Cohen and Marks Final

8/12/2019 Cohen and Marks Final

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Infant Addition and Subtraction 1

Running Head: Infant Addition and Subtraction

How infants process addition and subtraction events

Leslie B. Cohen and Kathryn S. Marks

The University of Texas at Austin

Key words: infant cognition; addition, subtraction, familiarity preference.


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Abstract

Three experiments are described that assess 5-month-old infants' processing of addition

and subtraction events similar to those reported by Wynn (1992a). In Experiment 1, prior to each

test trial, one group of infants was shown an addition event (1 + 1) while another group was

shown a subtraction event (2 - 1). On test trials, all infants were shown outcomes of 0, 1, 2, and

3. The results seemed to require one of two dual-process models. One such model assumed that

the infants could add and subtract but also had a tendency to look longer when more items were

on the stage. The other model assumed that infants had a preference for familiarity along with

the tendency to look longer when more items were on the stage. Experiments 2 and 3 examined

the assumptions made by these two models. In Experiment 2, infants were given only the test

trials they had received in Experiment 1. Thus, no addition and subtraction or familiarity was

involved. In Experiment 3 infants were familiarized to either one or two items prior to each test

trial, but experienced no actual addition or subtraction. The results of these two experiments

support the familiarity plus more items to look at model more than the addition and subtraction

plus more items to look at model. Taken together, these three experiments shed doubt on Wynn's

(1992a) assertion that 5-month-old infants can add and subtract. Instead they indicate the

importance of familiarity preferences and the fact that one should be cautious before assuming

that young infants have sophisticated numerical abilities.


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How infants process addition and subtraction events

Learning the number system and how to manipulate it is one of the most difficult tasks a

young child encounters; it is a slow and laborious process taking years to complete (for example,

Fuson, 1988). Children study mathematics from their earliest school days to high school

graduation and beyond. However, like most areas of psychology, there are multiple perspectives

on this topic. Three major views on the development of numerical competence can be

distinguished. The empiricist view argues that children learn about numbers by observing

numerical transformations and noting the consistencies between events (Kitcher, 1984). Piagets

constructionist view argues that the number concept is built from previously existing

sensorimotor intelligence (Piaget, 1941/1952). In contrast, a more recent nativist view argues

that sensitivity to number is innate and even young infants possess strikingly mature reasoning

abilities in the numerical domain (Wynn, 1992b; 1992c).

Over the course of the last twenty years, researchers have explored questions about the

roots of numerical knowledge using looking time techniques with infants. The first area to be

investigated was called subitization. Subitization is the rapid, perceptual enumeration of small

sets, usually from one to four items. It is thought that adults subitize unless a display contains

more than four or five items, in which case they revert to counting (Balakrishnan and Ashby,

1992). Some researchers have suggested that infants may also have the ability to subitize small

arrays of items. Starkey and Cooper (1980), the first to propose infant subitization, found that

infants at 5.5-months of age were able to discriminate two from three dots, but not larger numbers of dots. Further research has since replicated Starkey and Coopers (1980) findings

both with neonates (Antell & Keating, 1983) and with 10- to 12-month olds, the latter using


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common objects instead of dots (Starkey & Cooper, 1980). Together this research may provide

evidence for the presence of numerical knowledge during early infancy.

However, more recent research is telling a different story. In contrast to previous studies,

Clearfield and Mix (1999a, 1999b) systematically manipulated contour length and area in the

standard subitization paradigm with 6- to 8-month old infants. They reported that infants

dishabituated to a change in either contour length or area, but not to a change in number. As a

result, they concluded that infants may actually be using continuous quantity rather than number

to discriminate between displays, and thus may not be subitizing. Holding mass constant,

Feigenson and Spelke (1998) reached a similar conclusion with 7-month old infants. Thus, the

conclusion that infants are subitizing remains controversial. Further investigation is still

necessary to determine infants actual subitizing ability as well as the age at which subitizing

first occurs.

A second body of evidence indicates that infants may be able to process numerical

information in one modality and then transfer it to another. Starkey, Spelke, and Gelman (1983,

1990) were the first to show that 6- to 9-month old infants might be able to enumerate sounds

and match them correctly with a visual display depicting that number. These results are even

more remarkable than those for subitizing because they suggest some primitive counting ability

by infants (Starkey, Spelke & Gelman, 1990). However, this research is also controversial. Other

laboratories, using infants of the same age, have been unable to replicate the original findings

(Moore, Benenson, Reznick, Peterson, & Kagan, 1987; Mix, Levine, & Huttenlocher, 1997). In

addition, Mix, Huttenlocher, and Levine (1996), using a procedure adapted for preschoolers,

found that three-year-olds are unable to correctly match auditory to visual numerosity. Thus, as


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with the subitizing results, there is no uniform agreement that infants under 6 months of age, or

even young children, are able to enumerate sounds and then match them with a visual display.

Given the evidence, albeit tentative, that young infants have some understanding of

number, Wynn (1992a) took the next step and asked to what extent infants are able to actively

manipulate the number system. In what has become a frequently cited paper, Wynn (1992a)

argued that infants as young as five months of age ...are able to calculate the precise results of

simple arithmetical operations (p. 750, emphasis added). In her first set of experiments, Wynn

showed infants a large stage on which various objects were inserted and removed. In the 1 + 1

condition, infants saw a doll placed on the stage. A screen then rotated up to occlude the middle

of the stage. Infants then saw a second doll placed behind the screen. When the screen rotated

back down, infants saw one of two outcomes. In the arithmetically possible event, there were two

dolls standing on the stage. In the arithmetically impossible event, there was only one doll

standing on the stage. A similar course of events took place in the 2 - 1 condition. Initially two

dolls were placed on the stage one at a time. After the screen rose to occlude the dolls, a hand

entered and removed one of the dolls. At the end of the trial, either one (arithmetically possible

event) or two dolls (arithmetically impossible event) were present on the stage. Wynn found that

infants looked significantly longer at the impossible outcome than at the possible outcome. In a

separate experiment (Wynn, 1992a, Experiment 3), showed infants 1 + 1 = 2 or 3. As with the

original experiment, she found that infants looked significantly longer at the impossible outcome

of 3. She argued that this was evidence that infants were actually predicting the precise outcome

of the event, rather than relying on simpler mechanisms such as directionality.Based on the results of her experiments, Wynn (1995a, 1995b) has argued that infants are

not only sensitive to number, they are able to manipulate small numerosities. In the course of her


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work, Wynn has made three major claims about infants abilities. The first is that infants

understand the numerical value of small collections of objects. Number is abstracted over

varying perceptual details (Wynn, 1992a; 1995b, 1996). Second, and related to the first, is that

infants knowledge is general and can be applied to varying items and different modalities (for

example, Starkey, Spelke, & Gelman, 1990). Third, she claimed that infants are able to reason at

the ordinal level and compute the result of simple arithmetic problems (i.e., add and subtract).

In contrast to Wynns innate, domain-specific, numerical approach, Simon (1997, 1998)

has argued that a non-numerical, domain-general set of competencies can account for the data

Wynn (1992a) presented. One is memory and discrimination. Another is the ability to

individuate a small set of items. The third is object permanence, and the fourth is the ability to

represent objects in terms of spatio-temporal characteristics (Simon, 1998).

