Abstract
Research with children and adults suggests that people’s math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study. Sixty-eight 6-year-old children participated in a 5-week study that either trained their visual ANS ability or their phonological awareness (an active control group). Immediately before and after training, we assessed children’s visual and auditory ANS precision, as well as their symbolic math ability and phonological awareness. We found that, prior to training, children’s precision in a visual ANS task related to their math performance – replicating recent studies. Importantly, precision in an auditory ANS task also related to math performance. Furthermore, we found that children who completed visual ANS training showed greater improvements in auditory ANS precision than children who completed phonological awareness training. Finally, children in the ANS training group showed significant improvements in math ability but not phonological awareness. These results suggest that the link between ANS precision and school math ability goes beyond visuospatial abilities and that the modality-independent ANS is causally linked to math ability in early childhood.
Highlights
Educated adults and children use at least two systems to represent and process numerical information: an approximate number system (ANS), which allows observers to form imprecise estimates of the number of items in a collection without verbally counting (Dehaene et al, 1998), and an exact number system, which allows them to represent precise cardinalities and which is essential for formal mathematics (Dehaene, 1992)
Prior work on the ANS has suggested that it may represent number in an amodal fashion, readily taking both sounds and visual objects as input, and that these intuitive number representations may be linked to school math performance
It has been proposed that visual ANS tasks measure sensitivity to visual area, visual density, or some other non-numeric visual feature, and that the ANS, has no inherent connection to school math ability other than being linked by general visuospatial performance
Summary
Educated adults and children use at least two systems to represent and process numerical information: an approximate number system (ANS), which allows observers to form imprecise estimates of the number of items in a collection without verbally counting (Dehaene et al, 1998), and an exact number system, which allows them to represent precise cardinalities and which is essential for formal mathematics (Dehaene, 1992). Effects of Visual ANS Training we have fewer than 10 items in our shopping cart, whereas we might use our exact number system to make sure we receive the correct change after paying for our groceries. Both the ANS and exact number representations support numerical reasoning, they represent number differently. Whereas the ANS is present from birth (Izard et al, 2009) and is found in non-human animals, including fish (Dadda et al, 2009), rodents (Meck et al, 1985), and primates (Cantlon and Brannon, 2006), the exact number system is uniquely human and is acquired slowly over the course of development as children learn to count (Wynn, 1992; Feigenson et al, 2004; Carey, 2009)
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