Early discrimination among small object collections

JOURNAL

OF EXPERIMENTAL

CHILD

PSYCHOLOGY

36, 124-138 ( 1983)

Early Discrimination among Small Object Collections R. J. RUSSAC University of North Floridu Two studies are presented which examine the young child’s ability to discriminate between two small object collections on the basis of numerosity and to maintain that discrimination across changes in number-related cues. A transfer procedure and counting tasks were also included. In Study I, 2-, 3-. and 4-year-olds were reinforced for choosing either a two- or three-item array when length-density cues were manipulated across two training phases of 20 trials each. Training was followed by a transfer task in which one- and four-item arrays were displayed. Most 2-year-olds were able to learn the discrimination while at the same time displaying little quantitative ability. Further. their transfer responses were transpositional in nature. In Study 2, 2-year-olds were given a similar discrimination task in which numerosity was contrasted simultaneously with length-density and area-brightness cues. Again. most children learned the discrimination and transferred that learning on the basis of relational cues.

Number researchers have long suspected that young children can discriminate among small discrete collections on the basis of numerosity, and that this ability exists prior to the acquisition of learned quantitative skills. Piaget (1965) provided the following norms for the “perceptual intuition” of number: l-3 at Age 3, l-4 at Age 4, and l-5 at Age 5 (p. 154). Likewise, Gelman (1972b) hypothesized that collections of one and two elements can be recognized perceptually, but that number estimators, particularly counting, must be used to quantify larger sets. A recent study by Starkey and Cooper (1980) has placed such informal observations of early quantitative ability on much firmer experimental ground. These researchers were able to show that by 22 weeks of age infants are capable of discriminating between two and three objects when presented with a “habituation-dishabituation-of-looking” procedure. Starkey and Cooper suggest that the basis for such early number recognition is subitizing. I thank Russell Drennen, Toni Talmadge, the teachers, parents, and children who helped with this study. Thanks also to Rick Powell for his advice on statistical analyses and Diane Powell for her help in organizing and typing the manuscript. Requests for reprints and correspondence related to this article should be sent to R. J. Russac. Department of Psychology, University of North Florida. 4567 St. Johns Bluff Road, S.. Jacksonville, FL 32216. 124 0022-0965/83 $3.00 Copyright All rights

0 1983 by Academic Press of reproduction in any form

Inc. reserved

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The present studies were intended to go beyond the Starkey and Cooper analysis in the following ways: First, while the Starkey and Cooper procedure controlled only for length-density cues, in Study 2 areabrightness cues were controlled for as well. Second, the young child’s ability to attend to relational cues associated with numerosity was examined. Third, children in Study 2 were asked specifically to indicate the numerosity of several small sets just by looking, thus providing a test for the Starkey and Cooper hypothesis that subitizing, as usually defined, is the basis for early number recognition. Specifically, children were presented with a simultaneous discrimination procedure in which they were required to (a) learn a reinforced discrimination between collections of two and three objects, (b) maintain that discrimination across a change in numberrelated cues, and (c) transfer the learned discrimination when presented with a variation of the transposition paradigm. In addition, several different tests for quantitative ability were administered. STUDY

1

Children in Study 1 were required to learn a discrimination between two small object collections, and then to retain that discrimination when presented with two new collections which maintained the cardinal values of the first stimulus set while altering their length-density relationship. Two-year-olds were chosen specifically because of their lack of quantitative experience, while 3- and 4-year-olds were also tested to provide a comparison with quantitative children. Method Subjects

Twenty-four children were tested at each of three age levels: 2-yearolds (M = 32.92 months, SD = 2.65); 3-year-olds (M = 43.79 months, SD = 2.86), and 4-year-olds (M = 52.08 months, SD = 2.55). An equal number of boys and girls were included at each age level. Children were selected from private day-care centers in a Southern metropolitan area. To assure a diverse group of participants, two centers were chosen which served children primarily from low socioeconomic backgrounds, while two other centers were included which catered to children from middle and high socioeconomic environments. Materials

