Poster group
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poster
Whilst recent research suggests that infants can represent absolutevalues in numerical relationships, there is little evidence of infants'ability to reason with relative quantity. Using visual habituationtechniques, we investigated whether 7-month-old infants coulddiscriminate and represent 'more-less' relations between continuousquantities. Results indicate that infants successfully habituated whenshown a series of blocks of different shapes and sizes in which theratio relation between the colored areas in each block remainedconstant. Infants demonstrated increased looking times (dishabituation)during subsequent testing when show stimuli displaying novel more-lessrelations. Further investigation reveals that infants' discriminationis based on qualitative magnitude relationships rather than theabsolute ratio between target areas. Results are discussed in relationto the cognitive development of quantitative representation in infancy.
poster
Recently, Wynn (1992) has argued that infants possess asophisticated understanding of the number system. In a series ofexperiments in which an object was added or removed from a stage, shereported that 5-month-old infants are able to add and subtract smallnumbers. One can posit at least three possible explanations for Wynn'soriginal findings. First, as Wynn suggested, infants may actually be ableto add and subtract. Second, infants may be sensitive to the direction ofchange, but not the amount of change, so that they anticipate that additionleads to more, rather than less, and that subtraction leads to less ratherthan more. Lastly, infants may anticipate some sort of change, but notnecessarily the direction of change. In other words, they may expect thatthe display should change but not how it should change. The purpose ofthis study was to test these three competing hypotheses. Sixty-four 5-month-old infants participated in the study. Ourapparatus and procedure were similar to Wynn's. In the addition condition,a stuffed monkey was placed on a large puppet stage. A screen was thenrotated up to occlude the monkey. A second monkey was then placed behindthe screen. When the screen was lowered zero, one, two, or three monkeyswere found sitting on the stage. In the subtraction condition, two monkeyswere initially placed on the stage and the screen was raised. One of themonkeys was then removed from the stage. When the screen was lowered,zero, one, two, or three monkeys were found sitting on the stage. A 2 (condition) x 2 (gender) x 4 (number of test objects) mixedANOVA revealed a significant condition by test object interaction. In theaddition condition infants looked significantly longer at one than at zeromonkeys and marginally significantly longer at one than at two, or threemonkeys. The difference between one and two, although not significant,does tend to replicate Wynn's finding. On the other hand, taken as a wholethese results are most consistent with the hypothesis that the infantsrecognized something had changed within the event, but not the direction ornumber associated with that change. In the subtraction condition, the performance of the femalesmirrored the performance of all infants in the addition condition. In thiscase, they looked longer at an outcome of two than at the other outcomes.In contrast, males looked longer as more items were placed on the stage andmay in fact have been sensitive to the direction of change. As a whole, it appears that the results of this study replicatethose of Wynn but for a reason different than the one posited by Wynn. Infact they indicate that a simpler, more perceptual, explanation issufficient to explain the infants' behavior. They also suggest gradualimprovement in the development of addition and subtraction over the firstyear of life. But that can only be verified by additional research.
poster
Infants' numerical competence has been explored extensively. Looking-timestudies demonstrate infants' dishabituation to changes in object number,and response to unexpected results of numerical transformations. However,these demonstrations leave open the question of whether infants representthe ordinal relationships between numbers: Do infants encode 2 as simply'different than' 1, or as 'more than' 1? Preliminary evidence that infants represent ordinal relationships waspresented by Hauser et.al. (1999). Macaques and infants were given achoice between two discrete quantities of a desirable food (e.g.: grahamcrackers), placed into opaque containers. Participants selected one ofthe two containers. Because they were expected to want to select thecontainer yielding more, this task assessed spontaneous ordinal judgments,with any opportunity for training eliminated by presenting only a singletrial. This new method revealed that both macaques and infants chose thecontainer with the greater number of food items. The present research further explores infants' ordinal abilities. Weaddress two remaining questions: 1) What are the upper limits of infants'ordinal representations? and 2) What is the effect of non-numericalvariables correlated with number of food placements? Fifty-five 10-monthold and 69 12-month old infants were presented with one trial each usingthe ordinal choice task described above. Both groups were tested withcomparisons of 1 vs. 2, 2 vs. 3, and 3 vs. 4. As shown in Figure 1, amajority of 10- and 12-month