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Developments in infants' search for invisibly displaced objects
INFANT
BEHAVIOR
AND
DEVELOPMENT
9,
15-25
(1986)
Developmentsin Infants’ Searchfor Invisibly DisplacedObjects* CATHERINE SOPHIAN Carnegie-Mellon University A study of 16. and 24.month-old infants’ performance on an invisible displacements tosk examined age differences in infants’ search patterns in relation to developing comprehensive scorch skills. The study focused on problems thot involved displacements omong three locations within either o threeor o fivelocation space. Three motor classes of comprehensive search skills were found at both ages: (1) persistence-continuing to search until the obiect is found; (2) nonredundancy-not searching o location more than once: and (3) systematic ordering-utilizing either the spotial arrangement of the locations or their temporal ordering in the displacement sequence to order successive searches omang them. The principal developmentol change was in the ordering of infonts’ searches, which corresponded increasingly to the temporal ordering of locations in the displacement sequence. invisible spatiol
displacements and temparol
comprehensive scorch ordering representation
Searching for hidden objects is a simple form of problem solving that even infants engage in. Research on infant search has played a central role in the study of early cognitive development ever since the groundbreaking work of Piaget (1954), who used it to study the development of object permanence and of the symbolic-representational abilities he thought underlay the emergence of object permanence in late infancy. A particularly intriguing search problem devised by Piaget is the invisible displacements problem he used to study the final stages of object permanence development. Here the infant does not directly see the target object being hidden but only observes a container in which the object has been placed move to several locations and emerge without the object. Piaget argued that a search pattern starting at the last location in the displacement sequence and reversing the path taken by the container reflected the mental representation of the object and its movements while it was concealed in the container. Consistent with his theory, he observed this pattern of search only at the end of the infancy period. Although Piaget’s observations have been replicated in subsequent investigations (see, e.g., Uzgiris & Hunt, 1975), several considerations cloud the l This research was supported by grant No. lRO1 HD1695-01 from the National Institute Child Health and Human Development. The author thanks Laurie Yengo for her help with data collection and data analysis, and Susan Somerville for helpful comments on a previous draft of this paper. Correspondence and requests for reprints should be addressed to Catherine Sophian at Carnegie-Mellon University, Department of Psychology, Schenley Park, Pittsburgh, PA 15213.
for
15
16
.
SOPHIAN
intepretation of these data as evidence for the acquisition of symbolic-representational abilities in late infancy. First, on logical grounds the reverse-ordered search pattern is not in fact any more appropriate than any other search sequence, since the object could have been left in any of the displacement locations (see Sophian & Sage, 1983). Therefore, infants who do not show that pattern cannot necessarily be assumed to lack the representational abilities for which Piaget wanted to test. Furthermore, several recent studies have provided other kinds of evidence suggesting that infants can in fact make some inferences about movements of an object that is concealed from view by 12-15 months of age, well before the reverse-ordered search pattern emerges (Haake & Somerville, 1985; Sophian, 1985). This counter-evidence to Piaget’s account of the emergence of symbolic representation in late infancy raises the puzzling question of why the changes Piaget observed in infants’ patterns of searching for invisibly displaced objects do occur. The present research examines invisible displacements performance from the perspective of recent work on comprehensive searching, rather than viewing it as a logical search problem that requires selecting some locations over others. In comprehensive search problems, all locations are equally good places to search and so the main issue is not to overlook any or search them more than once. In a study of preschoolers’ comprehensive search, Wellman, Somerville, Revelle, Haake, and Sophian (1984) identified three major components of comprehensive search: exhaustiveness or persistence in searching until the object was found or all the locations had been checked; nonredundancy, or avoiding re-searching locations that had already been examined; and systematic ordering of the search sequence. A recent study of invisible displacements performance (Bertenthal & Fischer, 1983) provides evidence of each of these components of comprehensive search even in infancy. The persistence of infants’ searching was found to increase between about 12 and 18 months, and high levels of nonredundant searching were observed among 16- and 24-month-olds. In addition, the 16- and 24-month-olds gave evidence of ordered searching in that they showed a significant tendency to search adjacent locations successively. The present study further examined developmental trends in these three sorts of comprehensive search skills between 18 and 24 months, to see whether they contribute to the emergence of reverse-ordered searching in late infancy reported in the Piagetian literature. An important component of the study was to examine alternative forms of systematic ordering in infants’ searches. Although Bertenthal and Fischer had observed no developmental changes in search ordering, as reflected in the degree to which infants searched adjacent locations, the adjacent searches they observed could reflect different kinds of ordering at different ages. Specifically, since locations that were adjacent spatially were also visited successively in the displacement sequence, adjacent searches could have occurred either because infants repeated the experimenter’s actions (or reversed them)-a temporal form of ordering that is central to Piaget’s account-or because they followed
SEARCH
FOR INVISIBLY
DISPLACED
OBJECTS
17