Stimuli for the discrimination and transfer procedures consisted of six 13.4 x 9.6 x 2.4-cm white cardboard boxes. Centered longitudinally on the top of each box was a linear array of one to four blue dots 0.7 cm in diameter. Two sets of training stimuli were used. The “equal-length” set consisted of two and three dots in arrays 5.7 cm long while the “equal-density” set was composed of two- and three-dot arrays spaced

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3 cm apart. The transfer set was comprised of a single dot centered on the box and of four dots spaced I .8 cm apart. The boxes were presented on a 30.5 x 23-cm black cardboard mat and shielded during transformations by a 35.7 x 30.5cm cardboard screen. Candies were used as reinforcers. A 28 x 21.6-cm white cardboard card was used for the enumeration and cardinality tasks. Centered longitudinally on the card was a linear array of 11 yellow “chicks” approximately 2 x 2.5 cm in size and spaced 0.3 cm apart. Procedure

Children were tested individually by the author. After a few minutes spent initially getting acquainted and putting the child at ease, testing began. The entire procedure was completed in one session with no apparent loss of interest on the part of the participants. For convenience, the procedure will be presented in four phases: two training phases, a transfer phase, and a quantitative assessment phase. Phase 2. Half the children at each age level were presented first with arrays of equal length while the rest were presented with arrays of equal density. Phase 1 began with a warm-up procedure. A piece of candy was placed under the box displaying the positive stimulus array as the child watched. For half the youngsters in each length-density condition the candy was hidden under the two-item array while for the others it was concealed under the three-item array. The experimenter explained, “I am going to hide a piece of candy under this box. (At the beginning of every trial in Phases 1 and 2 the boxes were positioned initially so that the positive stimulus array was in front of the negative array and closest to the child. The child was always allowed to watch the candy being hidden.) Then I am going to try to fool you by moving the boxes around. But you will always know where the candy is hidden, because it will always be under these dots (indicating the positive stimulus array with a sweeping motion of the hand). Can you show me the dots?” The child was required to show that (s)he had attended to the arrays by pointing to all the dots either collectively or individually. Some 2-yearolds pointed to a single dot, seemingly ignoring the rest. These youngsters were prompted with the question, “Are there any other dots?” until the entire array had been acknowledged. The boxes were then moved side by side and the child, who was allowed to witness the transformation only during warm up, was asked to find the candy. Most children easily found the candy on the first try. Those who were incorrect were given another warm-up trial. No child required more than two trials to find the hidden treat. The first training trial began as the experimenter said, “Now I am going to make it a little harder for you to find the candy, because I am not going to let you see where I move the boxes. But you will still know

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where the candy is hidden; it will always be under these dots (again pointing to the positive array). The candy was placed under the appropriate box as the child watched. Then a screen was situated between the child and the stimuli to hide the boxes as they were moved side by side and 2.5 cm apart. The reinforced array was positioned in accordance with two combined Gellermann (1933) series. The actual positional sequence for Phase 1 was: RRLLRLRRLL(R)LRLRRLLRR. The item in parenthesis denotes a change in the first position of the second series, ensuring that at least two position reversals were required in any given block of five trials. The screen was then removed and the child asked to “Show me where the candy is hidden.” During all training trials the child was allowed to watch the candy being hidden under the appropriate box, but was prevented from observing the subsequent positioning of the boxes by the cardboard shield. Correct responses were followed immediately with verbal praise and the child was allowed to place the candy in a candy jar. Incorrect responses were followed by the admonishment. “No, remember the candy is under this box (pointing to the positive array). Let’s try again.” The candy was left under the box for the next trial. At no time was any characteristic of the arrays, other than color, mentioned. On Trials 5, 10, and 15 subjects were asked specifically why they had chosen a particular box. Phase 1 ended when the child made five consecutive correct responses or at the end of 20 trials. Those children who did not meet criterion during Phase 1 training were excluded from Phases 2 and 3. going directly to Phase 4 instead. Phase 2. Children who met the criterion of five consecutive correct responses in Phase 1 were given an additional 20 trials for which the length-density cues were reversed. Those youngsters who were first trained on equal-density cues were now shown the equal-length stimulus pair, and vice versa. Two new Gellermann series were combined to generate a sequence of 20 positions for the positive array. Again, a change was made at Position 11. The combined series was: LLRLRRLLRR(L)RLLRLRRLL. Phase 2 ended with five consecutive correct responses or after 20 trials. Phase 3. All children who successfully met the Phase 2 criterion were presented immediately with a transfer of training task. The transfer task was intended to determine whether or not children were attending to relational aspects of the stimulus pair. Ideally, a standard transposition paradigm’would have been used. Children reinforced for choosing the two-item array would then be shown the same two-item array along with a new one-item display while those youngsters reinforced for choosing the three-item array would subsequently be shown the same three-item array paired with a new four-item array. In either case, a choice of the previously reinforced array (an “absolute” response) would indicate that

