Children tend to prioritize whole number information over relational information in proportional reasoning tasks, such that they judge a spinner with 4/10 red pieces as more likely to land on red than a spinner with 2/3 red pieces, because 4 > 2 (e.g., Hurst & Cordes, 2018a; Jeong et al., 2007). This whole number bias is hypothesized to be a driven by fluency in verbal counting in early childhood, which is thought to promote attention to whole number information. In this study, we explored (1) the relation between verbal counting abilities and whole number biases and (2) whether distinct framing contexts - either encouraging children to maximize the number of stickers won, or minimizing the number of stickers lost -differentially impact children's proportional reasoning. Three-to nine-year olds (N = 210, M-age = 5.7 years) chose which of two spinners they preferred to spin. Children in the Gain condition learned that if the spinner landed on red, they would win a sticker and if it landed on blue, nothing would happen; children in the Loss condition learned that if the spinner landed on red, nothing would happen, but if it landed on blue, they would lose a sticker. Counter to prior work, performance of both older (6-9 year olds) and younger (3-5 year olds) children revealed whole number biases. Notably, whole number biases were not related to counting abilities. Importantly, we find framing the task in a Loss scenario lessened whole number biases, suggesting that task framing can alter children's attention to whole number information in a proportional reasoning context.

Games are frequently used to promote math learning, yet the competitive and collaborative contexts introduced by games may exacerbate gender differences. In this study, 1st and 2nd grade children in the U.S. (ages 5-8; N = 274; 70% White, 15% Asian, 2% Black, 1% Native American, 14% mixed or other race; 17% Hispanic) played either a competitive, collaborative, or solo game to learn about a challenging novel math concept: proportion. Overall, both social contexts boosted perseverance and task attitudes. However, analyses revealed the competitive condition yielded gender differences in attention to proportion in the presence of competing cues, with older boys underperforming in the competition condition. Potential explanations for these findings, as well as implications for classroom math learning, are discussed.

The ability to engage in counterfactual thinking (reason about what else could have happened) is critical to learning, agency, and social evaluation. However, not much is known about how individual differences in counterfactual reasoning may play a role in children's social evaluations. In the current study, we investigate how prompting children to engage in counterfactual thinking about positive moral actions impacts children's social evaluations. Eighty-seven 4-8-year-olds were introduced to a character who engaged in a positive moral action (shared a sticker with a friend) and asked about what else the character could have done with the sticker (counterfactual simulation). Children were asked to generate either a high number of counterfactuals (five alternative actions) or a low number of counterfactuals (one alternative action). Children were then asked a series of social evaluation questions contrasting that character with one who did not have a choice and had no alternatives (was told to give away the sticker to his friend). Results show that children who generated selfish counterfactuals were more likely to positively evaluate the character with choice than children who did not generate selfish counterfactuals, suggesting that generating counterfactuals most distant from the chosen action (prosociality) leads children to view prosocial actions more positively. We also found age-related changes: as children got older, regardless of the type of counterfactuals generated, they were more likely to evaluate the character with choice more positively. These results highlight the importance of counterfactual reasoning in the development of moral evaluations. Research HighlightsOlder children were more likely to endorse agents who choose to share over those who do not have a choice.Children who were prompted to generate more counterfactuals were more likely to allocate resources to characters with choice.Children who generated selfish counterfactuals more positively evaluated agents with choice.Comparable to theories suggesting children punish willful transgressors more than accidental transgressors, we propose children also consider free will when making positive moral evaluations.

By the preschool age, children exhibit a diversity of prosocial behaviors that include both sharing resources and helping others. Though recent work has theorized that these prosocial behaviors are differentiated by distinct ages of emergence, developmental trajectories and underlying mechanisms, the experimental evidence in support of the last claim remains scant. The current study focuses on one such cognitive mechanism - numerical cognition - seeking to replicate and extend prior work demonstrating the strong link between children's numerical cognition and precise sharing behavior, and further examining its relationship to instrumental helping. In line with theoretical perspectives favoring the differentiation of varieties of prosocial behaviors, we hypothesize that numerical cognition underlies precise sharing, but not precise helping behavior. Eighty-five 3 to 6-year-old children completed two procedurally similar tasks designed to elicit sharing and instrumental helping behavior, in addition to a Give-N task measuring their symbolic counting skills. Despite the procedural similarity, and the implicit norm of providing half (5 out of 10) stickers in both tasks, children's counting proficiency predicted precise sharing, but not precise helping. These results indicate a unique relationship between children's developing numerical cognition and behavioral fairness, providing empirical support for claims that varieties of prosocial behavior are supported by distinct underlying mechanisms.

Recent work has probed the developmental mechanisms that promote fair sharing. This work investigated 2.5- to 5.5-year-olds' (N = 316; 52% female; 79% White; data collected 2016-2018) sharing behavior in relation to three cognitive correlates: number knowledge, working memory, and cognitive control. In contrast to working memory and cognitive control, number knowledge was uniquely associated with fair sharing even after controlling for the other correlates and for age. Results also showed a causal effect: After a 5-min counting intervention (vs. a control), children improved their fair sharing behavior from pre-test to post-test. Findings are discussed in light of how social, cognitive, and motivational factors impact sharing behavior.

Understanding division is critical for later mathematical achievement. Yet division concepts are difficult to grasp and are often not explicitly taught until middle childhood. Given the structural similarity between sharing and division, we investigated whether contextualizing division problems as sharing scenarios improved preschool-aged children's abilities to solve them, as compared with other arithmetic problems which do not share structural similarities with sharing. Preschoolers (N = 113) completed an addition, subtraction, and division problem in either a sharing context that presented arithmetic via contextualized sharing scenarios, or a comparable, linguistically-matched non-social context (randomly assigned). Children were assessed on their formal, verbal responses and their informal, non-verbal, action-based responses (abilities to solve the problems using manipulatives) to these arithmetic problems. Most critically, context predicted children's performance on the division, but not the addition or subtraction trial, supporting a structural link between sharing and division. Results also revealed that children's action-based responses to the arithmetic problems were much more accurate than their verbal ones. Results are discussed in terms of the conceptual link between division and sharing.