Education and culture are now hot topics. Mathematics, as an important subject, is often considered difficult and boring due to monotonous learning and lack of motivation. Therefore, it needs improvement by connecting mathematical materials with local culture to make it more relevant in everyday life. The purpose of this research is to determine the effectiveness of E-LKPD flat shapes on the collage of Joglo traditional houses based on ethnomathematics in the mathematics learning process of flat shapes material which is expected to enable students to love their ancestral culture. The research method used is descriptive qualitative with the type of design research. Design research consists of 3 stages, namely experimental preparation, experimental implementation, and retrospective analysis. Data collection techniques with observation, questionnaires, and documentation. The results of the study are the implementation of E-LKPD collage based on ethnomathematics of Joglo traditional houses on flat shapes material runs effectively and can foster a sense of love for ancestral culture. This conclusion was obtained based on the suitability between ALT and HLT. Furthermore, the results of this study can be the basis for the development of the next E-LKPD by utilizing other cultures that are close to the daily lives of student.

This study aims to describe and analyze the planning of mathematics learning based on a love-centered curriculum at Athalla Health Vocational School. The curriculum was developed in response to the low motivation and academic achievement of nursing and midwifery students, who often perceive mathematics as irrelevant to their future professions. The love-based curriculum emphasizes the integration of compassion, empathy, and care values into the teaching process to create a more supportive, enjoyable, and meaningful learning environment. This study employs a qualitative method with a case study approach, collecting data through in-depth interviews with teachers and students, classroom observations, and analysis of lesson planning documents. Through the implementation of a love-centered curriculum, it is expected that students’ motivation, conceptual understanding, and learning outcomes will improve. Furthermore, this research aims to demonstrate how mathematics learning integrated with humanitarian values can foster positive character traits such as empathy, responsibility, and collaboration, which are essential qualities for future health professionals.

This study aims to determine the effect of using the Rotating Wheel (DaPur) learning media on the understanding of multiplication concepts of second-grade students at Tugu Utara 03 Elementary School, North Jakarta. The study was conducted in February 2025 with a quantitative approach and quasi-experimental design. The research sample consisted of 60 students divided into two classes, namely class II A as the control group and class II B as the experimental group, each consisting of 30 students. Data collection was carried out through the administration of pre-tests and post-tests. The instruments used have been tested for validity and reliability, with the results that all questions were declared valid and reliable (Cronbach's Alpha = 0.896). Data were analyzed using an independent sample t-test. The results of the analysis showed that there was a significant difference between the post-test scores of students in the experimental class and the control class, with a t-value of 27.757 and a significance of 0.001 (<0.05). This proves that the rotating wheel media has a positive and significant effect on the understanding of multiplication concepts. The Spinning Wheel media has been proven to help students understand multiplication material in a more enjoyable and concrete way, thereby improving their abilities in the aspects of translation, interpretation, and extrapolation of concepts. Based on these results, it can be concluded that the Spinning Wheel (DaPur) media is effective for use in mathematics learning, especially multiplication material.

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

This 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 study aims to analyze the learning difficulties experienced by fifth-grade students at Yayasan Al-Hidayah and identify innovative solutions in the learning process. The research uses a descriptive quantitative method with data collected through questionnaires. The results indicate that students still face challenges in understanding the material, primarily due to the fast pace of the teacher's explanations, a lack of supporting media and teaching aids, and limited learning facilities. The most difficult subjects for students to understand are Mathematics, followed by English and Science. Despite these challenges, parental involvement in supporting the learning process is relatively good, and students tend to prefer interactive learning, such as educational games, group discussions, experiments, and the use of digital media. Based on these findings, there is a need for innovation in learning, focusing on technology-based learning, the use of more varied teaching aids, and the application of creative strategies to enhance motivation, understanding, and student learning outcomes. Such innovations are expected to provide more engaging and effective learning experiences for students, addressing the difficulties they encounter in learning.

In teaching mathematics subjects, a teacher must be competent in designing innovative learning materials so that they can develop students' potential, which is expected to affect their learning outcomes and which is one of the influencing factors in student success in mathematics lessons is learning style. This study applies a descriptive method. The purpose is to describe the form of learning difficulties experienced by grade VIII students at MTs SA Al Murtadho Kedungwaru in learning mathematics on phytagoras theorem material referring to aspects of each student's learning style. In determining a subject in a study, it is carried out using the purpose sampling technique. There are three learning styles that will be studied further in this study, namely visual, auditorial, and kinesthetic learning styles. The research subjects of six students were taken representatives from a total of 34 students, in each class two representatives will be taken for those who have a visual learning style, two students also with an auditorial learning style, and two more students with a kinesthetic learning style. The techniques used to obtain the necessary data will be distributed questionnaires, test questions, interviews with students, and documentary evidence. This study applies two ways by comparing data from observation results with interview results and will also compare a person's assessment with various points of view with other people's perspectives. The results found in the study stated that there are difficulties in students including difficulties in understanding concepts, problems, and answering questions related to the Pythagorean theorem. So teachers need to find a learning style that is suitable for each student in order to help students understand the material so that students can solve the questions given appropriately.

This study aims to improve student learning outcomes through the implementation of the Problem Based Learning (PBL) model assisted by PowerPoint media in Mathematics for Grade I students at SD IT Riyadhoturrohman. The research employs Classroom Action Research (CAR) conducted in two cycles. Each cycle consists of three meetings, following the stages of planning, implementation, observation, and reflection. The research subjects were 16 students from Grade I of SD IT Riyadhoturrohman. The Problem Based Learning model was chosen because it encouraged students to be actively involved in learning through solving contextual problems, while PowerPoint media was used to help visualize the mathematical concepts being taught. The results showed an improvement in students' learning outcomes from the pre-action stage to Cycle I, and a further increase in Cycle II. Additionally, students demonstrated improved participation, conceptual understanding, and teamwork skills. Thus, the implementation of the Problem Based Learning model assisted by PowerPoint media proved to be effective in improving the mathematics learning outcomes of Grade I students at SD IT Riyadhoturrohman.

This study aims to develop a junior high school mathematics e-module based on local culture at the Van der Wijck Fortress complex to enhance students’ mathematical reasoning skills and learning interest. Specifically, the objectives are: (1) to describe the characteristics of the local culture-based e-module that can improve reasoning ability and learning motivation, and (2) to produce a high-quality e-module that meets the criteria of validity, practicality, and effectiveness. The research employed the ADDIE development model (Analysis, Design, Development, Implementation, and Evaluation). The participants consisted of one teacher, 31 students in the experimental class, and 32 students in the control class at a public junior high school in Kebumen Regency. The instruments used included validation sheets for media and material, competency tests, mathematical reasoning tests, learning interest questionnaires, and practicality assessment forms for teachers and students. The results showed that the e-module possesses characteristics of being self-instructional, self-contained, stand-alone, adaptive, and user-friendly. Product validity was confirmed through expert validation with average scores of 4.26 for media and 4.35 for material (very valid). The validation of instruments obtained average scores ranging from 4.5 to 4.92, categorized as very valid. Practicality was demonstrated through teacher assessments of 92%, student assessments of 85%, and learning implementation of 94% (all very practical). Effectiveness testing using the Multivariate Hotelling’s T² test indicated significant differences between experimental and control classes in competency test scores, mathematical reasoning, and learning interest. Therefore, the local culture-based mathematics e-module is proven valid, practical, and effective in enhancing students’ mathematical reasoning and learning motivation.