Mathematical Concepts Research Articles

Analisis Kesulitan Siswa dalam Menyelesaikan Soal Pembagian Materi Bilangan Bulat dengan Menggunakan Metode Porogapit

The background of this research is the importance of mathematics in daily life and the difficulties experienced by students in understanding mathematical concepts, especially division. This study aims to analyze the difficulties of students in solving integer division using the porogapit method in grade IV of SD Negeri Legok II, Indramayu Regency. This study uses a qualitative approach with a descriptive method. The research subjects were 6 people who were selected using the purposive sampling technique. Data was collected through observation, interviews, tests, and documentation. Data analysis uses qualitative data analysis consisting of data reduction, data presentation, and conclusion drawn. The results showed that students experienced difficulties in three main aspects: understanding problems, performing division calculation operations, and solving problems. Most students have difficulty in the division calculation operation even though they already understand the porogapit method. This difficulty has an impact on the understanding and application of mathematical concepts in daily life. This research provides recommendations for improving learning methods that can improve students' understanding and ability in integer division

EFFECT OF BLENDED LEARNING EDUCATIONAL MODEL ON SECONDARY SCHOOL STUDENTS’ MATHEMATICS CONCEPTUAL UNDERSTANDING

The study was conducted to assess the effect of a blended learning educational model on grade ten students' mathematics conceptual understanding in Ethiopia. A non-equivalent pre-test and post-test quasi-experimental design was employed. Two intact classes from different schools were randomly selected and assigned to experimental (n=38) and comparison group (n=45). From the previous semester, students’ record book revealed that both groups have almost an equivalent mathematics performance. A one-way ANOVA and paired sample t-test were used to analyze the data. Moreover, to check the equivalence of the groups, the same pre-test was developed and administered. The result indicates that both groups were equivalent. The test covers tenth-grade topics relations and functions, polynomial functions, exponential functions, and logarithmic functions. The study shows that students instructed through the blended learning approach surpassed those taught via the conventional method in their comprehension of mathematical concepts. The one-way ANOVA statistical result revealed there is a notable disparity between groups with effect size of η2 =.269, which is a large effect size. Moreover, a paired sample t-test shows the experimental group showed a substantial mean difference of 14.327 with a very large effect size (d=1.016) when compared with the comparison group. Thus, the study shows that blended learning was more effective in improving mathematical conceptual understanding when compared with a conventional method of teaching. Based on the findings, the researcher recommends blended learning in mathematics education and suggests stakeholders and policymakers incorporate the model into the curriculum. Keywords: blended learning, conceptual understanding, educational model, lab rotation model, mathematical concept

Topological data analysis assisted machine learning for polar topological structures in oxide superlattices

Ferroelectric topological phases and phase transitions have been extensively investigated recently due to the rich physical insights and potential applications in next-generation electronic devices. However, precisely predicting the topological phase transitions under different internal and external conditions in polar oxide superlattice systems is challenging due to the complex energy competitions and highly nonlinear kinetics involved. Herein, we adopted a state-of-the-art mathematical concept called “persistent homology” from topological data analysis to extract the essential topological features for the polarization data in various topological structures. By implementing the persistent image as the descriptor, support vector regression (SVR) based convolutional neural network (CNN) models are developed for the automated and high precision classification and regression of topological states based on high-dimensional phase-field simulation data of the PTO/STO superlattice. Using this method, we can automatically construct the strain and electric field phase diagrams in seconds with high throughput phase-field data. We hope to spur further interest in the integration of state-of-the-art mathematical tools, machine learning algorithms, and condensed matter physics for predictions of topological phase transitions.

Eksplorasi Etnomatematika Geometri Bangun Datar Segitiga pada Pakaian Tradisonal Sortopi Khas Suku Batak Toba

Exploration of ethnomathematics in the context of flat geometry, especially triangles, in traditional Batak Toba clothing, is an interesting and important study. This study aims to reveal the relationship between mathematical concepts and local culture, and how geometric elements can be found in the design of Sortopi traditional clothing. This research method uses a qualitative approach with data sources, namely library studies, from several literature reviews according to the topic and purpose of the study. The results of the study show that Sortopi is a complement to traditional Batak clothing used by men as a crown or headband. The shape of Sortopi contains elements of isosceles triangle flat geometry, thus showing that cultural elements are inseparable from mathematics.