Both Simon and Wynn have made predictions regarding what infants should do in the

Wynn task. In fact, both approaches make the assumption that infants will compare sets of items

based upon a one to one correspondence between the sets and will respond more (i.e., look

longer) at arithmetically impossible events than at arithmetically possible events. However, there

are other possible reasons why infants may respond more to the impossible events than to the

possible events in the Wynn task.

One possibility is that infants understand that when material is added, the outcome should

be more, or less in the case of subtraction, but they dont know how much more or less. This

directional explanation would be consistent with a rudimentary understanding of the ordinal

property of numbers, an assumption made by Simon as well. Reasoning at this level would involve comparing the final outcome to the initial display based upon the relative amount of

material. As long as the outcome is consistent with the direction of transformation, i.e., greater


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than or less than, the infants should look less than when the direction of transformation is

violated. As we noted earlier, Wynn (1992a) presented some preliminary evidence (Exp. 3) that

infants are doing more than making an ordinal transformation, but as we shall see from our

Experiment 2, there may be another explanation for her results. In any case, it seems reasonable

at least to consider this directional hypothesis.

Another possible explanation, one that has not been addressed before in the context of

infant addition and subtraction, is that the infants are simply responding more to familiar than to

novel displays. That familiarity may be based upon either the number of objects in the display, or

as Clearfied and Mix (1999a; 1999b) and Feigenson and Spelke (1998) have proposed, the

overall quantity created by the objects. Since the 1960s theorists have proposed that organisms

are most interested in an intermediate, optimal level of stimulation (e.g. Berlyne, 1963; Hunt,

1965; McCall & Kagan, 1967). According to Berlyne, for example, that level of stimulation is

based upon the overall novelty, complexity, and incongruity of the display. Several experiments

in the 1960s and 1970s demonstrated that indeed young infants often responded more to a

familiar stimulus than to a novel stimulus. In fact, recently Roder, Bushnell, and Sasseville

(2000) reported another example of 4 1/2 month-old infants having a familiarity preference, prior

to a novelty preference.

These results regarding infants preferences for familiarity and novelty have been

summarized in the three-dimensional model presented by Hunter and Ames (1998). According to

this model, with repeated presentations of a stimulus, infants should display a familiarity

preference prior to a novelty preference. Furthermore, the extent of this familiarity preference

should depend upon the age of the infant, with younger infants showing a greater familiarity


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preference than older infants, and the complexity of the stimulus or event, with more complex

events producing greater familiarity preferences than simple events.

Based upon this type of model, one might well predict that the Wynn task could be

producing familiarity preferences. The infants are relatively young, approximately 5 months of

age. The task is quite complex, with noises, multiple objects and a hand moving in and out, and

both a screen and a Venetian blind going up and down. Furthermore, the infants have not been

habituated to any of the events so they would be expected to be in an early stage of processing

the objects, a stage when a familiarity preference is likely to occur. It is also the case that in the

addition event they receive many more exposures to the single object (the incorrect result) than

to the two objects (the correct result) whereas in the subtraction event they receive many more

exposures to the two objects (the incorrect result) than to the single object (the correct result).

Therefore, based upon the model provided by Hunter and Ames, the conditions would seem

optimal for infants to look longer at the impossible event, not because it is impossible, but

because it is more familiar.

One way of testing among these three explanations is to present infants with 0 and 3

objects as well as the 1 and 2 objects typically used in this task. The three different explanations

and the unique predictions generated from them are presented schematically in Table 1. Note that

all of them predict the same pattern of results reported by Wynn (1992a) and Simon et al.

(1995a) in the 1 and 2 object tests. However, they make different predictions regarding 0 and 3

objects. In the familiarity preference case infants would be responding most to the outcome they

had seen the most. That is, they would find the outcome that matched the initial state of thedisplay most interesting because they were in an early stage of encoding the display. In essence,

this explanation assumes only a same-different comparison between the initial and final displays.


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In contrast to this explanation, according to the directionality predictions, the infants may

have some ordinal understanding of the changes to the display. It is possible that infants

understand that when material is added, the outcome should be more (or less, in the case of

subtraction). This explanation would be consistent with a rudimentary understanding of the

ordinal property of numbers. It would also be consistent with comparing the final outcome to the

initial display based upon the amount of material rather than the number. As long as the outcome

is consistent with the direction of transformation, i.e., the directional hypothesis shown in

Table 1, the outcomes that result in more (for addition) and less (for subtraction) will result in

lower levels of looking.

Finally, the most sophisticated possibility shown in Table 1 would be the actual

computation of the outcome based not only upon direction, but also on the actual number. In

essence, this hypothesis assumes that infants are able to add and subtract small numbers,

consistent with Wynns (1992a) view.

_______________________________

Insert Table 1 about here.

_______________________________

The main purpose of our first experiment was to replicate previous findings within the

context of a larger set of test events that includes outcomes with 0 and 3 objects as well as 1 and

2 objects. In so doing we hoped to be able to evaluate the plausibility of the three explanations

just discussed.


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Experiment 1

Method

Participants

Eighty healthy, normally developing infants, five months of age (M = 21.90 weeks, SD =

1.22 weeks) participated in this study. Of the 80 infants, 85 % were Caucasian. The majority of

parents had at least a four-year college degree. An additional 31 infants participated but were

excluded from data analysis due to fussiness (N = 28) or persistent inattention (N = 3).

Apparatus

The apparatus was modeled as closely as possible on the Wynn (1992a) experiment. Each

infant sat in a car seat attached to a low table, facing a large puppet stage, 60 cm high by 80 cm

wide by 30 cm deep. The infant was separated from the stage by 100 cm. The parent sat behind

and to the right of the infant. The stage was constructed from bright yellow foam board. A door,

cut in the right side of the stage allowed the visible addition and subtraction of the objects (toy

monkeys). A hidden trap door in the back of the stage allowed an experimenter to add or remove

monkeys surreptitiously.

A screen, 35 cm wide by 18 cm high, rotated on a horizontal rod connected to the front of

the stage. An attached mechanism allowed a second, hidden experimenter to rotate the screen up

and down. When in the upright position, the side of the screen exposed to the infant was white. A

reading light with a 40-watt bulb was aimed at the center of the stage from above. Dim recessed

lights in the ceiling of the room provided additional indirect light. Finally, a large dark green

mini-blind hung over the stage and could be dropped down in front of the stage between trials.

Dark green curtains surrounding the stage concealed both experimenters.


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A Panasonic, low-light, black and white camera was positioned under the stage and

aimed at the infants face. This camera was connected to a monitor and Sony VCR in a separate

control room. One experimenter monitored the image of the infant's face, but remained blind to

the stage. When the infant fixated on the stage, the experimenter pressed a button connected to

an Apple Power Macintosh 8500 computer programmed to record the duration of fixation. The

computer signaled the beginning and ending of the trials. A Panasonic color camera, positioned

behind the infant, recorded the stage. In addition, the signal from each camera was routed into a

Videonics digital video mixer where the images were combined onto one tape. This tape was

used for reliability purposes. Looking time data from 20 participants were recoded. The mean

correlation between the two observation sessions was .93 (SD = .06).

