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The approximate number system (ANS) has attracted broad interest due to its potential importance in early mathematical development and the fact that it is conserved across species. Models of the ANS and behavioral measures of ANS acuity both assume that quantity estimation is computed rapidly and in parallel across an entire view of the visual scene. We present evidence instead that ANS estimates are largely the product of a serial accumulation mechanism operating across visual fixations. We used an eye-tracker to collect data on participants’ visual fixations while they performed quantity-estimation and -discrimination tasks. We were able to predict participants’ numerical estimates using their visual fixation data: As the number of dots fixated increased, mean estimates also increased, and estimation error decreased. A detailed model-based analysis shows that fixated dots contribute twice as much as peripheral dots to estimated quantities; people do not “double count” multiply fixated dots; and they do not adjust for the proportion of area in the scene that they have fixated. The accumulation mechanism we propose explains reported effects of display time on estimation and earlier findings of a bias to underestimate quantities.
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Children’s Estimation of Peripheral Information Drives Improvements in Approximate Number Sense
Children rely on their approximate number system (ANS) to guess quantities from a young age. Studies have shown that older children displayed better ANS performance. However, previous research did not provide an explanation for this ANS improvement. We show that children’s development in ANS is primarily driven by improved attentional control and awareness of peripheral information. Children guess the number of dots on a computer screen while being eye-tracked in our experiment. The behavioral and eye-tracking results provide supporting evidence for our account. Our analysis shows that children estimate better under the longer display-time condition and more visual foveation, with the effect of visual foveation mediating that of time. It also shows that older children make fewer underestimations because they are better at directing their attention and gaze toward areas of interest, and they are also more aware of dots in their peripheral vision. Our finding suggests that the development of children’s ANS is significantly impacted by the development of children’s nonnumerical cognitive abilities.
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- Award ID(s):
- 2000759
- PAR ID:
- 10517222
- Publisher / Repository:
- Proceedings of the Cognitive Science Society
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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