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This study aims to analyze students’ mathematical reasoning abilities in quadratic function material through the use of Desmos. The research employed a qualitative descriptive approach using a case study and usability testing method. Data were collected through post-tests and interviews involving students’ responses in solving quadratic function problems. The analysis focused on several indicators of mathematical reasoning, including procedural skills, conceptual understanding, and analytical ability. The results show that students generally demonstrate adequate procedural reasoning, particularly in substitution and computation tasks. They are also able to relate algebraic representations to geometric interpretations, such as determining intercept points and analyzing the direction of parabolas. However, limitations were found in conceptual understanding, especially in identifying graph characteristics without relying on procedural steps. The use of Desmos significantly supports the development of students’ mathematical reasoning by providing real-time visualization, facilitating exploration of function parameters, and enabling verification of results. Overall, Desmos contributes to enhancing procedural, conceptual, and analytical dimensions of mathematical reasoning, although its effectiveness depends on proper instructional design.

The Hartley transform provides a real-valued alternative to the classical Fourier transform, offering structural advantages for the analysis of real-valued signals. This paper presents a systematic study of the continuous Hartley transform, including its definition, inversion formula, Plancherel identity, and core operational properties such as shifting, modulation, and convolution. The analytical framework is developed in parallel with the classical Fourier theory to highlight structural similarities and distinctions between the two transforms. Furthermore, we establish a Hartley-type Heisenberg uncertainty principle using two complementary approaches: a direct method based on intrinsic properties of the Hartley kernel, and a Fourier-based method that exploits the algebraic relationship between the Hartley and Fourier transforms. These results provide a unified and rigorous foundation for understanding uncertainty relations within real-valued transform frameworks, and they demonstrate the continued relevance of the Hartley transform in harmonic analysis, integral transforms, and modern signal processing.

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 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.

Advances in technology and computers are utilized in various fields of contemporary applications, especially in cryptography and data security in graph theory applications. By understanding the concepts of graph theory, researchers and developers can design cryptographic algorithms that are stronger, more efficient and resistant to attacks. One of the cryptographic applications that has been implemented is the XNOR algorithm. This algorithm has been applied to encryption and decryption as well as the use of stream ciphers. By using 64 bits, the XNOR algorithm can expand encryption and decryption capabilities and increase the security of encrypted data. In this research, an analysis was carried out regarding information encryption and decryption algorithms with the application and development of the XNOR gate logic circuit method in Boolean algebra and graph theory. This research uses the example of the word MATH, which can be changed into a code or password and vice versa to secure information that you want to keep secret. Apart from that, an analysis of the graph formation of each character in the word MATH was also carried out using Python which produced semi-Euler and Hamilton graphs  

Mathematics is often perceived as a subject that is difficult for students to master, a notion that has been confirmed by numerous previous studies. One of the contributing factors is the limited variety of instructional media used in classrooms, which affects students' interest and comprehension. Many teachers still lack appropriate learning media to support blended learning approaches. This study aims to develop and implement multimedia-based Educational Instructional Media (EIM) that are valid, practical, and effective. The project utilizes video-based learning to deliver algebra concepts material for Grade VII students at SMPN 252 Jakarta and SMPIT Al-Qudwah. The development process follows the ADDIE model, which includes five stages: analysis, design, development, implementation, and evaluation. During the analysis phase, both learning needs and content requirements were mapped according to SAP (System Analysis and Product). The material was then divided into seven core sections. In the design stage, the curriculum structure, system flow, and user interface were developed. The development stage involved creating instructional content based on the analysis results. The content was then uploaded to the Moodle platform and presented using the Project-Based Learning (PjBL) model.

This study aims to examine the use of Macaulay2 software in improving students' computational thinking skills in mathematics learning, especially in abstract algebra material. Macaulay2 as an open-source Computer Algebra Sistem (CAS) provides a symbolic and algorithmic environment that encourages logical and systematic exploration of mathematical concepts. Literature reviews show that the use of Macaulay2 can strengthen conceptual understanding, train computational thinking, and introduce mathematical programming to students. However, technical challenges, limited Indonesian language teaching materials, and limited educational infrastructure are obstacles that need to be overcome through collaboration between educational stakeholders.