Stimuli

The toys used in this study were brightly colored stuffed toy monkeys. The main body of

the monkey was light blue. There were colored dots on the abdomen and stripes on the paws.

The ears of the monkey were bright red. A squeaker inside the monkey was pressed repeatedly

allowing the experimenters to draw attention to the object as it was moved across the stage.

Procedure

Infants were randomly assigned to either the addition or subtraction condition. Equal

numbers of male and female infants were assigned to each condition. Order of presentation of the

test trials was counterbalanced using a Latin Square.

Three experimenters worked together to run the experiment. The first two experimenters

were in the testing room, behind the puppet stage. One experimenter controlled the screen and visibly placed the monkeys on the stage. A second experimenter operated the mini-blind between

trials and secretly inserted and removed the monkeys through a trapdoor in the back of the stage


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to create the correct outcome for each test trial. The third experimenter sat in a control room and

recorded looking times on-line. Digi-Tech, hands-free walkie-talkies allowed the experimenter in

the control room to communicate the beginning and end of trials to the second experimenter in

the testing room.

Pre-test. Infants were presented with two trials to familiarize them with the rotation of the

screen, the movement of the hand, and the sight and sound of the monkey. In the first pre-test

trial, no items were placed on the stage. The screen began flat against the front of the stage and

rotated up to vertical. An empty hand entered the stage through the side door, tiptoed across

the stage from the side, went behind the screen, paused, and left the display empty. The screen

then rotated back in the opposite direction, until it returned to its starting point. Infants were

allowed to continue looking at the end of the event for an additional two seconds. The mini-blind

was lowered to end the trial.

In the second pre-test trial, infants saw an event identical to the test event except that the

outcome was not shown. In the addition condition, the stage began empty. A hand holding one

monkey entered the stage through the door on the side, placed the monkey on the stage, and

exited. The screen was rotated up to vertical. A second monkey was then added to the stage

through the side door and placed behind the screen. The empty hand left the stage through the

side door. For the infants in the subtraction condition, the stage also began empty. Two monkeys

were placed on the stage by the hand, one at a time, and the screen then was rotated up. An

empty hand entered the stage and removed one monkey from behind the screen and carried it off

the stage through the door on the side of the stage. Infants in both the addition and subtractioncondition were allowed to continue looking at the end of their second pre-test event for an

additional two seconds. Once again the mini-blind was lowered to end the trial.


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Test. Infants were shown eight test trials with each of the four outcomes presented twice.

The screen began flat against the front of the stage. The experimenter placed one monkey (in the

addition condition) or two monkeys (in the subtraction condition) on the stage, and the screen

was rotated up to vertical. The first experimenter then either added or subtracted one monkey

from the display through the door on the side of the stage. Hidden from sight, the second

experimenter added or removed monkeys as needed through the trap door to produce the

outcome for that trial. The screen was rotated down to its starting position to reveal the outcome

of the event. See Figures 1 and 2 for a schematic diagram of the experimental events.

_______________________________

Insert Figures 1 and 2 about here. _______________________________

Looking times to each display were recorded by the third experimenter in the control

room. A look was considered valid if it was longer than one continuous second. A trial was

terminated when the infant looked away from the display for longer than one continuous second

or when the infant looked at the display for a maximum of sixty continuous seconds. At the end

of each trial, the mini-blind was lowered across the opening in the stage to allow the first and

second experimenters to reset the display.

Results

A 2 Condition (addition vs. subtraction) x 2 Trial Block (first vs. second) x 4 Outcome

(0, 1, 2, and 3) x 2 Gender (male vs. female) ANOVA yielded a number of significant results.

The main effect of outcome was significant, F (3, 228) = 5.38, p < .01, as was the main effect of

trial block, F (1, 76) = 32.24, p < .01. The main effect of trial block indicated significantly longer

looking times during the first block (M = 8.29 s, SD = 6.15 s) than during the second block (M =

6.26 s, SD = 4.49 s) of test trials. There was also a significant main effect of gender, F (1, 76) =


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4.91, p < .05. Overall, males (M = 8.03 s, SD = 6.12 s) looked significantly longer than did

females (M = 6.53 s, SD = 4.64 s). However, gender did not interact with any other main effects

or interactions, so it was excluded from subsequent analyses.

The main question addressed by this study was whether looking times to zero, one, two,

and three items varied as a function of the addition or subtraction manipulation. The interaction

of interest was the Outcome x Condition interaction, which was significant, F (3, 228) = 3.12, p

< .05. The three-way Trial Block x Outcome x Condition interaction was also marginally

significant, F (3, 228) = 2.61, p = .052 and is shown graphically in Figure 3.

_______________________________

Insert Figure 3 about here. _______________________________

In order to understand this interaction we first ran separate analyses for each trial block

just on outcomes one and two, the same outcomes tested by Wynn. As shown in Table 1, all

three explanations predicted a Condition x Outcome interaction (i.e., they predicted that infants

should look longer at an outcome of one than an outcome of two in the addition condition, but

infants should look longer at an outcome of two than at an outcome of one in the subtraction

condition.

A 2 Condition x 2 Outcome ANOVA on the first block of test trials produced only one

significant result, the predicted interaction, F (1, 78) = 11.38, p = .001. In the addition condition

infants looked significantly longer at an outcome of one (M = 10.94 s, SD = 7.36 s) than at an

outcome of two, (M = 7.82 s, SD = 4.97 s), F (1, 39) = 6.40, p = .02. In the subtraction condition,

on the other hand, infants looked significantly longer at an outcome of two (M = 9.95 s, SD =

7.67 s) than at an outcome of one, (M = 7.09 s, SD = 6.96 s), F (1, 39) = 5.04, p = .03.

The only significant effect in the second block of trials was the main effect of outcome, F


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(1,78) = 7.92, p < .01. Infants looked significantly longer at an outcome of two (M = 7.24 s, SD

= 5.56 s) than an outcome of one (M = 5.53 s, SD = 3.24 s).

One final set of analyses examined just those outcomes that were novel, that is, zero, two,

and three in the addition condition and zero, one, and three in the subtraction condition. Each

explanation shown in Table 1 predicts a different pattern of results. The familiarity explanation

predicts short looks to all outcomes in both addition and subtraction conditions. The directional

explanation predicts an interaction with long looks to an outcome of zero in the addition

condition and long looks to an outcome of three in the subtraction condition. Finally the

computational explanation predicts the quadratic looking pattern of long, short, long in both

addition and subtraction conditions.

Once again separate analyses were run for each Trial Block. In these analyses Outcome

had three levels, zero, middle, and three, where the middle outcome was two for the addition

condition and one for the subtraction condition. The 2 Condition x 3 Outcome ANOVA for Trial

Block One yielded only a significant main effect for Outcome, F (2,156) = 4.60, p < .02.