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discrimination learning was the result of attending to some attribute of the positive stimulus. A choice of the new array (a “transposition” response) would be interpreted to mean that a relational cue existing between the two arrays was a salient feature for the child. However, novelty itself can be a very salient cue. A child might be led to pick the new stimulus array simply because it had not been displayed previously and thereby mimic a transposition response. To overcome the problem of novelty while still maintaining small set size, two new arrays of one and four dots were presented during Phase 3. This modification allowed for an assessment of transfer based only upon relational aspects of the arrays. Following the fifth consecutive correct response in Phase 2, the screen was again placed between the child and the stimuli and boxes displaying one and four dots were placed surreptitiously on the mat. For half the children in each set size condition the one-item array was placed in the same position as the positive array on the last training trial. The remaining youngsters saw the four-item array in the same position as the positive array on the last trial. A piece of candy was placed under both boxes. The screen was then removed and the child asked to find the candy. Phase 4. The quantitative procedures that comprised Phase 4 were presented to all children, whether they participated in Phase 2 and 3 or not. Three quantitative tasks were given: (a) rerbnl coL(nting-the ability to recite the ordered set of numerals; (b) enlrmeuntion-the ability to pair the ordered set of numerals with one and only one element of a collection, and (c) cardinaliry r-u/e-the realization that the last number named during enumeration corresponds to the cardinal value of the collection. Each child was first asked to count as high as (s)he could. The verbal prompt “What comes next?” was provided when the child hesitated. Children were stopped if and when they reached 20. Next a card displaying a linear array of 11 “chicks” was placed in front of the child who was asked, “Do you know what these are?” The child’s label was used in subsequent questions. The child was then asked, “Can you count the (chicks) for me?” and the ordinal position of the last item enumerated correctly was recorded. Omissions or reiterations in either number sequence or the objects pointed to were considered errors. A test for the cardinality rule was administered immediately following enumeration. Using a procedure suggested by Schaeffer, Eggleston. and Scott (1974), the array was covered after enumeration and the child asked how many objects were hidden. Results

The data for Study 1 were analyzed by means of a four-way (procedure x sex x age x reinforced set size) analysis of variance. No significant

