Veraksa Aleksander N.

Background. The development of psychological science in the context of educational practice stimulates researchers to seek for a scientific explanation of phenomena that are often used without proper justification. The article is devoted to the analysis of “math anxiety” in an interdisciplinary context. 
In 2000, the All-Russian conference “Mathematics and Society. Mathematics education at the turn of the century”, organized by academician V.A. Sadovnichy took place in Dubna. At the conference V.A. Sadovnichy convincingly substantiated the growing role of mathematics in the 21st century and the importance of its results and applications not only for specialists, but also in all spheres of society — from theoretical physics and computer technology to the humanities and art history. In this regard, V.A. Sadovnichy pointed out the danger and inadmissibility of pseudo-scientific sophistications and pseudo-pedagogical speculations in the field of the meaning and difficulty of mathematics as a subject of teaching and problems related to it. We will look at one of these pseudoscientific concepts, the so-called “math anxiety,” in this article.
Objective. The purpose of this article is to systematize and analyze data on “math anxiety” and critically comprehend this phenomenon. 
Method. The methodological basis of the article is the cultural-historical, as well as activity-based approaches, developed in line with leading Russian psychology schools of L.S. Vygotsky, A.N. Leontyev, A.R. Luria, P. Ya. Galperin, and others. 
Results. Developing the ideas of cultural-historical psychology and activity theory in the context of education, Russian psychologists emphasized the special importance of research focused on practical problems related to learning. At the same time, referring to “math anxiety” can distract researchers from the real problems in teaching mathematics and other subjects. The joint efforts of psychologists, teachers, psychiatrists, neurologists and other specialists are important for the successful solution of educational problems. The development of issues of the content and methods of mathematics education, a psychological analysis of the difficulties experienced by both children and teachers, will contribute both to the development of psychological science and to the strengthening of its connections with educational practice.

Background. The study of the psychological aspects of the introduction of older preschoolers into mathematics is relevant due to the widespread early teaching of elementary mathematical concepts. This practice often not only does not help, but may even harm the further development of the child, since the methods used for this do not take into account the specifics of both the age-psychological characteristics of the preschooler, and the results of psychological research in the field of content, methods and means applied to formation of initial mathematical representations.

Objectives. The aim of the study was to analyze the comparative effectiveness of different types of sign-symbolic mediation in the formation of initial mathematical representations in older preschoolers with different levels of development of regulatory functions.

Study Participants. The study sample included 133 older preschoolers (6–7 years old).

Methods. To assess the level of development of regulatory functions, the NEPSY-II subtests, the “The Dimensional Change Card Sort” technique and L.A.Wenger’s “Schematization” technique were used. To assess the level of development of methodological concepts, a set of tasks was used for each of the three values — length, area, and volume.

Results. Significant differences were found between the increase in mathematical skills of children who studied using both sign and symbolic means as compared to the children fr om the control group. There were no significant differences in this increase between children who were trained with the help of model tools and the control group. In groups wh ere symbolic means or sign means were used, children with different levels of regulation learned with equal efficiency, but the level of regulation turned out to be critical when learning according to the most complex programme — using model tools.

Conclusions. The effectiveness of mastering the initial mathematical concepts in older preschoolers is primarily due to the nature of the learning content, which should ensure the rationality of children’s actions. However, the more complex this content is and the more complex symbolic means are used in teaching, the more requirements are placed on the level of development of children’s regulatory functions.