Функциональный потенциал текстовых задач в постсоветской дидактике начальной математики.
Functional Potential of Verbal Problems in Post–Soviet Didactics of Primary Mathematics

Summary/Abstract: With the changes of primary education aims and programs of teaching Mathematics the functions of text sums has changed. The development of functional potential has taken two trends: 1) widening of the functions of text sums and 2) changing of the priority of some functions. The main functions of verbal problems in post-soviet didactics of primary Mathematics were: to form ideas about mathematical notions and relations (notion of number, revealing the sense of arithmetic operations and their qualities, notions of equality and inequality, introduction of basic quantities and their qualities, etc.); to develop thinking (logical, functional, spatial, intuitive) effectively; to introduce techniques of mental operations (analysis, synthesis, comparison, etc.); to develop attention; to train different kinds of memory; to develop emotionally-volitionally; to broaden general outlook; to form skills in doing sums to form ideas about sums (compound elements, structure); to introduce the basics of doing sums (different devices, generalized methods); to accumulate definite experience correlating with the text, subject, scheme and symbolic models. Moreover, some scientists and methodologists single out additional functions of verbal problems: as a separate subject of research when schoolchildren understand the so-called research comparing sums (conditions, demands, decisions); their transformation (data, content changes); independent composing of sums; doing sums in other ways, using different methods; the mean of stimulating different kinds of activity (cognitive, motivating, creative); the function connected with the realization of the idea of active teaching of Mathematics: learning the notions of full value and mastering skills in practical, verbal, thinking activities specially organized by the teacher and produced by schoolchildren. Work with verbal problems offers wide possibilities; for the realization of a general cognition model the text sum is viewed as a model of some life situation, doing it is viewed as the process of cognition applying different methods including modeling; the way of teaching Mathematics; acquaintance with the mathematical language; understanding of Mathematics as a special language for a description definite of situations occurring in other sciences and practical activities; understanding that doing sums has developed from Mathematics supposing that conversion of these sums to the language of Mathematics and a reverse conversion from the language of Mathematics into the language of this field to which sums belong; notions are the main components of mathematical contents. The quality of schoolchildren learning is defined by the level of mathematical training therefore, in our opinion, the main function of verbal problems is formation of mathematical notions and relations. The significance of a particular mathematical notion determines the quantity and variety of verbal problems used in the process of teaching.

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