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The aims of the present study were to investigate whether there is an association between visuospatial abilities, core number ability in enumerating small precise numbers, and arithmetic competence in young children, and to examine whether core number abilities are associated with general cognitive abilities. The results supported all four hypotheses. Consistent with the first two hypotheses, findings showed that children in the faster or larger subitizing profiles showed significant benefit in enumerating canonical dot arrays in the counting range compared to random arrays, whereas children in the slower or smaller subitizing profile showed little benefit. Results also showed a significant difference in SDA ability across DE profile membership, and that none of VSWM, basic RT, and IQ accounted for the differences in profile membership, supporting the third and fourth hypotheses.
Three distinct DE profiles were identified, namely slow, medium, and fast subgroups. At each set sizes in both canonical and randomized arrays, the RT of fast-profile children were significantly faster than medium profile, which, in turn, was faster than slow profile. For all three profiles, the RT increased with increases in dot array size in both randomized and canonical arrays, however, with steeper increases in RT for slow profile than medium and fast profiles. Consistent with the first and second hypotheses, when comparing all array pairs in the counting range, both medium and fast profiles responded to canonical arrays more rapidly than randomized arrays, whereas slow profile did not. Since canonical arrays offer an opportunity for set-based reasoning (Krajcsi, Szabó, & Mórocz, 2013), the significant benefit of enumerating canonical over randomized dot arrays for medium and fast profiles suggested that, these children are able to utilize set knowledge for identifying and reasoning the patterns in a set, allowing them to extract numerical information faster from canonical than randomized arrays. Therefore, these children appeared to possess good visuospatial abilities, which enable them to extract numerical information from patterns. With good visuospatial abilities, children in the superior profiles would be able to extract numerical information from larger set sizes, as pattern recognition can help with the enumeration of large numbers (Jansen et al., 2014).
In contrast, children in the slow profile may instead depend on their procedural counting abilities, such that they would have to count the dots even in the canonical arrays, explaining why children in this poorer profile showed insignificant benefit in enumerating canonical over randomized arrays. With a lack of set-based reasoning and poor visuospatial abilities, the ability of children in the poorer profile to extract numerical information from sets might be limited to only small set sizes, as poor visuospatial abilities result in an inability to extract numerical information from patterns, which also explained why slow-profile children have a smaller subitizing range as they would need to begin counting. According to Reeve, Humberstone, and Butterworth (2012), DE as an index of core numerical competence, assesses the capacity of numerosity as a property of sets. Thus, the current results demonstrated that there is an association between the core ability to enumerate small precise numbers, as indexed by the DE profiles, and visuospatial abilities in extracting numerical information from patterns.
Insofar as the capability to represent numerosities as a property of sets serves as a foundational capacity for developing arithmetic abilities (Butterworth, Varma, & Laurillard, 2011), an inability to represent sets, as indexed by a slow or poor subitizing profile, would therefore predict poor math competence. Indeed, in the current study, significant differences in SDA accuracy were identified across the DE profiles, with the accuracy decreasing from fast to medium to slow profiles, showing that the core number abilities of enumerating dot arrays appeared to support the acquisition of cultural number competencies. Therefore, similar to previous research findings (Gray & Reeve, 2016; Reeve et al., 2012), the current study showed that core numerical competences, specifically DE ability, are related to arithmetical attainment. The finding that the slow DE profile characterized by slower RT and steeper subitizing slope was associated with poorer SDA accuracy is important as it suggested that a poor subitizing profile in school-aged children could potentially act as an early diagnostic marker of emerging math difficulties such as dyscalculia (Gray & Reeve, 2014).
On the other hand, no significant differences were identified across the three DE profiles in their performances on Corsi Blocks, basic RT, and Ravens tasks. Since these tasks measure VSWM, cognitive processing speed, and IQ respectively, the results supported the hypothesis that none of VSWM, basic RT, and IQ would account for the differences in DE profile membership. Similar to Reeve et al. (2012), the present study provided additional support that individual differences in core number abilities, such as DE ability, are not associated with general cognitive abilities, and are therefore, domain-specific. This finding would have important implications for understanding the origins of numerical competencies, such that by clarifying the significance of different cognitive correlates which might underlie different math abilities patterns, more effective programs would be developed for intervention success.
Three limitations could be highlighted in the present study. First, children’s counting behaviors during DE and SDA problem-solving strategies were recorded but excluded in the results analysis. Including them in the analysis might reveal additional information on different approaches utilized by children in acquiring a particular number competence. Second, while the ability to combine two numbers in SDA is an instance of set-based reasoning, the current study did not account for the direct association between visuospatial abilities and SDA abilities. Finally, considering that many reasons could account for poor math performances, testing children on these standard tasks did not provide enough evidence for the characterization of their math abilities, as the slow profile may comprise children with varying numerical competencies or math learning deficits. This necessitates future studies to conduct longitudinal research to determine whether varying early math ability profiles represent differences, delays, or deficits in developmental pathway trajectories, as they might lead to different long-term outcomes. This would have significant implications for the early detection and development of appropriate intervention targeting different math difficulties.
In summary, the current study demonstrated an association between core number ability to enumerate precise small number (DE subitizing) and visuospatial abilities, as well as between DE subitizing and arithmetic competence in young children. Furthermore, the present study also contributed to the understanding that core number abilities are domain-specific and not associated with general cognitive abilities. Nonetheless, future studies should move beyond normative, age-as-a-proxy-for-development, forms of analysis, together with applying tests of capacity rather than attainment. Hopefully, a better understanding of the mechanism underlying math difficulties, including dyscalculia, can be achieved for its early detection and amelioration.

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