From the experience of working on the formation of the ability to structure educational material in mathematical disciplines
One of the learning outcomes is the formation of competencies related to the ability of students to solve professional problems based on knowledge of the basic laws of mathematical disciplines. This is ensured by the presence of a system knowledge base in mathematics. The authors consider the structuring of educational material to be a necessary condition for students to master the basic mathematical concepts, theorems and formulas. The article reveals the concepts of "structuring educational material", "structuring educational material in mathematical disciplines", lists the main goals of structuring educational material (development of a rational and economical structure of educational material; construction of educational material, taking into account the possibility of introducing elements of educational and cognitive activity). The authors formulated and revealed the main tasks of forming the skills to structure educational mathematical material (the ability to structure the definition of a mathematical object; the ability to structure mathematical statements, highlighting conditions, conclusions, etc.; the ability to structure mathematical material expressed in formulas; the ability to structure mathematical material necessary for solving applied problems). The article presents the following examples of tasks for the formation of skills for structuring educational material: establishing reciprocal relations of necessity and sufficiency between a concept and its features; construction of various forms of judgments, including necessary and sufficient features and their analysis; definition of concepts through genus and specific difference; analysis of species differences of objects and selection of requirements - the basis for building a classification; transfer of knowledge to a new situation, etc. Examples of assignments for the implementation of educational goals by structuring the educational material and the actions of students disclosed through the system (familiarization, understanding, application, analysis, synthesis, evaluation) are also given.