Infant number knowledge : a test of three theories.

Transcription

1 University f Massachusetts Amherst SchlarWrks@UMass Amherst Masters Theses February 2014 Dissertatins and Theses 2003 Infant number knwledge : a test f three theries. Erin N. Cannn University f Massachusetts Amherst Fllw this and additinal wrks at: Cannn, Erin N., "Infant number knwledge : a test f three theries." (2003). Masters Theses February This thesis is brught t yu fr free and pen access by the Dissertatins and Theses at SchlarWrks@UMass Amherst. It has been accepted fr inclusin in Masters Theses February 2014 by an authrized administratr f SchlarWrks@UMass Amherst. Fr mre infrmatin, please cntact schlarwrks@library.umass.edu.

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3 INFANT NUMBER KNOWLEDGE; A TEST OF THREE THEORIES A Thesis Presented by ERIN N. CANNON Submitted t the Graduate Schl f the University f Massachusetts Amherst in partial fulfillment f the requirements fr the degree f MASTER OF SCIENCE May 2003 Department f Psychlgy

4 INFANT NUMBER KNOWLEDGE: A TEST OF THREE THEORIES A Thesis Presented by ERIN N. CANNON Apprved as t style and cntent by: Neil E. Berthier, Member Melinda Nvak, Member Melinda Nvak, Department Head Psychlgy Department

5 ACKNOWLEDGMENTS I wuld like t thank my advisr, Richard S. Bgartz, fr his supprt and guidance. Frm the earliest stages he was pen t explring the questins I wanted t answer, patiently allwed me t think abut them, and challenged me t g beynd what was "easy." The research skills and life skills (and cnfidence') 1 have acquired frm this experience are invaluable, and 1 am grateful. I wuld als like t thank the members f my cmmittee, Neil Berthier and Melinda Nvak fr their helpful cmments and recmmendatins during this prcess. 1 wuld like t thank all the parents wh vluntarily came t the lab with their infants. I wuld especially like t thank all f the undergraduate research assistants, ver the past tw years, fr their help in building the stage, hurs f training, running subjects, and cding data. I culd nt have dne this withut them. I als thank the graduate students wh vluntarily helped me run subjects during their summer break. A special thank yu t Dawn Melzer, my fficemate, my clleague, my friend, fr always helping me keep things in perspective during all f the highs and lws. Thank yu t my family fr their encuragement and "phne supprt." It might have taken a while, but I did it! iii

6 1 TABLE OF CONTENTS Page ACKNOWLEDGEMENTS... LIST OF TABLES LISTOFHGURES Ill VI Vll CHAPTER L INTRODUCTION ^ The Theries: Backgrund 4 The Accumulatr Mdel 5 The Object-File Mdel 9 The Perceptual Prcessing Mdel 12 Review f Previus Research Testing the Mdels 14 The Present Study METHOD 28 Participants 28 Apparatus 28 Equipment 30 Prcedure 30 Intrductin Phase 3 Cnditin 2 3 Familiarizatin Trials 32 Test Trials 33 Cnditin 3 ^4 Familiarizatin Trials 34 Test Trials 34 iv

7 ^nau,ns 2 and 3: Tests fr the Accumulatr, Perceptual Prcessmg. and Ubject-File Mdels. """''""Fne'Mdr 4. DISCUSSION '"^ P-c^tuarp.ces^ The Accumulatr Perceptual Prcessing ^ ENDNOTES Object-Files BIBLIOGRAPHY 77 V

8 LIST OF TABLES Table Page 1. Llng Time Predictins fr Each Thery in Cnditins 2 and 3, fr Sequence A Event»-vciii Lldng Time Predictins fr Each Thery in Cnditins 2 and 3, fr Event L^vcm Sequence B Lldng Time Predictins fr All Theries in Cnditin 2/3, fr Bth Event Sequences Sixteen Trial Type Orders fr Pssible/Impssible Pairings Event Sequences (A r B) tested in 16 Trial Type Orders fr Cnditins 2 3 and 2/3 ' ' 67 vi

9 LIST OF RGURES Figure Page 1. Sequence x Side Interactin fr First Lk Acrss All Three Cnditins Type x Number Interactin fr Length f First Lk within Blck 1 f Cnditin 2/ Number x Sequence Interactin fr Length f First Lk within Blck 1 f Cnditin 2/ Side X Sequence Interactin fr Length f First Lk within Blck 1 f Cnditin 2/3 5. Sequence x Side x Number Interactin fr Length f First Lk within Blck 1 f Cnditin 2/3: A) Tw Objects Revealed, B) Three Objects Revealed Length f First Lk (in Secnds) t Pssible and Impssible Events f Tw Objects Revealed n the Left and Right Sides Length f First Lk (in Secnds) t Pssible and Impssible Events f Three Objects Revealed n the Left and Right Sides 74 vii

10 CHAPTER 1 INTRODUCTION In the past 20 years, an abundance f evidence has suggested that infants, ranging in age frm days ld t 12 mnths ld, are sensitive t numersity (Antell & Keating, 1983; Starkey & Cper, 1980; Starkey, Spelke, & Gelman, 1990; Strauss & Curtis, 1981; Wynn, 1996). Infants discriminate between small sets f dts presented linearly, regardless f spatial (i.e., length and density) cues (Starkey & Cper, 1980; Antell & Keating, 1983). Starkey and Cper (1980) suggested that this number discriminatin is limited t small sets because the infants culd make a tw-dts versus three-dts discriminatin but nt fur versus six. Similar results were fund when pictures f threedimensinal bjects were presented in randm patterns and sizes (Starkey et al., 1990; Strauss & Curtis, 1981). In these studies, infants lked lnger (therefre, "discriminated") at arrays that were different in number frm what he r she was initially habituated t. Yung infants als discriminate number in less discrete frms f presentatin. Starkey et al. (1990) fund six-mnth-lds discriminated number acrss perceptual mdalities in that they preferentially attended t bject presentatins that crrespnded with the number f drum beats heard (but see Mix, Levine, & Huttenlcher, 1997 r Mre, Benensn, Reznick, Petersn, & Kagan, 1987). Infants further discriminate even less tangible events such as actins. Wynn ( 1996) shwed infants dishabituated frm watching tw jumps f a puppet when presented with a nvel three jump sequence. Bijeljac-Babic, Bertncini, & Mehler (1993) fund that newbrns discriminated multisyllabic utterances, i.e., utterances f tw syllables frm three syllables. These infants 1

11 hwever, als failed t discriminate fur frm six, similarly t Starkey & Cper's (1980) findmg. The abundance f evidence in different types f experiments suggests that yung infants have sme, albeit limited, number representatinal system present early in life. One means f investigating the rbustness f infants' prpsed numerical representatins has been t use tasks in which a transfrmatin has been made n a represented set f entities (e.g., Kechlin, Dehaene, & Mehler, 1997; Simn, Hesps, & Rchat, 1995; Ul.er, Carey, Huntley-Fenner, & Klatt, 1999; Wakely, Rivera, & Lander, 2000; Wynn, 1992; Wynn & Chiang, 1998). Studies invlvmg a physical transfrmatin differ frm habituatin studies in that a vilatin f expectatin prcedure is used. The infant is presented with a sequence f bject-based events, during a brief cclusin sme transfrmatin is made n the number f bjects, and an expectatin f the resulting number is assumed t be frmed. Lnger lking at an utcme is assumed due t a mismatch between the expectatin and what is in perceptin. Sme f these studies using the vilatin f expectatin paradigm have been interpreted as shwing that infants pssess even greater capabilities than numerical representatin. The infant's ability t frm an expectatin that may be number-based, and then use that expectatin t discriminate a perceived set f entities may invlve further reasning. Therefre, sme researchers have taken the psitin that transfrmatin studies exhibit infants' numerical reasning abilities (Wynn 1992, 1995; Wynn & Chiang, 1998). The landmark "transfrmatin" study by Wynn (1992), and subsequent variatins (e.g., Simn et al., 1995; UUer et al., 1999; Wynn & Chiang, 1998), in which infants as yung as five mnths ld seemingly perfrmed simple additin/subtractin calculatins. 2

12 have supprted tw mdels f early numerical reasnmg. The first mdel is the "accumulatr," a member f a class f analg-magnitude mdels. In shrt, this mdel psits the wrkings f a neural mechanism specialized t deal with number, based n the same pnnciples as the cunting system. The secnd mdel is the "bject-file" mdel, which rests n a mechanism f selective attentin, calling upn physical knwledge nly. Bth mdels have been supprted in the literature. Due t the wide variability in prcedures and results, researchers thus far have been unable t prvide a clear cntrast between these mdels, nr t accunt fr the infants' verall perfrmance using nly ne mdel. Cnsequently, researchers such as Xu and Speike (2000) and Wynn (persnal cmmunicatin, December 12, 2000) have suggested that perhaps bth hypthesized mechanisms cntribute t the develpment f enumerative abilities, and their relative cntributins may depend n the size f the set being wrked upn. Hwever, a third explanatin has recently emerged, and quickly gained supprt frm bth habituatin and transfrmatin studies. There is evidence t suggest that a sphisticated cgnitive system specialized fr number may nt be necessary t accunt fr the previusly accepted "sensitivity." Instead, simple perceptual factrs may be adequate in accunting fr infants' behavirs. Primarily, the infants may be shwing familiarity/nvelty preferences, preferences fr "mre" t lk at, and sensitivity t changes in spatial dimensins. These factrs are ften cnfunded with the arithmetically pssible and impssible utcmes in the transfrmatin studies (Chen & Marks, 2002; Simn et al., 1995; Wynn, 1992). The present research will cntrast these three psitins and test the assumptins upn which they are based, shedding light n the underlying nature f 10-mnth lds' knwledge f number. Specifically, the 3

13 experimental design will allw fr a determinatin f whether abilities exhibited in these tasks are based n the use f an accumulatr cunting mechanism, an bject-based attentinal mechanism, r simple perceptual prcesses. The Theries: Backgrunrl Wynn (1992) changed the apprach f studying infant number knwledge, frm the previusly standard habituatin paradigm, t a vilatin f expectatin paradigm. Wynn claimed that tlve-mnth-lds, ver three experiments, shwed evidence that they culd "calculate" the results f simple arithmetical peratins n a small set f bjects. In the first experiment, there were tw cnditins; additin and subtractin. In the additin cnditin, each trial began with the infant seeing ne dll n the puppet stage. The experimenter's hand entered the stage t the infant's right side, and held up the dll t call attentin t it. A screen rtated up t cclude the ne dll, and a secnd dll was brught nt the stage frm the right-hand side, tapped n the flr, squeaked, then placed behind the screen as the infant lked n. The screen rtated dwn t reveal either ne r tw dlls, an impssible r pssible event, respectively. In the subtractin cnditin, the infants initially were shwn tw bjects n the stage. The experimenter's hand entered frm the right side, wiggled and squeaked them ne at a time, then exited the stage empty-handed. The screen rtated up, and the empty hand returned, tk the right-mst dll frm behind the screen, squeaked and tapped it n the stage flr in the infant's sight, then exited the stage t the right with the dll in hand. The screen then rtated dwn t reveal either ne (pssible) r tw (impssible) dll(s). Wynn predicted lnger lking in bth cnditins t the impssible, r arithmetically incrrect, utcmes. Indeed, the 5-mnth-Ids discriminated the pssible utcmes (1 + 4

14 1-2 and 2-1 = 1) frm the impssible (1 + 1 = 1 and 2-1 = 2). These resuus were replicated in a secnd experiment. In a third experiment, infants crrectly discriminated a = 2 event frm a 1 + I = 3 event. The five-mnth-lds lked lnger at three dlls than at tw, indicating that nt nly did the infants have an expectatin fr the utcme t be "mre than ne," but that the infants had an expectatin t see "exactly" tw dlls. In accrdance with the hyptheses, the infants lked lnger t impssible events in bth the additin and subtractin cnditins, in all three experiments. Althugh Wynn (2000) claims these findings t be "rbust and cnsistent," as they have been partially replicated in ther labs (Simn et al., 1995; Uller et al., 1999), there has als been sme failure t replicate as well (e.g., Feigensn et al., expt 7, 2002; Pirier, 2001; Wakely et al., 2000). Mrever, a study by Kechlin, Dehaene, and Mehler, (1997) claims "infants lked reliably lnger at impssible events than at pssible events" (p. 98), and is ften cited as such. But this finding was nly significant in the subtractin cnditin (2-1 = 1 r 2), with n difference in lking time in the additin cnditin ( = 1 r 2). This difference has yet t g reprted in the literature. Stiil, Wyrm's (1992) findings led t the claim that infants "pssess true numerical cncepts" (p. 750) by the age f five mnths. The infants were able t encde numerical relatinships, make internal manipulatins, and represent a numerically meaningful utcme. This was demnstrated by the precisin f their calculatins. Wynn (1992) suggested that the arithmetical abilities demnstrated supprt fr an innate mechanism f enumeratin. She psited the "accumulatr mdel" as the best fitting accunt fr enumerative abilities evidenced at birth in infants and animals (Wynn, 1995, 1998). 5

