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..Whole number arithmetic, fractions, simple algebra, and measurement, with performance on these tests predicting employability and wages in adulthood, controlling for other factors.

Abstract Three- to 5-year-old children participated in one of 4 counting experiments. On the assumption that performance demands can mask the young child's implicit knowledge of the counting principles, 3 separate experiments assessed a child's ability to detect errors in a puppet's application of the one-one, stable-order and cardinal count principles. In a fourth experiment children counted in different conditions designed to vary performance demands. Since children in the errror-detection experiments did not have to do the counting, we predicted excellent performance even on set sizes beyond the range a young child counts accurately. That they did well on these experiments supports the view that errors in counting-at least for set sizes up to 20-reflect performance demands and not the absence of implicit knowledge of the counting principles. In the final experiment, where children did the counting themselves, set size did affect their success. So did some variations in conditions, the most difficult of which was the one where children had to count 3-dimensional objects which were under a plexiglass cover. We expected that this condition would interfere with the child's tendency to point and touch objects in order to keep separate items which have been counted from those which have not been counted.

Abstract Assessed the impact of linguistic differences in ordinal number names on children's acquisition and use of ordinal numbers and their understanding of ordinal concepts. Elementary school children (aged 5.4-10.6 yrs) in China and the US performed a series of tasks assessing understanding of ordinal numbers and concepts. The results show differences in the acquisition and use of ordinal numbers corresponding to linguistic differences in ordinal names in their native languages. On tasks assessing children's conceptual knowledge of ordinal relations, a more complicated picture emerged. These results suggest that (1) children induce their language's set of ordinal number names by generalization based on rules sanctioned by early examples, and (2) the relation between ordinal names and ordinal concepts is a complex one, with language only one source of difficulty in understanding ordinal relations. Implications for studies of the relation between linguistic structure and cognitive development are discussed, in particular the possibility that effects of linguistic differences may vary for different levels of development and for different aspects of cognition. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

"When children are acquiring the symbolic system for representing numbers and learning about math in school, they're tapping into this primitive number sense," says Elizabeth Brannon, a professor of psychology and neuroscience at Duke University, who led the study. "It's the conceptual building block upon which mathematical ability is built." Understanding how infants and young children conceptualize and understand number can lead to the development of new mathematics education strategies, says psychology and neuroscience graduate student Ariel Starr. In particular, this knowledge can be used to design interventions for young children who have trouble learning mathematics symbols and basic methodologies. "Our study shows that infant number sense is a predictor of symbolic math," Brannon says. "We believe that when children learn the meaning of number words and symbols, they're likely mapping those meanings onto pre-verbal representations of number that they already have in infancy," she says. "In fact our infant task only explains a small percentage of the variance in young children's math performance. But our findings suggest that there is cognitive overlap between primitive number sense and symbolic math. These are fundamental building blocks."