title: Toddler subtraction with large sets: further evidence for an analog-magnitude representation of number.
abstract: Two experiments were conducted to test the hypothesis that toddlers have access to an analog-magnitude number representation that supports numerical reasoning about relatively large numbers. Three-year-olds were presented with subtraction problems in which initial set size and proportions subtracted were systematically varied. Two sets of cookies were presented and then covered. The experimenter visibly subtracted cookies from the hidden sets, and the children were asked to choose which of the resulting sets had more. In Experiment 1, performance was above chance when high proportions of objects (3 versus 6) were subtracted from large sets (of 9) and for the subset of older participants (older than 3 years, 5 months; n = 15), performance was also above chance when high proportions (10 versus 20) were subtracted from the very large sets (of 30). In Experiment 2, which was conducted exclusively with older 3-year-olds and incorporated an important methodological control, the pattern of results for the subtraction tasks was replicated. In both experiments, success on the tasks was not related to counting ability. The results of these experiments support the hypothesis that young children have access to an analog-magnitude system for representing large approximate quantities, as performance on these subtraction tasks showed a Weber's Law signature, and was independent of conventional number knowledge.
authors.affiliation: School of Psychology, University of Queensland, Australia. vps@psy.uq.edu.au
authors.forename: Virginia
authors.initials: V
authors.lastname: Slaughter
authors.forename: Dorian
authors.initials: D
authors.lastname: Kamppi
authors.forename: Jessica
authors.initials: J
authors.lastname: Paynter
mesh_terms: D002657:Child Development / Q000502:physiology*; D002675:Child, Preschool; D003071:Cognition / Q000502:physiology*; D003210:Concept Formation / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D011340:Problem Solving / Q000502:physiology*