The use of games as playful pedagogical materials to problematize decolonial practices in educational environments

This article analyzes the relevance of working on decolonial issues through playfulness in mathematics. Methodologically, this is a bibliographical research, with a qualitative approach and reports of practices carried out with Youth and Adult Education classes and in Elementary School I. According to Educational Legislation, it is crucial to think about new methods that contribute to a movement of resistance and rupture in favor of the decolonization of schooling. In addition to contributing to the consolidation of mathematical concepts and countering patterns of Eurocentric colonial power, games provide reflections on conscious consumption, thus breaking with the capitalist system, which, according to Krenak, has the power of co-optation. Among the results and conclusions, playfulness in mathematics helps to promote inclusive education that values diversity.

Implementasi Etnomatematika pada Materi Kesebangunan dan Kekongruenan dengan Rumah Adat Karo

This article discusses the Karo traditional house, a review from Etnomathematics. Karo is located in North Sumatra and has high value history, culture and artifacts. One of these artifacts that still survives is the Karo traditional house. This traditional house not only functions as a protector for its residents but also has a deep function and meaning in accordance with the customs and culture of the community. In Karo traditional houses, the form, function and motifs of the aesthetic elements depict the close relationship between humans and their natural environment. Examining the aesthetic elements of Karo traditional houses which contain geometric concepts. Without studying geometric concepts in mathematics, Karo people have applied geometric concepts in everyday life, reflected in creating aesthetic elements in Karo traditional houses. The method used is literature study

Eksplorasi Etnomatematika pada Bangunan Cagar Budaya Ukiran Relief Istana Maimun di Kota Medan

Ethnomathematics is a field of study that combines mathematical concepts with cultural elements in people's lives. Maimun Palace, as one of the Malay cultural heritages located in Medan, North Sumatra, offers many examples of the application of ethnomathematics in its architecture and design. This research aims to explore how mathematical concepts, such as geometry, symmetry, fractals and proportions, are implemented in the building structure, ornaments and spatial layout of the Maimun Palace. The palace's architecture reflects a blend of local Malay, Islamic, Indian and European cultural influences, each of which carries unique mathematical values. In addition, symbolic elements of certain numbers are also found in the palace design, reflecting the cultural beliefs and philosophies of the local people. The results of this research show that the Maimun Palace is an important example of how mathematics is not only applied in a technical context, but is also influenced by beliefs, aesthetics, and cultural traditions. This study contributes to increasing understanding of the relationship between mathematics and culture and the importance of preserving cultural heritage through a multidisciplinary approach such as ethnomathematics. The method used is qualitative using library research

The Effectiveness of Missouri Mathematics Project Learning Models for Improving Students’ Mathematical Connection Ability on Junior High School

Mathematical connection ability is one of the high level abilities but is still classified as low because students' understanding of the conceptual material given by the teacher, there are still students going through steps in working on the problems given, such as describing a symbol, in completing mathematical concepts, therefore This research aims to examine the effectiveness of using the Missouri Mathematics Project Learning Model carried out at MTs Ibnu Sina Jl. Tegal Overtime No. 105, Pamekaran, District. Soreang, Bandung Regency, West Java 4091, by taking a sample of 60 students consisting of control and experimental classes. The research method used in this action was the experimental method. Based on the results of descriptive analysis of students' mathematical ability data before being given treatment, it showed the highest score was 70, the lowest score was 55 and the average score was 61. Meanwhile, the results of descriptive analysis of students' mathematical ability data after being given The treatment showed the highest score of 70, the lowest score of 55 and the average score of 61. Those given the treatment showed the highest score of 87, the lowest score of 69, and the average score of 77.83. So the average mathematical connection ability of students after being given treatment is higher than the students' mathematical ability before being given treatment.

