Отправна позиция на статията е комбинаторна задача от Фестивала на младите математици 2025, изследваща максималния брой различни транспозиции, които могат да бъдат извършени върху дадена пермутация така, че началното разположение да бъде възстановено. Показана е връзка с редицата A011848 от Онлайн енциклопедията на целочислените редици (OEIS) и е доказано обобщение за максималната дължина на поредица от различни транспозиции, свързваща два елемента на симетричната група \(S_{n}\).

В статията се разглеждат някои специфични подходи, които са ефективни в обучението по математика на ученици с разстройство от аутистичния спектър (РАС). Описват се някои характеристики на учениците с аутизъм, както и са посочени някои методологични подходи в тяхното обучение по математика. Разгледан е математически модел, който дава възможност за постепенно разширяване и добавяне на нов учебен материал. Описани са и примерни задачи, които биха били подходящи в обучението на учениците с разстройство от аутистичния спектър в общообразователния клас.

The transformation of geometric figures is one of the important topics in the school geometry course. Their study was primarily focused on the classical analytical representation. At the same time, the constructive component has been considered to a lesser extent. However, it allows for a more visual representation of the geometric meaning of each transformation. Thus, the task was set to use the example of the operation of parallel translation of figures, relying on the constructive nature of geometry to reveal important components in the formation of students’ understanding of such transformations. The main body of the article presents examples supported by diagrams and worked solutions. On this basis, the authors illustrate how, in their view, the study of geometric transformations may be modified by shifting the emphasis toward geometric constructions, the practical implementation of student STEM projects, and the use of artificial intelligence technologies. The concluding section summarizes the material and outlines directions for further research on this topic, including the prospects for implementing the proposed theoretical model in educational practice.

The integration of Artificial Intelligence (AI) and Mixed Reality (MR) in education is revolutionizing the way learners interact with digital content. This paper explores how AI-powered adaptive learning systems, combined with Unreal Engine 5 (UE5), can enhance immersive educational experiences. UE5 provides high-fidelity virtual environments, enabling interactive and engaging simulations that respond dynamically to learners’ needs. AI algorithms analyze user interactions, preferences, and cognitive load to personalize content in real-time, fostering deeper engagement and improved knowledge retention. The study examines key applications, including gesture recognition, voice interaction, and real-time adaptation of virtual learning environments. Challenges such as optimization for real-time performance, ethical considerations, and user accessibility are also discussed. The findings highlight the potential of AI-driven MR experiences in reshaping education, making learning more accessible, interactive, and personalized.

Статията представя модел на урок по информационни технологии с интегрирани STEM елементи, реализиран чрез ролеви игри и изкуствен интелект (AI). Поставените задачи на учениците включват работа с AI чатботове, които симулират известни учени, за да развият изследователски умения и критично мислене. Описани са методика, инструменти, критерии за оценка, резултати и ограничения на модела.

Analysis of student test results is an important stage in the learning process. It provides valuable information about the effectiveness of the learning process, identifies problem areas and develops measures to address them. The problem of choosing a method for assessing the level of training, the quality of knowledge, skills and abilities is extremely important. In order to improve the efficiency of the educational process in the discipline "Programming", a comprehensive analysis of student test results was carried out. The study included both quantitative data analysis (average score, percentage of correct answers) and qualitative analysis of typical mistakes and difficulties faced by students. Five tests covering the entire spectrum of the C programming discipline were selected for the study. The use of the R programming language allowed for in-depth data analysis and a detailed picture of students’ learning achievements. The study proves that data analysis can be a powerful tool for improving the educational process. A detailed analysis of the test results of students allowed us to identify weaknesses in the curriculum and develop a model that can predict student performance. The analysis can be used to create more individualized curricula and improve the overall efficiency of the educational proces.

The maze as a didactic tool plays an important role in mathematics education because it provides a unique way to develop important skills. Solving mazes requires students to actively engage and apply various heuristic methods, which stimulates their creative thinking and ability to make effective decisions. This study focuses on the use of mazes and analyses the maze-solving strategies used by students aged 7 to 12 years to overcome them. Results from a study of 159 primary school students show that the most effective strategies are eliminating dead ends, simulating passage, and recording decisions. The study highlights the importance of promoting the development of students' own strategies and systematically recording their procedures as key elements for enriching mathematics education.