papers by Abdullah Kurudirek
Journal of Applied Mathematics and Informatics, 2025
This study explores the properties of translation surfaces with non-zero constant total curvature... more This study explores the properties of translation surfaces with non-zero constant total curvature in multidimensional isotropic space. We begin by defining translation surfaces as manifolds generated by translating a given surface along a direction in the ambient space. Our focus is on surfaces exhibiting not constant total curvature, which implies that the intrinsic geometric properties are uniform throughout the manifold. A theorem on the existence of a translation surface from a given total and mean curvature in a multidimensional isotropic space is proven.
International Journal of Social Sciences & Educational Studies, 2025
Mathematics performance in Iraq has been of concern to education stakeholders in the post war yea... more Mathematics performance in Iraq has been of concern to education stakeholders in the post war years. This research aims to identify the causes of poor mathematics achievement in secondary schools in Iraq according to the teachers' point of view. An online questionnaire was used to collect data from 110 mathematics across the major cities of Iraq. The data was then analyzed using the Minitab software, employing t-tests techniques, analysis of variance, and general descriptive statics methods. Results indicate that among others, parental involvement, pedagogical approaches, mathematics teachers' anxiety, and the learners' weak mathematics foundation during the early years are factors that affect students' performance. Recommendations and suggestions to improve the situation are clearly discussed in the study.
Educenter: Jurnal Ilmiah Pendidikan, 2025
In this study, we investigate mathematical misconceptions, particularly prevalent among high scho... more In this study, we investigate mathematical misconceptions, particularly prevalent among high school students, and offer solutions. The primary aims of our research include identifying the most common mathematical misconceptions, uncovering their underlying causes, and evaluating research-based solutions that have successfully addressed these issues. For this study, data were collected using a mixed-methods approach in Stirling Schools operating throughout Iraq. Data were gathered via a diagnostic test, as well as teacher interviews and classroom observations. The test revealed conceptual, procedural, and application problems, while interviews and observations gave qualitative information about the sources of misunderstandings and teaching tactics. The data analysis blended quantitative mistake classification with qualitative theme analysis to provide a complete picture of misunderstandings and effective training approaches. In light of the data obtained, we can state that misconceptions typically stem from a lack of conceptual understanding, over-reliance on procedural methods, and contextual misunderstandings. Additionally, it has been shown that conceptual education, visual aids, and peer-supported learning help eliminate mathematical misconceptions. These valuable findings hold significant implications for educators seeking to improve students' mathematical knowledge by emphasizing the importance of concept-based learning and providing opportunities for re-education. Through this study, we offer key insights into how widespread mathematical misconceptions can be effectively addressed, contributing meaningfully to mathematics education.
Journal of Advancements in Education, 2024
The exploration of mathematics often involves encountering extraordinary challenges, intricate pu... more The exploration of mathematics often involves encountering extraordinary challenges, intricate puzzles, sophisticated mental games, paradoxes, and thought-provoking sophisms. Delving into captivating examples has the potential to engage, enlighten, and inspire students, fostering a drive for discovery. This research paper aims to elucidate some intriguing mathematical sophisms and their implications within the realm of mathematics education. Several factors impact the establishment of an evolving educational setting for teaching mathematics from a humanistic viewpoint. The methodology adopted in this paper is a multi-case study that involves showcasing specific examples, highlighting these characteristics, and implementing mathematical concepts without strictly adhering to their assumptions, which can lead to logical inconsistencies. Students frequently need help with topics such as dividing an equation by zero or extracting a nonnegative square root. The tactics and stages of erroneous thinking that give rise to sophisms are intricately linked to various mathematical principles, including square roots, trigonometry, equations, differentiation, logarithms, geometry, binomial expansion, and integration. The requirements for developing a healthy learning environment with cheerful sensations are undoubtedly expressed. As a result, these emotions will stimulate students' thinking, link with their cognitive interests, and aid them in their future undertakings. This exploration delves into sophisms associated with each of these mathematical notions. It is our aspiration that those with an interest in mathematics will perceive the concepts presented in this article as a catalyst for future mathematical research.
