Certainty in numerical judgments develops independently of the approximate number system

Recent work has shown that the precision with which children reason about their ANS certainty improves with age: when making simple number discrimination decisions, like deciding whether there are more blue or yellow dots on the screen, older children are better able to differentiate trials that they answered correctly vs. incorrectly. Here, in two experiments, we examine whether the age-related improvement in ANS certainty is accounted for by children's: (1) increasing ability to properly "calibrate" their certainty judgements (i.e., a reduction in over-confidence with age); (2) improving precision of the ANS representations themselves; and/or (3) the improvement of children's ability to represent and reason about certainty in general. By testing children in a child-friendly "relative" certainty task, we find that 3-7 year-olds' (N = 161) certainty in their ANS decisions develops independently of both ANS acuity and calibration abilities. These results hold even when non-numeric perceptual features, such as the density and cumulative area, are controlled for. We discuss these results in a broader context of children's general ability to reason about certainty and confidence.