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.

Babaeva, T.I., Gogoberidze, A.G., Solntseva, O.V. (2019). Comprehensive educational program of preschool education “Childhood” . St. Petersburg, Detstvo-Press Publ. (In Russian)

Bailey, D., Siegler, R., Geary, D. (2014). Early predictors of middle school fraction knowledge. Developmental Science. 17 (5), 775–785. https://doi.org/10.1111/desc.12155

Buneeva, R.N. (2019). The main educational program of preschool education “Kindergarten 2100”. Comprehensive educational programs for the development and upbringing of children of infant, early and preschool age. Publ. 3rd ed., rew. Moscow, Balass Publ. (In Russian)

D’iachenko, O.M. (1975). About the possibilities of using a schematized image by preschool children. PhD dissertation (Psychology) , Moscow, MGPU. (In Russian)

Davydov, V.V. (1962). Analysis of the structure of the account as a prerequisite for building a program in arithmetic. Moscow, Psihologicheskii institut RAO Publ. (In Russian)

Davydov, V.V., El’konin, D.B. (1966). Age-related opportunities for learning knowledge. Moscow: Prosveshchenie Publ. (In Russian)

Dienes, Z., Golding, E. (1975). Les Premiers Pas En Mathématique Logique et Jeux Logiques. Paris.

Duncan, G., Dowsett, C., Claessens, A., Magnuson, K., Huston, A., Klebanov, P., Japel, C., Pagani L. S., Feinstein L., Engel M., Brooks-Gunn J., Sexton H., Duckworth K. (2007) School readiness and later achievement. Developmental Psychology, 43 (6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428

El’konin, D.B. (1978). Psychology of the game. Moscow, Pedagogika Publ. (In Russian)

El’konin, D.B. (1989). Selected psychological works. Moscow, Pedagogika Publ. (In Russian)

Enik O.A., Bolotnikova O.P., Shchetinina V.V., Sidiakina E.A. (2015). Formation of the ability to manage their behavior in children aged 6–7 years. Sovremennye problemy nauki i obrazovaniia, 6, 356. https://science-education.ru/ru/article/view?id=22968 (accessed: 05.05.2021). (In Russian)

Gal’perin, P.Ia. (1985). Teaching methods and mental development of the child. Moscow, Moscow State University Press. (In Russian)

Gal’perin, P.Ia., Georgiev, L. S. (1960). On the question of the formation of initial mathematical concepts. In: Doklady APN RSFSR (pp. 31–66). (In Russian)

Göbel, S., Watson, S., Lervåg A., Hulme C. (2014). Children’s arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25 (3), 789–798. https://doi.org/10.1177/0956797613516471

Gutkina, N.I. (2009). Psychological readiness for school. 4th ed., rew., add. St. Petersburg, Piter Publ. (In Russian)

Gutkina, N.I. (2010). Psychological readiness for school in the context of the problem of continuity between preschool and school education. Psikhologicheskaia nauka i obrazovanie, 15 (3), 106–115. (In Russian)

Il’enkov, E.V. (1991). Philosophy and culture. Moscow, Politizdat Publ., 381–387. (In Russian)

Jordan, N., Kaplan, D., Ramineni, C., Locuniak, M. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45 (3), 850–867. https://doi.org/10.1037/a0014939

Karabanova, O.A. (2005). Developmental psychology. Lecture notes. Moscow: Airis-press. (In Russian)

Khiltunen, E.A., Borisova, O.F., Mikhailova, V.V. (2014). Approximate basic educational program of preschool education “Kindergarten according to the Montessori system”. Moscow, Natsional’noe obrazovanie Publ. (In Russian)

Kirichek, K.A. (2018). Formation of ideas about the area among preschoolers. Sovremennoe doshkol’noe obrazovanie. Teoriia i praktika, 2, 14–21. https://cyberleninka.ru/article/n/formirovanie-predstavleniy-o-ploschadi-u-doshkolnikov (accessed: 01.06.2021). (In Russian)

Klibanoff, R., Levine, S., Huttenlocher, J., Vasilyeva M., Hedges L. (2006). Preschool children’s mathematical knowledge: the effect of teacher “math talk”. Developmental Psychology, 42 (1), 59–69. https://doi.org/10.1037/0012-1649.42.1.59

Korepanova, M.V., Kozlova, S.A., Pronina, O.V. (2019). My math. Textbook on the cognitive development of children 5–7 (8) years old: In 3 parts. Moscow, Balass Publ. (In Russian)

Kudriavtsev, V.T. (2016). The main educational program of preschool education “Paths” . Moscow, Ventana-Graf Publ. (In Russian)

Leontiev, A.N. (2000). Lectures on general psychology. Moscow, Smysl Publ. (In Russian)

Leslie, A. (1987) Pretense and representation: The origins of “theory of mind”. Psychological Review, 94 (4), 421–426. https://doi.org/10.1037/0033-295X.94.4.412

Lykova, I.A. (2011). About the originality of the picture of the world of a preschool child. Pedagogika iskusstva, 4, 1–10. http://www.art-education.ru/electronic-journal/o-svoeobrazii-kartiny-mira-rebenka-doshkolnika (accessed: 01.06.2021). (In Russian)

