Methodical aspects of the formation of new competencies in students for the development of tasks for students within the framework of a modular approach
Authors: Perevoshckikova E. N. , Bychkov A. V. 
Published: March 2021

Introduction. The article highlights the methodical aspects of preparing a future teacher of mathematics for the development of assignments for students, presents various methods of involving students in the activity of developing assignments at the stage of formalization of a real situation, reveals the features of building an educational module aimed at formation of students' competencies in developing tasks for the formalization stage when solving tasks. The article reveals the stages of formations of actions that are part of the modeling, and drawing up adequate exercises on their basis.

Materials and Methods. The study is based on a systematic approach that allows us to consider the learning process as a system aimed at the methodological preparation of students for the design of tasks for the formation of schoolchildren's ability to model; the activity approach provides a phased formation of the actions that are part of the modeling; a modular approach that ensures the construction of an educational module for the formation of new competencies in the design of tasks in future mathematics teachers, aimed at the formation of modeling actions in schoolchildren; a competence-based approach, on the basis of which the methodical foundations of the formation of new competencies in students are identified.

Results. It was found that the process of methodical preparation of future teachers for the development of assignments for students should be built taking into account the specifics of future professional activities; the structure of practical lessons within the educational module should be built in accordance with the activity approach, which ensures the gradual formation of the actions that are part of the modeling. The organization of students' work on the analysis of the structure and content of tasks presented in the works of domestic and international studies, will allow students to be included in the work on identifying the composition of actions necessary to solve practice-oriented tasks, on the selection of situations, for the formalization of which mathematical knowledge and skills are needed to model, for constructing the plot of practice-oriented tasks. The methods of organizing the activities of students at motivational and content stages are highlighted, examples of constructed tasks are given.

Discussion and Conclusions. The article discusses the stages of identifying the actions that are part of the formalization in the process of analyzing real situations, formulates methods for including students in the activity of drawing up the conditions of the problem and formulating various questions for schoolchildren, allowing them to be included in the compilation of a meaningful and mathematical model of the situation presented in task. The conclusion formulated in the article is that in the process of forming new competencies in future mathematics teachers, it is necessary to organize their activities for the selection of a set of actions that make up the modeling and to drawing up a plot and questions for a practice-oriented task based on the selected actions.