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main effects or interactions were found for procedure (equal length versus equal density presented first) or sex, allowing the data to be collapsed across these variables. The results of Phase 1 broken down by reinforced set size are depicted in Fig. 1. Seven 2-year-olds (.29) failed to meet the Phase 1 criterion of five consecutive correct responses and went immediately to Phase 4. The remaining 2-year-olds and all 3- and 4-year-olds met criterion and proceeded to Phase 2 training. Analysis of variance revealed a highly significant decrease in the number of errors made with increasing age, F(2, 66) = 15.410, p < .00005. A further Scheffe post hoc analysis of the data indicated that the age effect was due to the large number of incorrect responses made by 2-year-olds as compared to the older age groups (p < .Ol). A second finding, indicated in Fig. 1, is a discrepancy between number of errors made on the twoversus three-item arrays at age 2. However, analysis failed to reveal either a significant main effect for set size or an age by set size interaction. Those children who moved on to Phase 2 training had little difficulty overcoming the change in length-density cues. No child failed to meet criterion. Indeed, very few errors were made at all during the second phase of training. Specifically, 13 errors were made by 2-year-olds. seven errors by 3-year-olds, and two errors by 4-year-olds. Apparently, a discrimination was learned in Phase 1 that had as its basis a cue other than length-density. The results of the transfer task presented during Phase 3 are straightforward: transposition was the predominant mode of response at all age levels. The proportion of transposition responses at each age was .82 for 2-year-olds, .79 for 3-year-olds. and .92 for 4-year-olds. Data for the quantitative tasks presented during Phase 4 are summarized in Table 1. Little evidence of quantitative ability was seen among the 2year-olds tested. One-quarter of the children were unable to count and nearly three-quarters were unable to enumerate. Only one child answered the cardinality question correctly, but failed to meet Phase 1 criterion. This means none of the youngsters who made the appropriate discrimination were able to derive the cardinal values of the collections by counting and then use the obtained values for numerical comparisons. It might be, however, that the process of enumeration itself provided a sensorymotor basis for the discrimination. Yet here again only three subjects were able to enumerate enough objects correctly to encompass the training and transfer stimuli (that is, to enumerate at least four items) and one of these children did not pass Phase 1 training. It should also be noted that few children pointed to the dots and only one counted spontaneously during training. Failure to find evidence of quantitative skills among the 2-year-olds is further supported by the fact that only four children provided quantitative

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PERFORMANCE

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Procedure

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1

ASSESSMENT

2

TASKS

AT THREE

AGE

LEVELS

3

4

Counting

M SD P(OY fY1t-u PC201

2.71 2.27 0.25 0.00 0.00

(2.33) (2.64) (0.41) (0.00) (0.00)

9.96 6.60 0.00 0.50 0.21

16.42 5.57 0.00 0.87 0.62

1.33 3.13 0.71 0.08 0.04

(0.67) (1.72) (0.75) (0.00) (0.00)

6.96 4.16 0.04 0.46 0.25

9.25 2.94 0.00 0.67 0.62

Enumeration

M SD pm P(l1) Cardinality rule’

a Values in parentheses are for children given the quantitative tasks only. b Proportion of children who met several criterion levels (criteria are given in parentheses). ’ Proportion of children who answered the cardinality rule question correctly.

justifications for their answers: one child counted; a second subitized“See these two dots; these (pointing to the nonreinforced array) are three”; a third used both strategies, and a fourth child raised three fingers to indicate the positive array. However, learning the discrimination seemed little related to quantitative justifications. The counting child failed to meet criterion while the other three made 0, 1, and 6 errors, respectively, during Phase I training. In order to avoid contamination of the discrimination procedure by exposure to the quantitative tasks, the latter were always presented after the training and transfer phases. The failure to counterbalance, while intentional, may nevertheless have somehow affected performance during Phase 4. To investigate this possibility, an additional group of 2-yearolds was given only the quantitative procedures. The results of this further test of quantitative ability (for N = 12. M = 29.58 months, SD = 3.15) are shown in parentheses in Table 1. On every task, the amount of quantitative ability was less than that displayed by children who were given the discrimination procedure. Discussion

The rapidity with which children learned to discriminate between two small collections increased markedly between ages 2 and 3. The fact that this improvement parallels an increase in quantitative ability (see Table 1) supports Celman’s (Gelman, 1972a; Gelman & Tucker, 1975) belief