Informatics is a subject that is desired to be able to contribute computational thinking skills based on logic, as well to the ways to think in solving a problem more effectively, efficiently and optimally in various fields of life that are now inseparable from the use of computers also provides technological skills where the binary system has several basic gates, namely NOT, AND and OR which are basic gates have symbols, truth tables, and gates that must be remembered and balanced according to the provisions in Boolean algebra, Basically students have difficulty understanding it because the teacher's method when delivering the material still uses the method of delivering practice, group work, lectures, questions and answers, and short quizzes. However, the practice carried out in this class only describes the input of the truth table which is depicted on the board and after that the basic gate is made using symbols, so this training is carried out to improve the skills of students who get an 85% increase and are categorized as being able to implement and are stated to have increased in Skill.

This study aims to analyze students' difficulties in understanding algebraic concepts in the implementation of the Merdeka Curriculum. This type of research uses a descriptive research method with a qualitative approach. Data collection techniques include interviews, questionnaires, and three written tests. Based on the results of interviews and questionnaires conducted by teachers with the school principal and mathematics teachers, the school has implemented the Merdeka Curriculum despite limitations in resources. The Merdeka Curriculum contributes to teachers in terms of teaching modules and freedom in creativity in learning, although training is still needed. The results of the student questionnaire indicate that the majority of students have difficulty understanding algebra, especially in identifying variables, but the majority of students feel that classroom learning is interactive and enjoyable. Most students feel helped by the example questions provided by the teacher. The written test results show that students have difficulty with the use of positive and negative signs, coefficients, constants, algebraic operations, and determining variable values. This indicates that the majority of students have not yet achieved mastery of the algebra material. It can be concluded that the implementation of the independent curriculum at SMP IT Az-Zahira Khatulistiwa supports teachers in the algebra learning process through the use of teaching modules, but students still struggle to understand algebraic concepts due to the limited use of educational media, which is constrained by the school's facilities.

This study aims to describe students' difficulties in translating word problems into mathematical models in algebra material. Using a qualitative approach, the subjects were seventh-grade students at SMP Negeri 2 Tasikmalaya in the 2024/2025 academic year. Data were collected through questionnaires, interviews, and documentation. The results show that students struggled to understand the meaning of word problems and convert them into correct equations. Common errors included misconceptions about algebraic symbols, such as treating variables as fixed numbers and misusing the equal sign. In addition, students had difficulty identifying essential information needed to construct a mathematical model. Learning activities that focused only on procedural calculations further contributed to these challenges. This study recommends the use of more contextual and meaningful learning approaches, such as Problem-Based Learning and Realistic Mathematics Education, to help students better understand the relationships within problems and accurately express them through appropriate mathematical representations..    Penelitian ini bertujuan untuk mendeskripsikan kesulitan siswa dalam menerjemahkan soal cerita ke dalam model matematika pada materi aljabar. Dengan pendekatan kualitatif, subjek penelitian adalah siswa kelas VII SMP Negeri 2 Tasikmalaya tahun ajaran 2024/2025. Data dikumpulkan melalui angket, wawancara, dan dokumentasi. Hasil penelitian menunjukkan bahwa siswa mengalami kesulitan dalam memahami makna soal cerita dan menyusunnya menjadi persamaan yang tepat. Kesalahan yang muncul meliputi pemahaman yang keliru terhadap simbol aljabar, seperti menganggap variabel sebagai angka tetap dan tidak tepat menggunakan tanda sama dengan. Selain itu, siswa juga tampak kesulitan menentukan informasi penting yang diperlukan untuk membangun model matematika. Pembelajaran yang hanya berfokus pada prosedur perhitungan turut memperkuat kesulitan ini. Penelitian ini merekomendasikan penggunaan pendekatan pembelajaran yang lebih kontekstual dan bermakna, seperti Problem-Based Learning dan Realistic Mathematics Education, agar siswa dapat lebih memahami hubungan antar informasi dalam soal dan menyusunnya dalam bentuk model yang benar.

This study aims to develop teaching materials based on the TESMER approach on algebra material to improve the quality of mathematics learning at the junior high school level. TESMER as a development model is designed to bridge learning theory with classroom learning practices through systematic stages, namely the analysis, design, formative experiments, and retrospective reflection stages. The algebra material focused on includes algebraic forms, algebraic operations, and simple problem solving. This study uses a design research approach by involving teachers and students in the development process. The results of expert validation show that the teaching materials are included in the very valid category, with high assessments in the aspects of content integration, presentation, and language. Limited trials show that the teaching materials are practical to use by teachers and are liked by students. In addition, there was a significant increase in students' conceptual understanding and logical thinking skills after using the teaching materials. These findings recommend the TESMER approach as an effective framework in developing contextual algebra learning devices that are oriented towards meaningful learning.