olds chose the greater number withcomparisons of 1 vs. 2 (13/16 infants of both ages), and 2 vs. 3 (12/1610-month olds; 13/16 12-month olds). For both ages, the upper limit ofdiscrimination was 3 vs. 4, at which infants failed to choose the largernumber at above-chance levels (5/12 10-month olds; 8/16 12-month olds). Several non-numerical correlates could have influenced infants' decisions.Infants could have succeeded by monitoring the overall presentation timeat each container, or by keeping track of the overall amount of ediblesubstance. These possibilities were tested with combined groups of 10-and 12-month olds. An attention-control condition addressed the firstpossibility by equating the time spent at and attention drawn to eachcontainer. Infants saw 1 cracker + an empty handwave vs. 2 crackers.This manipulation did not affect infants' performance: 12/16 infants chosethe greater number (see Figure 2). An area-control condition addressedthe second possibility by equating the overall amount of edible materialplaced in each container. Infants saw 1 large cracker vs. 2 smallcrackers, with both yielding an equal amount of edible material. Equatingoverall quantity did influence infants: only 10/16 selected the greaternumber. These results suggest that infants have access to ordinal representationsin the first year of life. Comparisons appear limited to small numbers ofitems, although performance with large number sets (with Weber fractionsequated to conditions of demonstrated success) is currently beingexplored. While infants' behavior appears to be based on discretenumerical representations, item size also influences performance. Ongoingstudies are currently addressing this relationship between number andcontinous quantity.
poster
Human infants represent approximate numerosity and discriminate sets ofobjects whose difference ratio is large (Xu & Spelke, in press). Infants also appreciate how addition or subtraction transforms objectarrays (e.g., Wynn, 1995). Research from preschoolers neverthelessprovides evidence that children learn number words slowly (Wynn, 1992). The present research investigates how the infants' numberrepresentations contribute to 3-year-old children's developingknowledge of number word meanings.One experiment investigated whether children who do not know the exactmeanings of their counting words nevertheless have mapped each wordonto an approximate numerosity. First, we probed how high childrencould count and whether they understood each counting word using asimple 'give a number' comprehension task (after Wynn, 1992). LikeWynn's subjects, most children could count to ten or higher, but fewcould correctly give a requested number of objects above 'two.' Next,we probed children's partial knowledge of higher counting words. Inone condition, children were shown a set of objects denoted by a knowncounting word (e.g., one fish) and a second set denoted by a highercounting word (e.g., eight fish). Children were asked to 'point to theone/eight fish' and did so successfully, as in previous research (Wynn,1992). In the second, critical condition, children were shown twolarger sets of objects differing by a 2:1 ratio (e.g., four vs. eightfish). When asked to 'point to the four/eight fish,' children pointedrandomly to the two piles. This finding provides no evidence that3-year-old children have mapped the words in their count sequence to arepresentation of approximate numerosity. A second study investigated whether young children appreciate thatwords such as 'four' and 'eight' change their application when the setsare transformed by addition. After the counting and exactcomprehension pretests, children were shown two piles containingadjacent numerosities whose words they produced when counting butfailed to comprehend (e.g., five vs. six fish), they were told that onepile had five fish, that pile then underwent either a number-relevanttransformation (an object was added) or an irrelevant transformation(the objects were rearranged), and children were asked to point to thesame or a different number of objects. If children understand thatnumber words denote specific numerosities, they should infer that a setlabeled as 'five fish' will still be labeled as 'five' if the objectsare rearranged, and that it will no longer be labeled as 'five' if afish is added. Contrary to this prediction, children pointed to thetwo piles at random in every condition of this experiment. Incontrast, children responded correctly in a followup experiment inwhich the pile with the named number of objects underwent notransformation. These findings provide evidence that young childrentreat number words as mutually exclusive in a direct test, but thatknowledge does not derive from any specific link between the numberwords and representations of numerosity and addition. In summary, young children do not appear to relate their countingwords to either of the number representations found in infants. Infants discriminate between sets of objects when their numerositydiffers in a 2:1 ratio, but 3-year-old children do not map countingwords to these approximate number representations. Moreover, infantstake account of addition in their representations of visual arrays, but3-year-old children evidently do not view such transformations asrelevant to the application of counting words. In the domain ofnumber, a long, indirect path links the infant's concepts to thechild's language.