15 The Accumulatr Mdel In 1983, Meek and Church prpsed a neural mdel that accunts fr bth perceptual timing and enumerative abilities in rats. Their mdel prvides a mechanism fr making numerical discriminatins. It is based n the premise that cntinuus quantities are stred in memry in terms f a system that is analgus t the principles f cunting (Gallistel, 1990). Discriminatin between tw quantities ccurs when a magnitude stred in memry is cmpared t what is in perceptin. When in cunting mde, there is a neural pacemaker generating pulses at cnstant intervals. A gate pens and clses in ne-t-ne crrespndence with each item t be cunted, allwing the pulses t enter a strage area where they are incrementally accumulated. The final pulse, r gate clsure, is tagged with a single analg value, representing the entire amunt. Gallistel and Gelman (1992) suggested that, in humans, these analg representatins are symblic representatins cmparable t numerical integers, and are later mapped nt number wrds. Bth the prpsed accumulatr mechanism and verbal cunting are guided by and dependent upn principles f ne-t-ne crrespndence, rdinality, and cardinality (Gallistel, 1990; Gallistel & Gelman, 1992). Therefre, it is plausible that such a mechanism, which perates n similar principles t cunting, may underlie preverbal cunting abilities in humans. Evidence fr an accumulatr mechanism has been fund in rats (Meek & Church, 1983), pigens (Rberts & Mitchell, 1985), mnkeys (Brannn & Terrace, 1998), human adults (Whalen, Gallistel, & Gelman, 1999), yung children (Huntley-Fenner, 2001; Huntley-Fenner & Cannn, 2000), and infants (Wynn & Chiang, 1998; Xu & Spelke, 2000). Hwever, the means by which the mdel is tested varies, depending n the 6

16 assumptin investigated. Fr example, the mdel allws fr tests f distance etlects, Weber's law, and cardmality. Of central imprtance here is cardinality. Because the last item is tagged with a single analg representatin f the accumulated value, this has implicatins fr memry. The mechanism stres ne value in memry, as ppsed t a separate representatin fr each item that has entered the accumulatr. This implies that there is n capacity limit n the quantity that can be accumulated and held in memry. Als, there can be several accumulatrs wrking at ne time. Althugh there are n limitatins t the values wrking accumulatrs can hld, the questin f hw many accumulatrs can be wrking at ne time has yet t be investigated. Anther peratin assumed in the mdel is the cmparisn f values. The value given t the stred amunt is cmpared t either a value in perceptin, r anther value in memry. Because a cmparisn f analg magnitudes is being made, discriminatin is best when differences are large (e.g., 8 versus 16 as ppsed t 8 versus 12). This is cnsidered t be the distance effect subject t Weber's Law. Hwever, a cmparisn f tw versus three items is nt necessarily much mre difficult than discriminating tw frm ne, because the numbers are still relatively small. Likewise in tasks f numerical estimatin, as the number f items t be estimated gets large, errrs increase in a cnstant prprtin t the assciated cmparisn magnitude, i.e., the value held in memry (see Gallistel & Gelman, 1992, Whalen, Gallistel, & Gelman, 1999). Distance effects are indirectly due t this scalar variability in the stred value, and are simply a functin f the rati f the pair f numbers (Gallistel & Gelman, 2000). Unless the rati between tw quantities is als large (e.g., 1:2), a simple discriminatin task will becme increasingly difficult as numbers (r quantities) increase (Gallistel & Gelman, 1992). 7

17 Evidence fr the accumulatr, based n the Weber's Law principle alne, has been btained in estimatin tasks frm aduhs (Whalen et al., 1999) and yung children (Huntley-Fenner, 2001 ), as well as discriminatin tasks lking at distance effects in yung children (Huntley-Fenner & Cannn, 2000) and infants (Xu & Spelke, 2000). The infant studies testing specifically fr the accumulatr mdel have emplyed bth the vilatin f expectatin paradigm (Wynn, 1992; Wynn & Chiang, 1998) and the habituatin paradigm (Xu & Spelke, 2000). Accrding t the mdel, when there is discrepancy between the accumulated value held in memry and the value held in perceptin, this mismatch will elicit lnger lking frm the infants. In the study by Xu & Spelke (2000), infants wh were habituated t displays f eight dts were fund t dishabituate (lked lnger) when presented with displays f 16 dts, but did nt dishabituate t 1 2 dt displays. The six-mnth-lds discriminated r detected the numerical difference between eight and 16, but nt eight and 12. This finding supprted the accumulatr mdel, in that the infants appeared t detect numerical mismatches within the cnstraints f the Weber's Law fractin. By six mnths the infant can discriminate between tw numerically large sets f items presented in a 1:2 rati, but nt 2:3, where the rati is smaller. The infant arithmetic results fund by Kechlin et al. (1997), Simn et al. (1995), & Uller et al. (1999), partial replicatins f Wynn (1992), can be interpreted by a different accunt f early enumeratin. This accunt addresses the arithmetic studies and interprets their results in terms f the infant's knwledge and representatinal abilities fr bjects. The infant's ability t track bjects thrugh space, frm a representatin f an ccluded bject, and hld this infrmatin in memry may accunt fr the results f the 8

18 transfrmatin studies, nt number, per se. This nn-numencal, representatinal accunt cnstitutes the basis fr a very different srt f interpretatin: the bject-file mdel. The Object-File Mdel Initially prpsed by Kahneman & Treisman (1984), the bject-file mdel was suggested as a mediating representatinal mechamsm between perceptin and lng-term memry. The hypthesized accunt states that fr every item in perceptin, a file is created and identified by the spatitempral infrmatin regarding that bject's lcatin. Hwever, with nline prcessing, features and prperties may gradually be added t the file. Further, each bject-file can remain intact during mtin, thereby implying that bjects can be individually tracked (Kahneman, Treisman, & Gibbs, 1992). Trick and Pylyshyn (1993, 1994) expanded n the bject-file framewrk, as a means f describing attentinal differences fr subitizatin and cunting prcesses. Accrding t their mdel, the individuatin and enumeratin f an item is a preattentive parallel prcess. Indices are created fr each item, assigned a variable name r reference tken, and a pinter is assigned t that item's lcatin. They further assumed that these indices perate n perceptual representatins, (as ppsed t retinally-based r higherrder representatins), and therefre there is an upper limit t hw many can be kept track f at ne time. The mdel accunted fr sme f the results in the early infant habituatin literature such as Starkey and Cper (1980), where yung infants discriminated tw frm three, but nt fur frm six. They psited that this was because the limit n the number f individual representatins held in memry is very small (2-3 items) in early infancy, and bth fur and six exceeded the capacity f items that culd be tracked and held in memry.^ 9

19 Leslie, Xu, Tremulet, & Schll (1998) prpsed a mdel f a wrking bject-file system t accunt fr the infant arithmetic studies (e.g., Wynn, 1992, Simn et al, 1995). They prpsed an bject-file may take n the fllwing prperties: 1) the index is a 'mental tken' serving as a pinter tward an bject in sme lcatin; 2) the index itself is nt a representatin f the bject prperties and features, hwever, this infrmatin can be -bund' t the index; and 3) because the mechanism invlved in indexing is a prcess f selective attentin, it is limited in capacity. Leslie et al. (1998) cited evidence t suggest this limit is n greater than fur, and later tested specifically fr this limit (Leslie, 1999). T this pint, there is n definitive evidence f an exact limit. It may vary between individuals in the range f tw t fur items. Simn et al. (1995) replicated Wynn (1992), but argued against a specific number mechanism. They indicated that in Wynn's experiment arithmetically incrrect events were als physically impssible events. The mere impssibility f an bject's physical appearance r disappearance was enugh t elicit lnger lking n these additin and subtractin tasks. Cnsequently, knwledge exhibited in the task may be due t the infant's physical bject knwledge. T uncnfund physical pssibility frm anthmetical calculatins, Simn et al. (1995) tested the r 2-1 peratins with the 1 r 2 numerical utcmes, using fur different utcmes fr each peratin. Fr the additin cnditin, the infant saw ne Elm dll, then a secnd Elm dll was added. Then, ne f fur different utcmes was revealed: 1) tw Elm dlls (pssible), 2) ne Elm dll (arithmetically impssible), 3) ne Ernie and ne Elm (arithmetic pssible/identity impssible), and 4) ne Ernie dll (arithmetically and identity impssible). The five-mnth-lds cnsistently lked lnger 10

20 at the tw arithmetically impssible events, as in the Wynn study, but were nt bthered by changes m the identity f the bjects. Simn et al. argued fr a -nn-numericaf explanatin (Simn, 1997) f tracking bjects, analgus t the bject-file system. The bject-file mechanism has the infants paying attentin t the lcatin f bjects withut encding featural infrmatin. At five mnths, it is questinable as t whether the infant has mastered the cncept f bject permanence. Tracking bjects mving behind a screen first and fremst draws the infant's attentin t spatitempral details. When tracking the mere existence f bjects, identity tends t be ignred. The infants in this study are yung enugh that tracking tw bjects places high demands n their attentin and memry system, thereby nly allwing fr spatitempral infrmatin t be encded, causing the lnger lking t the arithmetically impssible events. Objects mve cntinuusly thrugh space and time, frm ne lcatin t anther. This appearance f an bject shwing spatitempral cntinuity is what elicits an bjectfile t be pened. Kechlin et al. (1997) lked at this rle by replicating Wynn's study, with ne variatin; after the bjects were placed behind the screen, the bjects were rtated such that, when revealed, they were nt in the exact lcatin n each trial. They fund the slight variatin in placement did nt affect lking time. Infants cntinued t lk lnger at the arithmetically incnsistent utcmes, but in the subtractin cnditin nly. Yet, this finding was interpreted as verall evidence fr an bject tracking system which tracks bjects thrugh space, and leaves a mental tken pinting t "'smewhere behind the screen." Kechlin et al. (1997) favred this bject-based apprach ver a number mechanism because the pattern f results fllws the cnstraints f bject-based knwledge and reasning. Further, the authrs distinguished between infants 11

21 manipulating bject representatins in these transfrmatin studies and infants perfnning numencal peratins. The lnger lking is elicited by the mismatch f mental tkens (f bjects) placed in ne-t-ne crrespndence with what is in perceptin. The Perceptual Prcessing Mdel A study by Clearfield & Mix (1999) als challenged the claims f the infant habituatin wrk, namely that infants are respnding differentially t changes in number. They suggested results culd be due t changes in mre salient perceptual variables such as cntur length. They pinted ut that in all f the habituatin studies, such cntinuus variables were highly crrelated with number, thereby making the number claim suspect. Clearfield & Mi.x habituated six- t eight-mnth-ld infants t displays f tw r three squares, all f equal size. At test, the infants were shwn displays f either the familiar number & nvel cntur length, r a nvel number & familiar cntur length. The infants nly dishabituated t changes in cntur length, and nt t changes in the individual number f squares. They suggested, that at the very least, when shwn stimuli in which cntinuus variables (such as cntur, brightness, area, etc.) are separated frm the number variable, infants will attend t changes in the mre salient cntinuus variable. A series f experiments by Feigensn, Carey, & Spelke (2002) has recently supprted the previus finding by pitting number against surface area in bth habituatin and transfrmatin studies. First, they replicated the habituatin study f Starkey & Cper (1980), using ne versus tw discriminatin tests with six-mnth-lds, with cntinuus extent (surface area) and number cnfunded, as in the riginal experiment. 12

22 In the fllwing fur experiments, they habituated infants t a number f bjects and tested them n either familiar number/nvel extent, r nvel number/familiar extent. The infants cnsistently failed t dishabituate t changes in number. Feigensn et al. (2002) als replicated the transfrmatin study f Wynn ( 1 992), with number and extent cnfunded. Then in the fllwing experiment, extent was separated frm number. Specifically, infants were tested n a = 1 r 2 transfrmatin. On all trials infants saw ne small bject placed n stage, the ccluder rtated up, and a secnd small bject was added. The screen rtated dwn t reveal either tw large bjects (twice the surface area f the tw small bjects, but expected number) r ne large bject (surface area equal t the tw small bjects, but unexpected number). The events invlving unexpected extent resulted in significantly lnger lking times than the unexpected number events. Althugh the authrs f this study seemed t favr an bject-file interpretatin, they pinted ut that the infants were prbably drawing upn multiple mechanisms (bth physical representatins and number representatins). Nevertheless, the simplest perceptual variables shuld nt be ver lked in favr f these higher rder prcesses (Feigensn et al., 2002). Chen & Marks (2002) tested the hyptheses that results in the simple arithmetic studies culd stem frm three pssibilities: the actual cmputatin f the transfrmatin, familiarity preferences, r directinality preferences (i.e., frming an expectatin based n knwledge that additin yields "mre" and subtractin yields "less"). Fllwing Wynn (1992), five-mnth-lds were tested in either an additin cnditin (I + 1) r subtractin cnditin (2-1). Hwever, ver eight trials, the infants saw fur different utcmes (zer, ne, tw, r three bjects). Each utcme was presented twice, nce in 13

23 each blck f fur trials. Results differed frm thse f Wynn. Fr the first blck f trials, the infants lked lnger at the familiar number f bjects (ne in the additin cnditin, and tw in the subtractin cnditin). The respnses t these events were cnsidered t be due t familiarity preferences, because it was the riginal number f bjects seen n the stage befre any transfrmatin had ccurred. Althugh the interpretatin is different, the finding is als cnsistent with Wynn ( 1992). Hwever, in the secnd blck f trials, fr bth cnditins, the infants lked lnger at tw than at ne r zer. They cncluded that either the infants were adding r subtracting (as Wynn suggested), r alternatively, they were shwing a familiarity preference and a preference t lk lnger at mre bjects. In a secnd experiment, Chen & Marks tested fr this familiarity preference, by excluding any warm-up trials, and any intrductry expsure t the stimuli. This time, in the first blck f trials, n difference in lking time was fund between the ne, tw, and three bjects. Hwever, in the secnd blck f trials, the infants shwed a psitive linear trend in their lking behavir. In ther wrds, they lked lnger at ne than at zer, at tw than at ne, and lnger at three than tw bjects. They interpreted this as strng evidence that the numerical abilities claimed fr infants can als be explained in terms f simpler mechanisms. In this case, a preference fr familiarity plus a tendency t lk lnger at mre bjects. Review f Previus Research Testing the Mdels The three mdels described are all plausible explanatins fr the infant arithmetic literature. Yet they are different psitins assuming different prcesses. It is difficult t separate the cnfunds in many f the experiments. This has resulted in ambiguus 14

