Developmental Science 5:2 (2002), pp 186–212© Blackwell Publishers Ltd. 2002, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.Blackwell Publishers LtdARTICLE WITH PEER COMMENTARIES AND RESPONSEHow infants process addition and subtraction eventsLeslie B. Cohen and Kathryn S. MarksDepartment of Psychology, The University of Texas at Austin, USAAbstractThree experiments are described that assess 5-month-old infants’ processing of addition and subtraction events similar to thosereported by Wynn (1992a). In Experiment 1, prior to each test trial, one group of infants was shown an addition event (1 +1) while another group was shown a subtraction event (2 − 1). On test trials, all infants were shown outcomes of 0, 1, 2 and3. The results seemed to require one of two dual-process models. One such model assumed that the infants could add and subtractbut also had a tendency to look longer when more items were on the stage. The other model assumed that infants had a preferencefor familiarity along with the tendency to look longer when more items were on the stage. Experiments 2 and 3 examined theassumptions made by these two models. In Experiment 2, infants were given only the test trials they had received in Experiment1. Thus, no addition and subtraction or familiarity was involved. In Experiment 3 infants were familiarized to either one or twoitems prior to each test trial, but experienced no actual addition or subtraction. The results of these two experiments supportthe familiarity plus more items to look at model more than the addition and subtraction plus more items to look at model.Taken together, these three experiments shed doubt on Wynn’s (1992a) assertion that 5-month-old infants can add and subtract.Instead they indicate the importance of familiarity preferences and the fact that one should be cautious before assuming thatyoung infants have sophisticated numerical abilities.Learning the number system and how to manipulate itis one of the most difficult tasks a young child encoun-ters; it is a slow and laborious process taking years tocomplete (for example, Fuson, 1988). Children studymathematics from their earliest school days to highschool graduation and beyond. However, like most areasof psychology, there are multiple perspectives on thistopic. Three major views on the development of numer-ical competence can be distinguished. The empiricistview argues that children learn about numbers byobserving numerical transformations and noting theconsistencies between events (Kitcher, 1984). Piaget’sconstructionist view argues that the number concept isbuilt from previously existing sensorimotor intelligence(Piaget, 1941/1952). In contrast, a more recent nativistview argues that sensitivity to number is innate and evenyoung infants possess strikingly mature reasoning abilit-ies in the numerical domain (Wynn, 1992b, 1992c).Over the course of the last 20 years, researchers haveexplored questions about the roots of numerical knowl-edge using looking time techniques with infants. Thefirst area to be investigated was called subitization. Sub-itization is the rapid, perceptual enumeration of smallsets, usually from one to four items. It is thought thatadults subitize unless a display contains more than fouror five items, in which case they revert to counting(Balakrishnan and Ashby, 1992). Some researchers havesuggested that infants may also have the ability to sub-itize small arrays of items. Starkey and Cooper (1980),the first to propose infant subitization, found thatinfants at 5.5 months of age were able to discriminatetwo from three dots, but not larger numbers of dots.Further research has since replicated Starkey andCooper’s (1980) findings both with neonates (Antell &Keating, 1983) and with 10- to 12-month-olds, the latterusing common objects instead of dots (Starkey & Cooper,1980). Together this research may provide evidence forthe presence of numerical knowledge during early infancy. However, more recent research is telling a differentstory. In contrast to previous studies, Clearfield and Mix(1999a, 1999b) systematically manipulated contourlength and area in the standard subitization paradigmwith 6- to 8-month-old infants. They reported thatinfants dishabituated to a change in either contourlength or area, but not to a change in number. As aresult, they concluded that infants may actually be usingAddress for correspondence: Leslie B. Cohen, Department of Psychology, Mezes Hall 330, University of Texas, Austin, TX 78712, USA; e-mail:[email protected] addition and subtraction 187© Blackwell Publishers Ltd. 2002continuous quantity rather than number to discriminatebetween displays, and thus may not be subitizing. Hold-ing mass constant, Feigenson and Spelke (1998) reacheda similar conclusion with 7-month-old infants. Thus, theconclusion that infants are subitizing remains controver-sial. Further investigation is still necessary to determineinfants’ actual subitizing ability as well as the age atwhich subitizing first occurs.A second body of evidence indicates that infants maybe able to process numerical information in one modal-ity and then transfer it to another. Starkey, Spelke andGelman (1983, 1990) were the first to show that 6- to 9-month-old infants might be able to enumerate soundsand match them correctly with a visual display depictingthat number. These results are even more remarkable thanthose for subitizing because they suggest some primitivecounting ability by infants (Starkey et al., 1990). How-ever, this research is also controversial. Other laboratories,using infants of the same age, have been unable to replic-ate the original findings (Moore, Benenson, Reznick,Peterson & Kagan, 1987; Mix, Levine & Huttenlocher,1997). In addition, Mix, Huttenlocher and Levine (1996),using a procedure adapted for preschoolers, found that3-year-olds are unable to correctly match auditory tovisual numerosity. Thus, as with the subitizing results,there is no uniform agreement that infants under 6 monthsof age, or even young children, are able to enumeratesounds and then match them with a visual display.Given the evidence, albeit tentative, that young infantshave some understanding of number, Wynn (1992a) tookthe next step and asked to what extent infants are ableto actively manipulate the number system. In what hasbecome a frequently cited paper, Wynn (1992a) arguedthat infants as young as 5 months of age ‘are able tocalculate the