Mikhailova, Z.A, Poliakova, M.N., Ivchenko, T.A., Berezina, T.A., Nikonova, N.O., Rimashevskaia, L. S. (2017). Educational field “Cognitive development” (Methodical set of the program “Childhood”): educational and methodical manual. St. Petersburg, Detstvo-Press Publ. (In Russian)

Obukhova, L.F. (1972). Stages of development of children’s thinking. Moscow: MGU im. M.V.Lomonosova. (In Russian)

Paramonova, L.A. (2018). Origins: A comprehensive educational program of preschool education. 6th ed. rew. Moscow, TTs Sfera Publ. (In Russian)

Peterson, L.G., Kochemasova E.E. (2018). Practical mathematics course for preschoolers: methodological recommendations. Parts 1, 2. Moscow, BINOM. Laboratoriia znanii Publ. (In Russian)

Peterson, L.G., Lykova I.A. (2019). Comprehensive educational program of preschool education “World of discoveries” . 5th ed., rew. and add. Moscow, BINOM. Laboratoriia znanii Publ. (In Russian)

Piaget, Zh. (1994). Favourite psychological works. Moscow. (In Russian)

Podd’iakov, N.N. (2010). Mental development and self-development of a child: from birth to six years. St. Petersburg, Rech’ Publ. (In Russian)

Pomoraeva, I.A., Pozina, V.A. (2020). Formation of elementary mathematical representations: Lesson notes: 6–7 years. 2nd ed., corr. and add. Moscow, Mozaika-Sintez Publ. (In Russian)

Ritchie, S., Bates, T. (2013). Enduring links from childhood mathematics and reading achieve- ment to adult socioeconomic status. Psychological Science, 24 (7), 1301–1308. https://doi.org/10.1177/0956797612466268

Rose, H. (2006). Do gains in test scores explain labor market outcomes? Economics of Education Review, 25 (4), 430–446. https://doi.org/10.1016/j.econedurev.2005.07.005

Salmina, N.G. (1988). Sign and symbol in training. Moscow State University Press. (In Russian)

Sarama, J., Clements, D. (2009). Building blocks and cognitive building blocks: Playing to know the world mathematically. American Journal of Play, 1 (3), 313–337.

Schneider, M., Grabner, R., Paetsch, J. (2009) Mental number line, number line estimation, and mathematical achievement: Their interrelations in Grades 5 and 6. Journal of Educational Psychology, 101 (2), 359–372. https://doi.org/10.1037/a0013840

Shapovalenko, I.V. (2004). Developmental psychology. Moscow. (In Russian)

Shevelev, K.V. (2019). Partial general education program of preschool education “Formation of elementary mathematical representations in preschoolers” . Moscow, Binom. Laboratoriia znanii Publ. (In Russian)

Sultanova, M.N. (2021). Math before school: a guide for children 6–7 years old. In 2 parts. 5th ed., stereo. Moscow, Ventana-Graf Publ. (In Russian)

Taruntaeva, T.V., Alieva, T.I. (2015). The development of mathematical concepts in preschoolers. Moscow, TTs Sfera Publ. (In Russian)

Usova, A.P. (1981). Kindergarten education. Ed. 3rd, corr. Moscow, Prosveshchenie Publ. (In Russian)

Venger L.A., Kholmovskaia V.V. (1978). Diagnostics of intellectual development of preschoolers. Moscow, Pedagogika Publ. (In Russian)

Venger, L.A. (1986). Development of cognitive abilities in the process of preschool education. Moscow, Pedagogika Publ. (In Russian)

Venger, L.A., Slobodchikov V.I., El’konin D.B. (1988). Problems of child psychology and scientific creativity of D.B.Elkonin. Voprosy psikhologii, 3, 20–29. (In Russian)

Veraksa, A.N., Aslanova, M. S., Bukhalenkova, D.A., Veraksa, N.E., Liutsko, L.N. (2020). Assessing the effectiveness of differentiated instructional approaches for teaching math to preschoolers with different levels of executive functions. Education Science, 10 (7), 181. https://doi.org/10.3390/educsci10070181

Veraksa, A.N., Gorovaia, A.E., Kisel’, A.V. (2014). The possibilities of using symbolic and symbolic means in teaching preschoolers (on the example of mastering the rainbow phenomenon). Psikhologicheskaia nauka i obrazovanie, 6 (2), 19–34. (In Russian) https://doi.org/10.17759/psyedu.2014060202

Veraksa, N.E., Komarova, T. S., Dorofeeva, E.M. (2019). “From birth to school”. Innovative preschool education program. Ed. 5th (innovative), corr. and add. Moscow, Mozaika-Sintez Publ. (In Russian)

Vygotskii, L. S. (1983). History of the development of higher mental functions. Sobr. soch.: In 6 vols. Vol. 3 (pp. 132–133). Moscow, Pedagogika Publ. (In Russian)

Vygotskii, L. S. (2004). Psychology of child development. Moscow, Smysl Publ., Eksmo Publ. (In Russian)

Watts, T., Duncan, G., Clements, D., Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89 (2), 539–555. https://doi.org/10.1111/cdev.12713

Watts, T., Duncan G., Siegler, R., Davis-Kean, P. (2014). What’s past is prologue: relations between early mathematics knowledge and high school achievement. Educational Researcher, 43 (7), 352–360. https://doi.org/10.3102/0013189X14553660

Zaporozhets, A.V. (1986). Selected psychological works. Moscow, Pedagogika Publ. (In Russian)