24 results. Cnsequently, many f the studies t date can be interpreted as supprting mre than ne mdel. Baillargen, Miller, & Cnstantin (1994) cnducted arithmetic studies with 10- mnth-lds. Instead f seeing an bject placed n stage befre cclusin, the infants initially saw the empty stage. After a screen raised, tw bjects were added, ne at a time. Tw (crrect) r three (incrrect) bjects were then revealed, and the infants lked lnger at the three bjects, as the authrs predicted, based n the impssibility f the event. In a secnd experiment, they tested a = 2 r 3 calculatin. The screen was raised, tw dlls were simultaneusly placed behind it, fllwed by ne dll being placed. The infants lked lnger at tw bjects than at three, in this case. In a third experiment, they tested a = 2 r 3 calculatin, the difference being that the bjects were placed behind the screen ne at a time. There was n difference in lking time t tw r three bjects. The authrs suggested this was due t the requirements f the calculatin. Three updates t their representatin f what was behind the screen was required, rather than simply tw in the previus experiments. They cncluded that infants have "intuitin" abut additin, but abilities are still very limited. Uller et al. (1999) intended t test an integer-symbl mdel (i.e., accumulatr) against an bject-file mdel. The variable f particular interest was the placement f the first bject n the stage. In the first tw experiments, eight-mnth-lds were tested in a = 1 r 2 test. Half f the infants watched ne bject first placed n the stage, and then ccluded (the "bject-firsf task), as in Wynn's (1992) task. The ther half saw the empty stage, the screen rtated up, and the first bject was placed (the "screen-firsf task), as in the Baillargen et al. (1994) task, fllwed by the adding f the secnd bject. 15

25 Lnger lking at ne bject (the impssible utcme) was nly fund m the bject-first cnditin. Hwever, in a third experiment, the 10-mnth-ld infants did lk lnger at ne bject (the impssible utcme) in the screen-first = 1 r 2 task. Nte that, althugh the 10-mnth lds did ^succeed" at the task when the eight-mnth-lds did nt, the = 2 r 3 in the Baillargen et al. study still exceeded their capacity m a screen-first prcedure, suggesting this ability is very primitive. These studies prvide tw imprtant pieces f evidence: 1) the placement f an bject n the stage befre cclusin facilitated lnger lking t the incrrect utcme, and 2) a develpmental prgressin frm five t 10 mnths f an increasing capacity t handle the demands f the task. Fr bth reasns, Uller et al. supprt an bject-file mdel. The bject n the stage sets up an initial representatin f what is expected t be there. When the bject is ccluded, and a secnd bject is added, the initial representatin is updated t include tw bjects. The yunger babies struggle with the screen-first cnditin fr the fllwing reasn: When the first bject is placed behind the screen, they have t build an initial representatin fr "smething is nw behind the screen," cnstructed frm this brief initial perceptual experience. This is shrtly fllwed by the secnd bject added, requiring an update t the representatin f what is behind that screen. The infant hlds a representatin with ne bject-file, then tw bject-files. This invlves memry fr hw many items are behind the screen, attentin t the additin, updating the existing representatin (mre than nce in the screen-first cnditin, such that they are perating upn peratins), and therefre, at least sme crude frm f bject permanence t hld a representatin f smething behind the ccluder. These demands n memry are nt f issue t the accumulatr, which simply 16

26 et al. pinted ut that in the bject-first events by Wynn (1992) and Kechlin et al. hlds the last "cunt" value in memry. Nr des the initial set up in the bject-first cnditin differ frm the screen-first prcedure (fr the accumulatr). Furthermre, Uller (1997), five-mnth-lds were tested, and results f lnger lking t ne bject ver tw bjects were much less rbust. By the time the infants were eight mnths ld, they succeeded utright in the bject-first task, and, by ten mnths, in the screen-first cnditin. This gradual develpmental prgressin is indicative f the expected imprvements in infrmatin-prcessing, and these prcessing demands are precisely what an bject-file system wuld rely upn. In a final experiment, Uller et al. (1999) tested eight-mnth-lds in a screen-first, = 1 r 2 task nce again. The gal was t see if the eight-mnth-lds culd succeed when the prcessing demands are reduced. If s, it wuld be strnger evidence f an bject-file mechanism at wrk in these tasks. T reduce the demands placed n memry, they used a tw-screen prcedure, where ne bject was placed behind each screen. Hence, the tw screens served as perceptual lcatin markers, which wuld perhaps help the infants individuate the bjects, and pssibly facilitate the representatinal cnstructin by prviding greater spatitempral infrmatin. As predicted, the eightmnth-lds did succeed, they lked lnger at the impssible event (ne bject) than the pssible. Using the tw-screen prcedure facilitated eight-mnth-lds' success at the task. Therefre, Uller et al. (1999) favred this attentin-based mdel which calls upn physical representatins and knwledge, and has the capacity t imprve bth in accrdance with infrmatin-prcessing refinements that nrmally develp with age and with the reductin f prcessing demands within the task. 17

27 On the assumptin that a limited capacity bject-file mechanism was being used, Leslie (1999) attempted t find the limit f bjects that culd be tracked and represented by 10-mnth-lds. The infants were tested in either a 2-1 = 2 (unexpected) cnditin, r a (expected) cnditin. The slight change in methdlgy frm previus arithmetic studies (i.e., the cnstant utcme) was used t avid baseline prblems and required the infant t set up a specific expectatin fr tw bjects. The infants did lk lnger verall in the unexpected cnditin than the expected. Hwever, when tested in a 3-1=3 r 3-0 = 3 prcedure, there was n difference in lking times between the tw grups. Therefre, it was cncluded that 10-mnth-lds lacked a specific representatin fr three bjects, which may be cded as "many" r "mre than tw." Furthermre, he tested whether there was a general glbal (r ttal) limit t the number f bjects that culd be tracked at ne time, r if this limit was a "per set" limit, leaving the pssibility f perhaps tw bjects f ne kind (e.g., identity) and, ne r tw bjects f a different kind tracked and stred in memry. The cnclusin drawn by Leslie nly tuched upn the issue f a glbal limit. S the questin f whether this representatin is a glbal r per set limit was still unanswered at this pint. Xu & Carey (1996) had 12-mnth ld infants tracking ne duck and ne truck, tw distinct items needing t be represented. But was this just tw "things" being tracked, r was it specifically "ne truck" and "ne duck?" Leslie and his clleagues did several experiments t test if identificatin by feature served as an imprtant marker held in the infant's frmed representatin. If s, such a finding might implicate per set tracking limits. In ne experiment, 12-mnth-lds were shwn ne triangle placed behind a screen, then ne disk behind the screen. The screen was then 18

28 remved t reveal the disk and the triangle (expected) r tw disks (unexpected) r tw triangles (unexpected). A similar prcedure was used t test fr size discriminatins. The infants were shwn a small disk and a large triangle. The screen was then taken away t agam reveal the small disk and large triangle (expected) r the large disk and small triangle (unexpected). The infants lked lnger at the incnsistent utcme. Furthermre, Leslie et al. (1998) fund that althugh 12-mnth-ld mfants did appear t encde lcatin, shape, and size when tracking tw sets cntaining ne bject, changes in the clr f the bjects went undetected. They claimed this was because nt all featural infrmatin had been bund t the index. It was previusly established that 12-mnth-lds culd track tw distinct bjects in a simultaneus fashin, and hld quite a bit f featural infrmatin in their representatin. S Leslie (1999) tested t see if this number "tw" again was a glbal limit r per set, by increasing the number t three bjects. Twelve-mnth-lds were familiarized t the fllwing scene: An ccluding screen was raised n the stage. Tw frgs were placed behind the screen, fllwed by ne fish placed behind it. Each bject was then individually lifted and again shwn t the infant fr tw secnds, then replaced. At test, the screen drpped t reveal either tw frgs and ne fish (expected event) r ne frg and tw fish (the unexpected event). The infants shwed n difference in lking times t the events. Leslie (1999) cncluded the change in numersity f the tw sets went unnticed. He claimed that in the first year f life, the infant has a tracking limit f ne bject per set, and an verall glbal limit t track tw bjects. There are a few prblems with Leslie's (1999) argument. Spatitempral features are first t be encded, the mst salient feature t the bject-file system. Leslie et al. 19

29 (1998) indicate that an individual file can have featural infrmatin bund t it, but this infrmatin is nt bligatry fr creating a new file. Thus, in the previus study, identity features may nt be bund yet. This is a gradual prcess requiring mre expsure, greater prcessing demands, r mre efficient encding strategies that develp ver time. As we see, in a set f tw bjects, 12-mnth-lds seem t be able t encde and bind sme, but nt all features t the index. What has been encded and bund can be retrieved frm memry in cnjunctin with the index, and cmpared t what is in perceptin. Hwever, if files are pened fr three bjects, increased prcessing demands may in turn cause the infant t simply encde the spatitempral infrmatin, withut features bund t the index. Cnsequently, three indices r "pinters" at the screen wuld in fact be pened. Upn cmparisn f the tw fish and ne frg (the unexpected event), there wuld be n mismatch t what is held in memry. This is cntradictry t Leslie's (1999) claim that the Umit f the bject-file must be tw. If the system is mst respnsive t tracking bjects t sme lcatin, then it wuld be expected that when three bjects were hidden, and three revealed, there shuld be equal lking time. The finding that there was differential lking t tw featurally different items means that the featural infrmatin was able t be encded int the file, and may have facilitated retrieval. But the lack f differential lking t three bjects, changed in features, may simply mean that the featural infrmatin was nt available upn retrieval f the files frm memry. Perhaps by 12 mnths f age the infants actually are able t track three items. The nly indicatr that three bjects may be ver their tracking limit is the 3-0 = 3 versus the 3-1 = 3 test, but this may be misleading because f the ambiguity f a "zer" 20

30 transfrmatin. The hand entering the stage, ging behind the screen, and then exiting the stage empty, culd simply be a distractin and disruptive t what is held in memry. A secnd prblem with this study is that the authr claims that tw frgs, and ne fish placed behind ne screen, cmprise tw sets f bjects. Yet, the bject indexing system is lcatin sensitive. As the Uller et al. ( 1999) paper emphasized in the final experiment, distinct lcatin markers (tw separated screens in that case) are fundamental t the bject-file mechanism. Because the three bjects behind the ne screen nly varied in identity, it was the nly cue t facilitate the retrieval f thse files in memry. As previusly mentined, featural infrmatin may nt have initially been bund t the file. Anther pssibility is that the bjects, all placed in ne lcatin (behind ne screen) was mre indicative f ne set f bjects t be tracked. On the ther hand, if tw screens were used in the display area, the distinctin f tw sets wuld have been perceptually mre salient and culd have facilitated the encding f featural infrmatin. All this study can tell us is that three general bjects were tracked behind a screen. The change in identity, similar t the results f Simn et al (1995) went undetected. Because the infants saw three bjects placed behind ne screen in bth cnditins, and shwed equal lking time in bth the expected and unexpected cnditins, which bth revealed a ttal f three bjects, it cannt be determined whether the three bjects exceeded their tracking limit (as the authrs claimed), r was handled by a feature-insensitive tracking system that culd track three bjects. Furthermre, the same utcme (equal lking times between cnditins) wuld als be expected if an accumulatr mechanism were respnsible. Three bjects were placed, therefre the accumulatr stred a value equivalent t three in memry. The accumulatr is nt respnsive t identity issues. It is specific t number. 21

31 Or, by the Chen & Marks perceptual accunt, the infants in bth cnditins may have had n expectatin at all f what was t be revealed behind the screen. Instead, they may lk fr a lnger time at three bjects than anything less than that number, simply because three is mre t lk at. Because bth grups cntained three bjects, they each had the same amunt f "stuff ' t lk at and therefre the grups wuld nt differ in their lking times accrding t this perceptual mdel. The questin f whether tracking limits are f glbal number r per set remains unclear t this pint. Furthermre, mst studies favring an bject tracking system, cannt rule ut the pssibility f a number mechanism r perceptual mechanisms as cntributrs t the btained results. The current study makes unique predictins fr each mdel. Additinally, the design allws fr the determinatin f tracking limits, given that an bject-file system is utilized in the task. The Present Study The vilatin f expectatin paradigm was used in this study t test 10-mnthlds in a tw-screen, additin task. Infants' lking times were measured as they were presented with a ttal f five bjects, which exceeds any representatinal capacity limits previusly prpsed. One bject was placed n the left-hand side f the stage, behind an unraised screen. Then the left side screen was raised, ccluding the ne previusly placed bject. One bject was added behind the left, raised screen. Then ne bject was placed n the right hand side f the stage, behind an unraised screen. The right side screen was then raised, ccluding the ne bject, and tw bjects were simultaneusly added behind that screen. Therefre, nly tw updates had t be made, ne per screen lcatin. The 22

32 sequence f events were cunterbalanced, such that half f the infants saw ne bject added behind the left screen, and tw added behind the right screen, and half the infants saw tw bjects added behind the left screen and ne added behind the right. There were eight test trials in which the infants always watched this same sequence f events. On fur f the trials, the right screen was lwered t reveal the bjects, and n the ther fur trials, the left screen was lwered. There were three cnditins tested between subjects: 1 ) tw bjects revealed n each trial; 2) three bjects revealed n each trial, and 3) tw r three bjects revealed. Therefre, in the first tw cnditins, all infants were presented with eight trials f the same sequence presentatin, and all infants in the same cnditin saw the same number f bjects in each utcme. Bth the physical and arithmetical pssibility and impssibility f the event depended n which screen was lwered and what had been placed behind the screen. In the third cnditin, fur trials revealed tw bjects and fur trials revealed three bjects. Each infant saw tw trials f tw bjects, which were arithmetically pssible, tw trials f tw bjects that were impssible, tw trials f three bjects pssible, and tw trials f three bjects impssible. T demnstrate, if the infant was in the "tw bjects revealed" cnditin, and watched ne bject added behind the left screen (fr a ttal f tw), and tw bjects added behind the right screen (fr a ttal f three), then the left screen was lwered, t reveal tw bjects. This wuld be a physically pssible event. Hwever, if the right screen was lwered, and revealed tw bjects, this wuld be a physically and arithmetically impssible event. Therefre, the accumulatr mdel wuld predict lnger 23

