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.

The paper presents an analysis of the current Bulgarian curricula in Mathematics, Physics and Astronomy, Chemistry and Environmental Protection, Biology and Health Education, Geography and Economics, Computer Modeling, and Computer Modeling and Information Technologies. Some discrepancies in the chronology of intersubject relationships were identified. The study can serve as a guideline for improving the work of the committees involved in the preparation of new curricula.

This article examines the challenges of teaching a text-based programming language (Python) at the beginning of the secondary school stage, when students enter with uneven prior preparation and varying levels of confidence in writing program code. The focus is on overcoming this imbalance by transferring principles from foreign language teaching and applying the P.A.N. (Planning, Active Learning, Non-stop Practice) methodological framework within a project-based environment. A pedagogical scenario is proposed for working with the list and dictionary data structures in the context of a student project titled “Nutrition Calculator”. Through a sequential “linguistic” introduction of concepts (lexicon, syntax, and semantics of code) , controlled practices, and spiral learning exercises, the article demonstrates how the transition to associative structures facilitates the modeling of real-world data, enhances code readability, and supports the formation of sustainable programming habits. Indicators of progress are discussed, including solution accuracy, code quality, and self-assessment of competencies.

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.