Best Practice STEM-Based Differentiated Mathematics Learning for Improving Learning Outcomes and Self-efficacy of High School Students

Learning outcomes and self-efficacy are important learning factors. Mathematics learning outcomes can reflect the extent to which students have developed as learners, while self-efficacy reflects students' self-confidence in their own abilities in solving mathematical problems. This study was based on a qualitative approach, best practice. This best practice uses the STAR flow (“Situasi, Tantangan, Aksi, Refleksi”). The situation at SMAN 1 Mande, especially class XI, shows low learning outcomes and lack of self-efficacy. The challenge faced is planning and implementing differentiated learning to improve learning outcomes and student self-efficacy. Through a STEM-based differentiated learning approach, researchers designed and implemented contextual learning on the theme of global warming with integrating science, technology, engineering and mathematics. The results of this best practice indicate an increase in learning outcomes and student self-efficacy. STEM-based differentiated learning can also improve understanding of mathematical concepts at the high school level. Researcher recommend that educators embrace differentiated learning strategies by customizing their approaches to accommodate the diverse needs such as students' level of readiness, interests, and student’s learning profile. The significance of comprehending student characteristics, such as learning styles and thinking abilities is paramount, especially in the implementation of student-centered learning. Additionally, educators are advised to prioritize aligning learning objectives with the curriculum, ensuring relevance and engagement. This various approach aims to create a dynamic learning environment to resonates with students individualized level. Develop interventions to address students' lack of confidence in solving mathematical problems can improve self efficacy.

Analisis Kemampuan Mahasiswa Matematika FMIPA Unimed dalam Menyelesaikan Pertidaksamaan Nilai Mutlak dengan Berbantuan Python

This research aims to analyze the ability of Unimed FMIPA Mathematics students in solving absolute value inequalities with the help of the Python program. The problem faced is that students often have difficulty solving inequality problems manually. The purpose of this research is to see the effectiveness of using Python in helping to solve absolute value inequalities and how it affects understanding of mathematical concepts. The method used was qualitative research with a sample of 20 fifth semester students of the Mathematics Study Program, FMIPA, Medan State University. Students are given absolute value inequality problems to solve manually and with the help of Python. Data was collected through online tests and questionnaires using Google Form. The research results show that the majority of students feel that using Python is very helpful in solving absolute value inequalities. As many as 95% of students consider Python to be effective in making it easier to solve mathematical problems and increasing understanding of the concept of absolute value.

Formalising the Double-Pushout Approach to Graph Transformation

In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and demonstrating their properties. We establish the uniqueness of derivations, drawing upon Rosens 1975 research, and verify the Church-Rosser theorem using Ehrigs and Kreowskis 1976 proof, thereby demonstrating the effectiveness of our formalisation approach. The paper details our methodology in employing Isabelle/HOL, including key design decisions that shaped the current iteration. We explore the technical complexities involved in applying higher-order logic, aiming to give readers an insightful perspective into the engaging aspects of working with an Interactive Theorem Prover. This work emphasizes the increasing importance of formal verification tools in clarifying complex mathematical concepts.

Analisis Hambatan Belajar Siswa dalam Menyelesaikan Soal Cerita Konsep Perkalian Bilangan Cacah

Effective education in this context involves preparing students to explore and apply mathematical knowledge in various situations, providing a strong foundation for the development of intelligence and thinking skills. This research focuses on the challenges faced by 4th-grade students at SDN 4 Sukajaya in solving word problems related to multiplication of whole numbers. The object of this study is the students' difficulty in understanding the concept of multiplication, while the subjects are 10 students who experience difficulties and a class teacher. The research method used is qualitative with a descriptive approach, aiming to provide a detailed account of the problems faced by students. The study found learning obstacles among 4th-grade students at SDN 4 Sukajaya in solving word problems involving the concept of multiplication of whole numbers. These obstacles include: 1) difficulty in understanding the problems, 2) difficulty in identifying mathematical concepts, and 3) difficulty in calculations. The contributing factors are: 1) internal factors, such as motivation, intelligence, behavior, attitude, and students' physical condition (e.g., fatigue), and 2) external factors, such as facilities, teacher quality, and curriculum. Efforts to address these obstacles include: regular problem-solving practice, the use of varied and enjoyable teaching methods and media to boost motivation, and cooperation between teachers and students in monitoring learning progress