33 lking at the arithmetically impssible event (right screen dwn) than the pssible event (left screen dwn). Predictins f the bject-file mdel in this example wuld vary, depending n the number f bjects the infant culd keep track f in memry. It is generally accepted that the infant cannt track mre than fur bjects. Therefre, the presence f five bjects exceeds the infant's representatinal strage limits. The questins f interest are as fllws: What is the actual limit f items that can be tracked? When presented with an verlad, which indexes get drpped frm memry; the first nes established, r the mst recent? Or, by verlading the attentinal tracking system with mre than it can handle, will this be disruptive and cause the infant t resrt t relying n either an "analgmagnitude" mechanism, r simple perceptual prcesses t reduce the wrk f the attentinal system? The issue raised in the latter questin is a plausible ne that has never been fully addressed. In sme f the previus transfrmatin studies, it appears that the increase in prcessing demands (due t the number f bjects, the number f updates, and the number f event sequences and event utcmes the infant is expsed t), may lead the infant t resrt t sme ther mechanism, either perceptual r number, which may r may nt elicit lnger lking t an incrrect utcme. As demnstrated in the Uller et al. (1999) experiments, reducing prcessing demands f the task may increase the likelihd f an bject-file mechanism being used successfully. Therefre, the demands placed n the bject-file mechanism were reduced as much as pssible by: 1) using tw distinct and separate screens which serve as perceptually available lcatin markers, 2) placing ne bject n the stage befre the screen ccludes it, as in Uller et al.'s (1999) bject-first 24

34 cnditins, and 3) reducing the number f updates t tw, (ne per lcatin) by adding tw bjects in at ne time, as in Baillargen et al. (1994). Als, it may be the case that the infants fall back n perceptual mechanisms when presented with a greater variety f sequence events r utcmes, as in Pirier (2001), which presented fur different sequence events within eight trials, and Chen & Marks (2002) in which fur different utcmes were revealed ver eight trials. The majrity f studies arguing fr bject-file r accumulatr mechanisms have used a standard "ne presentatin sequence - tw different utcmes' design (e.g., Uller et al., 1999; Wynn, 1992), r a 'tw different sequence - ne utcme' design (e.g., Leslie, 1999; Wynn & Chiang, 1998). The additin f the third cnditin addressed this issue. Ifthereisne mechanism that deals with bject knwledge and number, and it is rbust, then lking times shuld be cnsistent with ne f the mdels' predictins in all three cnditins. If infants rely slely n perceptual variables, such as lking at mre bjects, then this shuld be exhibited by lnger lking at the three bject tnals than the tw bject trials in the "reveal tw r three" cnditin. Additinally, they wuld exhibit verall lnger lking in the "reveal three" cnditin than in the "reveal tw" cnditin, with n ther differences within each f these cnditins". Hwever, if the presentatin f fur different utcmes is respnsible fr the "perceptual accunt," then the infants wuld exhibit the lnger lking at three items than tw items in the "reveal tw r three" cnditin nly, and culd actually tit the predictins f a different mdel fr the "reveal tw" and "reveal three" cnditins. T address the frmer questins, regarding tracking limits, predictins can be exemplified using the prcedural example f tw bjects placed left, three bjects placed 25

35 right. In this case, assume the ten-mnth-ld infant has a tracking capacity f tw bjects, and can nly hld n t the first tw in memry, but lses the final three (primacy hypthesis). If the left screen rtates dwn and reveals the tw bjects, this is cnsistent with what is in memry; the number f files initially pened fr that lcatin matches the number f bjects in perceptin. Therefre, there shuld nt be lng lking time fr that trial. Hwever, when the right screen rtates dwn t reveal tw bjects, the infant wuld have n files pened in memry fr this lcatin. This type f mismatch may yield lnger lking^ On the ther hand, what if the infant has a capacity t hld tw bject-files, but nly retains the final tw (recency hypthesis)? Then, if the left screen is lwered t reveal tw bjects (a pssible event), the infant shuld lk relatively lng due t the fact that n files were pen fr the bjects at that lcatin. If the right screen is lwered t reveal tw bjects (an impssible event), and the infant has kept nly tw files pen in that lcatin, then lking time wuld be relatively shrt, as there wuld be a match between the files in memry and in perceptin. This is an instance where a distinctin is made between the accumulatr and the bject-file. The bject-file system, with a limit f the last tw bjects (bjects 4 and 5 placed n the stage) prvides the basis fr viewing tw bjects revealed n the right as "cnsistent," whereas the accumulatr wuld register this as "incnsistent" mth the value fr three bjects previusly placed behind the screen. In cntrast, if the infant is simply relying n perceptual prcesses, there shuld be n preference fr either event f seeing tw bjects. Rather, fr the perceptual prcessing mdel, lking times shuld be fairly invariable frm trial t trial, yet, n average, shuld yield shrter lking times than the average f the "reveal three" cnditin. 26

36 A list f all predictins made by the theries is presented in Tables 1-3. Table 1 displays the predicted lking times fr the "reveal tw bjects" cnditin and "reveal three bjects" cnditin fr Event Sequence A, and Table 2 displays predictins fr these cnditins, fr Event Sequence B. Nte that fr each mdel, the predictins (presented in the crrespnding rw) acrss the tw cnditins are unique. It is assumed that if ne mdel is rbust, the pattern f lking will fit the predictins fr bth cnditins. These tw cnditins can make unique predictins fr tracking up t three items nly. The "reveal tw r three" cnditin makes unique predictins which include the infant tracking up t fur bjects, as presented in Table 3, with bth Event Sequences included in this table. Fr Table 3, each mdels' predictins are represented by rw. Nte that fr this table, each bject placed is assigned a number, meaning the rder f placement. S, fr Event Sequence A, tw bjects are placed behind the lett screen, (bjects "1" and "2") and then three bjects are placed behind the right screen (bjects "3," "4," and "5," respectively). Fr Event Sequence B, bjects "1" "2" and "3" wuld be placed behind the left screen, and bjects "4" and "5" wuld be placed behind the right screen. Each clumn displays a predictin fr trials f Event Sequence (A r B), number f bjects revealed in the trial (2 r 3), and the screen lwered (right r left), as well as whether the utcme was cnsidered pssible r impssible. 27

37 0 CHAPTER 2 METHOD Participant?, Frty-eight full-term 1 0-mnth-ld infants participated in this study (M = 1 mnths; fur days, range = 9;20-10;15). The 28 males and 20 females were randmly assigned t ne f three cnditins (16 infants tested per cnditin). Participants were identified and recruited thrugh state birth recrds fr the Amherst, Massachusetts vicinity. Parents were cntacted via letter and a fllw up phne call. Written parental cnsent was btained fr each infant. Participatin was vluntary, and a certificate was given in appreciatin. Apparatus Objects were presented n a puppet stage with an pening 48 cm high, 85 cm wide and 37.5 cm deep, and raised 102 cm frm the flr. The stage flr was made f black fam bard. The side walls were cvered in black fabric, with a hle n each side fr the experimenter's hand t enter. The back wall was made f yellw fam bard, which had a black grid pattern (58 cm ) t camuflage the lines frm the hidden trap drs. The tw trap drs were cut ut exactly n the black gridlines, each 7.62 cm frm center stage. Each dr measured high cm x cm wide. A black curtain was attached at the frnt f the stage. The experimenter pulled n a string t raise the curtain s the stage display culd nt be seen between trials. At the beginning f each trial, the curtain drpped dwn t reveal the stage. The rm lighting was dimmed during the entire experiment, with the exceptin f the stage lighting: tw 40 Watt tubular light bulbs tward the frnt f the stage, and ne 1 5 Watt flurescent placed directly abve the 28

38 center f the stage, ut f the infant's direct line f sight. This Ughting minimized the amunt f shadws cast by the screens and bjects. Classical music was played in the backgrund at a lw vlume, which helped mask any sund made by the pening and clsing f the trap drs. In the center f the stage were tw fam bard screens (22.9 cm high x 21.6 cm wide) each placed 3.81 cm frm center (7.62 cm apart). The left hand screen was attached t a plastic black pipe 1.6 cm in diameter, while the right hand screen was attached t a wden dwel, placed thrugh the pipe, measuring.95 cm in diameter. The entire extensin f the dwel frm stage left t its end pint, just past the right hand screen, was cm. The dwel extended just slightly past the right screen (2.22 cm) where it was fastened t the flr but culd still be rtated freely. The pipe, which held the dwel, extended cm frm stage left t right, ending at the pint just past center where the secnd screen, cnnected t the dwel, began. These rds were cntrlled by a secnd experimenter, wh sat n the left side rear f the stage, ut f the infant's sight. This experimenter used the dwel and pipe t rtate the screens up and dwn (frm flat against the stage flr up t a 90 degree vertical angle and back dwn) t cclude and reveal prtins f the stage. When the screens were rtated up, they were white in clr, distinctly different frm the black flr, sides, and yellw backgrund. When the screens rtated dwn, they were black and blended with the flr clr. The bjects used in this study were rectangular red fam blcks with plastic ggly eyes and a yam smile ( 1 5 cm high X 7.5 cm wide) and wuld squeak when squeezed. The experimenter wre lng black glves t blend in with the surrunds, s as t fcus the infant's attentin n the bject. 29

39 Equipment A vide camera, discretely placed at the frnt f the stage, atp the stage ceiling, recrded each infant straight n. A secnd camera, placed behind the infant recrded the events as they ccurred n the stage. A vide mixer, in a separate rm, allwed the tw camera inputs t be recrded nt ne tape. The pnmary large image was the view f the infant, while the smaller insert at the bttm f the screen revealed the event that ccurred n the stage. A mnitr was placed in a separate rm s an experimenter culd cde the infants' lking times nline. The nline cding infrmatin fed int a cmputer. The prgram accumulated the lking time, and signaled (via an audible beep) the end f each trial, s that each trial was infant-cntrlled. Prcedure Infants sat in an infant seat, placed 30 cm frm the frnt f the stage. They were placed at a height where their eyes were apprximately at the midpint f the rtating screens ( 12 cm abve the stage flr). The parent sat behind the child, and was asked nt t interact with the child during the test trials. Three experimenters were needed fr the experiment. The first was psitined behind the stage, ut f the infant's view, and presented the bjects. The secnd experimenter sat at the side f the stage, als ut f the infant's view, and cntrlled the rtatin f the screens. A third experimenter was at the cmputer in a separate rm, viewing the infant and cding lking time. Infants were assigned at randm t ne f three cnditins: reveal tw bjects; reveal three bjects; r reveal tw r three. The cnditins will hereafter be referred t as Cnditin 2, Cnditin 3, and Cnditin 2/3, respectively. All infants went thrugh the same intrductin prcedure. 30

40 Intrductin Phase Fllwing the methd used in ther studies, using a duble-screen prcedure (e.g., Wynn & Chiang, 1998; Uller et al, 1999, expt 4) the infants were expsed t the experimenter's glved hands, and als given ne f the bjects, and encuraged t manipulate and explre it fr 60 s. The infant was then intrduced t the stage. The curtain was lwered and raised twice. Then the infant viewed the tw screens rtate up t vertical separately, the left screen raised t vertical and lwered, fllwed by the right. Next, the left screen rse t the vertical, then the right. While bth screens were raised, the glved hand entered frm ne side, mved in frnt f the screen, stpped at center between the screens and tapped the flr. The hand retracted, tapped the flr at the ther side f the screen, then mved behind the screen t center and tapped the flr, then the back wall, t emphasize the slidity. Then the hand retracted, and bth screens lwered. Then the right screen rse, fllwed by the left. The experimenter repeated the sequence entering frm the ther side, s that the infant had seen the hand enter frm bth sides f the stage, and the hand mve behind and between bth screens. This has been suggested t nt nly help the infant understand the bundaries f the slid flr and back wall, but als the bundaries f the screens. The partially hidden trajectry f the glved hand serves as an additinal cue f tw slid screens separated in space at tw distinct lcatins (Uller et al., 1999). Cnditin 2 Eight infants in this cnditin were shwn an event sequence A, and the ther eight were shwn event sequence B. In Event Sequence A, the infant watched tw bjects placed behind the left screen, then three bjects placed behind the right screen. 31

41 This event sequence ccurred in the same rder n all familiarizatin and test trials. In Event Sequence B, the infant watched three bjects placed behind the left screen, and tw behind the right, always in that rder n all trials. Familiarizatin trials The familiarizatin trial prcedure was mdeled after similar studies that have used a vilatin f expectatin paradigm, in which the infant viewed the entire sequence f events (i.e., bjects presented n the stage, screens raised, bjects placed behind the right screen, then bjects placed behind the left screen) with the exceptin that the screens never rtated dwn t reveal an utcme. There were tw trials f this type. Each trial began when the curtain was raised, and ended 4 s after the sequence f events. All trials began with the infant seeing an empty stage. A glved hand entered frm the left side f the stage hlding ne bject, as the experimenter said, "Lk baby! Lk at this!" The experimenter then squeaked it nce and placed it n the left-hand side f the stage. The left screen then rtated up, ccluding the ne bject placed there, as the experimenter said, "Up ges the screen!" Next, ne bject was brught in frm the left, squeaked, and placed behind the left screen, while the experimenter said "Lk baby! Lk at this! Where's he ging? Where's he ging baby?" This script, and that belw, is taken frm the Wynn (1992) study, nt reprted in the paper, but btained frm Wynn (persnal cmmunicatin, December 12, 2000). A hand then entered frm the right side f the stage with anther bject, repeated "Lk baby... " squeaked it, and placed it n the right side f the stage. The right screen then rtated up, ccluding the bject n the right side, as the experimenter said, "Up ges the screen!" The hand reentered frm the right, this time hlding tw bjects, squeaked 32