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in the importance of early number estimators. However, 71% of the 2year-olds tested eventually made the appropriate discrimination while at the same time displaying little evidence of overt quantitative skills. These results support the findings of Starkey and Cooper and are very similar to those reported by Gelman (1972b) herself. In a replication of the “magic paradigm” using 2-year-olds, she found that 13 of 21 children t.62) were able to identify the “winner” array when criterion was set at five correct choices out of six. When those youngsters who failed were retested the next day, three more learned the discrimination (total P = .76). It is appealing to think that numerosity was the basis for the young child’s discrimination and, indeed, the data are completely in line with such an interpretation. However, to gain confidence in this hypothesis, several alternative explanations for the present findings must be considered. Pattern Recognition The use of linear arrays avoided the sort of pattern recognition suggested by Schaeffer et al. (1974)-namely linear, triangular, quadrilateral, etc. However, some 2-year-olds apparently found the center dot in the threeitem array particularly salient. Likewise, Gelman (1972b) stated that one of her 2-year-olds described the winning array as having a “middle” (p. 157). Such a strategy would explain the paradoxical fact that young children found the three-item array somewhat easier to discriminate than the two-item array. However, attending to a particular attribute of the positive array such as the middle dot precludes the type of transpositional response seen in Phase 3. Length-Density Cues While considerable research has indicated that length and density are particularly salient features to the young child, the ease with which they were ignored between Phases I and 2 suggest that they are not confused with number when small sets are involved. This is entirely in line with Gelman’s (1972a) finding based upon her “magic paradigm” and with the Starkey and Cooper data. Quantitative Estimators Results from Phase 4 indicate that 2-year-olds lacked overt counting skills. However, the use of a “large” (11-item) linear array in testing for enumeration and the cardinality rule may have masked some quantitative ability applicable to smaller set sizes. This possibility was examined in Study 2. Area-Brightness Cues Brainerd and Howe (1979) have suggested that the ratio of stimulus area to background area (as well as the associated difference in brightness

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between stimuli and ground) is typically confounded with number when several arrays are compared simultaneously. Further, Brainerd and Siegel (Note 1) have shown that area-brightness is a particularly salient cue to the young child. Since area-brightness cues explain the results obtained in Study 1 no less well than numeric cues, the two factors must be teased apart, a task also performed in Study 2. STUDY 2 A second study was designed to clarify the findings just presented in two ways: First, in Study 1 only a single perceptual cue, length-density, was contrasted with number, while in Study 2 two number-related cues were contrasted simultaneously with relative numerosity-viz., lengthdensity and area-brightness. Second, children in Study 2 were asked to subitize and/or to count collections of l-4 objects during Phase 4 as a test for quantitative ability when dealing with “small” numerosities. Method Subjects

Twenty-four 2-year-olds (M = 31.42 months, SD = 3.74) were tested in Study 2. An equal number of boys and girls were included. All children were selected from private day-care centers in a Southern metropolitan area. As in Study 1, the centers were chosen to provide subjects from a wide range of socioeconomic environments. Materials

The materials used in Study 2 were identical to those described previously, with the following exceptions: First, the stimulus arrays were constructed so as to contrast number with both length-density and areabrightness cues. The characteristics of the training and transfer arrays are summarized in Table 2. Second, stimuli for the Phase 4 quantitative assessment consisted of four cardboard cards 20.3 x 12.6 cm in size. On each card was a linear array of l-4 blue dots 1.9 cm in diameter and spaced 2 cm apart. Procedure Phases I to 3. Except for the elimination of the equal-length equaldensity counterbalance, the procedure used during training and transfer was the same as that described above. Phase 4. Stimulus arrays of one to four dots were presented in an order randomized for each child. The child was first asked, ‘Can you tell me just by looking how many dots there are?” as a test for subitizing, and then “Can you count the dots for me?” as a test for counting.

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TABLE CHARACTERISTICS STIMULI

Dimension Phase 1 Number Stimulus size Total area Length Density Phase 2 Number Stimulus size Total area Length Density Phase 3 Number Stimulus size Total area Length Density

