Abstract
Early number skills underlie success in basic arithmetic. However, very little is known about the skill profiles among children in preprimary education and how the potential profiles are related to arithmetic development. This longitudinal study of 440 Finnish children in preprimary education (mean age: 75 months) modeled latent performance-level profile groups for the early number skill components that are proposed to be key predictors of arithmetic (symbolic number comparison, mapping, and verbal counting skills). Based on three assessment time points (September, January, and May), four profile groups were found: the poorest-performing (6%), low-performing (16%), near-average-performing (33%), and high-average-performing children (45%). Although the differences between the groups were statistically significant in all three number skill components and in basic arithmetic, the poorest-performing children seemed to have serious difficulties in accessing the semantic meaning of symbolic numbers that was required in the number comparison and mapping tasks in this study. Interestingly, the tasks demanding processing between quantities and symbols also most differentiated the poorest-performing children from the low-performing children. Due to remarkable and stable individual differences in early number skill components, the findings suggest systematic support and progress monitoring practices in preeducational settings to diminish and avoid potential difficulties in arithmetic and mathematics in general.
Highlights
As an innate ability, children are able to quickly discriminate small sets of quantities without counting (1-4; subitizing range), and they can detect which of two presented quantities is larger if the difference between them is large enough (Dehaene, 2011; see von Aster, 2000; von Aster and Shalev, 2007)
It has been proposed that this ability is critical for the development of early number skills and especially for number concept skills for which children need to learn the quantitative meaning of small number words, and later on, to map verbal and quantitative representations to corresponding number symbols
Because this study focused on the prerequisite skills for arithmetic (NC, MS, and verbal counting skills (VC)), this task was included in post hoc analysis only as a sum score of eight items for testing potential differences in basic arithmetic between hypothetically meaningful profile groups
Summary
As an innate ability, children are able to quickly discriminate small sets of quantities without counting (1-4; subitizing range), and they can detect which of two presented quantities is larger if the difference between them is large enough (Dehaene, 2011; see von Aster, 2000; von Aster and Shalev, 2007). Children need to understand what can be counted and that the order in which the quantities are counted does not matter (Gelman and Gallistel, 1978) These principles are vital for exact object counting (see Krajewski and Schneider, 2009; Dehaene, 2011), which, in turn, relates to the development of number concept skills. This skill allows and strengthens the understanding of explicit number system (knowing the exact relationships between numbers) that can be seen as prerequisite for the ability to compose and decompose magnitudes and for learning efficient and flexible arithmetical calculation strategies (Krajewski and Schneider, 2009; Geary, 2013)
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