Keyword: «mathematics teaching methods»

A pressing problem in modern education, confirmed by both official data and local studies, is schoolchildren's inability to explore various problem-solving approaches, evaluate intermediate results, and select optimal solutions. The aim of this study is to demonstrate that engaging high school students in well-organized mathematical dialogue based on solving a series of modified tasks helps solve this problem. By task modification, we mean a partial change in the task data or the addition of new data, leading to qualitative changes in the solution process, increasing the number of solution options, or leading to the possibility of no solution. By solving and analyzing such problem series, students learn to identify patterns and build mathematical models. The empirical study, conducted during the 2024-2025 academic year at the Natural Sciences Lyceum of Peter the Great St. Petersburg Polytechnic University, involved the systematic inclusion of modified tasks series in the educational process. Sixty-four 10th-grade students participated in the experiment. Classes were conducted using both traditional methods and modified and dialogue-based learning. Testing, workbook analysis, and observation of student activity in class were used to evaluate the effectiveness of this approach. Logarithmic equations and inequalities formed the basis for the developed learning materials. The article provides an example of a series of tasks resulting from the modification of a simple example. Methods for gradually increasing the complexity of modified tasks, allowing for differentiated instruction, are discussed. The study demonstrates that dialogue-based learning, incorporating elements of task modification, leads to a deeper understanding of the material and promotes the development of students' research skills. The theoretical significance of the study is determined by the development of methods in which work with modified tasks is transformed from a discrete element of in-depth training into an integrated educational model implemented throughout the entire mathematics learning process. The study clarifies the role and methods of organizing educational dialogue in solving non-standard problems, demonstrating its importance for finding and reasoning about solutions. Since the implementation of the proposed methodology improves the quality of schoolchildren's mathematical training by purposefully developing their ability to solve not only standard problems but also creative, research-based ones, this study has practical significance.

This article substantiates the relevance of developing multi-level assignments in probability theory for high school students based on a survey of teachers, students, and pupils. The main challenges identified include the uneven level of student preparation, a lack of practical assignments, and low motivation. The content of the «Probability Theory» section for grades 10–11 is analyzed, and problem types are identified. A method for generating problems using neural networks is proposed, and examples of varying difficulty levels are provided.

This article addresses the common problem of declining mathematical literacy in schoolchildren in the context of the active use of digital technologies. We also analyze the key factors influencing the decline in mathematical thinking and examine the most common causes of mathematical literacy. We also propose strategies for addressing this situation.

This article presents the results of the development and testing of an online course on solving percentage problems for students in grades 5–11, created using the Stepik platform. As part of the pedagogical experiment, the academic performance of the control group (instruction using traditional methods) and the experimental group (using blended learning with the author's e-course) was compared.