In this have a look at, a new mathematical model for FDAE-based smart manage systems is proposed. The model carries fractional derivatives blended with algebraic constraints to symbolize prolonged memory results. We describe a numerical method to solve the proposed device and practice this version to robotics, self-reliant cars, and sensible prosthetics. The Fractional Collocation Method is employed to resolve FDAEs, making sure accuracy and balance. To validate the proposed method, we introduce 3 examples: a simple FDAE demonstrating the accuracy of the numerical solution, a device of FDAEs modeling interdependent dynamic variables with algebraic constraints, and an FDAE with a nonlinear algebraic constraint, highlighting the approach's capability to handle complicated, nonlinear dynamics. Simulation results verify that FDAEs offer a more practical and powerful tool for designing and reading wise manage systems as compared to classical techniques.

The purpose of this study is to describe the effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on students' problem solving and mathematical communication skills, describe the effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on problem solving skills, and describe the effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on students' mathematical communication skills. This type of research is Quasi Experimental using Nonequivalent Control Group Design. This research was conducted at SMP Negeri 1 Malinau, North Kalimantan City with 60 students from two 9th grade classes. The instruments used in this study were descriptive test questions of problem solving ability, mathematical communication and observation sheets for the implementation of Outdoor Learning Math learning activities using GPS-based mobile technology-assisted math traces. The results showed that there was an effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on students' problem solving and mathematical communication skills together, there was no effect of Outdoor Learning Math using mobile technology-assisted math traces on problem solving skills, and there was no effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on mathematical communication skills. Therefore, for future researchers to expand the scope of materials such as geometry, statistics and probability, algebra, arithmetic and add student motivation variables.

This study discusses the history and development of the number system in India and its influence on the evolution of mathematics worldwide. The Indian number system has evolved since the Indus Valley Civilization and has undergone significant innovations, such as the invention of the number zero by Brahmagupta and the development of the place value system, which forms the basis of the modern decimal number system. This research employs a qualitative method with a library research approach, involving the analysis of various written sources, such as books, academic journals, and historical articles on the Indian number system. The findings indicate that the Indian number system has had a profound impact on the advancement of mathematics, particularly after it was introduced to the Islamic world by scholars such as Al-Khwarizmi, who later disseminated it to Europe, making it the foundation of the numerical system used today. Additionally, the Indian number system contributed to the development of various branches of mathematics, including algebra, calculus, and number theory, and served as the foundation for modern technology, including computers and calculators. Therefore, understanding the history of the Indian number system should be reinforced in mathematics education, accompanied by further research on its applications in contemporary science and technology.

This work introduces the concept of neutrosophic AT-ideals in AT-algebra and presents some associated facts and theorems. The homomorphism of neutrosophic AT-ideals in AT-algebra is examined, and some findings pertaining to them under homomorphism are derived.

Learning discrete mathematics, particularly on the topic of equivalence in propositional logic using propositional algebra laws, often presents challenges for students due to its abstract nature and the logical thinking skills required. This study aims to analyze the effectiveness of using ChatGPT as a learning aid to enhance students' understanding of this topic. The research employed a quantitative method with a post-test only control group design, involving two groups of students: an experimental group using ChatGPT and a control group utilizing conventional learning methods. Data were collected through a post-learning achievement test. The results showed that the average score of the experimental group (85.47) was significantly higher than that of the control group (66.78). The independent t-test results yielded a significance value of < 0.05, indicating a significant difference in learning outcomes between the two groups. Furthermore, the calculation of Cohen's d showed a value of 0.959, categorized as a large effect size. These findings indicate that the use of ChatGPT as a learning aid has a significant impact on students' learning outcomes. With its interactive and responsive features, ChatGPT helps students grasp complex propositional logic material more easily. This study recommends utilizing AI-based technologies like ChatGPT as an innovative learning strategy, particularly for abstract topics in discrete mathematics.

