Effectiveness of Different Teaching Resources for Forming the Concept of Magnitude in Older Preschoolers with Varied Levels of Executive Functions.

Background: Studies have shown the great importance of early mathematical development as a predictor of subsequent success, which poses the question of how to organize preschool mathematical education with a view to the children's age characteristics, including their cognitive development. In other words, mathematical concepts and actions should be formed with the help of teaching resources appropriate to the child's development. Objective: To determine the effectiveness of three teaching resources (examples, models, and symbols) in formation of the concept of magnitude in older preschoolers (ages 6-7) with different levels of executive function. Design: Four training programs (with 15 twenty-minute lessons each) were developed and conducted in a formative experiment for older preschoolers with different levels of development of executive functions. The lessons addressed the concept of magnitude (length, area, volume), using different types of teaching resources: exemplars (in traditional and game variants), models, and symbols. The total sample of 116 subjects (44% boys) was divided into 4 groups for each of the programs, plus a control group in which no sessions were conducted. The groups were equalized according to the initial level of development of concepts of magnitude and the level of development of executive functions. Results: There was a statistically significant increase in the quality of mastery of the concept of magnitude in three experimental groups ("symbolic," "traditional," and "traditional with imaginary characters") compared with the control group. The formative effect of the "model-building" program showed no significant differences from the effect of the child's natural development (the control group). We also showed that children with a low level of regulation learned mathematical concepts more effectively with the "symbolic" program; children with a medium level of regulation with the "symbolic" and any variant of the "traditional" program; and children with a high level of regulation with the "symbolic" and "model-building" programs. Conclusion: The findings underline the importance of both the type of teaching resources used and the level of development of voluntary regulation, when teaching mathematics to preschoolers.