TDPU, 2013
"Topology of Minkowski Metric" investigates the mathematical structure and features of the Minkow... more "Topology of Minkowski Metric" investigates the mathematical structure and features of the Minkowski space, which is essential to the study of special relativity and theoretical physics.
International Journal of Social Sciences & Educational Studies, 2024
This paper goes into the challenges faced in the teaching of geometry, emphasizing its foundation... more This paper goes into the challenges faced in the teaching of geometry, emphasizing its foundational principles. It investigates an alternate viewpoint by relating geometric principles to verses from the Holy Quran, implying that geometric conceptions have a spiritual and intellectual dimension. The historical contributions of Islam to geometric sciences are also examined, emphasizing the confluence between religion and geometry. The historical context of geometry in Islamic education is also explored, with an emphasis on the substantial contributions of some Muslim scholars to the topic between the 9th and 15th centuries. The literature overview presents much research on geometry education, including inquiry-based techniques, academic talent profiles, and the impact of various teaching methods on student achievement. Despite the variety of teaching methods, obstacles such as curriculum issues, teacher training, and student attitudes continue. In addressing the complexity of geometry teaching, the methodologies section highlights the significance of appropriate research design. The traditional teaching style and activity-based teaching/learning are addressed as two opposing methods. The latter is praised for its ability to foster innovative learning experiences. The results and discussion section critically assesses the "Foundations of Geometry" curriculum at top universities, identifying issues that need to be revised to line with contemporary expectations. The obstacles to teaching geometry are examined, including students' apathy and lack of prior knowledge, and solutions such as real-world examples, continual professional development, and activity-based teaching approaches are proposed. Finally, the article proposes a comprehensive reevaluation of geometry education that takes historical, religious, and current perspectives into account. It emphasizes the need for dynamic teaching methods, technology integration, and a revamped curriculum to make geometry more accessible and entertaining for students.
International Journal of Social Sciences & Educational Studies, 2024
This article addresses the sustainability of using digital technologies in mathematics education.... more This article addresses the sustainability of using digital technologies in mathematics education. The paper emphasizes the need to understand how we can improve mathematics learning processes and the role of technology in these processes. Technology encompasses various fields such as science, manufacturing, services, and transportation, covering a wide range from machines to methods. The use of technology in mathematics education should also be evaluated within this scope. The article examines how digital technologies are used in mathematics classes and how this usage affects students' mathematics learning processes. Technological advancements, ranging from graphic calculators to web-based applications, have transformed mathematics instruction. However, it is an important question whether technology is used only to access answers more quickly or to improve how mathematics is learned. Especially when there are numerous equations and programming languages in mathematics classes, the limitations of material presentation must be considered. Additionally, this research highlights the importance of using platforms for implementing online learning policies.
Zenodo (CERN European Organization for Nuclear Research), Aug 20, 2023
This thesis has three chapters related to Banach cores and statistical convergence. In the first ... more This thesis has three chapters related to Banach cores and statistical convergence. In the first chapter, some preliminary definitions, concepts, and theorems are given, which will also be needed in other chapters. After defining matrix transformations using infinite matrices, definitions of regularity, conservative, almost convergence, and Banach limits are mentioned. In addition, some theorems and results about Banach limits are given. In the second chapter, the concept of the core is briefly explained. Definitions of K-core, B-core, and theorems derived from these cores are given. Moreover, the
Mathematics and Statistics, Oct 31, 2023
Currently, the study of the geometry of semi-Euclidean spaces is an urgent task of geometry. In t... more Currently, the study of the geometry of semi-Euclidean spaces is an urgent task of geometry. In the singular parts of pseudo-Euclidean spaces, a geometry associated with a degenerate metric appears. A special case of this geometry is the geometry of Galileo. The basic concepts of the geometry of Galilean space are given in the monograph by A. Artykbaev. Here the differential geometry "in the small" is studied, the first and second fundamental forms of surfaces and geometric characteristics of surfaces are determined. The derivational equations of surfaces, analogs of the Peterson-Codazzi and Gauss formulas are calculated. This paper studies the development and isometry of surfaces in Galilean space. Moreover, the isometry of surfaces in Galilean space is divided into three types: semi-isometry, isometry and completely isometry. This separation is due to the degeneracy of the Galilean space metric. The existence of a development of a surface projecting uniquely onto a plane in general position is proved, as well as the conditions for isometric and completely isometric surfaces of Galilean space. We present the conditions associated with the analog of the Christoffel symbol, providing isometries of the surfaces of Galilean space. An example of isometric, but not completely isometric surfaces in G 3 is given. The concept of surface development for Galilean space is generalized. A development of the surface is obtained, which is uniquely projected onto the plane of the general position. In addition, the Gaussian curvature of the surface has been shown to be completely defined by Christoffel symbols.
