Socialization of Early Prosocial Behavior: Parents' Talk about Emotions is Associated with Sharing and Helping in Toddlers.

What role does socialization play in the origins of prosocial behavior? We examined one potential socialization mechanism, parents' discourse about others' emotions with very young children in whom prosocial behavior is still nascent. Two studies are reported, one of sharing in 18- and 24-month-olds (n = 29), and one of instrumental and empathy-based helping in 18- and 30-month-olds (n = 62). In both studies, parents read age-appropriate picture books to their children and the content and structure of their emotion-related and internal state discourse were coded. Results showed that children who helped and shared more quickly and more often, especially in tasks that required more complex emotion understanding, had parents who more often asked them to label and explain the emotions depicted in the books. Moreover, it was parents' elicitation of children's talk about emotions rather than parents' own production of emotion labels and explanations that explained children's prosocial behavior, even after controlling for age. Thus, it is the quality, not the quantity, of parents' talk about emotions with their toddlers that matters for early prosocial behavior.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.