Abstract
Objective: The main goals of school mathematical education are the development of intellectual students, the formation of thought qualities characteristic of mathematical activities and the acquisition of specific mathematical knowledge, the skills and skills necessary for practical application, and the formation of research skills. Theoretical Framework: The problem and purpose of the study is to identify the possibilities of problem-searching tasks in mathematics as a way for school students to develop research skills in updated content situations. Method: A method has been developed to build selected skills based on the corresponding system. It has been established that collective or group forms are most effective in creating problem situations in the classroom. Group or individual forms are most effective for testing a hypothesis and finding a solution to a problematic task. Result and Conclusion: The article also highlights the main blocks of research skills of schoolchildren and problem-search tasks in algebra and geometry developed for these blocks and methods for the formation of these skills. The basic principles for constructing a system of tasks focused on the formation of each block and each skill that we have chosen are determined. Research Implications: Implementation of these goals necessitates updating the system of school mathematical education, which is designed to ensure a harmonious combination of the interests of the individual and society. Originality/value: It contributed to the activation of students’ activities and their positive motivation for learning activities carried out in the classroom and at home.