42 them, and placed them behind the right screen, while repeatmg "Lk baby! Where are they ging'^ Where are they ging Baby?" The curtain then clsed, and the event was repeated fr ne mre trial. Infants in the Event Sequence B saw tw bjects added behind the left screen, and ne bject added behind the right, in that rder. Test trials There were eight test trials. On fur f the test trials, the left screen rtated dwn t reveal an utcme f tw bjects. On the ther fur test trials, the right screen rtated dwn t reveal an utcme f tw bjects. Therefre, in Event Sequence A, the left side revealed resulted in an arithmetically pssible event, whereas the right side revealed resulted in an impssible event, and vice versa fr Event Sequence B. The eight test trials cntained tw blcks f fur pssible/impssible utcme pairings, (fur blcks f P/I and I/P cmbinatins) such that a pssible event always directly preceded r fllwed an impssible event. There were a ttal f 16 unique trial type rders, as shwn in Table 4. All trial type rders were used in each cnditin, half with Event Sequence A, and half with Event Sequence B. Table 5 displays the balancing f Trial Type and Event Sequence acrss cnditins 2, 3, and 2/3. Test trials began when the curtain lwered, revealing the empty stage. The infants saw the same prcedure as in the familiarizatin trials, except that at the end, ne f the screens lwered t the stage flr t reveal an utcme f tw bjects. If the infant watched tw bjects placed behind the screen that was t be lwered, and tw bjects were revealed, this was cnsidered a "pssible" trial type. If the infant watched three bjects placed behind the screen that was t be lwered, and tw bjects were revealed, this was cnsidered an "impssible" trial type. Fr this t ccur, the experimenter 33

43 surreptitiusly remved ne bject thrugh a trap dr in the back wall while the screen was still rtated up t venical. On trials where the number revealed was cnsistent with the number placed, a trap dr was als pened and clsed, t keep any sund made by its pening cnsistent thrughut all trials. Lking times were measured frm the mment the screen lwered until the infant had either lked away fr 2 secnds, r when 30 s had elapsed. The cmputer cllecting the data beeped t signal the end f the trial. The curtain was then raised t cclude the stage. Ten secnds elapsed befre the start f the next trial. Cnditin 3 Familiarizatin trials Familiarizatin trials were exactly the same as in cnditin 2. Half f the infants in this cnditin saw Event Sequence A and half saw Event sequence B. Test trials Test trials were als exactly the same as Cnditin 2, except that three bjects were revealed when ne f the screens was lwered. Therefre, n trials cnsidered t be "impssible" (meaning, tw bjects were placed behind a screen, but three were revealed), the experimenter surreptitiusly added ne bject thrugh the trap dr behind the screen. Again, infants were randmly assigned t a Sequence and Trial Type rder, which were the same impssible/pssible sequences as in cnditin 2. Hwever, the screens revealed (left side r right side) fr pssible and impssible trials are ppsite that f cnditin 2. Fr example, in Cnditin 3, Event Sequence B ("3B"), after three bjects are placed behind the left screen and tw behind the right, revealing three bjects behind the left screen wuld be a "pssible" trial type, and revealing three bjects behind 34

44 the right screen wuld be an "impssible" tnal type. In cntrast, an infant in Cnditin 2B, if given the same rder f PA trials (as shwn in Table 5), the "pssible" tnal type wuld be the right screen revealing the tw bjects, and the "impssible" trial type wuld be the lett screen revealing tw bjects. Fr this reasn, each P/I trial rder alternated by Event Sequence A r B. This methd balances trial type with side revealed. Cnditin 2/3 Familiarizatin trials Infants watched the same familiarizatin trials as in the previus tw cnditins. Half were presented with Event Sequence A and half with Event Sequence B. Test trials Infants in this cnditin were tested n trials similar t the previus cnditins, with ne exceptin: they were expsed t fur different utcmes, as ppsed t tw. In the previus tw cnditins the infants watched the same event sequence, always fllwed by the same utcme number. Trials varied nly by which screen was lwered. In cnditin 2/3, the infants watched the same event sequence (A r B) with the fllwing utcmes revealed: 1 ) left screen lwered t reveal tw bjects, 2) left screen lwered t reveal three bjects, 3) right screen lwered t reveal tw bjects, and 4) right screen lwered t reveal three bjects. Whether r nt a trial was a pssible r impssible trial type depended n which event sequence was presented and what was revealed. Each infant saw tw trials f tw bjects revealed/impssible event, tw trials f tw bjects/pssible event, tw trials f three bjects/impssible event, and tw trials f three bjects/pssible. The eight trials were blcked int tw blcks f each f the fur utcme events. Tw bject trials were paired with three bject trials, and pssible 35

45 trials were paired with impssible trials, and randmized within each blck. Sixteen sequences f P/I events resulted, as shwn m Tables 4 and 5. In additin t the Pssible/Impssible cmbinatins paired, trials alternated by number f bjects revealed. Therefre, the tirst 4 trials had ne trial f each kind (pssible/tw bjects, impssible/three bjects, impssible/tw bjects, and pssible/three bjects). Measures The dependent measure f interest in the study was lking time (in secnds) frm the lwering f the revealing screen until the infant had lked away frm the display fr 0.5 secnds r lnger. Because the expenment is testing a ptentially fragile memry, it is assumed here that any srt f lk-away frm the bjects will decrease attentin t and memry fr them. This is a slightly different measure than thse typically used in lking time studies. Mst studies using lking time measures use "ttal lking time" measured by the length f time lking at the display until 30 s had elapsed, r the infant had lked away fr tw secnds. Hwever, upn review f the previus lking time studies with infants, ne can see that the majrity f infants are in the mnth range in age. Ten- t twelve- mnth ld infants are ften mre difficult t study in a lking time paradigm, because they are much mre active at this age, and d nt want t be sitting still fr very lng. The infants wh were included in this study were able t sit still during at least fur trials, but they did have sme lk-aways f up t 1.9 secnds lng befre ever having a tw secnd lk-away. It nly takes half a secnd fr an infant t cmpletely turn his face away frm the display and back again. These brief lk-aways culd interfere with the memry f events that just tk place n the stage. Fr this reasn, 0.5 secnd lk-aways were used as the cut-ff fr lking time t 36

46 each trial. In the present cntext, this is a mre sensitive measure f attentin than time until a tw secnd lk-away. Hwever, analyses were cnducted n 'ttal lking time" als, because the trial lengths did use the cnterin f a 2 s lk-away fr the trial t end. These results, as well as detailed analyses f the number f "shrter than 2 s lkaways" can be fund in the appendix. Design and analy ses The study was a factrial design with Cnditin and Event Sequence as betweensubjects variables, and Trial Type and Number as within-subjects. The first variable f interest was cnditin, tested between-subjects. Cnditin 2 infants always saw an utcme f tw bjects. Cnditin 3 infants always saw an utcme f three bjects, and Cnditin 2/3 infants saw utcmes f bth tw and three bjects. Therefre, the variable number f bjects (tw r three) was tested between-subjects fr Cnditin 2 and 3, and within-subjects fr Cnditin 2/3. Trial type designates the within-subjects variable fr impssible versus pssible events. Other variables lked at were tests fr differences in event sequence A and B (between-subjects) and side revealed (right r left screen, withinsubjects) were als cnducted. N effects were predicted fr these variables. An accumulatr mechanism shuld prduce a significant main effect f trial type in the mnibus ANOVA acrss all three cnditins, and in all ther analyses. If the mechanism is rbust, infants shuld cnsistently lk significantly lnger t arithmetically impssible trials than pssible nes, regardless f the cnditin r the event sequence they were tested in. If the perceptual prcessing psitin is crrect, there shuld be a main effect f number, such that the infants lk lnger at utcmes f three bjects than at utcmes f tw bjects. Hwever, an mnibus ANOVA cannt test the 37

47 vanable number f bjects. If the perceptual prcessing is crrect, there culd ptentially be a slight effect f cnditin due t the nature f utcmes in cnditins 2 and 3. This psitin can therefre nly be analyzed by testing Cnditin 2 versus Cnditin 3 separately (a test f the vanable cnditin = a test f the variable number), and testing fr number within Cnditin 2/3 separately. Cntrasts were cnducted fr the Object-tile predictins made m Tables 1-3. If the Object-file mechanism is dminating the respnse, average lking times shuld fit ne f the patterns (presented in the Table rws), and shuld be significant fr all three cnditins if this mechanism is rbust. 38

48 CHAPTER 3 RESULTS Interbserver Reliahility A primary bserver (ENC) scred lking time n each trial fr all 48 infants, and a secndary bserver (KO) scred lking time n each trial fr 18 f the 48 infants. A mask was placed ver a prtin f the mnitr t prevent the bservers frm seeing which events ccurred. A Pearsn's r f.91 indicated interbserver agreement was high. The primary bserver's judgments were used fr analysis. Omnibus Analysis: Test fr the Accumulatr and Perceptual Prcessing Mdels Analyses were cnducted using the length f each infant's lking time t an event prir t the first lk away. A3x2x2x2 ANOVA was perfrmed fr Cnditin (2, 3, r 2/3) x Trial Type (Pssible r Impssible) x Blck (Blck I = trials 1-4 r Blck 2 = trials 5-8) x Event Sequence (A r B), with cnditin and sequence as betweensubject variables, and blck and trial type as within-subject variables. There was a significant effect f blck, F(l, 42) = 14.69, p <.01, where length f first lk was greater in blck 1 (M = 5.68, SD = 2.05) than in blck 2 (M = 4.36, SD = 1.35). There was als a significant effect fr trial type, F(l, 42) ^ 5.39, p <.05. Over all three cnditins, the length f the infants' first lks was lnger fr arithmetically impssible trials (M = 5.41, SD = 2.08) than fr arithmetically pssible trials (M = 4.62, SD = 1.39). There were n significant interactins. Because attentin is best at the beginning f the experiment, the fllwing analyses are nly fr thse trials in Blck 1. Using the first fur test trials nly fr 39

49 analysis shuld yield the mst reliable data fr the fllwing reasns: 1 ) Critenn fr the data being included in the analysis was that the infant had t cmplete fur test trials. Therefre, all f these data pints are included in the analysis. Althugh the average number f trials cmpleted by infants in this study was 7.06 (SD = 1.22,), the number cmpleted ranged frm fur trials (3 infants) t eight trials (26 infants). Therefre the means in Blck 2 are nt reliable. Experimenters als agreed that by trial 5, infants shwed an increasing amunt f disinterest and fussiness, therefre sme trials were excluded frm the analysis, r the experiment ended early if the child became t fussy t sit in the seat, thereby cmpleting fewer tnals. 2) Analyses within all Cnditins shwed a significant effect f Blck, with lking times in the fur tnals cnsistently lnger than in the last fur trials. A detailed analysis within each blck f each cnditin, using dependent measures first lk, ttal lking time, and number f lk-aways can be fund in the appendix. When the abve ANOVA was repeated fr trials within blck 1 nly, there were n significant effects r interactins fund acrss all three cnditins. The previus effect f trial type is misleading, as it was largely influenced by the last fur trials. If the accumulatr is the underlying mechanism influencing behavir in this task, it shuld be present acrss all trials. The accumulatr mechanism is nt a learning-based mechanism that imprves with experience. Therefre, the mnibus analysis including blcks 1 and 2 shuld nt be taken as supprt fr the accumulatr. The data fr length f first lk was receded t test fr effects f Side the bjects were revealed (right r left), and tested in an ANOVA fr Cnditin, Sequence, and Side within the first fur trials. The variable side culd nt be included in the previus 40

50 analysis because it is cnfunded with trial type. Fr example, in Cnditin 2, given event sequence A, the impssible trials were always revealed n the right side, and the pssible trials were always n the left side. In Cnditin 2, given event sequence B, impssible trials were always revealed n the left side, and pssible trials were always revealed n the right side. An verall preference fr ne side might play an influential rle in these results, and shuld be cnsidered when interpreting this data. In the ANOVA there was an effect f side, F( 1, 42) = 3.95, p =,05, such that infants lked slightly lnger t the bjects revealed behind the right screen (M = 6. 17, SD = 3.28), than t the bjects revealed behind the left screen (M = 5. 19, SD = 2.03). This slight preference fr the bjects revealed frm behind the right screen may be due t: 1) an inherent preference t lk tward the right side, 2) the side f presentatin always went frm bjects placed behind the left-side screen and then behind the rightside screen (a recency effect), r 3) sme factr due t the experimental variables being manipulated (e.g., cnditin r sequence). Fr this reasn, the side variable was included in all subsequent analyses. There was a side x sequence interactin, F{ 1, 42) = 4.09, p =.05, as shwn in Figure 1. Althugh there was n difference in the length f the first lk t either side when presented with sequence A, the infants preferred t lk at the bjects revealed frm behind the right side when presented vsdth sequence B. This difference between left and right side revealed in sequence B is significant, t(23) = -2.76, p =.01. Cnditins 2 and 3: Tests fr the Accumulatr. Perceptual Prcessing, and Object-File Mdels. Analyses fr Cnditin 2 and 3 were cnducted t test the predictins fr all three theries. An ANOVA was cnducted fr variables sequence, cnditin, and trial type. 41

