The Quality of Mathematical Education in the Context of Semiotics

Abstract

The content of mathematics education takes on a specific form of existence in a variety of shellsverbal and non-verbal, which are created with the help of sign and symbol means of a different nature. The language is the main means. In teaching signs and symbols perform a substitutional, cognitive, and communicative function; build up an informational basis of students' learning activities. In mastering learning contents signs and symbols are the subject of study, and an instrument of knowledge. Operating sign and symbolic means is a necessary component of students' learning activities, which is directly related to semiosis in students' training activities and enrichment of the conceptual structures possessed and acquired by the students. Mastering different means of fixing the training material contents and every kind of sign and symbolic activity, namely-substitution, coding (decoding), schematization, and modeling is the basis of the information culture and a prerequisite for the development of each student's personality. The selection and use of sign and symbol means should be made on the basis of the analysis of conflicts between the logical and visual. Such conflicts may have not only an objective, historically conditioned character. Most often they are generated by subjective factors-the advent of the students' misunderstanding of the contents of the material and the negative attitudes to the possibility to understand the content, inability to place content in different sign and symbolic shell, the presence of adhesions (but not a dialectical unity) of content and form which were formed in the prior learning students' experience, etc. Adequate conditions for the training and development of all students in the course of mathematics acquisition are created through a comprehensive, systematic and activity approaches to the use of verbal and non-verbal sign and symbol means. Thus, the new goal in teaching mathematics is the ensuring of the two processes unity: the formation of subject knowledge, skills and abilities, on the one hand, and the experience of independent sign and symbolic activities of students, on the other hand.

Didactic analytics as a component of professional training for math teachers

“…На цьому рівні здійснюється аналіз знаково-символічних засобів (ЗСЗ) фіксації у зовнішньму плані навчального математичного змісту, які використано в підручнику та інших засобах навчання. Особливості ЗСЗ (вербальних і невербальних) докладно висвітлено нами в ряді публікацій [8][9][10].…”

Why Do Students Make Errors when Solving Problem in Semiotic Representation?

“…In comparison, Tarasenkova and Kovalenko expound that semiotics and semantics of mathematical tasks arranged in teaching mathematics for elementary school students education [10]. Tarasenkova, notwithstanding, reveals a new aim in teaching mathematics is ensuring of the unity of the two processes: first the formation of subject knowledge, skills, and abilities, both of which mark experience independently and the students' symbolic activities [11]. In addition, semiotic components could also appear in generalization pattern activity include gesture, words, and symbols [12].…”

Specifications of the University Course "Methods of Teaching Mathematics in Higher Education Institutions"

“…Under the educational reform in Ukraine one of the main objectives of higher education is to ensure providing special training for students, cultivate their personal qualities for them to become qualified and highly skilled experts who know how to work creatively [1][2][3][4][5][6][7][8][9][10].…”