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The knowledge and skills a student needs in order to perform well on mathematics competitions are usually more and at a higher level compared to school mathematics. But school mathematics, and particularly perfecting the main properties, theorems, lemmas and postulates from the school curriculum, as well as when and how to apply them, can significantly impact the students’ performance on mathematics competitions. This paper discusses a specific example of a problem given on a team selection test for selecting a national team for a regional competition, and the mistakes from the school mathematics which the tested students made, without looking for reasons or explanations of these mistakes. [ABSTRACT FROM AUTHOR]

Тhe paper includes problems from the team selection tests for the national team for JBMO 2023, as well as model solutions and short comments on the performance of the contestants. The materials included can be useful for the groups for preparation for junior high school math contests. [ABSTRACT FROM AUTHOR]

The paper describes activities for developing the notion of symmetries. The activities were performed by a group of children between the ages of 5 and 9 and a parent of two of them. Through play and active work the group explores symmetries in sports, architecture, biology, language, music and mathematics. The activities were carried out outdoors in nature. Ideas for complementary activities with computers are presented. As a result the children demonstrate the ability to recognize symmetries in areas and situations different from the ones set in the activities they performed. This proves the main thesis of the paper: the nature of mathematics can be captured successfully in an informal environment at any age. [ABSTRACT FROM AUTHOR]

The paper discusses a traditionally construed as problematic aspect of Kant's philosophy of mathematics: the place and importance of nonEuclidean geometry in the structure of mathematics. Kant's conception of pure intuition in mathematics is usually considered incompatible with the existence of mathematics, leaving no place for the latter. In this paper I argue that we can find a place for them, provided we know where to look. Of key importance in this respect is the concept of symbolic construction, which Kant employs in his discussion of algebra. The concept makes it possible to sidestep the limitations related to the requirement of constructibility in pure intuition. The development of Hilbert's formalism in the philosophy of mathematics can be seen as a continuation of this move that makes manifest its full potential, which was not, and even could not, be realized by Kant. [ABSTRACT FROM AUTHOR]

The paper contains the team selection tests for the team of Bulgaria at the Junior Balkan Math Olympiad 2021 as well as an overview of the team results. The included materials can be useful for the math contest preparation classes in Junior high school. [ABSTRACT FROM AUTHOR]

The paper examines questions that are essential to the philosophical interpretation of modern logic. The enormous number of different non-classical logics leads some philosophers to doubt the possibility of classifying them. Our objective requires a classification corresponding to the philosophical interpretation and importance of the systems rather than to their formal technical elements. This will not be a classification in the precise sense of the word, but a “typologization”, since a system may have different interpretations and the demarcation will not be strictly exclusive. I propose the following “typologization” of logics, corresponding to their philosophical evaluation (this is a “typologization”, and maybe even a classification, of the basic, most important and crucial philosophical-methodological interpretations of logical systems): “Logical systems serving as bases for a mathematical theory”; “Logical systems – attempts for the explication of logical inference”; “Logical systems expressing epistemological aspects. Logical systems related to ontological aspects”; “Logical systems as pure mathematical models without philosophical justification”; “Applied logic”; “Quasi-logical studies of language”. [ABSTRACT FROM AUTHOR]

The present paper analyzes the State Educational Standards, the State Educational Requirements and the school programs in Mathematics and Technologies and entrepreneurship in the 5th grade with respect to the real possibilities for integrating knowledge in Mathematics and Technologies and entrepreneurship. A concrete option for implementing an integrated learning process is proposed. [ABSTRACT FROM AUTHOR]

The paper presents the experimental mathematics as a problem environment for students’ research activities. Such an area is available to students who have different level of mathematical competence. The organization of students’ research activities in experimental mathematics environment is a basis for their preparation for work in the form “Science 2.0”. Students will learn the following main characteristics of Science 2.0: working on a project, participation in crowd-sourcing, research network, computer supported research. [ABSTRACT FROM AUTHOR]

The paper is dedicated to a practical problem in mathematics. A didactic scenario is proposed for a mathematical class lesson, based on a multiple representation applying dynamic drawings and spreadsheets. [ABSTRACT FROM AUTHOR]

The paper presents the idea of parallel formation of skills for didactic design in electronic and traditional form. A conceptual model is proposed to realize this idea in a methodological course for future teachers. Some concrete examples of platforms are shown to describe teaching scenarios and software to create didactic materials for mathematical teaching, which can be used in applying the described model. [ABSTRACT FROM AUTHOR]

The paper is dedicated to the Twelfth International Olympiad in Linguistics. The problems of the Olympiad are presented and their methodological solutions are proposed. [ABSTRACT FROM AUTHOR]