Educenter, Jan 25, 2024
This study emphasizes the importance of adding life skills education to school curricula, recogni... more This study emphasizes the importance of adding life skills education to school curricula, recognizing that not all students' paths will lead to traditional employment. While not all students will become doctors, engineers, or lawyers, they will all go through a process of growth. Every individual needs key life skills necessary for resilience, adaptation, and effective management of daily life. This study aims to explore the important role of education in preparing the developing generation to live at the desired level by emphasizing the importance of empowering schools to shape a more productive future. This study utilizes the case study research approach. In this technique, researchers remain outside of the situation under investigation, focusing on the examination of many aspects and components that may interact. as a result, a holistic education, active families, and a developing curriculum with 21st-century skills enable children to overcome social barriers and prepare them for postsecondary education and the workforce. This study proposes a holistic strategy that emphasizes life skills alongside academic coursework, developing individuals who are adaptable and ready to face future challenges by revisiting the traditional educational tripod.
International Journal of Social Sciences & Educational Studies, 2024
This paper goes into the challenges faced in the teaching of geometry, emphasizing its foundation... more This paper goes into the challenges faced in the teaching of geometry, emphasizing its foundational principles. It investigates an alternate viewpoint by relating geometric principles to verses from the Holy Quran, implying that geometric conceptions have a spiritual and intellectual dimension. The historical contributions of Islam to geometric sciences are also examined, emphasizing the confluence between religion and geometry. The historical context of geometry in Islamic education is also explored, with an emphasis on the substantial contributions of some Muslim scholars to the topic between the 9th and 15th centuries. The literature overview presents much research on geometry education, including inquiry-based techniques, academic talent profiles, and the impact of various teaching methods on student achievement. Despite the variety of teaching methods, obstacles such as curriculum issues, teacher training, and student attitudes continue. In addressing the complexity of geometry teaching, the methodologies section highlights the significance of appropriate research design. The traditional teaching style and activity-based teaching/learning are addressed as two opposing methods. The latter is praised for its ability to foster innovative learning experiences. The results and discussion section critically assesses the "Foundations of Geometry" curriculum at top universities, identifying issues that need to be revised to line with contemporary expectations. The obstacles to teaching geometry are examined, including students' apathy and lack of prior knowledge, and solutions such as real-world examples, continual professional development, and activity-based teaching approaches are proposed. Finally, the article proposes a comprehensive reevaluation of geometry education that takes historical, religious, and current perspectives into account. It emphasizes the need for dynamic teaching methods, technology integration, and a revamped curriculum to make geometry more accessible and entertaining for students.
International Journal of Social Sciences & Educational Studies, 2024
This article addresses the sustainability of using digital technologies in mathematics education.... more This article addresses the sustainability of using digital technologies in mathematics education. The paper emphasizes the need to understand how we can improve mathematics learning processes and the role of technology in these processes. Technology encompasses various fields such as science, manufacturing, services, and transportation, covering a wide range from machines to methods. The use of technology in mathematics education should also be evaluated within this scope. The article examines how digital technologies are used in mathematics classes and how this usage affects students' mathematics learning processes. Technological advancements, ranging from graphic calculators to web-based applications, have transformed mathematics instruction. However, it is an important question whether technology is used only to access answers more quickly or to improve how mathematics is learned. Especially when there are numerous equations and programming languages in mathematics classes, the limitations of material presentation must be considered. Additionally, this research highlights the importance of using platforms for implementing online learning policies.
