How do children map symbolic number words to continuousand noisy perceptual magnitudes? We explore how 5- to 12-year-olds attach novel units to number, length, and area byexamining whether verbal estimation performance is primarilypredicted by access to number words, the precision ofchildren’s underlying perceptual systems, or a more generalprocess in structurally aligning number words with perceptualmagnitudes. We find that from age five onward, children canreadily form novel mappings between number words andperceptual magnitudes, including dimensions they have noexperience estimating in (e.g., length, area), and even whenfaced with completely novel units (e.g., mapping a collectionof three dots to “one” unit for number). Additionally,estimation performance was poorly predicted by the noise intheir underlying perceptual magnitudes and number wordaccess. Instead, we show that individual differences inchildren’s abilities to translate continuous perceptual signalsinto discrete categories underlie verbal estimationperformance.

From something as simple as judging the time to more complicated behaviours like answering trivia questions, ourcognitive systems always provide us with a representation of confidence: the probability of being correct. The developmentof confidence has been a long-standing issue in cognitive and developmental science. However, most studies assess children’sconfidence through either extensively trained numerical or verbal scales (“I am sure”), or by asking children to gamble on theiranswer. These measures stand to confuse metacognition with the development of language and inhibitory control. Here, wevalidate a novel model and task that measures individual and developmental differences in confidence relatively (“Are you moreconfident in X or Y”). Subsequently, we apply this task to demonstrate that metacognitive abilities of children aged 5–8 showsignificant development in the domain of intuitive number representations. These results are discussed in a broader context oftheory and measurement of metacognition.