the spatial ordering of the locations in the array. The present study attempted to disentangle spatial and temporal ordering by testing infants on “nonlinear” displacement problems, on which the displacement sequence did not correspond to the spatial ordering of locations (e.g., left-right-middle), as well as on more standard “linear” displacements (left-middle-right or right-middle-left), On the nonlinear problems, infants who are ordering their searches on the basis of the spatial arrangement of the locations in the array should show a different search pattern than those who are ordering their searches on the basis of the temporal ordering of locations in the displacement sequence. For instance, if the experimenter visited the locations in the order left-right-middle, an infant using spatial ordering would search left-middle-right or right-middle-left, whereas an infant using temporal ordering would search left-right-middle (the forward temporal order) or middle-right-left (the reverse temporal order). Some evidence concerning the role of spatial versus temporal ordering on the linear displacements problems was similarly obtained by examining regularities in infants’ patterns of searches across problems that varied in whether the experimenter proceeded from left-to-right or from right-to-left. METHOD Subjects Twenty-six 16-month-olds (480 to 508 days; M=491 days) and 25 24-montholds (721 to 749 days; M=733) participated. There were approximately equal numbers of boys and girls in each group. All children lived in the metropolitan area around the university and were brought to a laboratory on campus for testing. Materials Two sets of five plastic cups, one red and one yellow, were used as hiding places. Each cup was 7.5 cm tall and 6.2 cm in diameter and was lined with a fur-like fabric to eliminate noise cues. Matching lids, made from cardboard circles covered with felt, fitted on top of the cups. The cups were positioned in a semicircular array on a 27 x 58 cm felt-lined tray for the search trials. A variety of small, attractive toys served as target objects. Each toy was small enough to be completely concealed within the experimenter’s hand. Procedure Infants were tested individually by a female experimenter in a single session of about lo-15 min. The infant sat on a parent’s lap across a table from the experimenter. Testing began with a few warm-up trials, during which the infant retrieved an object first from a single cup and then from one of two cups. Immediately thereafter, the experimental trials were administered. There were four experimental conditions, representing the factorial combination of the number of locations in the search space (three vs. five) and
18
SOPHIAN
the kind of displacement sequence used (linear, i.e., left-middle-right or rightmiddle-left vs. nonlinear, e.g., left-right-middle). For the five-location conditions, five cups were positioned in a semicircular arrangement on the tray so there were approximately equal spaces between them and all were about equidistant from the infant. For the three-location conditions, three cups were placed in any three adjacent positions out of the five used in the five-location conditions, with the particular subset of positions selected varying randomly across trials. In both the three-location and the five-location conditions, three cups were visited in the displacement sequence. For three-location problems, of course, these comprised all the cups that were present. For five-location problems, three adjacent cups made up the displacement locations, and the other two were control locations. The particular subset of cups used as displacement locations varied randomly across trials. The experimenter began each displacement problem by attracting the child’s attention to a toy, which she then concealed behind the fingers of one hand, held with the fingers pointing downward. She then moved this hand to the first location in the displacement sequence, uncovered the cup with her other hand, inserted the fingers of the hand in which she had concealed the toy into the cup briefly, and then covered the cup again using the other hand. She visited the second and third locations in the displacement sequence in the same manner. For linear displacement problems, she always went to the locations in either a left-to-right or right-to-left sequence,with the direction of movement varying randomly across problems. For nonlinear displacement problems, she used one of the other four possible orderings, and again the particular ordering varied randomly across problems. In all conditions, the toy was left equally often in the first, second, and third locations in the displacement sequence. Thus, the infant could not tell from the experimenter’s actions exactly where the toy would be. While the experimenter performed the displacement sequence, she kept the tray pulled back so that the cups were just out of reach of the child. After completing the displacement sequence, she showed the child that she no longer had the toy, and, after about a l-s delay, she pushed the tray forward to allow the child to search. If the child’s first search was unsuccessful, the experimenter returned the cup, now uncovered, to its original position on the tray, removed the cover from sight, and allowed the child to continue searching. The same procedure was followed for all subsequent searches until the child either found the object or ceased searching altogether. If the child stopped searching before finding the object, the experimenter initiated a series of prompts designed to encourage the child to complete the problem. These prompted searches, however, were not included in the analyses. All of the problems within each condition were presented together in a blocked fashion. In order to ensure that sufficient data were obtained to examine sequences of searches among the displacement locations, infants were given a variable number of problems within each condition. Each condition was presented until two problems had been completed on which the infant had
SEARCH
FOR INVISIBLY
DISPLACED
OBJECTS
19
