From "1, 2, 3" to "Fractions We See": Trajectories and Early Contributors to Children's Rational Number Development

How do children construct increasingly complex numerical concepts across early development? Through a series of four studies, this dissertation explores numerical development, beginning with children’s acquisition of the natural number system and gradually extending into learning of rational numbers (in particular, fractions). The current work reveals a set of four core findings that characterize the layered developmental trajectory followed by young learners. First, the hierarchical nature of early natural number skills is more nuanced and less strictly sequential than previously recognized; Study 1 finds evidence that mastery of the Cardinality Principle is not a prerequisite for learning more advanced quantity relations skills. Instead, only partly-consistent cardinality task performance at a particular quantity is required to apply this quantity in magnitude comparison or rudimentary operations contexts. Second, natural number and fraction talk co-occur across early development, though on vastly different scales favoring natural number. Study 2 finds that fraction talk first begins to emerge, though infrequently, before formal schooling (as early as 30 months of age, and in nearly half of participants by age 5).  This appearance occurs substantially earlier than is often studied, and follows a pattern that centers on the quantity of one half, emphasizes part-whole structures, and focuses on examples of single items divided into pieces. Third, the pattern of part-whole prioritization, especially for food items and sharing contexts, is preserved in parent-child fraction conversations elicited by light-touch, open-response prompts in Study 3A. The number of real-world fraction examples discussed in these prompted conversations positively predicts children’s post-conversation fraction knowledge, implying the utility of illustrative examples as an exploratory learning tool. Finally, in efforts to experimentally evaluate the effect of prompts featuring real-world fraction examples, Study 3B finds that targeted prompts successfully lead parent-child dyads to discuss relevant fraction examples, and that children’s emerging knowledge of fractions is especially supported by discussion of an infrequently-referenced format: continuous quantities (e.g. cups of water). Taken together, these studies suggest that numerical development is more overlapping and interleaved than traditionally assumed. Rather than mastering concepts one at a time in strict sequence, children are capable of engaging with increasingly complex numerical ideas using partial and still-developing knowledge.