Subsequent linear and quadratic trend tests produced a significant linear trend, F (1,156) =

9.124.60, p < .005. Infant looking times increased regularly from the zero outcome, (M = 6.43 s,

SD = 4.43 s), to the middle outcome, (M = 7.46 s, SD = 6.02 s), to the three outcome, (M = 8.85

s, SD = 5.63 s). The quadratic trend did not approach significance, F (1,156)


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longer at one than two. The main question, though, is what is the best way to explain these

findings? One possibility is that the infants were actually adding and subtracting. However, other

explanations are also possible and the present experiment was designed to enable us to decide

among them.

By adding outcomes of zero and three to the original outcomes of one and two, we were

able to assess three distinct processing explanations. The familiarity explanation states that

infants should look longest at the outcome that is most familiar to them. The most familiar

outcome will correspond to the first number of items on the stage (prior to the addition or

subtraction manipulation). In the case of addition, this would be an outcome of one. In the

subtraction condition, it would be an outcome of two. The directional assumes only a directional

understanding of addition and subtraction. In this case, infants would look longer at outcomes in

the opposite direction than expected. In the case of addition, outcomes of zero and one are

directionally incorrect and should both be looked at longest. In subtraction, outcomes of two and

three are directionally incorrect and should be looked at longest. Finally, a pure computational

explanation would predict that infants should look longest at all of the arithmetically incorrect

outcomes.

The present data, particularly the obtained linear trend, do not unequivocally support any

of these explanations. The first one outlined was a simple familiarity preference. Although

infants do show a preference for one in the addition condition and two in the subtraction

condition, as predicted by a familiarity preference, their looking times also should be equally low

at the other novel outcomes, zero, middle, and three in both conditions. Instead, their lookingtimes displayed an increasing linear trend. Thus, a simple familiarity preference, by itself, cannot

account for the data.


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The second alternative was a qualitative understanding of the direction of the operation.

Infants should look longer at events that violate the directionality of the operation. In the addition

condition, infants should look longer at the zero outcome than at the middle or three outcome. In

the subtraction condition, they should look longer at the three than at the middle or zero

outcome. Whereas the data from the subtraction condition are consistent with this strategy, the

data from the addition condition are not. Infants showed the opposite pattern of looking times.

The final possibility outlined was true computational reasoning. This explanation predicts

that infants should show increased looking times to all of the impossible events. In the case of

the addition condition, two is the only possible outcome. Looking times to the outcomes of zero,

middle (i.e., two in addition), and three should follow a high (impossible), low (possible), high

(impossible) pattern. Similarly in the subtraction condition, one is the only possible outcome.

Thus, looking times to the outcomes of zero, middle (i.e., one in subtraction) and three should

follow the same high, low, high pattern. The data clearly do not support this model either.

Infants' looking times to the novel outcomes of zero, middle, and three showed a strong linear

increasing trend and no hint of a quadratic trend as predicted by the computational model. Thus,

when both zero and three are included as alternatives, the results from this study are not

consistent with knowledge of addition and subtraction.

From the point of view of a purely arithmetic reasoning interpretation, the most troubling

finding was that in both the addition and subtraction conditions infants did not look very long at

the zero outcome even though in both conditions it was an impossible event. Wynn (1995a) has

attempted to account for the zero problem by assuming that infants look longer at impossibleevents, except when the outcome is zero. However, her argument is not entirely clear. On the one

hand, she argues that zero is a privileged entity that cannot be represented using Meck and


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Church's (1983) accumulator mechanism, the mechanism she uses to explain the addition and

subtraction. Because the accumulator's neutral position is the same as the result of an operation

ending in zero, the mechanism cannot distinguish between the two conditions. Thus, infants can

not form numerical expectations when the outcome of an event is zero. However, the correct

outcome in the present experiment is not zero, so that argument does not seem to apply. On the

other hand, Wynn and Chiang (1998) report that infants can distinguish between outcomes of

zero in a magical versus expected disappearance situation, with infants tending to look longer at

zero in magical as opposed to expected disappearances. Because both our addition and

subtraction conditions could be considered cases of "magical disappearances" (zero is never the

correct result of the operation), we assume Wynn would predict infants will look longer at zero

in those situations as well. However, since we found that infants in both the addition and

subtraction conditions tended to look less at zero, this prediction fails to account for the results

found in Experiment One.

On the other hand, one could make the common sense assumption that infants should

look more when there is more to look at, i.e., when there are more objects on the stage. That

assumption clearly fits with the linear trend found in looking times to novel outcomes. A two-

process explanation combining this "more to look at" prediction with Wynn's arithmetical

reasoning hypothesis would probably fit the present data.

However, combining the "more to look at" assumption with a familiarity preference

would also fit the data. Considering familiarity first, as we noted earlier, Hunter and Ames

(1988) outlined a theoretical model in which familiarity and novelty preferences are based on theage of the infants, the complexity of the task, and the amount of time infants have to process the

events. Recently Bogartz, Shinskey, and Shilling (2000), Shilling (2000), and Cashon and Cohen


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(2000) have all reported familiarity preferences with the violation of expectation method

(Baillargeon, 1987; Baillargeon, Spelke, & Wasserman, 1985) used for studying object

permanence .

In the present experiment, which can also be considered an example of the violation of

expectation method, on each trial the infants saw either one object on the stage and then another

one added or they saw two objects on the stage and then one subtracted. In the addition

condition, over the course of the 8 test trials they saw one object 10 times and zero, two and

three objects only 2 times each. Infants looked longer at the outcome that they saw most

frequently, namely one object. Infants in the subtraction condition saw two objects 10 times, and

zero, one, and three objects only twice each. They showed this same pattern of looking longer at

the outcome that was most frequent, in this case two objects. More support for the familiarity

preference comes from considering each block of four trials separately. In both the addition and

subtraction conditions, the results from the first block of trials alone mirrored the results of the

data as a whole. In contrast, in the second block of trials, some evidence of the "more to look at"

assumption was present. Infants looked significantly longer at an outcome of two than at an

outcome of one regardless of condition. This disappearance of the familiarity effect would be

expected given the large number of repetitions of the basic addition or subtraction event. On the

other hand there is no reason to expect such a disappearance based upon the computational

explanation.

Wynns (1992a) claim is that infants are able to precisely calculate the result of simple

arithmetic problems. To examine the hypothesis that infants were using an imprecise, directionalstrategy, she also showed infants 1 + 1 = 2 or 3. Presumably this design would rule out any

explanation based upon familiarity as well since both 2 and 3 would be novel. She reported that


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infants looked longer at the impossible event, 1 + 1 = 3. However, this evidence should only be

considered suggestive given that the difference in looking times to two versus three did not reach

statistical significance using a traditional two-tailed test. We also found no significant difference

between 2 and 3 in our addition condition. Thus, at this point, evidence that infants look longer at

3 than at 2 items after an addition manipulation should still be considered tentative. Even if one

found that 3 items were looked at more than 2 items, it is imperative that controls for looking

longer when there are more items to look at be included.

The possibility that infants look longer the more there is to look at was really an ad hoc

assumption based upon an inspection of the test data in Experiment 1. In order to provide an

independent test of this assumption we conducted Experiment 2. The procedure of Experiment 1

was simplified to its most basic elements, just a presentation of the eight test trials. No warm-up

was given, no addition or subtraction was presented, and infants were not familiarized to any of

the 4 outcomes.

