However,

these data should be interpreted with caution, given that the 11-branch trials were always presented after children had participated in another experiment on a 6-branch tree, and also had received a familiarization trial to orient them to attend to the tree. In the present research, we tested whether children who do not yet possess symbols for large exact numbers (subset-knowers) are nonetheless able to give judgments pertaining to large exact find protocol quantities. To do so, the children were provided with one-to-one correspondence cues indexing the objects of a set: cues that made exact numerical differences accessible to perception. In conditions where the set to be reconstructed was comprised of the same individual items throughout the trial (no transformation in Experiment 1; the identity-preserving events in Experiment 4), the children were able to discriminate 5 from 6 puppets. The information conveyed by the one-to-one correspondence cues proved essential to the children’s success, as their performance dropped when these cues were not informative

(Experiment 5). Our findings therefore provide evidence that children understand at least some aspects of Hume’s principle BTK inhibitor before they acquire symbols for exact numbers: they understand that one-to-one correspondence provides a measure of a set that is exact and stable in time, even through displacements and temporary occlusions. However, as soon as a transformation affecting either the identity of the set to be reconstructed (the puppets) or the identity of the one-to-one correspondence cues (the branches) was applied (additions and subtractions in Experiment 2, substitutions in Experiment 4), our participants ceased to perform exact discriminations on large sets. In contrast,

Experiment 3 provided evidence that children performed near ceiling when the same addition and subtraction events were applied to small sets, thus excluding memory for the transformation itself as the source of the children’s difficulty. Furthermore, Experiment 4 presented a minimal contrast between two events that each resulted in no change in number: one event that did not affect the identity of the individual members buy Afatinib of the set (one puppet exiting and re-entering the box) and one event that did (one puppet exiting the box and another, featurally identical puppet entering the box). Although the same puppet movements occurred through the opening of the box in these two conditions, children succeeded at reconstructing the sets in the former case and failed in the latter. Interestingly, children did not ignore the transformation altogether, for they did not expect the end set to stand in a similar one-to-one relation to the branches of the tree as the starting set. Rather, whenever the identity of the items in the set of puppets changed, the children appeared to give up on the one-to-one correspondence cues and switched to a generic strategy, searching until they felt the box was empty.