#### Susan Carey, David Barner, **Ontogenetic Origins of Human Integer Representations**. Trends in Cognitive Sciences, Volume 23, Issue 10, 2019, Pages 823-835, DOI: 10.1016/j.tics.2019.07.004.

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children\u2019s understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume\u2019s principle (that one-to-one correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.