Abstract
The proposed article presents the results of experimental data, through which it was revealed that teachers had the most difficulties: when compiling assignments for practice-oriented tasks in the context of the PISA-2021 program concept; when establishing formative and developing links between the algorithm for solving practice-oriented problems and thinking of the 21st century. A meaningful and comparative analysis of scientific papers and textbooks in mathematics made it possible to conclude that the methodological base for compiling educational tasks in the context of the formation and development of mathematical literacy among schoolchildren is not sufficiently developed. In this regard, this study is aimed at developing approaches to solving this modern topical problem. To solve this problem, the article proposes a cognitive method of teaching, a method of reducing this task to assessment-learning tasks in the context of the PISA-2021 program concept. The problem of identifying by teachers the influence of the stages of problem solving on the development of students' mathematical reasoning is considered. The paper developed tasks illustrating the methodology for applying cognitive-activity learning approaches that would contribute to the development of mathematical reasoning in schoolchildren. The use of such a technique in teaching involves the creation of a problem situation, independent solution of tasks, interpretation of the solution of the task. The proposed approach to designing tasks for problem situations can be effectively used in the preparation of new generation textbooks in the Republic of Kazakhstan.