Educenter: Jurnal Ilmiah Pendidikan, 2024
This study emphasizes the importance of adding life skills education to school curricula, recogni... more This study emphasizes the importance of adding life skills education to school curricula, recognizing that not all students' paths will lead to traditional employment. While not all students will become doctors, engineers, or lawyers, they will all go through a process of growth. Every individual needs key life skills necessary for resilience, adaptation, and effective management of daily life. This study aims to explore the important role of education in preparing the developing generation to live at the desired level by emphasizing the importance of empowering schools to shape a more productive future. This study utilizes the case study research approach. In this technique, researchers remain outside of the situation under investigation, focusing on the examination of many aspects and components that may interact. as a result, a holistic education, active families, and a developing curriculum with 21st-century skills enable children to overcome social barriers and prepare them for postsecondary education and the workforce. This study proposes a holistic strategy that emphasizes life skills alongside academic coursework, developing individuals who are adaptable and ready to face future challenges by revisiting the traditional educational tripod.
Mathematics and Statistics, 2023
Currently, the study of the geometry of semi-Euclidean spaces is an urgent task of geometry. In t... more Currently, the study of the geometry of semi-Euclidean spaces is an urgent task of geometry. In the singular parts of pseudo-Euclidean spaces, a geometry associated with a degenerate metric appears. A special case of this geometry is the geometry of Galileo. The basic concepts of the geometry of Galilean space are given in the monograph by A. Artykbaev. Here the differential geometry "in the small" is studied, the first and second fundamental forms of surfaces and geometric characteristics of surfaces are determined. The derivational equations of surfaces, analogs of the Peterson-Codazzi and Gauss formulas are calculated. This paper studies the development and isometry of surfaces in Galilean space. Moreover, the isometry of surfaces in Galilean space is divided into three types: semi-isometry, isometry and completely isometry. This separation is due to the degeneracy of the Galilean space metric. The existence of a development of a surface projecting uniquely onto a plane in general position is proved, as well as the conditions for isometric and completely isometric surfaces of Galilean space. We present the conditions associated with the analog of the Christoffel symbol, providing isometries of the surfaces of Galilean space. An example of isometric, but not completely isometric surfaces in G 3 is given. The concept of surface development for Galilean space is generalized. A development of the surface is obtained, which is uniquely projected onto the plane of the general position. In addition, the Gaussian curvature of the surface has been shown to be completely defined by Christoffel symbols.
Eurasian Journal of Science and Engineering, 2024
The introduction of the Galilean plane within the affine plane parallels the familiar concepts of... more The introduction of the Galilean plane within the affine plane parallels the familiar concepts of the Euclidean plane, extending the realm of geometric exploration. The fundamental concepts of lines, triangles, squares, and circles are important in both planes, allowing for a smooth transition between these mathematical environments. The noteworthy aspect is the discovery that cycles in the Galilean plane have properties similar to circles in the Euclidean plane. This paper contributes to the mathematical literature by carefully deriving and establishing features of cycles in the Galilean plane, exhibiting their startling resemblance to Euclidean circles. The use of the inscribed angle as an alternative definition of the circle is particularly insightful, providing a faster and more intuitive explanation of some findings than the usual definition. Such comparative assessments not only broaden our understanding of various geometries but also give us chances to streamline the learning process. The paper argues for the inclusion of Galilean geometry in the high school curriculum by highlighting these parallels. It implies that exposing students to various geometrical systems not only broadens their mathematical perspectives but also fosters a larger and more inclusive vision of the subject, potentially inspiring increased interest and acknowledgment of Galilean geometry among students.
