INFO-2024 CONTEST
Mathematical concepts and algorithms are present in the basic and advanced informatics courses of primary and secondary schools, in the tasks of the Unified State Exam and tasks of Olympiads and competitions in programming. the content lines of mathematics and informatics overlap in many ways, mainly in the sections of discrete mathematics: mathematical logic, graph theory, combinatorics, number systems, modular arithmetic, etc. the article provides examples of mathematical tasks that are useful when studying various sections of the informatics course. the use of semi-invariants and invariants in solving mathematical tasks and verifying programs is considered. Examples of tasks on non-traditional number systems that are used in creating hardware and software for personal computers are given. the issues of remainder arithmetic related to modern information encryption standards are discussed. Most of the tasks included in the article are created for well-prepared and motivated students. they were proposed by the authors at various Olympiads and competitions in informatics for schoolchildren in the Yaroslavl region.
The article considers the capabilities of spreadsheet processors in the context of developing students' analytical competency. It defines analytical competency and identifies its components (abstract-logical, critical, systemic, problematic, figurative, algorithmic, creative, associative, and reflexive). It considers the role of Olympiad tasks in the educational process as a means of developing analytical critical thinking, developing data handling skills, and the ability to make informed decisions. the author's tasks on the theme "Spreadsheet processors" are provided for conducting the Olympiad for both high school students and junior university students. It is concluded that developing students' analytical thinking is a complex problem that includes increasing the abstractness of thinking, developing logic, developing a creative approach to solving problems, etc.
The article provides a rationale for introducing schoolchildren to voxel modeling technology, describes the possibility of using the MagicaVoxel modeling environment to teach schoolchildren the basics of voxel modeling during extracurricular activities at school and during classes at the Quantorium children's technology parks, and describes several original practical works on voxel modeling, covering the most commonly used tools of the modeling environment. Methodological developments in the form of practical works will be useful for teachers teaching modeling at school, for conducting classes using the MagicaVoxel voxel modeling environment from 2nd to 11th grade. Teaching the basics of voxel modeling based on this methodological development will help students develop skills in three-dimensional voxel modeling, and the ability to apply information technology to solve creative problems.
The article discusses the use of virtual geocaching technology in extracurricular activities in informatics. Virtual geocaching is an educational technology that is a game in which students travel around the virtual world, learn interesting facts about cities and countries, complete applied tasks and receive geographic coordinates of new "treasures" for the correct solution. unusual for pedagogical practice, the virtual geocaching technology helps to activate the educational and cognitive activities of students who actively respond to the use of new digital tools in learning. the article presents the author's course on extracurricular activities "Around the world in 34 hours" aimed at developing meta-subject competencies of 9th grade students. the presented methodological recommendations, author's approaches to organizing the game, constructing geolocations, as well as the proposed tasks can be used by teachers of different subjects when planning and organizing extracurricular activities.
TEACHING PRACTICES
The multilayer model of computer is its representation as a sequence of layers (levels): from physical encoding of the values 0 and 1 to application software. Each layer has a specific meaning for forming a complete picture of knowledge. In the article the traditionally distinguished layers of the model are compared with the content of the established at the school informatics course. It is shown that in the program of advanced course for grades 10–11 the material that is to one degree or another related to each of the layers can be found. however, in light of the urgent need for domestically produced computing equipment and its element base, the proportion of studying some layers should be increased. based on the analysis of the federal work programs for the school informatics course, specific recommendations are provided on possible improvement of the discipline content. the article will be useful for teachers, as well as for pupils interested in computers and wishing to connect with them future specialty.
The article actualizes the necessity of using interactive teaching methods when studying the theme "Elements of algebra of logic" in the basic informatics course of secondary school. Interactive teaching methods are considered as a means of activating the cognitive activity of students, motivating them to learn, creating conditions for involving students in studying the subject. The choice of the theme is due to its importance for the formation of universal learning actions that are components of logical thinking and are necessary for studying other themes of the informatics course, as well as other subjects. The purpose of this article was to describe the methodological aspects of using interactive teaching methods aimed at improving the level of logical thinking of students when studying the theme "Elements of algebra of logic". The possibilities of specific teaching methods in the formation of individual components of logical thinking are considered. Methodological recommendations for the use of interactive teaching methods in the process of conducting one of the lessons on the theme "Elements of algebra of logic" are presented.
FINAL CERTIFICATION IN INFORMATICS
The article presents methodological approaches to solving the data analysis problem included in the Unified State Exam (USE) in informatics since 2025. It is shown that for any shape of clusters, it is possible to separate them by a set of straight lines parallel to the coordinate axes or by inclined lines. an accelerated algorithm for finding cluster centers is proposed, which allows to significantly reduce the computation time and thus to solve the problem for data sets containing more than 10,000 points in an acceptable time. complex versions of the problem, as compared with the demonstration version of the control and measuring materials, are considered: the presence of anomalies that should be ignored when searching for the cluster center, and clusters of complex shape. a comparison of various approaches to dividing data into clusters, including the dbscan algorithm and the k-means method, is carried out.
The article proposes methods for solving some tasks from the computer based Unified State Exam in informatics using spreadsheets as an alternative to the traditionally accepted method of solving problems by coding. In particular, the tasks 13, 23, 26 presented in the 2025 demo version are considered.
Due to the fact that it is not always possible to allocate a sufficient number of hours to study the theme "programming" within the school course, and also due to the fact that not all students have time to deeply master the skills of coding, the option of solving tasks using spreadsheet processors looks very realistic and attractive. It should be noted that in many cases this method allows you to solve tasks quite quickly and accurately, since spreadsheets allow you to visually present the data being processed and it is easier for students to navigate them and find the required answer.
The article may be useful for students planning to take computer based Unified State Exam in informatics, informatics teachers to prepare students for the exam, as well as for studying the theme "spreadsheets" in a school informatics course.
The solutions to the problems in the article are implemented using the LibreOffice calc electronic processor. additional materials are attached to the article in the form of files with tasks solutions in the format of the specified spreadsheets.