to search at least two of the displacement locations before finding the toy. On the average, this requirement resulted in presenting 2.98 problems per condition to the younger children and 3.08 to the older children. RESULTS The results are presented in three parts, corresponding to the three kinds.of comprehensive search skills identified in the introduction-persistence, nonredundancy, and systematic ordering. Persistence The mean proportion of problems on which children continued to search until they found the target object averaged .92 at 16 months and .97 at 24 months. Because of ceiling effects, only nonparametric analyses were used to compare the age groups. Thirteen of the 26 16-month-olds and 18 of the 25 24-montholds continued searching until they found the object on every single problem, and 20 16-month-olds and 22 24-month-olds met a slightly less stringent criterion, leaving no more than one problem incomplete out of the eight or more they received. These age differences were not significant, x2 (1) I 1.75, p > .lO. A more stringent measure of persistence can be obtained by considering only those problems on which the object was not in the first place the infant looked, so that at least two locations had to be searched to find the object. The 16-month-olds continued searching until they found the object on an average of .89 of these problems, and the 24-month-olds did so on an average of .96 of them. Nonredundancy The average number of locations infants searched more than once was .04 per problem at 16 months and .06 per problem at 24 months. Only 5 of the 26 16month-olds and 9 of the 25 24-month-olds ever searched redundantly, and only 3 16-month-olds and 4 24-month-olds did so more than once. These age differences were not significant, x2 (1) 5 1.06, p > .lO. Systematic Ordering Evidence regarding systematic ordering in infants’ searches was derived from those problems on which the infant searched at least two of the displacement locations before either quitting or finding the object. Two searches are sufficient to specify a complete ordering of the displacement locations, since only one location remains once two have been searched.’ There were two problems that met this constraint in each condition for each infant, since we had preI This specification does not requireassuming that, if infants had searched further on problems where they only went to two locations, they would necessarily have searched the remaining location next (although the nonredundancy results suggest that in general they would have). Rather, it is based on the recognition that any complete search pattern infants might have shown, had they continued searching long enough to get to all the locations, would necessarily have involved visiting the third location at a later point in time than the two locations he or she had already visited before stopping searching.
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sented additional problems when necessary to ensure that this much data on search sequences was available. Initial analyses gave little evidence of either spatially or temporally ordered searches in the nonlinear displacement conditions. On the average, only .41 of infants’ search sequences matched either the left-to-right or the right-to-left spatial order, and .23 matched either the forward or the reverse temporal order (chance = .33). Therefore, detailed analyses will be reported only for the linear displacement problems, where there was more evidence of systematic ordering. Here, .51 of the 16-month-olds’ search sequences and .69 of 24-month-olds’ were either left-to-right or right-to-left patterns and correspondingly matched either the forward or reverse temporal sequence. Of these, .81 at 16 months and .73 at 24 months were optimal searches in that they did not include any repetitions or searches at nondisplacement locations, and the infant continued searching until the object was found. There was a significant increase in ordered search sequences with age, F( 1,48) = 4.30, p< .05, but no age difference in the proportion of those searches that were optimal, F< 1. Both age groups showed significantly more ordered searches than would be expected by chance, ts 2 2.62, ps < .05. While ordered search on any single linear displacement problem could reflect either spatial or temporal ordering, across problems the two kinds of ordering can be separated to some extent because the direction of displacements varied. Thus, consistent search in the left-to-right spatial order (or in the right-to-left spatial order) would result in search sequences that corresponded to the forward temporal order on some problems but to the reverse temporal order on others; and likewise consistent search in the forward temporal order (or in the reverse temporal order) would result in search sequences that sometimes corresponded to the left-to-right spatial order and sometimes to the rightto-left spatial order. Accordingly, the proportion of each infant’s ordered search sequences that corresponded to a single spatial or temporal order was examined. Consistent searching in a left-to-right or right-to-left order would provide unambiguous evidence that infants based their searches at least in part on spatial factors, while consistent searching in a first-to-last or last-to-first order would clearly indicate some use of temporal information to structure searches. It is not possible to conclude from either kind of pattern that infants relied wholly on one kind of information to the exclusion of the other, however; evidence for spatial ordering does not rule out some degree of temporal ordering as well, or vice versa. Indeed, the occurrence of more ordered search in the linear displacement conditions than in the nonlinear ones suggests that both spatial and temporal information played a role in the ordering of infants’ searches. The kinds of ordering infants showed in the linear displacements conditions are summarized in Table 1. The only significant pattern at 16 months was a spatial pattern in the three-location condition. Here infants’ searches followed a right-to-left spatial ordering significantly more often than expected by chance
SEARCH
Mean
Proportions
FOR
INVISIBLY
DISPLACED
TABLE 1 of Infants’ Ordered-Search to Specific Spatial or Temporal
OBJECTS
21
Sequences Orderings Age
Problem/Type
of
Three-Location
Lineor
Ordering
f6-month-olds
that
Correspond
Group 24-month-olds
Displacement
Left-right
spotiol
ordering
.21
.65
Right-left
spotiol
ordering
.79
.35
Forword
temporal
ordering
.60
.00
Reverse
temporal
ordering
.32
.20
Five-Location
Linear