Experiment 2

Experiment 2 was designed to examine the possibility of a simple preference for more

items over fewer items. Infants were given the same test trials infants had received in Experiment

1. That is, they received two blocks of 0, 1, 2, and 3 items presented in a Latin Square order.

However, unlike Experiment 1, prior to each test they did not see a hand adding or subtracting

items. They also did not receive any familiarization with 1 or 2 items prior to each test trial.

Method

ParticipantsSixteen healthy, normally developing infants, five months of age (M = 21.79 weeks, SD

= 1.23 weeks) participated in this study. Of the 16 infants, 69 % were Caucasian. The majority of


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parents had at least a four-year college degree. One additional infant participated but was

excluded from data analysis due to fussiness.

Apparatus and Stimuli

The setup of the room and stage were identical to that used in Experiment 1. Looking

time data from four randomly chosen participants were recoded as a test for reliability. The mean

correlation between the two observation sessions was .96 (SD = .02).

Procedure

Infants were randomly assigned to one of four presentation orders, counterbalanced using

a Latin Square. Equal numbers of male and female infants participated in the experiment.

Two experimenters worked together to run the experiment. The first experimenter was in

the testing room, behind the puppet stage. She had control of the mini-blind and presentation of

the objects. The other experimenter sat in a control room and recorded looking times on-line.

Digi-Tech hands-free walkie-talkies allowed the experimenter in the control room to

communicate the beginning and end of each trial to the experimenter in the testing room.

Infants were shown four different test trials in a counterbalanced order, with each of the

four outcomes presented twice. When the mini-blind in front of the stage was raised, 0, 1, 2, or 3

objects were sitting on the stage. No manipulation of the display took place in this experiment.

Looking times to each display were recorded by one of the experimenters. A look was

considered valid if it was longer than one continuous second. A trial was terminated when the

infant looked away from the display for longer than one continuous second. At the end of each

trial, the mini-blind was dropped in front of the stage to allow the experimenter to reset thedisplay.

Results


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Figure 4 provides looking times to each number of objects for each block of trials. 2 Test

Block (first or second) x 4 Outcome (0, 1, 2, or 3) ANOVA revealed a main effect of outcome, F

(3, 45) = 4.48, p < .01 and a main effect of trial block, F (1, 15) = 13.96, p < .01. There was a

significant linear increase in looking time as the number of items presented on the stage

increased, F (1, 45) = 10.82, p < .01; but no significant quadratic trend, F (1, 45) = 2.56, n.s.

Infants also looked significantly longer at the first block of trials (M = 9.85 s, SD = 6.97 s) than

at the second block of trials (M = 6.05 s, SD = 4.46 s). Although the interaction between

outcome and trial block was not significant, we were interested in comparing the looking times

across the two blocks of trials. Results of the first trial block revealed no significant difference

among outcomes. In contrast, in the second block, there was a significant main effect of outcome

F (3, 45) = 4.02, p < .05, and once again, a significant linear trend, F (1, 45) = 11.61, p < .005.

_______________________________

Insert Figure 4 about here. _______________________________

Discussion

The primary result from this experiment was that infants showed increased looking times

as the number of items to look at increases. That result was significant in the overall analysis,

and it was significant in the second trial block, but not the first trial block. Apparently, infants

must be given sufficient time to process the overall testing situation before this preference is

evident. These results are consistent with the results of Wynns (1992a) Experiment 3. In that

experiment, she found that during the pretest, there were no significant differences in looking at

two and three items. However, when presented with 1 + 1 = 2 or 3 in the test trials, infants

appeared to look longer (albeit not significantly) at the impossible event with three items. The

two blocks of our experiment can be compared to the pretest and test trials of Wynn (1992a). In


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our first four trials, there was no preference for more objects. However, there was a linear

increase in looking time, as more items were placed on the stage in the second block. Based upon

the present results, one could argue that Wynn (1992a) did not find pretest differences because

the infants in her experiments were not sufficiently familiar with the testing situation to show

such a preference. Thus her apparent, albeit not significant, demonstration that infants in an

addition condition looked longer at 3 items than at 2 items, could simply have reflected an

emerging tendency for longer looking, the more items there were to look at.

Experiment 3

Experiment 3 was designed to be an independent test of the possibility that a familiarity

preference would develop in this type of complex event. The experiment examined what would

happen if infants were familiarized with either one or two objects prior to receiving the test items

used in Experiment 2. Unlike Experiment 2, half of the infants were shown 1 item prior to each

test trial. The other half were shown 2 items prior to each test trial. Thus, in this experiment the

infants had an opportunity to develop a familiarity preference, but no opportunity to respond on

the basis of addition or subtraction. Unlike Experiment 1 the infants did not receive warm-up

trials, the sight of a moving hand, or other features of that experiment's procedure. The goal of

Experiment 3 was not to replicate directly all aspects of Experiment 1 except addition and

subtraction. The goal was simply to add familiarization experience with either one or two objects

to the test trials of Experiment 2. The reason was to determine whether a familiarity preference

would be superimposed on the previously found linear trend of looking longer as the number of

items on the stage increased. As in previous experiments, infants were given two blocks of testtrials with 0, 1, 2, or 3 items.

Method


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Participants

Sixteen healthy, normally developing infants, five months of age (M = 21.22 weeks, SD

= .85 weeks) participated in this study. Of the 16 infants, 56 % were Caucasian. The majority of

parents had at least a four-year college degree. An additional 3 infants participated but were

excluded from data analysis due to fussiness.

Apparatus and Stimuli

The setup of the room and stage were identical to that used in Experiment 1. Looking

time data from five randomly chosen participants were recoded for reliability purposes. The

mean correlation between the two observation sessions was .99 (SD = .001).

Procedure

Infants were randomly assigned to either the one-item familiarity condition or the two-

item familiarity condition. Equal numbers of male and female infants were assigned to each

condition. Two experimenters worked together to run the experiment. The first experimenter was

in the testing room, behind the puppet stage. She was responsible for controlling the mini-blind

as well as the events taking place on the stage. The other experimenter sat in a control room and

recorded looking times on-line. Digi-Tech hands-free walkie-talkies allowed the experimenter in

the control room to communicate the beginning and end of each trial to the experimenter in the

testing room.

Test trials

As in Experiments 1 and 2, infants were shown two sets of four test trials in a

counterbalanced, Latin Square order, with each of the four outcomes presented twice. The screen began flat against the front of the stage. Either one or two objects were on the stage at the

beginning of each trial. Infants saw this configuration for approximately 2 seconds. The screen


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was then rotated up to vertical to hide the stage. The experimenter added or removed objects as

needed through the trap door to produce the outcome for that trial. The screen was then rotated

down to its starting position to reveal the outcome of the event.

The experimenter in the control room recorded looking times to each display. A look was

considered valid if it was longer than one continuous second. A trial was terminated when the

infant looked away from the display for longer than one continuous second. At the end of each

trial, the mini-blind was dropped across the front of the stage to allow the experimenter to reset

the display.