51 There were n significant effects within the first fur trials f these cnditins. The Accumulatr mdel predicted lnger lking fr the impssible trials. Hwever, this mdel was nt supprted, as impssible trials (M = 5.69, SD = 2.92), yielded lking times acrss bth cnditins similar t the pssible trials (M = 5 4 1, SD = 2 64) The Perceptual Prcessing Mdel predicted n difference in pssible versus impssible test trials within Cnditins 2 and 3, s this part f the predictin was supprted. Hwever, the crucial secnd part f the Perceptual Prcessing predictin, namely the lnger average lking time t events in Cnditin 3, fr which mre bjects were revealed n each trial, was nt supprted. In fact, the infants actually lked lnger, n average, in Cnditin 2, where tw bjects were revealed (M = 5.91, SD = 2.04), than in Cnditin 3, where three bjects were revealed (M = 5. 19, SD = ). Hwever, this difference was als nt significant. When the data were recded fr the variable side, there were n significant effects r interactins. In testing fr the Object-file predictins n the dependent measure first lk, cntrasts were perfrmed based n the predictins made in Tables 1 and 2. There was a significant effect fr the predictin that the infants remember the last tw bjects placed behind the right-hand screen, F( 1, 28) = 5.49, p <.05. Nne f the ther Object-file predictins apprached significance. Cnditin 2/3: Tests fr the Accumulatr. Perceptual Prcessing, and Object-file Mdels. An ANOVA was cnducted within blck 1 fr between-subject variable sequence, and within-subject variables number and trial type. There was a significant effect f trial type, F(l, 14) = 6.30, p <.05, with lnger first lks t the impssible trials 42

52 (M , SD = 2.94) than t the pssible (M = 5. 14, SD = 1.68). The type x number interactin was significant within this these first fur trials, ( 1, 14) = 9.56, p <.01. As shwn in Figure 2, tw bject trials did nt differ in lking times t different trial types (Mtw/pssible = 5.98, SD = 2.76; Mtw/impssible = 5.24, SD = 2.60). But, lking times differed cnsiderably fr three bject tnals (Mthree/pssible = 4.30, SD 1.34; Mthree/impssible= 8.24, SD = 4.50). T-tests revealed these means were significantly different fr the fllwing cmparisns: a) tw bjects/pssible versus three bjects/pssible, t(15) = 2.43, p <.05; b) tw bjects/pssible versus three bjects/impssible, t(15) = -2.30, p <.05; c) tw bjects/impssible versus three bjects/impssible, t(15) = -2.71, p <.05; d) three bjects/pssible versus three bjects/ impssible, t(15) = -3.35, p_<.01. There was als an interactin f sequence x number, F(l, 14) = 4.43, p =.05, as displayed in Figure 3. There was lnger lking time t three bjects when infants were tested in sequence B, than in sequence A, and very little difference lking at tw bjects, regardless f whether the infant was initially presented with sequence A r B. A t-test revealed the difference between tw bjects and three bjects revealed in sequence B was significantly different, t(7) -2.43, p <.05. When receded fr side, there were n significant main effects. There was the side X sequence interactin, F(l, 14) = 9.56, p <.01, as displayed in Figure 4. Whereas sequence A shwed a decrease in lking time frm left side t right side, sequence B shwed an increase. Even mre infrmative was a sequence x side x number interactin, as shwn in Figure 5. Althugh there was little difference between presentatin sequence and side when tw bjects were revealed, there was much mre variability when three bjects were revealed. Mrever, Figure 5a reveals that there was n effect f trial type 43

53 when tw bjects were revealed. When tw bjects were revealed n the left, infants lked lnger if given sequence A, which was a "pssible" trial, than sequence B, which was an "impssible" trial. When tw bjects were revealed n the nght, there was n difference in lking time. In Figure 5b, this sequence x side interactin fr three bjects revealed appears t be the surce f the trial type effect in Cnditin 2/3. When three bjects were revealed n the left side, infants lked lnger if given sequence A, which was an "impssible" tnal, than infants in sequence B, which was a "pssible" trial. When three bjects were revealed n the right side, infants lked lnger when in sequence B, which was an "impssible" trial, than thse in sequence A, which was a "pssible" trial. Althugh the significant effect f trial type fund in Cnditin 2/3 fits the predictin f the Accumulatr mdel, these interactins d nt. Therefre, there is limited supprt fr this mdel, because the Accumulatr cannt accunt fr the influences f side revealed and presentatin sequence n lking time behavir. Thus, a different srt f explanatin may be required in interpreting this data. The Perceptual Prcessing mdel predicted lnger lking in this cnditin t the three bject trials than tw. This mdel was nt supprted by the data, as lking t three bjects (M 6.27, SD = 2.35) was nt significantly different than t tw bjects (M = 5.61, SD = 2.28). Hwever, as can be seen in the type x number interactin in Figure 2, lnger lking ccurred when three bjects were revealed if it was als an impssible trial. Furthermre, mean lking time was even greater, as shwn by Figure 5b, when three bjects were revealed, it was an impssible trial, and it ccurred n the right side. This result may, in part, be due t sme cntributing influence f perceptual prcessing. 44

54 T test fr the pssibility f the Object-file mechanism being used in this cnditin, cntrasts were perfrmed n trials within Blck 1, based n the predictins made in Table 3. There was a significant effect f the infants remembering the last fur bjects presented, F(l, 14) = 5.99, n<.05. This effect appears t be a prduct f cnfunding factrs, inflating the rightmst clumn mean in Table 3; that being fr sequence B, three bjects, right side, impssible; rather than real supprt fr the Objectfile predictins, and will be addressed in the discussin t fllw. 45

55 CHAPTER 4 DISCUSSION If there were nly ne numerical prcessing mechanism respnsible fr number and bject knwledge, the candidates being the Accumulatr, the Object-lilc, and Perceptual Prcessing mechanisms, and it was rbust, then the lking times displayed by 10-mnth-lds wuld be cnsistent with its predictins acrss all three cnditins. The present study des nt cnsistently supprt ne f the three mechanisms. N single mechanism accunted fr the infants" respnses in this number-based task. Rather, the results shw a cmplex pattern, requiring a cmplex explanatin. Specifically, the results can be interpreted in terms f all three mechanisms cntributing t the pattern f lking behavirs. The strngest evidence verall favrs the Object-file mdel. The results best fit the predictins made fr Cnditins 2 and 3. This is because f the significant cntrast indicating that infants remembered the last tw bjects placed behind a screen. This interpretatin is further supprted by the lack f any interactins in these cnditins, as nne were predicted by the mdel. In cntrast. Cnditin 2/3 appears t fit the predictin f the Accumulatr mdel, namely lnger lking at the impssible trials. Hwever, the Accumulatr mdel als des nt predict the presence f any interactins. Therefre, the interactins fund in Cnditin 2/3 weaken the argument fr an accumulatr accunt fr lking behavir in this task. The Accumulatr If the infants used an accumulatr mechanism t discriminate quantity then, in all cnditins, they wuld lk lnger t the arithmetically impssible test trials than t the 46

56 pssible trials. At first glance, this appeared t be the case, because the Omnibus analysis f all eight trials shwed this pattern f lking. Yet, when the mnibus analysis was repeated fr the first fur trials nly, when attentin was at its best, the effect disappeared. Mrever, the means displayed in Figures 6 and 7, which separate tw bject trials frm three bject trials, reveals the "Trial Type" effect seems t be cming nly frm the three bject trials in Cnditin 2/3. Cnditin 2/3 taken by itself, appears t prvide sme supprt fr the Accumulatr mdel. Infants in that cnditin lked lnger t arithmetically impssible trials than pssible trials. This finding supprts the findings f Wynn (1992) and thers. An analg-magnitude mechanism culd explain the data fund in Cnditin 2/3, t a degree. The pattern f lnger lking t the impssible events nly appears in trials with three bjects revealed, but nt tw bjects. This finding is similar t that fund in Kechlin et al. (1997). In their study, in the 2-1 subtractin cnditin lnger lking times t tw bject (impssible) trials was slely respnsible fr the "pssibility effect." Lking t the impssible additin trials (1 + 1 = 1) was nt different frm the pssible additin trials (1 + 1=2). In this sense, the pssible/impssible trial type effect ccurred n the trials with the greatest number revealed and with arithmetical impssibility. The results in Cnditin 2/3 fit the same pattern. These results n mre supprt the interpretatin that all infants lked lnger t impssible trials than t pssible, than did the results f Kechlin et al., despite their making such claims, and thereby cntradicting their wn results. Lking lnger t impssible trials was nly fund in Cnditin 2/3, and ccurred nly when three bjects were revealed. The questin nw becmes, if the Accumulatr mechanism was used t make numerical calculatins in Cnditin 2/3, the 47

57 attentinally mre demanding cnditin, why was it nt respnsible fr perfrming the simpler, mre repetitive calculatins needed in Cnditins 2 and 3? Perceptual Prnre«;«;in The results d nt supprt the Perceptual Prcessing Mdel as the sle mechanism in guiding lking behavir. There were n significant effects f number in any f the cnditins tested. Of curse, the Perceptual Prcessing Mdel cannt be cmpletely discunted because the Chen & Marks (2002) mdel, which these predictins were based n, takes the psitin that it is the effects f familiarity and a tendency t lk lnger t larger numbers f bjects ("mre") that elicit the lnger lking. By nly testing ne piece f the assumptins made by the mdel C^mre" versus "less"), the present results may nt be an entirely accurate reflectin f the mdel because there was never a "familiar number" utcme. Althugh the number variable was nt significant, it did interact with ther variables in Cnditin 2/3, in such a way that reflects a preference t lk at "mre," given the right circumstances. In Cnditin 2/3 the infants lked lnger t the impssible trials, as previusly discussed. Interestingly, the lngest lking times were fund when three bjects were revealed AND the trial type was impssible, as reflected by the Type x Number interactin in Figure 2. This culd be because f sme perceptual prcessing. Within Cnditin 2 and within Cnditin 3, the same number f bjects were always revealed. In cntrast, in Cnditin 2/3 different numbers f bjects were revealed n different trials. The varied number utcmes presented may have cntributed t the differential lking pattern acrss trials because sme trials had "mre" t lk at, and 48

58 sme had "less," whereas in Cnditins 2 and 3, the "amunt" t lk at was always the same acrss trials. But, t take the perspective that the differences in "amunf ' are eliciting these differential lking patterns, ne culd argue the lking behavirs are exclusively perceptually-based. There is evidence that infants d respnd t simple changes f amunt in tasks meant t be number-based. Fr example, Starkey & Cper (1980) shwed that fur mnth-lds dishabituated t arrays that changed in number (tw r three dts). This was nt nly a change in number, but als a change in amunt. Hwever, in a similar habituatin prcedure, Clearfield and Mix (1999) fund that infants did nt dishabituate t changes in number, but nly t changes in cntur length f the stimuli. One f greater relevance t the present study is Feigensn, Carey, & Spelke's (2002) results. In a transfrmatin study they pitted number against "cntinuus extent" (i.e., surface area). They fund that infants lked lnger t changes in extent than t changes in number. Mrever, Feigensn, Carey, & Hauser (2002) fund that when given the chice, 10- t 12-mnth ld infants will discriminate based n extent rather than number. These studies shw that infants may be mre sensitive t perceptual changes alng a cntinuus dimensin rather than discrete number per se. Is it pssible then t interpret the present results as due t the detectin f changes in amunt nly? This is a difficult claim t make in the present study, because a change in number was cnfunded with a change in amunt. In the task, if the infant watched tw bjects placed behind a screen, and then tw bjects were revealed, it was a same number/same amunt trial. If the infant watched tw bjects placed behind a screen, then three bjects were revealed, this is a different number/different amunt trial. The 49

59 predictins made by the accumulatr mdel wuld be the same as a mdel that predicted lnger lking t changes in amunt. Therefre, if the results were cnsistent in finding lnger lking t impssible trials than t pssible tnals, then determining whether the mechanism used t make this discriminatin was number-based r perceptually-based culd nt be teased apart. This perceptually-based accunt f lking behavir faces the same prblems as the number-based accumulatr psitin. The data fr Cnditins 2 and 3 fail t supprt that infants were respnding based n perceptual changes in amunt (which were the arithmetically impssible trials). The nly significant change in amunt detected was fr three bjects in Cnditin 2/3. Likewise, this psitin fails t accunt fr the finding f Starkey & Cper (1980), where infants failed t detect the perceptual change in amunt f fur dts frm six dts presented. While this was used as evidence fr an accumulatr, number-based mechanism, taken tgether these data argue against the psitin that infants nly are respnding t perceptual changes in amunt. Such an argument culd be made that this is because sme ther mechanism was invlved in the task, which has implicatins fr memry and set-size being represented. Perhaps in the present study, as earlier suggested, it is the ccurrence f different number utcmes facilitating differential lking t "mre" (three bjects) than "less" (tw bjects) when these utcmes smetimes invlved a perceptual change in amunt (pssible r impssible). In a recent study by Feigensn, Carey, & Hauser (2002) 10- and 12- mnth-lds watched tw crackers, f equal size, placed in a cntainer. Then they watched three crackers, all same size as the previus tw, placed int a secnd cntainer. The infants were then given the chance t crawl t ne f the cntainers. The infants 50

60 reliably chse the cntainer hlding three crackers, indicating they understd, and preferred the cntainer that had "mre." In the present lking time study, there des seem t be smething special abut revealing "mre" bjects than "less" bjects. Nt nly did three bjects elicit lnger lking in Cnditin 2/3 when the trial was impssible, but a three-bject trial als elicited lnger lking when it was revealed n the nght side. An examinatin f several studies by Wynn reveals that fr all experiments in which a claim fr the accumulatr mechanism was made, all imprtant actins and manipulatins ccurred n the infant's right side. Fr example, in the Wynn & Chiang (1998) study, a duble-screen prcedure was als used. It differed frm the present study, in that bth screens were lwered at the same time n all test trials. Hwever, all bject transfrmatins (i.e., the additin r subtractin f an bject) were always made n the right side. Therefre, any arithmetical differences that needed t be detected were always n the right. S, either there is sme inherent preference fr the right side, r the Accumulatr and Object-tlle mechanisms wrk mst efficiently when bjects revealed are thse t the right. But this side preference is nt a prperty f the Accumulatr mdel. On the ther hand, the idea f a preference fr lking at "mre" bjects in cnjunctin with being revealed n the right side (the mst recently transfrmed bjects) is a plausible ne. The preference strngly appears t implicate the demands placed n memry. Because memry demands shuld nt be a prblem fr the Accumulatr nr Perceptual Prcessing in this task, but they are prblematic fr Object-file mechanism, the latter mdel may best explain this result. 51