Mathematical Approaches to Cryptographic System Design

In the digital age, cryptographic systems are the most important part of safe communication. To protect data security, confidentiality, and validity, they need strong design frameworks. The math methods used in this paper are very important for designing and analyzing secure systems. As basic ideas, it looks at number theory, math, and complexity theory, with an emphasis on both old and new methods. Some important topics are the creation of prime numbers, modular arithmetic, elliptic curves, and finite fields, which are the basis for many encryption methods. The paper also talks about how complexity theory can be used to measure the strength of cryptography. It specifically talks about issues with discrete logarithms and integer factorization, which are at the heart of popular protocols like RSA and ECC. It also looks into lattice-based cryptography, which is seen as a strong option to quantum threats, and shows how hard it is to solve lattice issues. The study also looks at the design principles of symmetric cryptography, mainly block ciphers and stream ciphers, and how they use permutation groups and linear algebra to make sure that key plans and spread methods are safe. The paper also looks at secure hash functions, focusing on collision resistance, pre-image resistance, and how they are made using mathematics concepts such as Merkle-Damgård and sponge functions. Advanced topics like homomorphic encryption and zero-knowledge proofs show how mathematics and cryptography are increasingly coming together. They show how they can be used to make operations safe on protected data and privacy-preserving protocols. This paper gives a full picture of how mathematical theories and methods are used to build strong cryptographic systems by combining strict mathematical models with real-world cryptographic needs. The discussion stresses that the field is always changing because of new threats and improvements in computers. It also calls for constant scientific progress to make cryptography stronger against future problems.

The Sublime of Consciousness

Abstract The aesthetic tradition has identified as paradigmatically sublime such objects as imposing mountains and intense storms, as well as monumental art. But the tradition also acknowledges less paradigmatic cases, including sometimes mathematical structures or abstract concepts. In this paper, we argue that there is also a case for considering phenomenal consciousness—the experiential quality of subjective awareness—as a sublime phenomenon. One appreciates this, we argue, when one is struck by (fitting) awe upon contemplating (a) the perplexing existence of something like phenomenal consciousness in an otherwise completely material universe and (b) the role of consciousness in injecting meaning and value in an otherwise brutally factual reality.

Games in Mathematics Education: Trends and Methodological Approaches in the Context of the Congress of European Research in Mathematics Education (CERME) Review

This study aimed to examine the studies on digital games presented in The Congress of European Research in Mathematics Education (CERME) using a systematic analysis approach in terms of research method, data collection tool, and how they define digital games. Sixteen studies related to games were selected from the proceedings. The findings of the research revealed that the number of studies on games has increased in recent years, and the interest of the mathematics education community in this subject has gradually increased. It was seen that qualitative research approaches were used in most of these studies. As a data collection tool, a semi-structured or clinical interview form was mainly used. To reach more comprehensive results, it is necessary to give importance to quantitative research approaches and even to prefer the use of both approaches together. It was indicated that the tendency towards mathematical reasoning and puzzle games has continued predominantly in recent years. Although it was seen that the number of studies on digital games has increased in the last five years, only six studies in total were presented at the CERME. Moreover, three digital games developed by using the tools in the context of dynamic geometry environments were found. Another significant finding was that most of these studies did not define games. Only a few studies that defined the game considered the game as a tool used to acquire a mathematical concept or knowledge. Based on the findings, it can be argued that digital games are not among the interests of the mathematics education community. Finally, it was observed that mathematical theorems and approaches were central to the studies reviewed. Games were generally defined as tools within these studies. Therefore, future research should particularly consider fundamental game features such as game mechanics to create more integrated research environments with mathematics education.

The pedagogical insights of mathematics teachers integrating artificial intelligence in rural upper primary schools of Namibia

This paper presents a qualitative intervention study that explores the pedagogical experiences of mathematics teachers integrating Artificial Intelligence (AI) technologies into teaching mathematics in rural upper primary schools in Namibia. The Technological Pedagogical Content Knowledge (TPACK) framework, which intersects teachers’ understanding of technology integration with pedagogical techniques and subject matter knowledge, was adopted for the study. The research involved 13 mathematics teachers selected through purposive sampling. Data collection included two sharing circle discussions, lesson observations, and semi-structured interviews. A thematic analysis approach was employed to interpret the collected data. The findings reveal a diverse range of AI tools used by the selected teachers, such as Geogebra, Khan Academy, Virtual Tutors, and various problem-solving mobile applications, including Photomath, Mathway, and Microsoft Math Solver. These AI resources were noted for enhancing the visualisation of mathematical concepts, providing adaptive learning experiences, and promoting independent, paced learning that supports learners' learning styles. Teachers reported a marked improvement in learners’ comprehension and problem-solving abilities attributable to AI integration. Despite the benefits of AI in education, challenges remain, particularly in rural areas. Key issues include inadequate infrastructure, limited access to devices, and the need for ongoing teacher training in technological pedagogical content knowledge. Additionally, the lack of culturally relevant AI technologies hinders effective AI-supported learning in diverse contexts. Greater investment in localised AI educational tools is needed to achieve equitable and effective learning outcomes.

