In this short note we present the use of a form of binary symmetry in trigonometry in order to present naturally grouped trigonometric identities in a compact way. This approach is more conceptual and, in particular, replaces a tedious consideration of similar cases.

Анализирани са актуалните учебни програми по предметите математика, физика и астрономия, химия и опазване на околната среда, биология и здравно образование, география и икономика, компютърно моделиране, компютърно моделиране и информационни технологии. Набелязани са някои разминавания в междупредметни връзки. Проучването може да послужи като насока за подобряване на работата на комисиите по изготвяне на бъдещи нови учебни програми.

Статията разглежда предизвикателствата при преподаването на текстов програмен език (Python) в началото на гимназиалния етап, когато учениците постъпват с неравномерна предварителна подготовка и различна увереност при писане на програмен код. Фокусът е върху преодоляването на дисбаланса чрез трансфер на принципи от чуждоезиковото обучение и прилагане на методическата рамка П. А. Н. (планиране, активно учене, непрекъснати упражнения) в проектно базирана среда. Предлага се педагогически сценарий за работа със структурите от данни „списъци“ и „речници“ в контекста на ученически проект „Хранителен калкулатор“. Чрез последователно „езиково“ въвеждане на понятия (лексика, синтаксис, семантика на кода), контролирани практики и спираловидно упражняване се демонстрира как преходът към асоциативни структури улеснява моделирането на реални данни, повишава четливостта и подпомага формирането на устойчиви навици в програмирането. Обсъждат се индикатори за напредък: точност на решенията, качество на кода и самооценка на компетентностите.

This study explores the use of artificial intelligence (AI) tools to support personalized learning in classroom environments, as well as their integration into project-based learning activities implemented within STEM interest clubs in the context of the Bulgarian school system. The research aims to examine the attitudes of teachers and students toward AI-supported personalized learning and to evaluate its potential impact on students’ motivation and academic achievement. A quasi-experimental research design with pre-test and post-test measures was implemented between 2023 and 2025. Data were collected from 129 teachers, 86 students, and 42 parents through structured questionnaires, DigCompEdu-based self-assessment instruments, and classroom observations. The findings reveal an improvement in student achievement, increasing from 70% to 83% following the implementation of AI-supported personalized learning activities. Furthermore, 95% of students reported positive attitudes toward learning with AI-based tools, while 67% of teachers perceived AI chatbots as useful instructional support instruments. Nevertheless, nearly half of the teachers expressed a need for additional professional development, and most parents reported concerns regarding the use of AI tools without the supervision of a teacher or mentor. The results suggest that AI technologies can significantly support personalized learning when combined with clearly structured, pedagogically grounded learning activities and appropriate teacher guidance. However, the study is limited by the absence of a control group and its focus on a single national educational context. Future research should therefore involve larger and more diverse samples in order to further validate these findings.

Robots, along with AI and VR technologies, are among the most compelling tools in education. While technology providers highlight innovative learning opportunities, scholars discuss various ways of integrating robots, either within specific subjects such as informatics and programming, or for developing more general social skills. Numerous case studies demonstrate fragmented practices of using robots in schools and universities, overlooking their broader role in preparing new generations for the future of work. At the same time, many educational institutions explore practical and conceptual questions for providing training on robotics, ranging from investments in hardware and teacher training, to benefits for learning, future skills, teaching methodologies, among others. The objective of this paper is to investigate some of the key challenges and opportunities for integrating robots in educational settings. Based on a literature review, it critically examines the main issues educators face to understand how, why, and to what extent robots might be integrated in teaching and learning. Building on Bloom' s taxonomy, the purposes and opportunities of using robots in class are carefully evaluated, taking into consideration as well their impact on innovative teaching and assessment. A special section is dedicated to the development of educational robotics in Bulgaria. Findings of this study indicate that a more holistic perspective is needed to prepare students not only to work with robots, but also to design, evaluate, and critically analyse their role in the near future. The discussion evaluates more strategic views about using robots in education. The conclusion and future work sections outline the next steps in defining the new roles of robots in education.

Machine learning (ML) is being increasingly used in mathematics and computer science education, but the educational value of machine learning is not theorized or assessed evenly. The current studies focus on predictive accuracy, automation, and personalization, which raises the question of whether such applications are relevant to supporting higher-order disciplinary learning. This gap is filled by the current study, which is a qualitative systematic review based on the PRISMA framework of open-access and Q1/Q2 peer-reviewed articles published between 2014 and 2025. Through reflexive thematic analysis, sixteen studies were synthesised in four dimensions of analysis, namely application types, evaluation practices, cognitive support, and pedagogical integration. The results show that there is a systematic predominance of predictive analytics and performance-based assessment, but little overt scaffolding in problem solving, abstraction, and conceptual knowledge. Notably, ML systems are frequently used as back-end analytics and not as a learning-focused instructional tool. This review is novel in that it is a discipline-specific, cognition-based synthesis, shifting the ML paradigm from outcome prediction to pedagogically grounded cognitive scaffolding. Such a point of view provides practical design and assessment guidelines to narrow the divide between ML innovation and disciplinary learning in the education of mathematics and computer science.