2

OF TRAINING USED

AND

IN STUDY

TRANSFER 2

First array

Second array

2 5.02 cm’ 10.05 cm’ 3.80 cm 2.00 cm

3 3.32 cm’ 9.95 cm’ 8.10 cm 3.00 cm

2 3.32 6.63 8.00 6.60

cm’ cm’ cm cm

I 15.39 cm’ 15.39 cm’ -

-

3 5.02 15.07 5.70 1.50

cm’ cm’ cm cm

4 3.32 cm’ 13.27 cm’ 8.10 cm 1.70 cm

Results A two-way (sex x reinforced set size) analysis of variance was performed on the data from Phase 1. Again, no significant main effects or interactions were found for either variable. The mean number of errors during Phase 1 training are shown in Fig. 1. Overall, 1.5 of 24 children C.62) successfully met criterion. In terms of mean number of errors for combined set sizes, children who successfully met Phase 1 criterion found it no more difficult to make the appropriate discrimination under the conditions imposed in Study 2 than they did in the first study. Two children failed to meet Phase 2 criterion after successfully completing Phase 1. One child was reinforced for choosing the two-item array and the other for choosing the three-item array. If these two youngsters are removed from the analysis of Phase 2 results, however, only a single error was made by the remaining 13 subjects. It appears therefore that most youngsters learned a discrimination in Phase 1 that depended on a cue other than length-density or area-brightness. While the focus of this study was on the perceptual basis for the learned discrimination, it is also useful to look at the reason some children were unable to meet criterion. Based upon informal observations made during

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testing, the hypothesis that position was the feature attended to by those who failed to meet Phase 1 criterion was tested using a 2 (success versus failure) x 2 (position reversal versus no position reversal) chi-square design. That is, children’s correct and incorrect responses were compared with whether or not the positions of the stimuli had been reversed on a particular trial. Results of this analysis, x*(l) = 16.90, p < .OOl, indicate that position was indeed an important cue for those children who did not learn the discrimination. More than four times as many errors were made on trials involving position changes than on those that did not. Results from the transfer of training phase again indicate that the learned discrimination involved a relational cue. Eleven of thirteen children (.85) gave a transposition response-i.e.. chose the new stimulus array with the same relationship to its pairmate as the originally reinforced stimulus array held to its counterpart. As in Study 1, little evidence of quantitative ability was found during Phase 4, even though smaller set sizes were presented. Specifically, six children were able to subitize and two to count the single-item array. Two children subitized the two-item array. Again, as in Study 1, an additional group of children were tested on the quantitative tasks alone. The results (for N = 12, M = 31.33 months, SD = 2.46) were similar to those just recounted-six children subitized and three children counted the one-item array. One child subitized the two-item display. Another youngster counted the one- and four-item arrays correctly. Discussion

The data for Study 2 remain in concordance with the hypothesis that relative number was the basis for the learned discrimination, and further that it provides a particularly salient cue for the young child. Even in the face of simultaneous changes in two perceptually relevant cues between Phases 1 and 2, the discrimination was maintained. In addition, there was very little evidence that the learned discrimination resulted from the use of quantitative estimators such as counting. Of course, the possibility that some form of quantification was being used cannot be ruled out completely since obtaining an accurate estimate of the young child’s number ability is extremely difficult. As Gelman and Gallistel (1978) have pointed out, young children may use counting procedures different from adults, or may rely only on certain components of the adult counting process. However, three findings from the present studies suggest that most 2-year-olds tested were not applying learned quantifiers: First, physical prompts, such as pointing or successive fixations, which are required by the young child to establish an accurate one-toone correspondence between quantifier and object (Saxe & Kaplan, 1981), were rarely seen. Second, there was little counting during the procedure itself and few justifications based on quantification. Third, the studies

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failed to show evidence of significant quantification across four different counting procedures incorporating both large and small set sizes. Perhaps, as Starkey and Cooper (1980) suggest, a “perceptual enumeration process called subitizing . . . underlies [the capacity to recognize small cardinal values]” (p. 1033). However, here a problem of semantics arises. Subitizing, as originally defined by Kaufman, Lord, Reese, and Volkmann (1949) and as typically used since, denotes the ability not only to recognize small cardinalities directly but also to provide the correct numeric label. For example, Beckmann (cited in Gelman, 1972b) defined subitizers as youngsters who provided a numeric label (e.g., “It looks like two”) and who displayed no overt counting (p. 129). It seems possible that a young child may be able to discriminate among small numerosities without yet having the ability to label them. If this is true, then it is important to distinguish between the perceptual recognition of infants and very young children and the somewhat later appearing skill of labeling perceptually derived cardinahties (subitizing) which may, as Gelman suggests, require quantification skills. Study 2 provides some tentative evidence for just such a distinction, viz., with the exception of the single-item array, almost no subitizing ability was apparent in Phase 4. GENERAL DISCUSSION

