Keyword: «research skills»

The article is devoted to the problem of developing the skills of cognitive and research activities in primary school students in the lessons of the surrounding world, organizing more effective and productive activities of students in class and extracurricular activities and using various research tasks and modern teaching aids.

The article discusses the essence of research skills of primary school students in teaching mathematics, the components and directions of formation. Pedagogical methods are also presented, with the help of which research skills are formed. The inclusion of research methods in the educational process allows students not only to master subject competencies, but also to develop the ability to think analytically and independently search for solutions.

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.