HRPUB Mathematics and Statistics, 2023
Currently, the study of the geometry of semi-Euclidean spaces is an urgent task of geometry. In t... more Currently, the study of the geometry of semi-Euclidean spaces is an urgent task of geometry. In the singular parts of pseudo-Euclidean spaces, a geometry associated with a degenerate metric appears. A special case of this geometry is the geometry of Galileo. The basic concepts of the geometry of Galilean space are given in the monograph by A. Artykbaev. Here the differential geometry "in the small" is studied, the first and second fundamental forms of surfaces and geometric characteristics of surfaces are determined. The derivational equations of surfaces, analogs of the Peterson-Codazzi and Gauss formulas are calculated. This paper studies the development and isometry of surfaces in Galilean space. Moreover, the isometry of surfaces in Galilean space is divided into three types: semi-isometry, isometry and completely isometry. This separation is due to the degeneracy of the Galilean space metric. The existence of a development of a surface projecting uniquely onto a plane in general position is proved, as well as the conditions for isometric and completely isometric surfaces of Galilean space. We present the conditions associated with the analog of the Christoffel symbol, providing isometries of the surfaces of Galilean space. An example of isometric, but not completely isometric surfaces in G 3 is given. The concept of surface development for Galilean space is generalized. A development of the surface is obtained, which is uniquely projected onto the plane of the general position. In addition, the Gaussian curvature of the surface has been shown to be completely defined by Christoffel symbols.
International Journal of Statistics and Applied Mathematics
Global trends in mathematics education show that modern teaching methods are rapidly evolving at ... more Global trends in mathematics education show that modern teaching methods are rapidly evolving at the national, regional, and global levels. In this regard, teaching non-Euclidean geometry concepts in schools can be essential in developing students' spatial imagination and enhancing scientific inquiry competencies. This paper aims to engage and increase students' interest in geometry science by introducing the fundamental concepts of several non-Euclidean geometries. With this aim, we will first give you a modern definition of geometry and move towards the exciting and fun world of non-Euclidean geometry. Of course, remember that the target audience we will talk about these issues is talented students in secondary and high schools.
International Journal of Statistics and Applied Mathematics, 2023
Global trends in mathematics education show that modern teaching methods are rapidly evolving at ... more Global trends in mathematics education show that modern teaching methods are rapidly evolving at the national, regional, and global levels. In this regard, teaching non-Euclidean geometry concepts in schools can be essential in developing students' spatial imagination and enhancing scientific inquiry competencies. This paper aims to engage and increase students' interest in geometry science by introducing the fundamental concepts of several non-Euclidean geometries. With this aim, we will first give you a modern definition of geometry and move towards the exciting and fun world of non-Euclidean geometry. Of course, remember that the target audience we will talk about these issues is talented students in secondary and high schools.
There have been many investigations into the factors that underlie variations in individual stude... more There have been many investigations into the factors that underlie variations in individual student performance in high school physics courses. Numerous studies report a positive correlation between students’ mathematical skills and their exam grades in high school physics The purpose of my study was to determine the effect of mathematical misconception that is one of the reasons the lack of students success in kinematics teaching.
OALib, 2015
In this paper, we have tried to indicate the own properties of polygons in Galilean geometry usin... more In this paper, we have tried to indicate the own properties of polygons in Galilean geometry using the Affine concepts as well. The relationships between an angle and a side as well as the relationships between altitudes and medians concepts, and comparison of some special polygons have been examined carefully. In addition, the area concept has been mentioned. Finally, the paper was completed with a new idea, Theorem 6.
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papers by Abdullah Kurudirek
In the geometry of the Galilean plane, the formula for calculating the distance between points is divided into two parts, with each pair of points corresponding to one of these parts. On the Galilean plane, the similarity of figures can be defined exactly as it is on the Euclidean plane. However, there are three additional ways to define the similarity of figures on the Galilean plane that have no analogs in Euclidean geometry.