Longitudinal pathways of numerical abilities in preschool: Cognitive and environmental correlates and relation to primary school mathematics achievement.

Abstract

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated with them. We applied a person-centered approach to a 5-year longitudinal study (N = 410, 213 boys) conducted in Belgium from preschool to grade 3. Preschoolers (Mage = 58.14 months, SDage = 3.51) were selected to represent the full range of socioeconomic backgrounds. We examined via Latent Profile Analysis the heterogeneous patterns that exist in preschoolers’ early numerical development using measures of counting, numeral identification, comparison, ordering, and arithmetic abilities. We investigated the association between the derived numerical ability pathways, general cognitive factors (working memory, language, spatial ability) and the home math environment. We also evaluated the relation of these early numerical ability pathways to later mathematics achievement in grade 1 and 3. Four longitudinal pathways emerged: a low (15%), below-average (28%), above-average (44%), and a high numerical ability pathway (13%). Differences between the four pathways were mostly quantitative. Most of the general cognitive factors contributed to pathway membership, whereas the home math environment and socioeconomic status (SES) did not. The pathways differed in mathematics achievement in grade 1 and 3, and most of these differences remained when the covariates were considered. The results highlight the heterogeneity that is already present in preschoolers’ numerical abilities and their predictive value for subsequent mathematics achievement.

General and math vocabulary contributions to early numeracy skills in a large population-representative sample

“…Findings of significant and even substantial correlations do not guarantee a purely linear relation, and the relation of variables can vary greatly at the extremes, especially when outcomes rest on a multiplicity of foundational skills. For example, Bakker et al (2023) found evidence for differences in the pattern of prediction to numeracy from other cognitive measures at the high end of the distribution with that in the low-and average-range. We are not aware of any research on either extreme of math vocabulary in the preschool period, although there is much evidence for very substantial variability in general vocabulary (Marchman and Dale, 2023).…”

“…However, the targeting, design, and interpretation of early intervention studies would benefit from greater understanding of the determinants, particularly general and math vocabulary, of extremely low and extremely high numeracy ability. Even less is known about extreme high performance in numeracy (see Bakker et al, 2023, for a review of what is known about variability across the full distribution of numerical ability).…”

Exploring the potential of a game-based preschool assessment of mathematical competencies

“…Early mathematical competencies are the basis for mastering more complex mathematical understanding (Fritz et al, 2018). Yet, despite the large amount of research on early mathematical competencies, there is not always consensus on the definition of these skills (Bakker et al, 2022). Most of the researchers seem to agree that apart from counting, early mathematical competencies include components such as the understanding of cardinality and the ability to compare magnitudes (Purpura and Lonigan, 2013;Purpura et al, 2017;Bakker et al, 2022).…”

“…Yet, despite the large amount of research on early mathematical competencies, there is not always consensus on the definition of these skills (Bakker et al, 2022). Most of the researchers seem to agree that apart from counting, early mathematical competencies include components such as the understanding of cardinality and the ability to compare magnitudes (Purpura and Lonigan, 2013;Purpura et al, 2017;Bakker et al, 2022). Children intuitively develop such concepts through personally meaningful activities that facilitate the learning process (Fisher et al, 2012).…”

“…Early mathematical competencies are highly heterogeneous among preschool children (Mähler et al, 2017;Cahoon et al, 2021;Bakker et al, 2022) but research shows that these competencies can be effectively promoted in kindergarten before school enrolment (Ehlert and Fritz, 2016;Moraske et al, 2018;Skillen et al, 2018a). The educational staff stimulates children's interest in further engaging with new mathematical concepts in the daily kindergarten routine, and potential developmental risks can be examined more intensively (Ministerium für Kultus, Jugend und Sport Baden-Württemberg, 2022).…”