When faced with a sentence like, "Some of the toys are on the table", adults, but not preschoolers, compute a scalar implicature, taking the sentence to imply that not all the toys are on the table. This paper explores the hypothesis that children fail to compute scalar implicatures because they lack knowledge of relevant scalar alternatives to words like "some". Four-year-olds were shown pictures in which three out of three objects fit a description (e.g., three animals reading), and were asked to evaluate statements that relied on context-independent alternatives (e.g., knowing that all is an alternative to some for the utterance "Some of the animals are reading") or contextual alternatives (e.g., knowing that the set of all three visible animals is an alternative to a set of two for the utterance "Only the cat and the dog are reading"). Children failed to reject the false statements containing context-independent scales even when the word only was used (e.g., only some), but correctly rejected equivalent statements containing contextual alternatives (e.g., only the cat and dog). These results support the hypothesis that children's difficulties with scalar implicature are due to a failure to generate relevant alternatives for specific scales. Consequences for number word learning are also discussed.

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5–7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard classroom settings, (b) improves students' mathematical abilities (beyond standard math curricula), and (c) is related to changes in basic cognitive capacities like working memory. MA students outperformed controls on arithmetic tasks, suggesting that MA expertise can be achieved by children in standard classrooms. MA training did not alter basic cognitive abilities; instead, differences in spatial working memory at the beginning of the study mediated MA learning.

We investigated the origins and interrelations of causal knowledge and knowledge of agency in 3-month-old infants, who cannot yet effect changes in the world by reaching for, grasping, and picking up objects. Across 5 experiments, n = 152 prereaching infants viewed object-directed reaches that varied in efficiency (following the shortest physically possible path vs. a longer path), goal (lifting an object vs. causing a change in its state), and causal structure (action on contact vs. action at a distance and after a delay). Prereaching infants showed no strong looking preference between a person’s efficient and inefficient reaches when the person grasped and displaced an object. When the person reached for and caused a change in the state of the object on contact, however, infants looked longer when this action was inefficient than when it was efficient. Three-month-old infants also showed a key signature of adults’ and older infants’ causal inferences: This looking preference was abolished if a short spatial and temporal gap separated the action from its effect. The basic intuition that people are causal agents, who navigate around physical constraints to change the state of the world, may be one important foundation for infants’ ability to plan their own actions and learn from the acts of others.