Young children interpret number gestures differently than nonsymbolic sets.

Researchers have long been interested in the origins of humans' understanding of symbolic number, focusing primarily on how children learn the meanings of number words (e.g., "one", "two", etc.). However, recent evidence indicates that children learn the meanings of number gestures before learning number words. In the present set of experiments, we ask whether children's early knowledge of number gestures resembles their knowledge of nonsymbolic number. In four experiments, we show that preschool children (n = 139 in total; age M = 4.14 years, SD = 0.71, range = 2.75-6.20) do not view number gestures in the same the way that they view nonsymbolic representations of quantity (i.e., arrays of shapes), which opens the door for the possibility that young children view number gestures as symbolic, as adults and older children do. A video abstract of this article can be viewed at https://youtu.be/WtVziFN1yuI HIGHLIGHTS: Children were more accurate when enumerating briefly-presented number gestures than arrays of shapes, with a shallower decline in accuracy as quantities increased. We replicated this finding with arrays of shapes that were organized into neat, dice-like configurations (compared to the random configurations used in Experiment 1). The advantage in enumerating briefly-presented number gestures was evident before children had learned the cardinal principle. When gestures were digitally altered to pit handshape configuration against number of fingers extended, children overwhelmingly based their responses on handshape configuration.

Connecting symbolic fractions to their underlying proportions using iterative partitioning.

Fractions are a challenging mathematics topic for many elementary and middle school students, and even for adults. However, a growing body of developmental research suggests that young children can reason about visually presented proportions, well before fraction instruction, providing insight into how fractions might be introduced to improve learning. We designed a card game to teach first and second grade children (N = 195, including a racially and economically diverse sample from the United States) about fractions in one of three ways. In the Actively Divided condition we iteratively divided an area model into equal-sized units, in the Predivided condition we used an area model with the end-state of the Actively Divided condition, and in the Nondivided condition we used a continuous representation of the fraction magnitude that was not divided into unit-sized parts. Children in the actively divided condition demonstrated larger improvements matching symbolic fractions and visual fractions (i.e., pie charts) than children in the other two conditions. Posthoc analyses of children's gameplay revealed that the actively divided condition may have provided a more optimal level of difficulty for young children than the predivided condition, which was particularly difficult, and the nondivided condition, which was trivially easy. These differences in gameplay performance provide insights into possible mechanisms for our results. We discuss open research questions highlighted by this work and implications of these findings for both the development of proportional reasoning and fraction learning. (PsycInfo Database Record (c) 2022 APA, all rights reserved).