The cognitive underpinnings of emerging mathematical skills: executive functioning, patterns, numeracy, and arithmetic.

BACKGROUND: Exposure to mathematical pattern tasks is often deemed important for developing children's algebraic thinking skills. Yet, there is a dearth of evidence on the cognitive underpinnings of pattern tasks and how early competencies on these tasks are related to later development. AIMS: We examined the domain-specific and domain-general determinants of performances on pattern tasks by using (a) a standardized test of numerical and arithmetic proficiency and (b) measures of executive functioning, respectively. SAMPLE: Participants were 163 6-year-olds enrolled in primary schools that typically serve families from low to middle socioeconomic backgrounds. METHOD: Children were administered a battery of executive functioning (inhibitory, switching, updating), numerical and arithmetic proficiency (the Numerical Operations task from the Wechsler Individual Achievement Test-II), and three types of pattern tasks. RESULTS: Contrary to findings from the adult literature, we found all the executive functioning measures coalesced into two factors: updating and an inhibition/switch factor. Only the updating factor predicted performances on the pattern tasks. Although performance on the pattern tasks were correlated with numerical and arithmetic proficiency, findings from structural equation modelling showed that there were no direct or independent relationships between them. CONCLUSIONS: The findings suggest that the bivariate relationships between pattern, numeracy, and arithmetic tasks are likely due to their shared demands on updating resources. Unlike older children, these findings suggest that for 6-year-olds, better numerical and arithmetic proficiency, without accompanying advantages in updating capacities, will no more likely lead to better performance on the pattern tasks.

Central executive involvement in children's spatial memory.

Previous research with adults found that spatial short-term and working memory tasks impose similar demands on executive resources. We administered spatial short-term and working memory tasks to 8- and 11-year-olds in three separate experiments. In Experiments 1 and 2 an executive suppression task (random number generation) was found to impair performances on a short-term memory task (Corsi blocks), a working memory task (letter rotation), and a spatial visualisation task (paper folding). In Experiment 3 an articulatory suppression task only impaired performance on the working memory task. These results suggest that short-term and working memory performances are dependent on executive resources. The degree to which the short-term memory task was dependent on executive resources was expected to be related to the amount of experience children have had with such tasks. Yet we found no significant age-related suppression effects. This was attributed to differences in employment of cognitive strategies by the older children.

Receptive vocabulary and semantic knowledge in children with SLI and children with Down syndrome.

Receptive vocabulary and associated semantic knowledge were compared within and between groups of children with specific language impairment (SLI), children with Down syndrome (DS), and typically developing children. To overcome the potential confounding effects of speech or language difficulties on verbal tests of semantic knowledge, a novel task was devised based on picture-based semantic association tests used to assess adult patients with semantic dementia. Receptive vocabulary, measured by word-picture matching, of children with SLI was weak relative to chronological age and to nonverbal mental age but their semantic knowledge, probed across the same lexical items, did not differ significantly from that of vocabulary-matched typically developing children. By contrast, although receptive vocabulary of children with DS was a relative strength compared to nonverbal cognitive abilities (p < .0001), DS was associated with a significant deficit in semantic knowledge (p < .0001) indicative of dissociation between word-picture matching vocabulary and depth of semantic knowledge. Overall, these data challenge the integrity of semantic-conceptual development in DS and imply that contemporary theories of semantic cognition should also seek to incorporate evidence from atypical conceptual development.

Exploring developmental differences in visual short-term memory and working memory.

Although visuospatial short-term memory tasks have been found to engage more executive resources than do their phonological counterparts, it remains unclear whether this is due to intrinsic differences between the tasks or differences in participants' experience with them. The authors found 11-year-olds' performances on both visual short-term and working memory tasks to be more greatly impaired by an executive suppression task (random number generation) than were those of 8-year-olds. Similar findings with adults (e.g., Kane & Engle, 2000) suggest that the imposition of a suppression task may have overloaded the older children's executive resources, which would otherwise be used for deploying strategies for performing the primary tasks. Conversely, the younger children, who probably never had the capacity or know-how to engage these facilitative strategies in the first place, performed more poorly in the single task condition but were less affected in the dual task condition. These findings suggest that differences in the children's ability to deploy task-relevant strategy are likely to account for at least part of the executive resource requirements of visual memory tasks.