Research beginning with Piaget reveals a change in infants’understanding of multistep, means-end action sequences:Whereas 12-month-old infants reason that (e.g.) one opens abox to access its contents, younger infants are more likely toreason that one’s goal is simply to open the box. Here weexplore the implications of this developmental change ininfants’ action understanding for infants’ social evaluations.Using a puppet show paradigm, we examined infants’evaluations of two agents who helped another agent to achieveeither the end or the means of a means-end sequence, bothbefore and after 12 months of age. In a subsequent preferencetest, 15-month-old infants reached for an End-Helper over aMeans-Helper, whereas 8-month-old infants did the reverse.These findings link infants’ evaluation of helpers to theirrepresentations of action plans, consistent with recentcomputational models of naïve psychology.

Do infants’ social evaluations privilege the outcomes of others’ actions, or the beliefs underlying those actions? In two experiments, 8-month-old infants viewed a protagonist who sought to grasp one of two toys, each inside a different box, as two other agents observed. Then, while the protagonist was away, the toys exchanged locations, either in the presence or absence of the two other agents. Thus, the agents had either true or false beliefs about the toys’ locations. When the protagonist returned, one agent opened the box that now contained the protagonist’s desired toy, whereas the other opened the box that previously contained that toy. When agents had true beliefs about the desired toy’s location, infants preferred the agent who opened the box containing that toy. When agents had false beliefs about that location, infants instead preferred the agent who opened the opposite box. Thus, infants' social evaluations privilege agents’ beliefs.

Research provides evidence that infants infer what others can and cannot see from their differing perspectives, but do infants appreciate that their own perspective on an object can differ from that of a person who views the same object from a different direction? First, infants were shown two faces with screens in front of or behind them. Infants correctly inferred that a face that was visible to them was occluded to a person sitting across from them. Then two experiments presented infants with two unscreened faces: one upright and one inverted. Infants attributed their own perspective on those faces to the other person: They did not appreciate that faces that were upright to them were inverted to the other person. Thus, infants appreciate that others may see things that they do not, but they fail to grasp not that others may experience the same visible objects differently than they do.

Commutativity–the fact that changing the order of operands in an operation does not change the result–is a fundamental principle of mathematics. How does its understanding develop in children? While this question has mostly been addressed for addition, here we focus on multiplication. We ask whether children’s formal learning of multiplication commutativity relies on pre-existing non-symbolic intuitions, or whether it is first learnt symbolically and only later elaborated as a general principle that extends to concrete situations. 2nd and 3rd graders received an intervention on commutative multiplication, before and after which they played a number comparison game testing their understanding of commutativity in symbolic and non-symbolic contexts. Our results suggest that the commutative principle of multiplication may not be available to intuition before formal teaching: perceiving that 2 groups of 3 dots and 3 groups of 2 dots contain the same number of dots requires mastering commutativity symbolically first.

In order to understand social relationships, humans must recognize cues of affiliation. When infants see interactionsbetween abstract, animated characters, they use imitation, helping, comforting, and exerted effort to predict who willapproach whom. Moreover, infants attend to and reach for characters who imitate other characters and those who helpothers. The present research builds on these findings and asks whether infants reach for human-animated puppets withdistinct and variable human voices who imitate, are imitated by, comfort, are comforted by, or move synchronously with aperson. At 12 months, infants reached more often for puppets who imitate a humans sound, and also for those who werenot targets of imitation. In contrast, infants did not reach more for puppets who comforted or synchronized their motionswith a human actor. By 12 months, therefore, infants show differentiated responses to different acts of social engagementby those whose social interactions they observe as third parties.