Previous studies have found that the development of mathematical abilities, along with the development of executive functions, predict students’ subsequent academic performance. The present study aimed to assess the effectiveness of teaching the concept of area to preschool children with different levels of cognitive processes (CP) including executive functions and short-term memory. The experiment introduced the concept by using three different instructional approaches: traditional, contextual, and modeling. The sample included 100 children aged 6–7 years (M = 6.5 years), of whom 43% were boys. Each experimental condition included children with low, middle, and high levels of CP, as determined based on the NEPSY-II subtests. The children with low CP levels showed higher results in assimilating the notion of area after being taught using the contextual approach. In contrast, children with high CP levels showed a higher mastery of the concept of area following the use of the modeling approach. The results suggest the importance of CP development in building ways of mastering mathematical content. This contributes to choosing the optimal path of teaching mathematics for preschoolers, taking into account the development of their cognitive processes to improve their academic performance.

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 e" ectiveness of three teaching resources (examples, models, and symbols) in formation of the concept of magnitude in older preschoolers (ages 6–7) with di" erent 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 di" erent levels of development of executive functions. ! e lessons addressed the concept of magnitude (length, area, volume), using di" erent types of teaching resources: exemplars (in traditional and game variants), models, and symbols. ! e 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. ! e groups were equalized according to the initial level of development of concepts of magnitude and the level of development of executive functions. Results. ! ere was a statistically signi# cant 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. ! e formative e" ect of the “model-building” program showed no signi# cant di" erences from the e" ect of the child’s natural development (the control group). We also showed that children with a low level of regulation learned mathematical concepts more e" ectively 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. ! e # ndings underline the importance of both the type of teaching resources used and the level of development of voluntary regulation, when teaching mathematics to preschoolers.

Background. Relevance of this study is determined by the increased interest in mathematical education in recent years. Teachers and researchers are concerned about the conditions and means of developing mathematical education. Along with this, there is no consensus on what constitutes mathematical abilities, what is their structure and development. Objective. Th e aim of this study is to compare the development of mathematical skills of fi rst-graders in diff erent educational programs and to identify specifi c to each program features. Sample. Th e study sample consisted of 434 fi rst-graders of Moscow schools (54.8% of boys), among which: 37.1% of fi rst-graders learn programs of increased complexity, 44% — traditional programs, 18.9% — developmental education program. Methods. An author’s set of tasks was developed to diagnose the mathematical skills of fi rst-graders in this study. It included “classical” tasks children must perform regardless of the training program and “specifi c” tasks that test the awareness of meaning of the mathematical actions performed. Results. Th e analysis showed that most of the classical mathematical skills are not related to the character of the program and it developed by all fi rst-graders in the course of training. However, complex arithmetic skills (working with twodigit numbers and searching for an unknown sum component) developed more eff ectively in programs of increased complexity. Specifi c skills related to reasonable action with a number (tasks for a number line or measurement) showed an ambiguous development dynamic. Conclusion. Th is study allows us to form a hypothesis that the selecting students for programs aff ects only the rate of development of a number of classical mathematical skills. Whereas specifi c skills are more dependent on the content of the program. It requires further study.

Relevance. There is growing interest in the market for educational applications in Russia. A significant number of these are aimed at preschoolers. Although much is known about the key features of preschoolers learning ( due to the cultural-historical approach as well ), there is still little research analyzing whether these features are taken into account in the design and methodology of mobile applications available on the market. Objective. To analyze math apps for preschoolers from the standpoint of cultural-historical theory. Design. We went to Google Play and AppStore with the query “mathematics for preschoolers” and selected four apps that are most popular among users and recommended by experts. We analyzed them according to the following criteria: (1) adult engagement, (2) quality of the child’s interactions with the application content, (3) types of content, (4) forms of material presentation and the correspondence of the method of number concept formation to the preschool age specifics, (5) the quality of mathematical content, that ensures the principle of continuity with the primary school curriculum. Results. None of the apps was based on developmental learning methodology, and none used opportunities for involving an adult in a dialogue and joint activities with a child. Not all the apps considered the characteristics of the age group in their design of content and the child’s interactions with the app. Only one of the apps provides continuity with the primary school curriculum. Conclusions. Scientific knowledge and practical achievements in the field of mathematical education for preschoolers are not always reflected even in the most popular programs. Our analysis allows to draw the attention of parents, teachers, and developers to important design elements that could make an app really educational for preschool children.