Article

A symbolic knowledge of numbers: A window into the early understanding of numeric structure

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Abstract

INTRODUCTION. Accumulating evidence, primarily from English-speaking children, indicates that acquisition of multi-digit numbers begins prior to formal math instruction. The present study replicated this phenomenon in a novel cultural/linguistic context and extended the current knowledge of early symbolic numeric development. METHOD. The study involved a sample of Russian preschoolers who took part in two testing sessions. In one session, children completed symbolic numeric tasks: writing and reading of multi-digit numbers. In another session, they completed a non-verbal intelligence task. Children’s performance on the two numeric tasks was compared, controlling for their general intelligence level. RESULTS. Russian preschoolers found the reading task more challenging than the corresponding writing task. In particular, when reading numbers that included two or three digits, children were more likely to make conceptual errors that revealed the difficulty of understanding the hierarchical structure of multi-digit numbers. In contrast, the frequency of errors in which the structure of the multi-digit number was preserved (for example, substituting one of the digits) was similar across the writing and reading tasks. DISCUSSION. Consistent with prior work, preschoolers in the present study revealed a partial knowledge of multi-digit numbers that emerges prior to formal instruction and is likely based on informal learning. The relative difficulty of the reading task-compared to the writing task-suggests that at the early stages of learning symbolic numbers children may require additional cues about numeric structure, which may be provided by spoken number names. The written numerals do not provide linguistic cues about numeric structure, making the reading task more challenging. Implications of these findings for early educational practice are discussed.

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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
Full-text available
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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
Full-text available
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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
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... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Chapter
Early childhood is the period of life in which the conditions of children’s development can have the longest and most significant impacts (Heckman and Masterov, Review of Agricultural Economics 29:446–493, 2007). One of the key activities in the early childhood period—play—will be considered in this chapter from a cultural–historical perspective. Based on theoretical approaches in play research and the research questions of interest to our laboratory at the Lomonosov Moscow State University, we conducted two studies. Based on the common anecdote that play is less valued today than in previous generations, Study 1 sought to explore that if there are significant differences in beliefs between the two generations (parents and grandparents) regarding the value of play in preschool childhood and their willingness to support children's free play in principle and in their participation together with their child or grandchild. Results suggested that the younger generation value play more for its potential academic value than did their parents and, plausibly as a result of this belief, will be more likely to engage in play with their child. The goal of Study 2 was to examine the impact that different roles (protagonist, sage, villain or the child’s normal role) can have on preschooler’s completion of executive functions (EF) tasks, as previous research has not examined whether the imaginary topics themselves might impact children’s real-world abilities differently. The results imply that different roles could have both positive and negative effects on performance on various tasks of EF. Moreover, for children with high levels of EF, it appeared beneficial to adopt a role, whereas low-EF children benefitted from skill training. Findings from this chapter are of a particular relevance for policymakers when developing educational programs as well as when designing teaching trainings for pedagogues and psychologists.
... For the assessment of math performance, several tasks used in prior research (Vasilyeva et al., 2016(Vasilyeva et al., , 2018 were utilized in the present study. One of these tasks-Number reading-assessed children's knowledge of written numerals and their ability to map written number symbols onto oral number words. ...
Article
The aim of this study is to explore the relationship between cooperative play and cognitive development in preschool age. The study involved 56 children aged 5-6 years (29 boys and 27 girls) of Moscow kindergartens. The article describes the main parameters of the observations of peer play (indicators of substitution, implementation of plan, play interaction). Analysis of the results revealed the presence of two correlation pleiades. The first one shows significant relationships between a child's ability to draw up a story and different play aspects associated with the development of the internal action plan and visual thinking (sustainability of play plot, subject substitution, substitution of playing space, organizing character of interaction, level of ideas). The second correlation pleiade centers around the unfolding of the play idea which is linked with the ability to understand emotions of others, with self-regulation of cognitive processes, and with visual memory. The obtained data show the presence of two sources of development in child play: one is associated with visual-imaginative thinking, and the other with partner interaction.
Chapter
Development of the preschoolers’ executive functions is a powerful predictor of the success of mastering early mathematical skills as well as of the further mathematical achievements at school (Bull and Lee, Child Development Perspectives 8:36–41, 2014; Fuhs et al., Developmental Psychology 50:1698–1709, 2014; Gilmore et al., PLoS ONE 8, 2013; Welsch et al., Journal of Educational Psychology 102:43–53, 2010; Willoughby et al., Child Neuropsychology: A Journal on Normal and Abnormal Development in Childhood and Adolescence 18:79–91, 2012, etc.). Despite a large body of research investigating the relation between executive functions and math skill development, there are multiple questions that still need to be addressed. One of them has to do with a distinct contribution of different components of executive functions to math achievement. Therefore, the present longitudinal study focused on examining the relationship between all three components of executive functions (working memory, inhibition, and cognitive flexibility) and different aspects of symbolic numerical development in children between preschool and early elementary school (from 5 to 8 years). The present investigation provided results that support and extend prior findings of the relation between early executive functions and math learning. Our results highlight the role of early math knowledge as a potential mediator of the relation between preschoolers’ executive functions and first graders’ math skills. This has to be taken into account when designing for children’s educational programs in mathematics.KeywordsChild developmentPreschool ageElementary school ageExecutive functionsEarly mathematicsSymbolic numeric skillsNumber knowledge
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