Psychological Analysis of the Means and Conditions for the Formation of Elementary Mathematical Representations in Preschoolers



The article aims to identify and describe the conditions as well as means of teaching that form the zone of proximal development when mastering elementary mathematical concepts (EMC) at an older preschool age (first of all, ideas about quantities: length, area, mass, volume, etc.). Also, the work analyzes the representation of these conditions and means of teaching in modern Russian preschool education programs developed on the basis of the Federal State Educational Standard for Preschool Education. The selection of programs was carried out on the basis of the PRISMA procedure, as a result of which 8 programs were selected out of 43 for analysis according to the selected criteria. Three types of the most common teaching tools were identified in situations when introducing new EMC: samples (visual or verbal instructions, rules), models (schematic representation of essential relations between objects) and symbols (symbolic representation of essential relations between objects). For the main learning conditions, the content and characteristics of those actions in which EMC data are assimilated were analyzed. It was shown that when organizing the formation of ideas about values in older preschoolers, it is psychologically more appropriate to select conditions that require the implementation of actions of selection by magnitude, indirect comparison, as well as measurement using conditional measures that is necessary in situations of representation of modeling or symbolization tools. The obtained results of the analysis of modern Russian preschool education programs indicate that most often they use only one tool — a visual sample or instruction, and the formation of ideas about the values is carried out solely on the basis of the action of direct comparison. The conducted research will make it possible to provide psychologically sound recommendations to teachers, educators and the administration of preschool educational institutions on the choice and implementation of EMC training programs.

General Information

Keywords: preschool education, elementary mathematical representations, teaching tools, sample, model, symbol

Journal rubric: Empirical and Experimental Research

Article type: scientific article


Funding. The study was supported by the Russian National Science Foundation grant no. 21-18-00584 “Comparative effectiveness of various means of forming elementary mathematical representations in preschool children and their impact on the development of cognitive skills”.

Received: 02.07.2021


For citation: Sidneva A.N., Plotnikova V.A., Solovieva Y., Lyutsko L.N. Psychological Analysis of the Means and Conditions for the Formation of Elementary Mathematical Representations in Preschoolers. Vestnik of Saint Petersburg University. Psychology, 2021. Vol. 11, no. 4, pp. 389–408. DOI: 10.21638/spbu16.2021.407. (In Russ., аbstr. in Engl.)


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Information About the Authors

Anastasiya N. Sidneva, PhD in Psychology, Senior researcher, Department of Educational psychology and Pedagogy, Faculty of Psychology, Lomonosov Moscow State University, Moscow, Russia, ORCID:, e-mail:

Valeriya A. Plotnikova, Student, Lomonosov Moscow State University, Moscow, Russia, ORCID:, e-mail:

Yulia Solovieva, PhD in Psychology, Director Master Program in Neuropsychological Diagnosis and rehabilitation, Faculty of Psychology, Autonomus University of Puebla, Puebla, Mexico, ORCID:, e-mail:

Lyudmila N. Lyutsko, PhD in Psychology, Associate Professor, Psychology and Education, Open University of Catalonia, Barcelona, Spain, ORCID:, e-mail:



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