The combined studies produced two additional findings that require further consideration. First, while results from the transposition procedure presented in Phase 3 suggest that 2-year-olds were responding, not only to the number of objects in the arrays, but also to their ordered relationship, two alternative hypotheses can be put forth: Children who transferred to the four-item array may have done so because, like the three-item array, it contained a “bunch.” However, such a strategy runs counter to what was found when transfer was to the single-item array. While both the two- and three-item arrays were true “collections” in the sense of containing multiple elements, the one-item array was not. A transfer strategy based upon the notion of “bunch” should have led to picking the four-item array regardless of which set size was reinforced. Alternatively, it is possible that children may simply have used some vague notion of “more” and “less” based on a variety of cues, both numeric and perceptual. It could be argued, for example, that in Study 2 the child based his judgment of “more” or “less” on length in Phase 1 but switched to a judgment based on stimulus size in Phase 2 (see Table 2). However, such a strategy seems unlikely to produce responses that are consistently transpositional. A second finding was that children were able to ignore not only lengthdensity cues, but also simultaneous and conflicting changes in areabrightness while making judgments based on relative number. The ease with which young children ignored these number-related cues is in apparent

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disagreement with work reported by Brainerd and Siegel (Note 1). These researchers described a series of experiments that suggest once all numberredundant cues such as length-density and area-brightness have been controlled, “children who lack formal instruction in number concepts cannot easily make [even] small number discriminations” (p. 9). Because a number of procedural differences exist between the Brainerd and Siegel study and the present studies, it is difficult to determine the precise reason for the discrepant outcomes. However, one possible explanation lies in the fact that Brainerd and Siegel apparently presented comparison stimuli whose relative size differed to a much greater extent than did the comparison stimuli in the present studies. This may very well have made relative size more salient to the young child than relative number. What this possibility implies is that, while very young children are in fact capable of attending to numerosity, they do not yet use this cue consistently when comparing small sets. Rather, they will choose the most obvious of several closely related perceptual cues in making their comparison. If true, then perhaps the importance of quantitative skills such as counting lies not only in the fact that they allow the child to quantify and compare collections beyond the range of perceptual discrimination, but also that with repeated use, they attune the child to the cultural importance of numerosity when dealing with collections, even when numerosity may be overshadowed by much more salient cues such as length-density or area-brightness. REFERENCES Brainerd, C. J., & Howe, M. L. An attentional analysis of small cardinal number concepts in five-year-olds. Canudian Jortrnal of Behuvioral Sciences. 1979. 11, 112-l 13. Gellermann, L. W. Chance orders of alternating stimuli in visual discrimination experiments. Journul of Genetic Psychology, 1933, 42, 206-208. Gelman, R. Logical capacity of very young children. Child Development, 1972. 43, 7590. (a) Gelman. R. The nature and development of early number concepts. In H. W. Reese (Ed.), Advances in child developmenf atld behat*ior (Vol. 7). New York: Academic Press, 1972. (b) Gelman, R., & Gallistel. C. R. The &/d’s understanding of number. Cambridge, Mass.: Harvard Univ. Press, 1978. Gelman, R., & Tucker, M. F. Further investigations of the young child’s conception of number. Child Development. 1975. 46, 167-175. Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. The discrimination of visual number. American Journal of Psychology, 1949. 62, 498-525. Piaget, J. The child’s conception qf number. New York: Norton, 1965. Saxe, G. B.. & Kaplan, R. Gesture in early counting: a developmental analysis. Perceptual and Motor Skills, 1981, 53, 851-854. Schaeffer, B., Eggleston, V. H., & Scott, J. L. Number development in young children. Cognitive Psychology. 1974. 6, 357-379. Starkey, P., & Cooper. R. G. Perception of number by human infants. Science. 1980, 210, 1033-1035.

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REFERENCE NOTE 1. Brainerd. C. J., & Siegel, L. S. How do WY knm thur mo rhings hatv the mm number? (Res. Bull. No. 469). London, Canada: The University of Western Ontario. Department of Psychology. November 1978. RECEIVED:

March 30. 1982:

REVISED:

July 14. 1982