Displacement
Left-right
spatial
ordering
.53
.42
Right-left
spatial
ordering
.47
.50
Forward
temporal
ordering
.60
.79
Reverse
temporal
ordering
.40
.21
(.50), r(18)=3.28, p< .Ol. At 24 months, in contrast, there was evidence of temporal ordering in both conditions. Search sequences corresponding to the forward temporal ordering occurred significantly more often than expected by chance, 1~~3.27, ps< .Ol. The developmental increase in temporally ordered search suggested by these results was corroborated by an analysis of variance on the overall proportion of infants’ search sequences on linear displacement problems that corresponded to the forward temporal ordering of the displacement locations. On the average, .34 of 16-month-olds’ search sequences fit this ordering, compared with .57 of the 24-month-olds’, F( 1,48) = 5.44, p< .05. A final analysis on systematic ordering in infants’ searches looked for consistencies in the way individual infants ordered their search sequences on the linear displacement problems. Combining data from the three-location and five-location conditions, this analysis looked for subjects whose search sequences were consistent with any single one of the four possible ordered search patterns (spatial: left-to-right; spatial: right-to-left; temporal: forward ordering; temporal: reverse ordering) on problems where only a single search had been made as well as on problems where a sequence of at least two searches had been obtained. Infants were classified as using a given search pattern if their searches were compatible with that pattern on all or all but one of the four or more linear displacement problems they received. By this criterion, 4 of the 16-month-olds and 12 of the 24-month-olds showed search in the forward temporal order. Again, this result represents a significant increase with age, x2 (1) = 4.87, p< .05 (corrected for continuity). Seven additional infants showed other regular search patterns. Two 24-month-olds consistently searched in accordance with the reverse temporal order. One 24-month-old consistently searched from right-to-left. Two 16-month-olds and 2 24-month-olds consistently moved from one end of the displacement locations toward the other by
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SOPHIAN
searching adjacent locations (Bertenthal & Fischer, 1983) without adopting either a consistent spatial order (i.e., always left-to-right or always right-to-left) or a consistent temporal one (i.e., corresponding always to the forward displacement sequence or always to its reverse). The rest of the infants did not show any regular ordering in their searches. DISCUSSION
Two kinds of developmental changes were observed in the way infants ordered their searches among the displacement locations. First, there was an increase in ordered searches of any kind, suggesting that the older infants were generally more systematic than the younger infants in searching a set of possible locations. And second, the ordered searches that did occur were more likely to correspond to the temporal ordering of locations in the displacement sequence at 24 than at 16 months. Both of these trends may contribute to the increase in reverse-ordered search in late infancy reported in the Piagetian literature, although that particular search pattern occurred only infrequently in the present study, even among the 24-month-olds. Increases in ordered searching were evident both in the proportions of linear displacement problems on which infants searched from left-to-right or right-to-left, and so in either the forward or reverse displacement order, and also in the numbers of individual infants who showed consistent kinds of ordering across the four or more linear displacement problems they received. Even at 24 months, however, a full half of the infants tested still did not use any form of ordering consistently. Thus, there was clearly substantial variability in this aspect of performance. However, the unclassifiability of many infants’ search patterns is not surprising in light of the stringency of the classification criteria used. In most invisible displacements work, infants are simply categorized as “passing” or “failing” the task according to a dichotomous criterion that puts every possible response pattern into one category or the other. In contrast, the classification system used here is more like those popularized in rule assessment work with much older children (see, e.g., Siegler, 1976) in that it specifies several systematic patterns of responding of interest while leaving a large number of other possible patterns as too complex or inconsistent to be interpreted. Rule assessment methodology has proven difficult to apply to children below 4 or 5 years of age (Siegler, 1978), apparently because of the greater variability intrinsic to very young children’s performance (Sophian, Larkin, & Kadane, 1985). In this context, the identification of specific kinds of ordering in even a minority of infants’ searches is an important result. The increase in temporally ordered searches with age fits well with the Piagetian idea that Stage 6 infants base their searches on a representation of the movements of the object during the invisible displacement sequence. However, in the present study, temporally ordered searches nearly always corresponded to the forward order of the displacement sequence, rather than the reverse order as reported in the Piagetian literature. The low frequencies of
SEARCH
FOR INVISIBLY
DISPLACED
OBJECTS
23
