6, p   = .24, ηp2=.14, and no interaction of Condition and Outcome Size, F(1,9)<1,ηp2<.01. Additional ANOVAs confirmed that, in each condition, the children searched longer for the 3rd puppet in the trials in which the transformation resulted in 3 puppets (puppet addition/subtraction condition: F  (1, 9) = 101.1, p   < .001, ηp2=.92; branch addition/subtraction condition: F  (1, 11) = 78.6, p   < .001, ηp2=.88). Furthermore, performance was significantly better with the small numbers of Experiment

3 compared to the large numbers of Experiment 2 (interaction between Experiment and Outcome Size for the puppet addition/subtraction condition: F  (1, 20) = 13.5, p   = .0015, Nutlin3 ηp2=.40; for the branch addition/subtraction condition: F  (1, 22) = 15.0, p   < .001, ηp2=.40). In the context of small numbers, children were able to remember and process addition and subtraction

transformations adeptly. They were equally able to do so whether the transformation affected a visible or an invisible set (branches or puppets). This finding converges with a host of research showing that children are able to infer and correct surreptitious transformations in small sets of objects (Gelman, 1972b and Gelman and Gallistel, 1986). The children’s success in Experiment 3 provided evidence that they were able to remember and understand the transformation events, thus excluding memory of the transformation events and other limits to processing the transformations as the reason for the children’s failure in Experiment 2. Three potential explanations for this failure remain. First, perhaps children were able to remember a transformation SCH727965 datasheet event while tracking a small set of objects, but remembering

both a transformation and a one-to-one mapping between branches and puppets exceeded their memory capacity. Indeed, in contrast to the conditions presenting large sets of puppets, it is possible that children SSR128129E did not use the branches to succeed with small sets, given that the set sizes did not exceed their object-tracking limit. Second, perhaps children remembered both the starting configuration and the transformation, but failed to combine these pieces of information so as to update their expectations for the final mapping between puppets and branches. In all the transformations used so far (additions and subtractions), the end configuration was different from the starting configuration, hence the need to update the mapping. Third, perhaps children of this age do not have a full understanding of whether transformations affect one-to-one mappings between sets; in other words, maybe children fail to recognize that relations established by one-to-one pairings follow the principle of Addition/Subtraction. Under this hypothesis, children in Experiment 2 were unsure whether the transformation events affected the one-to-one correspondence mapping between the branches and puppets, and thus they stopped attending to this mapping altogether.