61 Obiect-File<; One initial questin f this research asked if there is an bject-file system present and functining in the infant, then what is the actual limit f items that can be tracked"^ The results in this study supprt Leslie's (1999) claim that 10-mnth-ld mfants can keep track f and represent at least tw bjects. The results further supprt Leslie's suggestin that the tw-bject limit is glbal, because the infants in the present study did nt shw evidence fr remembering tw bjects n each side (a per set limit), which wuld have been supprted by a significant cntrast fr remembering the first tw bjects placed als. Hwever, the "first tw" cntrast was nt significant. Given that the tracking limit is a glbal ne, the secnd questin prmpting this study asked which indexes get drpped frm memry; the first nes established, r the mst recent? The cntrasts cnducted between Cnditins 2 and 3 indicated that the infants remember the tw mst recent indexes established. The mst recent bjects, always presented and then hidden behind the right screen, are mre salient in memry, whereas the indexes presented earliest (behind the left screen) are mst likely t get drpped frm memry. This alne culd explain the preferential lking t the right side. The issue f what might happen t these "drpped" indexes was cnsidered when making predictins based n the bject-file mechanism. One pssibility was that indexes "drpped" frm memry wuld elicit lnger lking time than events revealing an "expected," r "pssible" utcme. Hwever, the data did nt supprt this cnjecture. Lking times t events n the left side were nt lnger relative t the "pssible" utcmes revealed n the right side. This finding is similar t that f Wynn & Chiang 52

62 (1998). There, the infants watched an bject hidden behind each f tw screens. When the bject was taken away frm the nght-hand screen, the infants did nt lk lnger t the "magical appearance" f the bject n the right than they did t an "expected appearance" (when ne bject was added t the right-hand screen that previusly had nthing behind it). The argument made was that an accumulatr des nt hld an expectatin fr zer, s there was n expectatin, therefre n mismatch. It may be the case that an bject-file des nt hld the value zer either; that the drpped indexes fr bjects behind the left screen may simply decay r vanish and new files may be assigned when bjects are revealed n the left. This des nt require extra lking time t d, and there is n mismatch in perceptin, because n explicit expectatin was frmed due t these files being gne. While this accunts fr sme f the data in the present study (in Cnditins 2 and 3), it des nt accunt fr the impssible/three bject trials in Cnditin 2/3. These trials elicited lnger lking when bjects were revealed n bth the left and right sides. Hwever, if infants in Cnditin 2/3 relied n the Accumulatr mechanism fr these trials, the issue f "n expectatin" behind the left screen des nt apply. It is assumed by the mdel that there can be mre than ne accumulatr. Fr this study, nly tw accumulated values need t be held in memry, ne value fr the left screen, and ne value fr the right screen. There has been n previus evidence indicating accumulated values are drpped frm memry, unless the value is zer, which is nt the case here. The accumulatr can accunt fr part f the results in Cnditin 2/3, because the threebject trials elicited lnger lking t impssible trials, regardless f whether revealed n the left r the right side. As shwn in Figure 7, the pattern f lking was similar t bth 53

63 sides. N ther cnditin elicited a cnsistent pssible/impssible pattern f lking between sides revealed. In fact, f the means displayed in Figure 6 and 7, the Cnditin 2/3 - three-bject trials were the nly trials in which the differences were significant at the.05 level. But in Cnditins 2 and 3, where the lking times t the left were relatively shrt, the best fitting explanatin seems t be the right side preference due t drpped indexes, implicating the prbable use f an Object-file mechanism. Anther questin psed in this study was, wuld increasing the number f utcme types ver trials t fur be disruptive and cause the infant t resrt t relvin^ n either an "analg-magnitude" mechanism, r simple perceptual prcesses t reduce the wrk f the attentinal system? This questin was answered by the inclusin f Cnditin 2/3. It was speculated that the presentatin f fur different utcmes culd result in the infants lking lnger at three items than tw items in the Cnditin 2/3 nly, and culd actually fit the predictins f a different mdel fr the "reveal tw" and "reveal three" cnditins (Cnditins 2 and 3, respectively). This turned ut t be cnfirmed, althugh the results mst favr the accumulatr mechanism, r a numberbased explanatin, rather than Perceptual Prcessing. The reasn the findings best supprt a number-based mechanism, rather than the detectin f a perceptual change in amunt is because f the failure t detect changes in amunt when tw bjects were revealed. If infants were using ttal surface area as the primary cue, then they shuld have detected the change frm three bjects t nly tw. The finding that they did detect the difference when three bjects were revealed, suggests that sme ther mechanism was being used, which may have had smething t d with the greater number. Because the accumulatr is implicated as best dealing with larger numbers, utside f the 54

64 representatinal capacity, at this pint it seems the mst plausible mechanism. In Cnditin 2 and in Cnditin 3, where the trial utcmes were identical in number within cnditins (they nly varied by side revealed), the pssible decrease in verall attentinal prcessing demands demnstrated an efficient use f an attentinal tracking mechanism fr tw bjects. Neither the accumulatr nr perceptual prcessing can explain r accunt fr this pattern f lking in these cnditins. In Cnditin 2/3, there was a significant cntrast fr infants tracking the last fur bjects hidden, which appears t be arbitrary at first glance. Hwever, the effect is inflated due t the mean fr Sequence B/Three bjects revealed/right screen/impssible trials. If the bject-file cntrasts fr remembering the last tw bjects and the last three bjects hidden were als significant, then this cntrast fr the last fur bjects wuld be cnvincing. Because these ther cntrasts did nt apprach significance, it seems mst likely due t a cmbinatin f factrs such as: three bjects ("mre"). Event Sequence B (having last seen nly tw bjects hidden behind a screen), arithmetical impssibility, and a right side preference. Because all f these factrs seem t cntribute t greater lking time, the implicatins f the result are nt decisive. Leslie (1999) argued that the number f bject-files a 10-mnth-ld can hld in memry is tw. This was based n equal lking times fund in a 3-1 = 3 and 3-0 = 3 prcedure. Leslie cncluded that 10-mnth-lds lacked a specific representatin fr three bjects, which may be cded as "many" r "mre than tw." Earlier in this paper it was suggested that the presence f the hand mving in and ut in the 3-0 = 3 trials might have been disruptive t a fragile memry trying t retain three files, and they were nt successful due t this disruptin. The additin f a third file t memry is fragile at this 55

65 age, and cannt carry identity infrmatin in the file, as suggested by Leslie et al. (1998). But the system may be efficient enugh t hld a primitive third index, encding spatial lcatin infrmatin nly. The significant cntrast fr Cnditins 2 and 3 des supprt Leslie's (1999) claim f a tw-bject limit. But the present study des nt rule ut the pssibility f a fragile representatin develping fr a third bject held in memry. The pattern f lking times t events n the nght side is very different than t the left side. This may further implicate the memry and prcessing f bjects mst recently seen. T demnstrate, assume the 10-mnth-ld infant can represent the Uv bjects mst recently hidden behind the right screen. Furthermre, assume this infant is develping an ability t keep track f three bjects in memry, but this ability is nt cnsistently successful. There are fur scenaris that culd have taken place in this study: First, if tw bjects are placed behind the right screen, and tw are revealed, a shrt lking time t the event wuld be expected, because the infant can easily match the number f pen files in memry t the bjects in perceptin. This is a "pssible" utcme, and ccurred when infants were shwn Event Sequence B, with tw bjects revealed n the right. Secnd, if tw bjects are placed behind the right screen, and three bjects are revealed, this is a clear mismatch f the files in memry t what is in perceptin, and lnger lking t this event wuld be expected. This is an "impssible" utcme, and is what ccurred when infants were shwn Event Sequence B, with three bjects revealed n the right. Third, if three bjects are placed behind the right screen, then tw bjects are revealed n the right, the infant views this as cnsistent, r "pssible," because ability t pen and remember tw bject files is easiest, and readily accessible. It is mre difficult t remember the third, mre primitive file pened. This 56

66 third tile IS a graded representatin f srt (Munakata, 2001). In this case, there IS nt lnger lking t the event, which ccurred when infants were shwn Event Sequence A, with tw bjects revealed n the right side. But, in the furth scenan, the ability t hld three pen indexes in memry ccurs when three bjects are placed n the right, and three bjects revealed, as ccurred when infants were shwn Sequence A, three bjects revealed n the right side. The ability t pen this third file and hld it in memry is fragile, but the memry is facilitated by the revealing f three bjects immediately after they are hidden, with n ther disruptin. The third, graded representatin is strengthened by the presence f the third bject in perceptin. There is little chance f a 10-mnth ld infant remembering three bjects n the left. T many ther disruptins have taken place, such as bjects placed n the right, the raising f the right screen, and the passing f mre time. It is pssible t remember three n the right, if the three bjects are hidden, three files pened in memry, and then three bjects are revealed and matched up shrtly thereafter. This ntin that infants can remember at least the last tw bjects, and pssibly mre, can explain the facilitating effect f sequence B in this study. Assuming that anything placed behind the left screen has little r n chance f being remembered, sequence B gives the infant an advantage f nly needing t remember thse last tw bjects placed n the right. This results in lnger lking in sequence B t three bjects, than t any ther type f event, because this is mst likely t be detected as incrrect. The interactin f sequence with number, as fund in Cnditin 2/3 is imprtant, particularly because f the ease with which ne might have made a blanket statement that the accumulatr mechanism accunts fr the results f Cnditin 2/3. But the 57

67 accumulatr explanatin. The interactins f sequence with side revealed (Figure 1 accumulatr mechanism shuld nt be mtluenced at all by the presentatin sequence r the number f bjects revealed. The finding f n difference between tw bjects/pssible and tw bjects/impssible in Cnditin 2/3 was als a prblem fr the acrss all cnditins, and Figure 4, fr Cnditin 2/3), and sequence with number (Figures 3 and 5 in Cnditin 2/3) requires a mre cmplex explanatin than what is ffered by nly ne f these mdels. Therefre, it is pssible that this task created a cnflict between a develpin^ representatinal system (i.e.. Object-files) and a primrdial analg-magnitude system. If infants keep track f the tw mst recently seen bjects (n the right) and they are trying t remember a fragile representatin fr a third bject (but nly when presented n the right, as in sequence A) they might nt always be successful in their discriminatins. This culd be because the number f bjects appraches the bundary f the representatinal capacity in memry (tw r three bjects). The accumulatr, which is implicated in number discriminatin tasks that exceed the infant's representatinal ability (e.g., Xu & Spelke, 2000), may take ver at this pint. Such a mechanism can be used, as shwn in previus studies f adult estimatin (e.g., Whalen et al, 1999), and yung children's estimatins (e.g., Huntley-Fenner, 2001), when quantities are t great, r presented t rapidly, t cunt with accuracy. Furthermre, it supprts the argument that an accumulatr mechanism may be respnsible fr 5-mnth-lds' lking behavirs in additin and subtractin tasks (Wynn, 1992, 1995, 1997). Endwing the five-mnth-ld infant with the ability t add and subtract, r rather, make calculatins and frm expectatins abut the hidden bjects, is an extravagant claim t make, when it is nt 58

68 cnclusive as t whether infants can even represent and reasn abut hidden bjects at all at this age (Bgartz, Shinskey, & Schilling, 2000). But, the accumulatr des nt necessarily rely n bject representatin, it is nly a neural mechanism generating pulses f energy that are stred and tagged with an analg. The Object-file mechanism wuld nt be flinctinal at five mnths f age, because infants must have the ability t represent the hidden bjects. By 10 mnths, there is n dispute that infants are able t represent and remember hidden bjects. Therefre, in this task, either mechanism culd have been called upn, whereas with much yunger infants, an accumulatr culd be the nly number-based mechanism available. Then, given these tw mechanisms (Object-file and the Accumulatr) are bth available, what factrs decide their fates? Perhaps it is perceptual factrs, namely, the number f bjects revealed. As suggested by the Chen & Marks (2002) mdel, as well as by thers (e.g., Kechlin et al., 1997), lking at "mre" may take lnger than lking at "less," the simplest reasn being that there is mre "stuff t lk at when there is mre. If, 1 ) it takes lnger t lk at "mre," and 2) an impssible event typically elicits the lnger lking than pssible events, then, by this reasning, ne culd argue the lngest lking time shuld ccur n trials with "mre" (three bjects) that are als impssible, and the shrtest lking time shuld ccur n trials invlving "less" (tw bjects) that are pssible. On the ther hand, perceiving fewer bjects ("less") culd facilitate prcessing f the infrmatin that the amunt is equivalent t the files being held in memry. The perceptin f "mre" culd take lnger because there is mre t lk at, and the amunt may r may nt be t large t be represented in memry, at which pint the accumulatr may take ver. 59