Results

The results are shown separately for each block of trials in Figure 5. A 2 Familiarization

Condition (familiarization to one or two) x 2 Trial block (first vs. second) x 4 Outcome (0, 1, 2,

or 3) ANOVA revealed a significant three way interaction F (3, 42) = 6.17, p < .01. The

ANOVA also revealed significant outcome, F (3, 42) = 4.93, p < .01, and test block, F (1, 14) =

29.55, p < .01 main effects. Overall, infants looked longer at 1, 2, and 3, than they did at 0, F (1,

42) = 14.01, p


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infants looked significantly longer at one object (M = 22.47 s, SD = 8.87 s) than at two objects

(M = 11.82 s, SD = 5.57 s), F (1, 7) = 10.77, p = .01. In the two-objects familiarization

condition looking times were in the opposite direction with longer looking at two objects ((M =

20.60 s, SD = 16.84 s) than at one object (M = 14.69 s, SD = 10.07 s). However, the difference

between these two means did not reach statistical significance, F (1, 7) = 2.27, < .20, perhaps

because the N was so small.

As in Experiment 1, a final set of analyses examined only those outcomes that were

novel, that is, zero, two, and three in the one object familiarization condition, and zero, one, and

three in the two object familiarization condition. Once again, for the purpose of the analyses, the

outcomes were treated as zero, middle, and three, and separate analyses were run for each block

of trials. Outcome was significant for both the first block, F (2,28) = 3.54, p < .05 and the

second block, F (2,28) = 3.97, p < .05. The first block revealed a significant linear trend, F (1,28)

= 7.04, p = .01, with looking times increasing regularly from the zero object outcome, (M = 9.76

s, SD = 4.79 s, to the middle object outcome, (M = 13.26 s, SD = 8.00 s) to the three object

outcome, (M = 17.73 s, SD = 13.50 s). The second block of trials produced both a marginally

significant linear trend, F (1,28) = 3.20, p = .08 and a significant quadratic trend, F (1,28) = 4.73,

p < .05. These trends occurred because infants looked less at the zero outcome (M = 5.56 s, SD

= 2.76 s) than at either the middle outcome, (M = 8.88 s, SD = 4.68 s) or the three outcome, (M =

7.70 s, SD = 3.9 s.)

Discussion

The results of Experiment 3 are consistent with the two-process view that incorporates a preference for familiarity (e.g., Hunter and Ames, 1988) with longer looking when there are

more items on the stage. Infants who repeatedly saw one item at the beginning of the event had a


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significant preference for one item over two items. In contrast, infants who repeatedly saw two

items tended to have a preference (albeit not significant) for two items over one item. Also, this

tendency to look longer in the test at the number of items presented prior to the test occurred in

trial block one but not trial block two. The disappearance of the tendency with repeated exposure

(i.e., trial block two) is consistent with a familiarity effect as described by Hunter and Ames

(1988).

In the first block of trials infants demonstrated a clear increase in looking time as the

number of test items increased. An increase also occurred in the second block although the

tendency was for infants to look less at 0 items than at more than 0 items. Thus, in Experiment 3,

an experiment that included no addition or subtraction manipulation, we found evidence for both

a familiarity effect and a tendency to look longer when more items were on the stage.

Direct Comparison between Experiment 1 and Experiment 3 1

In Experiment 2 we asked whether infants would look longer when more items were on

the stage. The infants did. In Experiment 3 we added familiarization experience with either one

item or two items to the test trials in Experiment 2 and asked whether infants would show a

familiarity preference as well as a tendency to look longer when more items were on the stage.

They did. Strictly speaking, Experiment 3 was not designed to be a control for Experiment 1.

One can identify a number of differences between Experiments 1 and 3 in addition to the fact

that Experiment 1 included addition and subtraction whereas Experiment 3 did not. For example,

Experiment 3 did not contain the warm-up trials found in Experiment 1. Experiment 1 also had

the repeated appearance and disappearance of a hand, which was not present in Experiment 3. Nevertheless, in Experiment 1we argued that one possible reason for the results was that the

infants were displaying a familiarity preference on top of a preference for looking more when


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there were more items on the stage. Since those same two effects were found in Experiment 3, it

might be instructive to directly compare the results from Experiment 1 with the results from

Experiment 3.

Sixteen infants were tested in Experiment 3. In order to make the Ns comparable in the

two studies, we selected 16 infants from Experiment 1 that comprised the last complete,

counterbalanced group of infants run in the study. That is, the group included 8 males and 8

females. Four infants of each sex were in the addition condition and 4 were in the subtraction

condition. Also, each subgroup of 4 infants was assigned test trials according to a

counterbalanced Latin Square design.

We duplicated the types of analyses we had run previously in Experiment 1 and

Experiment 3 except that we added Experiment 1 versus 3 as an additional factor. As in those

experiments, separate ANOVAS were computed for each block of trials.

Our first set of analyses compared infants' looking times to outcomes of one versus two

items. On the first block of trials a 2 Experiment (Experiment 1 versus Experiment 3) x 2

Familiarization Condition (familiarization to one versus two items, which is also the same as

addition versus subtraction in Experiment 1) x 2 Outcome (one versus two items) ANOVA

yielded a significant main effect of Experiment; F (1,28) = 471, p < .05. On the first block of

trials infants looked longer overall during Experiment 3, (M = 17.40 s, SD = 11.44 s) than during

Experiment 1, (M = 10.87 s, SD = 9.98 s). The only other significant result was the

Familiarization Condition x Outcome interaction, F (1,28) = 15.27, p < .001. In both experiments

infants looked longer at an outcome of one item if they had been familiarized to one item, and they looked longer at an outcome of two items if they had been familiarized to two items. The 3-

way-interaction of Experiment x Familiarization Condition x Outcome did not approach


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significance. It produced an F < 1. The same ANOVA was run on the block two data, but no

significant differences were found. In summary, it appears, that although infants looked longer in

general during Experiment 3 than Experiment 1, they produced the same pattern of looking in the

two experiments. They looked longer at the familiar outcome than at the novel outcome.

Our final set of analyses compared Experiments 1 and 3 on infants' tendency to look

longer when there were more items on the stage. Once again, separate analyses were performed

for each block of trials. On Trial Block One the 2 Experiment x 2 Familiarization Condition x 3

Outcome (zero, middle, and three) ANOVA yielded two significant main effects. As in the

previous Block One analysis, infants looked longer in general during Experiment 3 (M = 13.58 s,

SD = 9.94 s), than during Experiment 1 (M = 8.48 s, SD = 7.55 s), F (1,28) = 6.75, p < .05.

Infants also looked longer overall when more items were on the stage as indicated both by a

main effect of Outcome F (2, 56) = 5.17, p < .01, and by the significant increasing linear trend, F

(1,56) = 10.189, p < .005. The quadratic trend did not approach significance. No significant

differences were found for the block two data. So once again, these analyses indicate that

although infants looked longer in general during Experiment 3 than Experiment 1, they produced

the same pattern of looking in both experiments. In this case the pattern was to look longer when

more items were on the stage.