reverse-ordered searching observed here converge with similar findings in several other recent studies (Bertenthal & Fischer, 1983; Corrigan, 1981) in questioning the generality of the Piagetian observations. Several important limitations on those classic observations emerge from these nonreplications. First, a factor that has been implicated by several lines of work is the accumulation of learning or practice effects over trials. Corrigan (1981) showed that infants are more likely to begin their searches at the last displacement location if the object is in fact repeatedly hidden there; and Bertenthal and Fischer (1981) similarly demonstrated that the Piagetian patterns are more likely to occur when the displacement problems are presented in the context of a whole series of simpler problems, as they often have been in Piagetian studies designed to assess the ordinality of object permanence tasks. The present results fit with these findings insofar as they again show little evidence of reverseordered search on a task that is quite similar to the traditional Piagetian one (especially in the three-location linear displacement condition) except that it does not provide these kinds of opportunities for learning. A different sort of factor that is evident in the present study is the kind of displacement sequence that is used in hiding the object. Infants show much less systematicity in ordering their searches when the displacement sequence does not correspond to the spatial ordering of the locations than when the traditional spatially ordered displacements are used. These results suggest that spatial relationships among the locations play at least a facilitative role in infants’ ordered searches. A more profound role of spatial factors may be as an alternative basis for search patterns that have traditionally been interpreted in relation to the displacement sequence (i.e., as either forward or reverse searches). The evidence that 16-month-olds’ ordered searches in the three-location linear displacement condition tended to fit a right-to-left spatial pattern rather than either a forward or a reverse temporal one underscores the possibility that some studies may have overestimated the prevalence of temporally based searches because they did not distinguish spatially ordered searches from them. While the only infant who consistently searched from right-to-left was a 24-monthold, the patterns in the group data for the 16-month-olds suggest that spatial influences nevertheless contributed to their ordered searches and indeed had more impact, for the sample as a whole, than did the temporal ordering of locations in the displacement sequence. In summary, the present results point to changes in infants’ comprehensive search skills, particularly in skills for ordering a sequence of searches, that could help to explain the developmental changes in infants’ search for invisibly displaced objects that have been reported in the Piagetian literature. At the same time, they call into question the generality of the search patterns that have been reported. These findings strengthen the argument that invisible displacements problems are not a good index of infants’ representational abilities by providing an alternative explanation for the developmental changes in in-
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SOPHIAN
visible displacements performance. At the same time, because infants’ invisible displacement performance has been the primary source of evidence for Piaget’s theory of the development of representation, the present results have an indirect bearing on that theory. By undermining the strength of the evidence Piaget cited to support his claim that representation emerges only at the end of infancy, the present results lend support to other lines of work indicating that infants may have some representational abilities substantially earlier. Piaget’s interpretation of infants’ search patterns on invisible displacement problems focused on their ability to infer the trajectory the object followed while it was concealed from view. He maintained that the reverse-ordered search he observed in late infancy was based on the inferred trajectory of the object, and correspondingly that the emergence of that search pattern reflected the acquisition of the representational abilities needed to infer the object’s unseen movements. This analysis has led to the widespread use of infants’ search patterns on the invisible displacement task to assess their level of cognitive development (e.g., Uzgiris & Hunt, 1975). However, it rests on two complementary premises, both of which are problematic: first, that infants who show the specified search patterns must be inferring the object’s movements, and second, that infants who do not search in those ways cannot yet infer the object’s movements. Corrigan (1981) and Bertenthal and Fischer (1983) have criticized the first of these premises, arguing that infants can arrive at the specified search patterns on a sensorimotor basis. This argument is supported by evidence from their work and also from the present study that the prevalence of the key search patterns in Piaget’s analysis depends on such task characteristics as regularities in the object’s hiding place across trials and spatial features of the displacement sequence. Sophian and Sage (1983) criticized the second premise of the Piagetian account of invisible displacement performance, noting that there is no logical reason why infants should show any particular search pattern even if they can infer the object’s movements, since the object could in theory end up in any of the displacement locations. The evidence of selective search in their study supports their claim that infants may understand the object’s movements well before they show the search patterns that have been the focus of Piagetian invisible displacement research. In recent years, the Piagetian tradition of looking at infants’ search for evidence of basic concepts like object permanence has increasingly given way to a newer tradition, which focuses on the search process itself as an early form of problem solving. The present work analyses the developmental patterns Piaget observed in infants’ invisible displacement performance within the framework provided by this newer problem-solving tradition. In shifting focus from the specific search patterns Piagetian work has emphasized to more general changes in comprehensive search skills, it connects the age differences in infants’ invisible displacement performance with developmental trends that extend across a wide range of age and search problems.
SEARCH
FOR INVISIBLY
DISPLACED
25
OBJECTS
REFERENCES Bertenthal. B. I., & Fischer, K. W. (1983). The development of representation cognitive analysis. Child Developmenr. 54, 846-857. Corrigan, R. (1981). The effects of task and practice on search for invisibly Developmental Review, 1. I-17.
in search:
A social-
displaced
objects.
Haake,
R. J., & Somerville, S. C. (1985). The development of logical search skills Developmental Psychology, 21, 116- 186. Piaget, J. (1954). The conslrucrion ofrealirv in /he child. New York: Basic Books.
Siegler, Siegler.
