The Representations Underlying Infants' Choice of More: Object Files Versus Analog Magnitudes

Abstract

A new choice task was used to explore infants' spontaneous representations of more and less. Ten- and 12-month-old infants saw crackers placed sequentially into two containers, then were allowed to crawl and obtain the crackers from the container they chose. Infants chose the larger quantity with comparisons of 1 versus 2 and 2 versus 3, but failed with comparisons of 3 versus 4, 2 versus 4, and 3 versus 6. Success with visible arrays ruled out a motivational explanation for failure in the occluded 3-versus-6 condition. Control tasks ruled out the possibility that presentation duration guided choice, and showed that presentation complexity was not responsible for the failure with larger numbers. When crackers were different sizes, total surface area or volume determined choice. The infants 'pattern of success and failure supports the hypothesis that they relied on object-file representations, comparing mental models via total volume or surface area rather than via one-to-one correspondence between objectfiles.

Evidence for a non-linguistic distinction between singular and plural sets in rhesus monkeys

“…If it is, then the signatures of PI should be found when small sets are presented one individual at a time, as in previous studies that document limits of PI in rhesus monkeys (Hauser & Carey, 2003;Hauser et al, 2000;Wood et al, 2008) and in human infants (Barner et al, 2007;Cheries et al, 2006;Feigenson & Carey, 2005;Feigenson et al, 2002). To explore this, we tested rhesus monkeys on the numerical comparisons of Experiment 1, but presented apples as independently moving objects that were hidden individually.…”

“…These data thus replicate previous studies in which separately moving objects are placed, one at a time, into separate buckets for choice. These previous studies find success when both sets are within the range of PI (1 vs. 2, 2 vs. 3, and 3 vs. 4), in the face of failures when one set is outside that range (Hauser et al, 2000;see Feigenson & Carey, 2003Feigenson et al, 2002, for parallel infant results). These data also suggest that the 3 vs. 5 success reported by Hauser et al (2000) was an anomaly a conclusion which is also consistent with that study's finding that rhesus monkeys fail at even 3 vs. 8.…”

“…According to theories of object-based attention and working memory, independently moving individuals trigger the assignment of visual indexes to objects (Pylyshyn, 2003), which can then be represented in working memory (Kahneman, Treisman, & Gibbs, 1992;Luck & Vogel, 1997). These representations permit the comparison of sets (e.g., held in two working memory models) on the basis of one-to-one correspondence, as well as on the basis of summed continuous variables, so long as both sets are within the limits of PI (Feigenson & Carey, 2003Feigenson et al, 2002). These facts regarding PI, in addition to the fact that AM representations are non-obligatory, allowed us to study the signatures of setrelational representations.…”

“…The primary signature of AM representations is scalar variability: error in the representation of numerosity grows linearly with the size of the set being represented. As a result, the discriminability of two sets is a function of 1 In fact, infants' choices are based on overall amount of cracker stuff, such that they should prefer 1 large cracker that amounts to more overall stuff than 2 small ones (Feigenson, Carey, & Hauser, 2002). However, this summing over continuous amount is limited to sets within PI: infants cannot sum over sets of 4 or more crackers.…”

Improving approximate number sense abilities in preschoolers: PLUS games.

“…This system relies upon the ratios between stimuli that are presented, known as Weber's fraction (w). Over development, children's ANS system increases in precision and children become better at discriminating between smaller ratios (Feigenson, Carey, & Hauser, 2002;.One dominant theory is that ANS abilities serve as a foundation for symbolic mathematics. Studies in both typical development and developmental disorders have shown that the ANS is predictive for number ability outcomes later on in life and that inter-individual differences in w can be explained by differences in ANS acuity …”