General Discussion

Three experiments were conducted to evaluate Wynn's (1992a) claim that five-month-old

infants can add and subtract. Experiment 1 was designed to test three competing hypotheses

concerning why infants would look longer at the incorrect number (one test item) in the addition problem and (two test items) in the subtraction problem. One hypothesis was that infants were

actually adding and subtracting. A second hypothesis was that they were responding at an ordinal


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level to more versus fewer items. A third hypothesis was that the infants were simply

demonstrating a greater response to the familiar test display. It should be noted that either of the

last two alternatives could be accomplished by attending to the overall quantity of objects rather

than the exact number of objects as suggested by Clearfield and Mix (1999a, 1999b).

The results of Experiment 1 did not support any of the three hypotheses independently.

However, the results were consistent with two possible dual-process explanations. One

explanation posited that infants could, in fact, add and subtract, but that their tendency to look

longer at the incorrect number was superimposed on a tendency to look longer when there were

more items on the stage. The other hypothesis was that infants were responding more to a

familiar outcome, but that this preference for familiarity also was superimposed on a tendency to

look longer when there were more items on the stage.

Experiment 2 tested whether, in fact, infants would look longer when more items were on

the stage. In Experiment 2, infants were given only the test items from Experiment 1 without any

prior warm up, familiarization, or addition and subtraction experience. Evidence was found

(overall and particularly on the second block of test trials) for a linear increase in looking as the

number of items in the stage increased.

In Experiment 3 infants were familiarized with either one item or two items before

encountering each test event. Thus, their experience was similar to that of Experiment 1, except

that there was no warm up period and no hand added or subtracted any items. Nevertheless, in

most respects their behavior mirrored that of infants in Experiment 1. As both the analyses of

individual experiments and the direct comparison of Experiment 1 with Experiment 3 indicated,in both experiments infants familiarized with one item looked longer at one item than at two

items in the test. Whereas infants familiarized with two items looked longer at two items than at


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one item in the test. There was also a tendency in both experiments for infants to look longer the

more test items there were to look at. Thus, Experiment 3 provided support for the familiarity

plus more items hypothesis over the addition-subtraction plus more items hypothesis.

One consistent difference between Experiment 1 and Experiment 3 was also found.

Infants looked considerably longer overall in Experiment 3 than in Experiment 1. Although the

reason for this difference in looking time is unclear, the nature of the events themselves may help

to explain it. In Experiment 1, infants saw items placed on a stage, and a hand enter and leave the

stage. These actions took approximately 20 seconds in the addition condition and 23 seconds in

the subtraction condition. During the majority of this time, infants were looking at the stage. In

contrast, in the third experiment none of these actions took place. Infants saw an item on a stage

for approximately 2 seconds, the screen rotate up, and the screen rotate down. The entire

sequence of events took approximately 10 seconds. Assuming that there is a maximum amount

of time infants will look at any event, the shorter procedure in Experiment 3 gave infants more

time to process the end of the event, possibly resulting in longer looking times. In any case,

despite the overall difference in looking times and the physical differences between Experiments

1 and 3, since type of experiment did not interact with the main findings of a familiarity

preference and a longer looking with more items preference, these two preferences should be

considered viable explanations for the results in Experiment 1. The present results also raise the

distinct possibility that other studies using the Wynn procedure, including Wynn's original

experiment, that have found apparent evidence for addition and subtraction, may merely have

found evidence for a familiarity preference.These experiments are not the only ones that have contradicted Wynn's (1992a) assertion

that young infants can add and subtract. In another recent report, Wakeley, Rivera, and Langer


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(2000) attempted to replicate Wynns studies with a more controlled procedure. They found that

infants did not look longer at the impossible events in the addition or the subtraction conditions.

Based on their findings, they argued that infants ability to compute the outcome of arithmetic

problems is fragile and inconsistent at best.

In response to this counter-argument, Wynn (2000) reported a number of studies that

have replicated the original results using that procedure as well as modified procedures. In

addition, Wynn discussed three potential methodological differences that may have affected

Wakeley et al's results. The first two relate to infant attentiveness to the events. The final one

relates to subject exclusion due to fussiness. The controls used in our procedure (i.e., presenters

being blind to the participant during trials) more closely matched those of Wakeley et al., yet we

did find the same differences (i.e., looking longer at one item in the addition condition and

longer at two items in the subtraction condition) reported by Wynn (2000). Thus, it seems that

these methodological differences cannot account for the null results found by Wakeley et al.

Why, then, did we find differences when Wakely et al. did not? According to our

predictions, infants should have shown a familiarity preference, just as they did in previously

published studies. We are not certain. One potential difference between our Experiment 1 and the

Wakeley et al. study is the length of the intertrial interval. In Wynn (2000) and in our procedure,

as soon as the stage was reset, a new trial began. On average, the intertrial interval was less than

six seconds with a standard deviation of one second. In contrast, Wakeley, Rivera, and Langer

used a consistent ten s inter-trial interval. Allowing more time to elapse between trials may have

made it more difficult for infants to become sufficiently familiar with the one object. The lack of a comparable subtraction condition also makes comparison between the two studies difficult.


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Perhaps Wakely, et al. are correct that the evidence for infant addition and subtraction is

fragile and inconsistent. However, no matter how carefully a study is done, it is difficult to

mount a convincing challenge against previously reported evidence when one fails to find a

significant difference. In essence it amounts to trying to prove the null hypothesis. That difficulty

is compounded when, as Wynn (2000) correctly points out, several other studies have replicated

her results. In fact, we did so in Experiment 1. The problem with Wynn's explanation is that we

also replicated her results in our Experiments 3, an experiment in which no addition or

subtraction was involved. It is much more difficult to counter a challenge when a set of

experiments first replicate the results in question and then show that those results can be

accounted for by a different, and in this case simpler, set of reasons.

The other studies reported by Wynn (2000) that have replicated her results all tested

infants on one and two items after a 1 + 1 event or a 2 - 1 event. To our knowledge, no previous

study has included controls for a possible familiarity preference. The one that may come closest

was reported recently by Uller, Carey, Huntley-Fenner and Klatt (1999). They argued they were

testing an "Object-file" model versus an "Integer-symbol" model. But from our point of view

they may also have been varying the familiarity of the objects during their test trials. In their

experiments they showed infants 1 + 1 = 1 or 2 when the items were either placed on the stage

first (object first condition) or the screen was placed on the stage first and the objects were

dropped behind the screen (screen first condition). In the object first condition infants had more

of an opportunity to build up a familiarity preference for one, the incorrect number. It is not

surprising, then, that in their first two experiments Uller et al. (1999) found 8-month-old infantsresponding more to the impossible event (or from our point of view the familiar event) only in

the object first condition. In contrast, in Experiment 3, 10-month-old infants responded to the


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impossible event even in the screen first condition. Perhaps, as suggested by Hunter and Ames

(1988), older infants need less familiarization time with the objects before showing a familiarity

preference.

Uller et al.s final experiment is more difficult to interpret from a familiarity preference

point of view. In this experiment two separate small screens were used instead of a single large

screen. In contrast to the first experiments, 8-month-old infants in the screen first condition now

looked longer at one item than at two items in the test. One could make the argument that with

two small screens and one object dropped behind each screen during familiarization, the infants

may have treated the familiarization period as two examples with one object rather than as a

single example with two objects. Perhaps that produced enough familiarization with one object

for 8-month-old infants to respond more during the test to one object than to two objects.