R. S. (1976). R. S. (1978).
in infancy.
Three aspects of cognitive development. Cogni/ive Psychology, 8, 481-520. The origins of scientific reasoning. In R. S. Siegler (Ed.), Children’s rhink-
ing: Whar develops?. Hillsdale, NJ: Erlbaum. C. (1985). Understanding the movements of objects: Early developments in spatial cognition. Brirish Journal of Developmenral Psychology, 3, 321-333. Sophian, C.. Larkin, J. H., & Kadane, J. B. (1985). A developmental model of search: Stochastic estimation of children’s rule use. In H. M. Wellman (Ed.), Children ‘ssearching: Thedevel-
Sophian,
Sophian. Uzgiris, Wellman.
opmenl of search skill and spatial represenraiion. C., & Sage, S. (1983). Developments in infants’ Esperimenral Child Psychology, 35, 143- 160.
Hillsdale. NJ: Erlbaum. search for displaced objects.
JournaloJ
I. C., & Hunt, J. M. (1975). Assessment in infancy. Urbana: University of Illinois Press. H. M., Somerville, S. C., Revelle, C., Haake, R. J., & Sophian, C. (1984). The development of comprehensive search skills. Child Development, 55, 472-481. 3 December
1984;
Revised
9 September
1985
n
BEHAVIOR
AND
DEVELOPMENT
9,
15-25
(1986)
Developmentsin Infants’ Searchfor Invisibly DisplacedObjects* CATHERINE SOPHIAN Carnegie-Mellon University A study of 16. and 24.month-old infants’ performance on an invisible displacements tosk examined age differences in infants’ search patterns in relation to developing comprehensive scorch skills. The study focused on problems thot involved displacements omong three locations within either o threeor o fivelocation space. Three motor classes of comprehensive search skills were found at both ages: (1) persistence-continuing to search until the obiect is found; (2) nonredundancy-not searching o location more than once: and (3) systematic ordering-utilizing either the spotial arrangement of the locations or their temporal ordering in the displacement sequence to order successive searches omang them. The principal developmentol change was in the ordering of infonts’ searches, which corresponded increasingly to the temporal ordering of locations in the displacement sequence. invisible spatiol
displacements and temparol
comprehensive scorch ordering representation
Searching for hidden objects is a simple form of problem solving that even infants engage in. Research on infant search has played a central role in the study of early cognitive development ever since the groundbreaking work of Piaget (1954), who used it to study the development of object permanence and of the symbolic-representational abilities he thought underlay the emergence of object permanence in late infancy. A particularly intriguing search problem devised by Piaget is the invisible displacements problem he used to study the final stages of object permanence development. Here the infant does not directly see the target object being hidden but only observes a container in which the object has been placed move to several locations and emerge without the object. Piaget argued that a search pattern starting at the last location in the displacement sequence and reversing the path taken by the container reflected the mental representation of the object and its movements while it was concealed in the container. Consistent with his theory, he observed this pattern of search only at the end of the infancy period. Although Piaget’s observations have been replicated in subsequent investigations (see, e.g., Uzgiris & Hunt, 1975), several considerations cloud the l This research was supported by grant No. lRO1 HD1695-01 from the National Institute Child Health and Human Development. The author thanks Laurie Yengo for her help with data collection and data analysis, and Susan Somerville for helpful comments on a previous draft of this paper. Correspondence and requests for reprints should be addressed to Catherine Sophian at Carnegie-Mellon University, Department of Psychology, Schenley Park, Pittsburgh, PA 15213.
for
15
16
.
