INTERRELATION OF SIGN-SYMBOLICAL ACTIVITY AND UNDERSTANDING WHEN TRAINING IN MATHEMATICS
Journal Title: Дидактика математики: проблемы и исследования - Year 2017, Vol 1, Issue 46
Abstract
The article reveals the key elements of the educational systems of developing learning math. From the point of view of the authors, they include the categories "meaning" and "understanding", the interpretation of the "understanding" assimilation of mathematics is specified. Another important element of developing learning mathematics is the assimilation of the results of symbolic-symbolic activity by trainees. Three plans have been singled out for mastering the symbolism for the organization of the "understanding" assimilation of mathematics: syntactic, semantic and pragmatic. Examples are given of working with mathematical symbols on the example of studying the concept of a function. The operations of symbolic-symbolic activity are considered: modeling, coding, schematization and substitution as applied to the educational field of "mathematics". The methodological recommendations on the formation of all operations of symbolic-symbolic activity are given. The interrelation of understanding and symbolic-symbolic activity promotes the use of various forms of representing facts, phenomena, concepts; the formation of an image (scheme) of the studied object or phe-nomenon, the use of empirical experience. This is important in connection with the need to understand the formal specific symbolic language of mathematics, to apply the method of mathematical modeling and to understand the abstract content of mathematical knowledge. Understanding contributes to the comprehension of information, is associated with the development of a landmark and objective-real situation. In the process of developing this type of understanding, for example, the mathematical concept, the learner relies on this verbal definition, on his entire past experience. In particular, when introducing a mathematical concept, the requirement of simultaneous introduction of a verbal formulation of a definition, its formalized symbolic record and illustration (diagram, figure, model) is practically mandatory. The realization of the relationship between understanding and sign-symbolic activity ensures the improvement of the quality of mastering the mathematical material by the students, its conscious perception, structuring and memorization.
Authors and Affiliations
Eleonora Breitigam, Irina Kuleshova
Keywords
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