Admittedly, this interpretation of Uller et al.'s Experiment 4 is highly speculative. But the

interpretation could easily be tested by running a subtraction condition as well as an addition

condition. When two screens are used, we would expect 8-month-olds to have more "trouble"

with subtraction than with addition. If the infants are becoming more familiarized with one

object in the two screen condition, they should tend to prefer one object in the test, which would

be the "impossible" result in an addition problem, but the "possible" result in a subtraction

problem.

It is clear that future research should follow Uller et al.'s example by testing older infants

and considering possible developmental changes in the processes underlying how infants treat

these events. An important question is whether infants progress from a simple preference for familiarity to more sophisticated approaches, such as the directional (i.e. ordinal) one, and

proceed to true addition and subtraction. Feigenson (1999) tested infants ranging from 12- to 18-


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months of age in a discrimination learning task involving the ordinal relationship between

numbers. She found that infants in this age range were capable of learning the correct rule (look

at the bigger number or look at the smaller number). Hauser, Feigenson, and Mastro (1999) also

found similar results using ten-month-olds in a procedure where they searched to retrieve either

one or two cookies. This evidence suggests that by 10 months of age, infants may be able to

reason about the events using the more complex, directional method. The studies by Uller et al.

(1999) also seem to suggest certain changes in processing by 10 months of age.

In conjunction with the issue of infant addition and subtraction, we believe that the

experiments presented here raise a more general and important issue. One should be cautious

about attributing sophisticated cognitive processes to young infants when simpler processes will

suffice. The fact that infants, particularly younger infants, sometime prefer familiarity in these

tasks is not an accident or fluke. Familiarity preferences have been reported repeatedly since the

early 1970's (e.g., Greenberg, Uzgiris, and Hunt, 1970; Rose, Gottfried, Mellow-Carminar, and

Bridger, 1982; Wetherford and Cohen, 1973). As we mentioned previously, Hunter and Ames

(1988) provide an excellent summary of this older literature. In addition, recent studies are also

beginning to report the same familiarity effect with 4- and 5-month-old infants in tasks similar to

those used in addition-subtraction studies. Bogartz, Shinskey, and Schilling (2000) and Schilling

(2000) both found that in object permanence tasks, in which one object repeatedly appeared and

disappeared behind an occluder, 5-month-old infants, for a time, also preferred familiar events.

Cashon and Cohen (2000) reported the same effect with 8-month-old infants in an animated

version of the events. The point is, that under some circumstances, familiarity preferences arereal, even predictable. Studies that rely on assessing infant visual preferences without first

habituating infants should add appropriate controls to rule out familiarity preferences as a


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possible explanation. Even studies that do habituate infants to a criterion but include non-

habituators along with habituators, should make certain their findings do not result from the non-

habituators who may still have a lingering familiarity preference (e.g., Cashon and Cohen, 2000;

Roder, Bushnell, & Sasseville, 2000).

Based upon the evidence presented in the present three experiments, Wynn's (2000)

claims notwithstanding, we believe it is still an open question as to whether 5-month-old infants

can actually add or subtract. Just as we mentioned in the introduction regarding research on

young infants' ability to subitize or to do cross modal matching based upon number, the evidence

is still in dispute. When certain abilities are attributed to young infants, simpler mechanisms can

sometimes account for the data. Clearly, further research is needed to delineate infants'

understanding of quantity and their development of numerical knowledge. Until that research

reveals convincing evidence of infants' numerical competence, we believe caution and parsimony

are the best principles to follow when trying to understand the development of infants' abilities.


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Author Notes

Leslie B. Cohen and Kathryn S. Marks, Department of Psychology.

This research was supported in part by NIH grant HD-23397 to the first author from the National

Institute of Child Health and Human Development. The first experiment presented in this article

was based upon a master's thesis to Kathryn S. Marks at the University of Texas. Portions of the

first two experiments also were presented at the 2000 meeting of the International Conference on

Infant Studies (Marks & Cohen, 2000). We would like to express our appreciation to Christina

Bailey and Tanya Sharon for their assistance on this project and to Elizabeth Chiarello and Cara

Cashon for their careful reading of the manuscript and their many suggestions for improving it.

Correspondence and requests for reprints should be sent to Leslie B. Cohen, Department of

Psychology, Mezes Hall 330, University of Texas, Austin, TX 78712. Electronic

correspondence may be sent via Internet to [[email protected]].


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Footnote

1. We wish to thank one of the outside reviewers for suggesting this comparison.


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Table 1

Predicted Looking Times Based upon Three Different, but Possible Explanations

Addition Task

Familiarity Directional Computational

1 + 1 = 0 Short Long Long

1 + 1 = 1 Long Long Long

1 + 1 = 2 Short Short Short

1 + 1 = 3 Short Short Long

Subtraction Task

Familiarity Directional Computational

2 - 1 = 0 Short Short Long

2 - 1 = 1 Short Short Short

2 - 1 = 2 Long Long Long

2 - 1 = 3 Short Long Long


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Figure Captions

Figure 1. Schematic drawing of the sequence of events in the Addition condition. First

one object is placed on the stage. The occluding screen is raised and a second object is placed on

the stage. Then the screen is dropped to reveal either 0, 1, 2, or 3 objects.

Figure 2. Schematic drawing of the sequence of events in the Subtraction condition.

Two objects are placed on the stage. The occluding screen is raised and one of the objects is

removed. Then the screen is dropped to reveal either 0, 1, 2, or 3 objects.

Figure 3. Infant looking times in Experiment 1 to 0, 1, 2, and 3 items on Block 1 and

Block 2 test trials when in either Addition or Subtraction conditions.


Block 2 test trials.


Block 2 test trials when familiarized with either one or two items prior to each trial.


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1 + 1 = 0, 1, 2, or 3

1. An object is placed on the stage 2. The screen rotates up to hide it.

3. A second object is added to the stage... 4. And is pushed behind the screen.

5a. The screen drops... 5b. To reveal zero objects on the stage.

5a. The screen drops... 5b. To reveal one object on the stage.

5a. The screen drops... 5b. To reveal two objects on the stage.

5a. The screen drops... 5b. To reveal three objects on the stage.

-OR-

-OR-

-OR-


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2 - 1 = 0, 1, 2, or 3

5a. The screen drops... 5b. To reveal zero objects on the stage.

5a. The screen drops... 5b. To reveal one object on the stage.

5a. The screen drops... 5b. To reveal two objects on the stage.

5a. The screen drops... 5b. To reveal three objects on the stage.

1. Two objects are placed on the stage 2. Screen rotates up to hide the objects.

3. One object is brought out from behind the screen... 4. And is removed from the stage

-OR-

-OR-

-OR-


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Addition Subtraction0

2

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ThreeTwoOneZero

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Addition Subtraction0

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Experiment 1


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Zero One Two Three0

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Experiment 2


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One Two0

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Experiment 3

Documents

Cohen and Marks Final