SOPHIAN
intepretation of these data as evidence for the acquisition of symbolic-representational abilities in late infancy. First, on logical grounds the reverse-ordered search pattern is not in fact any more appropriate than any other search sequence, since the object could have been left in any of the displacement locations (see Sophian & Sage, 1983). Therefore, infants who do not show that pattern cannot necessarily be assumed to lack the representational abilities for which Piaget wanted to test. Furthermore, several recent studies have provided other kinds of evidence suggesting that infants can in fact make some inferences about movements of an object that is concealed from view by 12-15 months of age, well before the reverse-ordered search pattern emerges (Haake & Somerville, 1985; Sophian, 1985). This counter-evidence to Piaget’s account of the emergence of symbolic representation in late infancy raises the puzzling question of why the changes Piaget observed in infants’ patterns of searching for invisibly displaced objects do occur. The present research examines invisible displacements performance from the perspective of recent work on comprehensive searching, rather than viewing it as a logical search problem that requires selecting some locations over others. In comprehensive search problems, all locations are equally good places to search and so the main issue is not to overlook any or search them more than once. In a study of preschoolers’ comprehensive search, Wellman, Somerville, Revelle, Haake, and Sophian (1984) identified three major components of comprehensive search: exhaustiveness or persistence in searching until the object was found or all the locations had been checked; nonredundancy, or avoiding re-searching locations that had already been examined; and systematic ordering of the search sequence. A recent study of invisible displacements performance (Bertenthal & Fischer, 1983) provides evidence of each of these components of comprehensive search even in infancy. The persistence of infants’ searching was found to increase between about 12 and 18 months, and high levels of nonredundant searching were observed among 16- and 24-month-olds. In addition, the 16- and 24-month-olds gave evidence of ordered searching in that they showed a significant tendency to search adjacent locations successively. The present study further examined developmental trends in these three sorts of comprehensive search skills between 18 and 24 months, to see whether they contribute to the emergence of reverse-ordered searching in late infancy reported in the Piagetian literature. An important component of the study was to examine alternative forms of systematic ordering in infants’ searches. Although Bertenthal and Fischer had observed no developmental changes in search ordering, as reflected in the degree to which infants searched adjacent locations, the adjacent searches they observed could reflect different kinds of ordering at different ages. Specifically, since locations that were adjacent spatially were also visited successively in the displacement sequence, adjacent searches could have occurred either because infants repeated the experimenter’s actions (or reversed them)-a temporal form of ordering that is central to Piaget’s account-or because they followed
SEARCH
FOR INVISIBLY
DISPLACED
OBJECTS
17
the spatial ordering of the locations in the array. The present study attempted to disentangle spatial and temporal ordering by testing infants on “nonlinear” displacement problems, on which the displacement sequence did not correspond to the spatial ordering of locations (e.g., left-right-middle), as well as on more standard “linear” displacements (left-middle-right or right-middle-left), On the nonlinear problems, infants who are ordering their searches on the basis of the spatial arrangement of the locations in the array should show a different search pattern than those who are ordering their searches on the basis of the temporal ordering of locations in the displacement sequence. For instance, if the experimenter visited the locations in the order left-right-middle, an infant using spatial ordering would search left-middle-right or right-middle-left, whereas an infant using temporal ordering would search left-right-middle (the forward temporal order) or middle-right-left (the reverse temporal order). Some evidence concerning the role of spatial versus temporal ordering on the linear displacements problems was similarly obtained by examining regularities in infants’ patterns of searches across problems that varied in whether the experimenter proceeded from left-to-right or from right-to-left. METHOD Subjects Twenty-six 16-month-olds (480 to 508 days; M=491 days) and 25 24-montholds (721 to 749 days; M=733) participated. There were approximately equal numbers of boys and girls in each group. All children lived in the metropolitan area around the university and were brought to a laboratory on campus for testing. Materials Two sets of five plastic cups, one red and one yellow, were used as hiding places. Each cup was 7.5 cm tall and 6.2 cm in diameter and was lined with a fur-like fabric to eliminate noise cues. Matching lids, made from cardboard circles covered with felt, fitted on top of the cups. The cups were positioned in a semicircular array on a 27 x 58 cm felt-lined tray for the search trials. A variety of small, attractive toys served as target objects. Each toy was small enough to be completely concealed within the experimenter’s hand. Procedure Infants were tested individually by a female experimenter in a single session of about lo-15 min. The infant sat on a parent’s lap across a table from the experimenter. Testing began with a few warm-up trials, during which the infant retrieved an object first from a single cup and then from one of two cups. Immediately thereafter, the experimental trials were administered. There were four experimental conditions, representing the factorial combination of the number of locations in the search space (three vs. five) and
18
SOPHIAN
the kind of displacement sequence used (linear, i.e., left-middle-right or rightmiddle-left vs. nonlinear, e.g., left-right-middle). For the five-location conditions, five cups were positioned in a semicircular arrangement on the tray so there were approximately equal spaces between them and all were about equidistant from the infant. For the three-location conditions, three cups were placed in any three adjacent positions out of the five used in the five-location conditions, with the particular subset of positions selected varying randomly across trials. In both the three-location and the five-location conditions, three cups were visited in the displacement sequence. For three-location problems, of course, these comprised all the cups that were present. For five-location problems, three adjacent cups made up the displacement locations, and the other two were control locations. The particular subset of cups used as displacement locations varied randomly across trials. The experimenter began each displacement problem by attracting the child’s attention to a toy, which she then concealed behind the fingers of one hand, held with the fingers pointing downward. She then moved this hand to the first location in the displacement sequence, uncovered