This research aims to describe how the effectiveness of differentiated learning strategies through giving structured assignments on class VII students' algebraic operations material in terms of: (1) student learning achievement, (2) student learning motivation, and (3) student learning achievement and student learning motivation simultaneously. This research is a quasi-experimental research with a pretest and posttest non-equivalent group design. This research is quantitative research with experimental methods, This type of research is a quasi-experiment, a pretest-posttest nonequivalent control group design. The subjects in this research were 66 students, divided into two classes, namely 33 experimental class students and 33 control class students. The data collection technique for student learning achievement uses a multiple choice test with 20 questions and an essay with 2 questions, while for data on student learning motivation uses a questionnaire in the form of a questionnaire with 25 questions. Data analysis used two sample t-test analysis using statistical formulas and the SPSS 27 for Windows program. The results showed that the differentiated learning strategy through structured assignments on the material of the operation of algebraic forms of seventh grade students was 1) ineffective in terms of student learning achievement, 2) effective in terms of student learning motivation, and 3) effective in terms of student learning achievement and student learning motivation simultaneously.

The purpose of this study was to develop AKM model mathematics questions using the Yogyakarta cultural context to determine the profile of mathematical literacy of high school students. This type of research is a design research type of development study using an emphasis on repeated cycle development using formative evaluation. This study developed a set of AKM model mathematics questions, with preliminary and prototyping stages. The subjects of the study were class X students of MAN 2 Wonosobo and were determined by partner teachers. Data analysis techniques used document analysis, walk through analysis, and test result analysis. The results of the study showed that: 1) a set of AKM model mathematics questions using the Yogyakarta cultural context that were compiled had met the valid criteria using the Formative Evaluation flow. 2) the results of the study of the profile of mathematical literacy of students in the field test subjects revealed that there were many students who had not completed, especially in the employ category where only 15% (6 out of 40 students) had completed it, namely on question number 8. Likewise in the formulate and interprete categories, both of which were no more than 17.5% of students who managed to get the maximum score. Likewise, in the content category, it can be seen that no more than 15% (6 out of 40 students) were able to obtain the maximum score on question number 8. Meanwhile, in the algebra domain, at least 32.5% (13 out of 40 students) managed to obtain the maximum score, namely on questions 23, 24 and 25. The same thing in the data domain can be seen to be higher than the number domain and geometry domain, although the percentage is quite low, namely 27.5% (11 out of 40 students) who obtained the maximum score.

This study aims to: 1) Describe the profile of students' mathematical literacy abilities in the personal context domain in solving algebra problems based on components in class VII students of SMP Negeri 9 Singkawang in the 2020/2021 academic year; 2) Describe the profile of students' mathematical literacy abilities in the personal context domain in solving algebra problems based on components in class VII students of SMP Negeri 9 Singkawang in the 2020/2021 academic year; 3) Describe the profile of students' mathematical literacy abilities in the personal context domain in solving algebra problems based on components in class VII students of SMP Negeri 9 Singkawang in the 2020/2021 academic year. This research method is a qualitative research method. The subjects in this study were 30 class VII A students. The object of this study is mathematical literacy abilities in algebra material. The data collection instruments were written tests and interviews in accordance with the strategic competency indicators that had been tested with content validity, construct validity, reliability, level of difficulty and discriminatory power. The results of the study showed that: 1) Of the 30 students who took the mathematical literacy ability test, in the personal context domain the average student score was 45.83 and was in the moderate category; 2) Of the 30 students who took the mathematical literacy ability test, in the work context domain the average student score was 57.22 and was in the moderate category; 3) Of the 30 students who took the mathematical literacy ability test, in the general context domain the average student score was 54.44 and was in the moderate category.

This research aims to determine the feasibility, practicality and effectiveness of using the Canva Application as a Mathematics Learning Media for Class VII Flat Building Material at SMP Negeri 1 Citeureup.This research adopts the ADDIE model stages (analyze, design, develop, implement, and evaluate). The analyze stage includes initial analysis, student analysis, concept analysis and formulating learning objectives. The design stage includes preparing learning media in the form of selecting appropriate media and designing learning content. The development stage includes the development of data collection instruments. The data collection instrument in this research was interviews with the teachers concerned. The implementation stage includes implementing the use of the Canva application. The evaluation stage includes the form of evaluation carried out at each ADDIE stage. The data analysis technique used is the validity coefficient by Aiken's V. The research results show that the learning media that has been developed is in the very good category and can be used in the learning process.