Young children have informal knowledge of fractions before learning about fraction symbols in school. In the current study, we followed 103 children in the Mid-Atlantic United States from the fall to the spring of first grade to characterize the development of individual differences in early informal fraction knowledge, as well as its relation to other mathematical and cognitive skills. Most children in our sample showed some early fraction knowledge at the beginning of first grade, especially with nonsymbolic fractions and halving, and this knowledge improved over the school year without explicit instruction in fractions. However, there were large individual differences in early fraction knowledge at the start of first grade, which explained significant variance in math achievement at the end of first grade, even when controlling for whole number knowledge and a variety of cognitive skills. Start-of-year whole number knowledge, but not spatial scaling or proportional reasoning, also predicted early end-of-year fraction knowledge. These data can inform activities for learning in the early years to foster both early fraction and integer knowledge in parallel, which may better prepare students for later formal instruction in fractions.

Algebra knowledge is an important gatekeeper to educational and economic opportunity. Both math education researchers and psychologists have shown that fractions may be a key to this gate (e.g., Hackenberg, 2013; Siegler et al., 2012). However, psychological and educational research on the fractions-algebra association has been disconnected, with separate frameworks, definitions, and designs. This integrative review synthesizes evidence from both disciplines about how and why fractions knowledge leads to stronger algebra knowledge. I suggest that the strength of causal evidence is limited by idiosyncratic measurement, limited longitudinal research, and imprecise definitions. I also review six plausible fractions-to-algebra mechanisms, which future research should empirically test. Throughout, I argue that more nuanced understanding of the fractions-algebra association will require interdisciplinary teams. Finally, I propose an integrative conceptual model of how fractions knowledge may lead to success in algebra and suggest new directions for collaborative investigation to inform developmental theory and educational practice.

Young children have informal knowledge of fractions before learning about fraction symbols in school. In the current study, we followed 103 children in the Mid-Atlantic United States from the fall to the spring of first grade to characterize development of and individual differences in early informal fraction knowledge, as well as its relation to other mathematical and cognitive skills. Most children in our sample showed some early fraction knowledge at the beginning of first grade, especially with nonsymbolic fractions and halving, and this knowledge improved over the school year without explicit instruction in fractions. However, there were large individual differences in early fraction knowledge at the start of first grade, which explained significant variance in math achievement at the end of first grade, even when controlling for whole number knowledge and a variety of cognitive skills. Start-of-year whole number knowledge, but not spatial scaling or proportional reasoning, also predicted early end-of-year fraction knowledge. These data can inform activities for learning in the early years to foster both early fraction and integer knowledge in parallel, which may better prepare students for later formal instruction in fractions.