69 The 10-mnth-ld is trying t represent bjects and quantities in the real wrld. The early perceptual prcesses and analg-magnitude mechanisms are cntributing t this rapidly develping ability t represent and remember. The findings reprted here supprt the Xu & Spelke (2000) suggestin that the use f an analg-magnitude mechanism r the use f an Object-file mechanism may depend n the size f the set being wrked upn. Future wrk t test the claims made herein wuld be helpful, such as reducing the numbers t ne and tw bjects hidden and revealed, and testing if the predictins hld up fr the bject-file mdel. The issue f a nght-side preference and a recency effect shuld be tested by presenting the bjects n the right side, then the left side. Als, testing 12-mnth-lds culd answer the questin f the fragile representatin f ''three bjects" in memry. By this age, the representatin may nt be s fragile. T summarize: 1) There is sme supprting evidence fr the Object-file mdel. Namely, 10-mnthld infants can successfully track and stre at least tw bjects in their memry. In Cnditins 2 & 3, the infants shwed lking behavir in accrdance with the predictin made between the tw cnditins fr representing and remembering the last tw bjects hidden behind a screen. 2) Analyses acrss all three cnditins indicated that infants' initial lks t an event were lnger fr arithmetically impssible events. Hwever, the effect nly ccurred in trials revealing three bjects in Cnditin 2/3. There was n difference in lking time t pssible and impssible events when tw bjects were revealed. Therefre, there is minimal supprt fr the Accumulatr Mdel, 60

70 which seems t be used in circumstances f high attentinal demand and the number f bjects revealed exceeds representatinal memry capacity. 3) The perceptual prcessing mdel cannt be cmpletely discunted in this experiment. Althugh the infants did nt always lk lnger t events revealing three bjects than events revealing tw bjects verall, there was smething unique abut the trials that revealed "mre" bjects (three), than "less" (tw). The trials that were arithmetically "impssible," elicited lnger lking times nly if three bjects were revealed, but nt when tw bjects were revealed. 4) Testing fr number-based representatinal abilities, r any higher-level cgnitive abilities, in a prcedure where the each infant is presented with the same events and the same number f bjects revealed has an imprtant advantage. The chance f btaining results due t simple perceptual prcesses as familianty preferences r size preferences are eliminated. In the present study. Cnditin 2 and Cnditin 3 prvide a srt f baseline fr Cnditin 2/3. The cmplex results f Cnditin 2/3 illustrate the delicacy f the prcessing that ccurs in the 10-mnth ld, and hw easily a seemingly simple change in prcedure can elicit a change in the interpretatin f results. Based n these results, it is suggested that 10-mnth-lds are in a transitinal perid f representatinal develpment, where tw mechanisms, an analg-magnitude mechanism (accumulatr) and an attentin-based bject-file system are in "cmpetitin" when faced with a task invlving a number f bjects just slightly ver what the limit the bject-file can track and represent. Whereas the bject-file attentin-based mechanism may be readily functinal fr representing small numbers f bjects at this age, the accumulatr 61

71 culd be best equipped t deal with prcessing larger numbers f bjects than can be represented and held in memry. Simple perceptual mechanisms, such as detectin f "mre" and "less" may be used as a btstrapping mechanism dictating which representatinal mechanism will dminate the infant's respnse. 62

72 1 u ^ 4) a: n Z z z z O n u c 3 C u CO c u > S > a: c c U 00 T3 U z a zo O z z z c z m c CO ri CO c "T3 C c U u Ji a z n a z O z Z 2 > 0 s c5 a c U - - C/2 O i O Z -J 55 z cu B 'mm c 'mm O CS 3 E 3 U E 3 es B. 4) O w. ID X)' O E CO E E E 63

73 T3 w V -C c s; «u ~ O Z -3 z O Z O a z z z > u a; 00 5 c a c U -Q c z z z -J s -a -a wv > s O C/3 O z ce: O C/3 a z C c/1 c g c U t3 ^ 5 S 2i i- O Z a: 0 a z z z.j -] _4J u CQ u 3 E 3 O < 4) E s CO 2 a. u 0) O IS C E E E J2 c (U 3 cr 00 c > 64

74 ^ CQ 8 c 4> 3 IT U n i3 T5 S «> c: -e c c z 2 z -J -J -J E- a: C/3 z -J z z z a z -a O Z -1 2 O z C/3 ~' S U - D c <u 1) X = - u i> E i3 u -a O I u -c 5 ^ II f- C/2 Z O -J O 00 f- O 5/3 O Z f- O X 00 z c z z z -J -J g 9 C/D G Z O c Z -J ~ c u. c 1) 71 CO < c _ O 8 8 «s ^ <5 3 ft O C/D z O z z z z -J a: O C/3 O z z z z z -J z c z -J 1) C J- ^ ^ C2 E w CO 00 t«^1 O f CO ^ 2 j z -J O a: 00 H E- fid fie: O O a: E 1/3 z z z z J Z E- O K z E- O (/5 CO O c CO O 45 a C T3 (U OX) x: 0) X)»0 _«"5 3 U O Si OS 2 av ii u Ok ect-fil m m T (N (N m T m (N i V iu iii '<a ect-fil ect-fil ect-fil ect-fil ect-fil S S O O O O O 1) 00 = S.E ^ > I A, c m CO 65

75 P Table 4: Sixteen Trial Type Orders fr Pssible/Impssible Pairings. Tnals 1-4 PIPI PUP IPPl IPIP Trials 5-8 PIPI PIPIPIPI PIPIPIIP PIPIIPPI PIPIIPIP PUP Piippipi prippiip piipippi PIIPIPIP IPPI IPPIPIPI IPPIPIIP IPPIIPPI IPPIIPIP IPIP IPIPPIPI IPIPPIIP IPIPIPPI IPIPIPIP Nte. = Pssible, I = Impssible. 66

76 Table 5: Event Sequences (A r B) tested in 16 Trial Type Orders fr Cnditins 7 3 ana 2/ j ' ' Trials PIPI PUP IPPI IPIP PIPI PUP IPPI IPIP Cnditin Cnditin Cnditin Cnditin 2 A B A B B A B A 2/3 A B A B 2 B A B A A B A B 2/3 B A B A 2 A B A B 3 B A B A 2/3 A B A B 2 B A B A '> A B A B 2/3 B A B A 67

77 Figure 1 : Sequence x Side interactin fr First Lk acrss all three cnditins 9-1 w 8 - C CO / «V) c D k c: (A i_ 4 - il at c 0) _i 1 4 Sequence A - -Sequence B 0 Left Side Revealed Right 68

78 Figure 2: Type x Number interactin fr Length f First Lk within Blck 1 Cnditin 2/3 10 n 0 A, Tw Three Number f Objects Revealed 69

79 Figure 3: Number x Sequence interactin fr Length f First Lk within Blck 1 f Cnditin 2/3 *- 4 - (A u il 3. Tw Three Number f Objects Revealed 70

80 Figure 4: Side x Sequence Interactin fr Length f First Lk within Blck 1 f Cnditin 2/3. w D C u Sequence A - Sequence B V) iz «* at c 0) Left Side Revealed Right 71

81 Figure 5: Sequence x Side x Number interactin fr Length f First Lk within Blck 1 f Cnditin 2/3. A) Tw bjects revealed M 14 u W 10 Sequence A Sequence B J< 8 "S 4 ir =*= 2 Left Side Revealed Right B) Three bjects revealed 14 (A ^12 u 4) W 10 Sequence A - Sequence B IL S 4 OI S 2 Left Side Revealed Right 72

82 Figure 6^Length f First Lk (in Secnds) t Pssible and Impssible Events Objects Revealed n the Left and Right Sides Pssible Impssible C2 -Left C2 -Right C2/3 -Tw C2/3- Tw Left Right 73

83 Figure T^Length f First Lk (in secnds) t Pssible and Impssible Events f Three Objects Revealed n the Left and Right Sides Pssible Impssible C3 -Left C3 -Right C2/3 -Three C2/3 -Three Left Right 74

84 ENDNOTES Trick and is'lyshyn (1994) used this bject-file type f mdel t accunt fr adult subitizatin, a rapid nnverbal enumeratin ability, which has been prpsed t utilize the same prcess r mechanism as infant preverbal enumeratin. Adults can typically subitize up t fur r five items. Ntice that the explanatin f failure in the Starkey & Cper (1980) fur t six cmparisn is due t the number f items being t large fr infants t track and hld in memry. It seems a plausible argument can be made that this is evidence fr a limited-capacity tracking mechanism which is limited t tw r three items in infancy, but with develpment, increases t fur r five. Hwever, the accumulatr mdel, which has als been suggested t underlie adult subitizatin, as well as the infant preverbal number studies discussed herein, can als accunt fr the failure f the fur-versus-six discriminatin. The numbers are large, but this mdel wuld psit that it was the 2:3 rati which is imprtant, in additin t the distance effect (there is nly a difference f tw), and therefre discriminatin is mre difficult than even a twversus-fur discriminatin (where the difference is als tw, but the rati f items is 1 :2). Thus, bth mdels can accunt fr the results f the Starkey & Cper (1980) study. In the study by Chen & Marks (2002), they claimed that the rle f perceptual prcesses is exhibited thrugh a lking preference fr the familiar, plus a tendency t lk at mre bjects. Because there is n "familiar" utcme in this study, predictins are made by this mdel slely n the assumptin f lnger lking t mre bjects. ^ It remains unspecified in the bject-file literature hw the infant will respnd t the lack f pen files in memry when the right screen reveals three bjects. N pen files might cnstitute a definite expectatin fr nthing (zer bjects) behind the 75

85 ccluder. In this case, the ^magical appearance" (Wynn & Chiang, 1998) f an bject culd elicit lnger l6kmg due t the mismatch between the perceptin f three bjects and the expectatin f zer bjects. Alternatively, the lack f pen files pinting t that particular lcatin might mean that n expectatin exists whatsever. This culd result in several pssibilities, nt all mutiially exclusive: 1) lking time is nt as lng t this ''appearance" (regardless f the number f bjects) than t an utcme that clearly mismatched (e.g., tw files had been pened and cmpared t three bjects in perceptin) because there was nt necessanly a mismatch in this case, simply assignment f new files t the bjects, 2) the assigning f new files t the bjects may r may nt result in lng lking times, because nthing is knwn abut the time invlved in "de-assigning" files frm ne lcatin and "re-assigning" them t a new lcatin, as described by Leslie et al. (1998), and 3) lnger lking may ccur t three bjects than tw, due t n expectatin and therefre falling back n a simpler perceptual mechanism f lking lnger at mre bjects. Cnversely, there may be equal lking time t tw and three bjects revealed in a lcatin with n files in memry, because n utcme was expected, and therefre bth are equally unexpected. Because it is unclear hw infants will react in such a case if they are using an bject-file mechanism, sme f the predictins invlving the ti-acking limits f tw r three bjects, where instances f n pen files fr a particular lcatin may ccur, are made with cautin. Patterns f lking are cnsidered when data was analyzed, t address these cncerns. Fr purpses f this thesis, the authr assumed in the predictins that the assigning f new bject files t a new lcatin invlves lnger lking time than if pened files were simply matched with thse in perceptin. 76

86 BIBLIOGRt^^HY ce, nenates. Baillargen, R., Miller, K., & Cnstantin g«n. J (1994^ Ten mnnth ^i^ unpunished.anuscir^^^^^^ r, Canfield, R. L., & Smith E. G. (1996). Number-based expectatins and sequential enumeratin by 5-mnth-ld mfants. Develpment.) P.yPhni.^ Clearfield, M. W., & Mix, K. S. (1999). Number versus cntur length,n infants' discriminatin t small visual sets. Psvchlmcnl Sr.iPnrP in Chen, L. B., & Marks, K. S. (2002). events. Develpmental Science S Hw infants prcess additin and subtractin Dehaene,S. (1992). Vaneties f numencal abilities. Cgnitin Feigensn, L., Carey, S., & Hauser, M. (2002). The representatin underlying infants' Object-file versus Analg magnitudes. Psvchlgical Sr.ienre n^t5vl56^''^" Feigensn, L., Carey, S., & Spelke, E. (2002). cntinuus extent. Cgnitive Psvchlev Infants' discnminatin f number vs. Gallistel, C. R. (1990). The rgamzatin f learning. Cambridge, MA: Bradfrd Bks/MIT Press. Gallistel, C. R., & Gelman, R. (2000). Nnverbal numerical cgnitin: frm reals t integers. Trends in Cgnitive Sciences Gallistel, C. R., & Gelman, R. (1992). Cgnitin Preverbal and verbal cunting and cmputatin. Huntley-Fenner, G. (2001). Children's understanding f number is similar t adults' and rats': numerical estimatin by 5-7-year-lds. Cgnitin. 78. B27-B40. Huntley-Fenner, G., & Cannn, E. (2000). Preschlers' magnitude cmparisns are mediated by a preverbal analg mechanism. Psychlgical Science

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88 C^r, G. (1980). Perceptin f number by human infants Science, M., & Pylyshyn, Z. V differently? A limited Review Wakeley, A., Rivera, S., & Langer. J. (2000). Can yung infants add and subtract? Child Develpment Whalen, J., Gallistel, C.R., & Gelman, R. (1999). Nnverbal cunting in humans The psychphysics f number representatin. Psychlgical Science Wynn, K. (1992). Additin and subtractin by human infants. Nature Wynn, K. (1995). Origins f numerical knwledge. Mathematical Cgnitin Wynn, K. (1996). Infants' individuatin and enumeratin f actins Psychlgical Science Wynn, K. (1998). Psychlgical fundatins f number: numerical cmpetence in human infants. Trends in Cgnitive Science Wynn, K. (2000). Findings f additin and subtractin m infants are rbust and cnsistent: Reply t Wakely, Rivera, and Langer. Child Develpment Wynn, K., & Chiang, W.-C. (1998). Limits t infants' knwledge f bjects: The case f magical appearance. Psychlgical Science Xu, F. & Carey, S. (1996). Cgnitive Psychlgy Infants' metaphysics: The case f numerical identity. Xu, F., & Spelke, E. S. (2000). Large discriminatin in 6-mnth-Id infants. Cgnitin. 74,B1-B11. 79

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