How do children progress from an initial understanding of set identity to the adult concept of numerosity? One possibility is that children first understand the principles buy Crizotinib of exact numerical equality as applied to small sets, through their object-tracking

system, and later extend those principles to large sets (Klahr & Wallace, 1973). As far as understanding the impact of addition and subtraction transformations on numerical equality, this seems a likely possibility, given children’s ability to predict the numerosity of small sets through addition and subtraction events. However, it remains to be shown that young children are able to handle substitution events with small numbers, since substitutions are necessarily more complex: they are formed of at least two simple events, one addition and one subtraction. Alternatively, experience with numeric symbols may play a crucial role in the acquisition of exact numerical equality. As children become CP-knowers, they assign a meaning to number words that is defined in

terms of the counting procedure. Although the impact of the transition to the CP-knower stage on children’s concepts of number is debated (Davidson et al., 2012 and Le Corre et al., http://www.selleckchem.com/products/Bosutinib.html 2006), all parties agree that, at a minimum, CP-knowers appreciate that to say that there are ‘five frogs’ means that if they count this set of frogs, they will end the count with the word ‘five’. Thus, CP-knowers have access to a representation that has the properties of exact numbers, and in particular, implies a relation of exact numerical equality between sets. As a result, whenever they are able to apply counting, or perhaps even when they can simulate the application Anacetrapib of counting, CP-knowers gain the ability to respond in accordance with a precise interpretation of number words. For example, contrary to subset-knowers, CP-knowers generalize number words correctly in face of two sets presented

in visual one-to-one correspondence (Sarnecka and Gelman, 2004 and Sarnecka and Wright, 2013), perhaps because this configuration enables them to predict how the results of counts would compare across these two sets. In other tasks where counting is not permitted, young CP-knowers sometimes revert to the same errors as subset-knowers (Davidson et al., 2012 and Sarnecka and Carey, 2008). Nevertheless, it is possible that, after the children have become CP-knowers, the counting procedure serves to scaffold the development of a concept of exact numerical equality between sets by providing children with a mental model from which they derive the properties of exact numbers.