Mathematical Concepts in Graphic Design

Graphic design involves the creation of visual content to effectively convey information to an audience. Concurrently, mathematics encompasses the study of numbers, shapes, and patterns, serving as the fundamental basis for various fields, including design. Despite the apparent disparity between these two disciplines, they are intertwined in multiple ways, giving rise to a potent amalgamation. This review paper aims to delve into the correlation between graphic design and various mathematical concepts and theories.

Pemanfaatan Teknologi untuk Meningkatkan Numerasi Peserta Didik SMP N 1 Kertanegara

Numeracy is very important for junior high school students to learn because it has a significant impact on daily life such as problem solving abilities, critical thinking abilities and the ability to apply mathematical concepts in various situations. The numeracy ability index at junior high school level in Purbalingga Regency is rated "below minimum competency" with a score of 1.73 (scale 1-3). Problems among students at SMP N 1 Kertaengara related to numeracy include students having difficulty understanding basic mathematical concepts and more complex mathematical concepts. Another problem is that the numeracy teaching methods used by teachers are still monotonous and do not use technology. Therefore, efforts are needed to increase student numeracy, one of the efforts that can be made by utilizing technology. This activity aims to improve understanding of numeracy by utilizing technology so that students' numeracy skills increase. There are 3 stages of training starting from preparation, implementation and evaluation. The results of this activity can improve numeracy skills in a more effective and enjoyable way by utilizing technology in learning.

Exploring geometry and measurement in the Perjuangan Subkoss Garuda Sriwijaya Museum: An ethnomathematics study

The Museum of Perjuangan Subkoss Garuda Sriwijaya is a museum that preserves the history of South Sumatra’s struglle against the Dutch and Japanese colonialists. This research aims to obtain the results of an ethnomathematics study from the Museum of Perjuangan Subkoss Garuda Sriwijaya regarding historical, philosophical, and mathematical aspects and implement it in the Merdeka Curriculum in mathematics for elementary schools. This research employs an ethnographic approach with a qualitative descriptive approach, utilizing observation, interviews, documentation, field notes, and data triangulation. The analysis techniques include data reduction, data presentation, verification, and conclusions drawings. The study involved three informants who had direct interaction with the Museum of Perjuangan Subkoss Garuda Sriwijaya. The results of this research shows that ethnomathematics studies offer several insights: the historical aspect introduces local history and culture through artifacts that supported the struggle during the physical revolution; the philosophical aspectteaches the values ​​of caring, cooperation, creativity, and diversity within society; and the mathematical concepts reveals the concept of geometry, including area, perimeter, volume of both two-dimensional figures and three-dimensional figures, and length measurement.

Collaborative Design Capacity for Enactment Framework: An Analytic Tool for Conceptualizing Pedagogical Design Capacity Within Social Context

ABSTRACTThis study examines an urban middle school teacher design team's capacity for creating integrated science, technology, engineering, and mathematics curricula. Using Brown's pedagogical design capacity (PDC) theory, which highlights interactions between personal and curricular resources, this paper introduces an extended framework that includes social interactions as key influences on teachers' design abilities. Findings show that individual teachers' spontaneous curriculum modifications were adopted by the team, becoming collective resources for ongoing redesign and improving their design capacity. Teachers effectively used each other as resources to address unexpected challenges in integrating science, engineering, and mathematics concepts. Three types of social interactions were identified as collaborative resources: (i) Storytelling: sharing experiences to make abstract concepts actionable for curriculum development; (ii) Protocols: structured methods to address curricular problems related to integration; and (iii) Assessment “for” curriculum redesign: using assessment tools to inform and improve the curriculum. The Collective Design Capacity for Enactment framework is introduced to describe PDC within a social context, highlighting the importance of social interactions in bridging curriculum use and development, thus extending the literature on PDC.