the cup with her other hand, inserted the fingers of the hand in which she had concealed the toy into the cup briefly, and then covered the cup again using the other hand. She visited the second and third locations in the displacement sequence in the same manner. For linear displacement problems, she always went to the locations in either a left-to-right or right-to-left sequence,with the direction of movement varying randomly across problems. For nonlinear displacement problems, she used one of the other four possible orderings, and again the particular ordering varied randomly across problems. In all conditions, the toy was left equally often in the first, second, and third locations in the displacement sequence. Thus, the infant could not tell from the experimenter’s actions exactly where the toy would be. While the experimenter performed the displacement sequence, she kept the tray pulled back so that the cups were just out of reach of the child. After completing the displacement sequence, she showed the child that she no longer had the toy, and, after about a l-s delay, she pushed the tray forward to allow the child to search. If the child’s first search was unsuccessful, the experimenter returned the cup, now uncovered, to its original position on the tray, removed the cover from sight, and allowed the child to continue searching. The same procedure was followed for all subsequent searches until the child either found the object or ceased searching altogether. If the child stopped searching before finding the object, the experimenter initiated a series of prompts designed to encourage the child to complete the problem. These prompted searches, however, were not included in the analyses. All of the problems within each condition were presented together in a blocked fashion. In order to ensure that sufficient data were obtained to examine sequences of searches among the displacement locations, infants were given a variable number of problems within each condition. Each condition was presented until two problems had been completed on which the infant had
SEARCH
FOR INVISIBLY
DISPLACED
OBJECTS
19
to search at least two of the displacement locations before finding the toy. On the average, this requirement resulted in presenting 2.98 problems per condition to the younger children and 3.08 to the older children. RESULTS The results are presented in three parts, corresponding to the three kinds.of comprehensive search skills identified in the introduction-persistence, nonredundancy, and systematic ordering. Persistence The mean proportion of problems on which children continued to search until they found the target object averaged .92 at 16 months and .97 at 24 months. Because of ceiling effects, only nonparametric analyses were used to compare the age groups. Thirteen of the 26 16-month-olds and 18 of the 25 24-montholds continued searching until they found the object on every single problem, and 20 16-month-olds and 22 24-month-olds met a slightly less stringent criterion, leaving no more than one problem incomplete out of the eight or more they received. These age differences were not significant, x2 (1) I 1.75, p > .lO. A more stringent measure of persistence can be obtained by considering only those problems on which the object was not in the first place the infant looked, so that at least two locations had to be searched to find the object. The 16-month-olds continued searching until they found the object on an average of .89 of these problems, and the 24-month-olds did so on an average of .96 of them. Nonredundancy The average number of locations infants searched more than once was .04 per problem at 16 months and .06 per problem at 24 months. Only 5 of the 26 16month-olds and 9 of the 25 24-month-olds ever searched redundantly, and only 3 16-month-olds and 4 24-month-olds did so more than once. These age differences were not significant, x2 (1) 5 1.06, p > .lO. Systematic Ordering Evidence regarding systematic ordering in infants’ searches was derived from those problems on which the infant searched at least two of the displacement locations before either quitting or finding the object. Two searches are sufficient to specify a complete ordering of the displacement locations, since only one location remains once two have been searched.’ There were two problems that met this constraint in each condition for each infant, since we had preI This specification does not requireassuming that, if infants had searched further on problems where they only went to two locations, they would necessarily have searched the remaining location next (although the nonredundancy results suggest that in general they would have). Rather, it is based on the recognition that any complete search pattern infants might have shown, had they continued searching long enough to get to all the locations, would necessarily have involved visiting the third location at a later point in time than the two locations he or she had already visited before stopping searching.
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sented additional problems when necessary to ensure that this much data on search sequences was available. Initial analyses gave little evidence of either spatially or temporally ordered searches in the nonlinear displacement conditions. On the average, only .41 of infants’ search sequences matched either the left-to-right or the right-to-left spatial order, and .23 matched either the forward or the reverse temporal order (chance = .33). Therefore, detailed analyses will be reported only for the linear displacement problems, where there was more evidence of systematic ordering. Here, .51 of the 16-month-olds’ search sequences and .69 of 24-month-olds’ were either left-to-right or right-to-left patterns and correspondingly matched either the forward or reverse temporal sequence. Of these, .81 at 16 months and .73 at 24 months were optimal searches in that they did not include any repetitions or searches at nondisplacement locations, and the infant continued searching until the object was found. There was a significant increase in ordered search sequences with age, F( 1,48) = 4.30, p< .05, but no age difference in the proportion of those searches that were optimal, F< 1. Both age groups showed significantly more ordered searches than would be expected by chance, ts 2 2.62, ps < .05. While ordered search on any single linear displacement problem could reflect either spatial or temporal ordering, across problems the two kinds of ordering can be separated to some extent because the direction of displacements varied. Thus, consistent search in the left-to-right spatial order (or in the right-to-left spatial order) would result in search sequences that corresponded to the forward temporal order on some problems but to the reverse temporal order on others; and likewise consistent search in the forward temporal order (or in the reverse temporal order) would result in search sequences that sometimes corresponded to the left-to-right spatial order and sometimes to the rightto-left spatial order. Accordingly, the proportion of each infant’s ordered search sequences that corresponded to a single spatial or temporal order was examined. Consistent searching in a left-to-right or right-to-left order would provide unambiguous evidence that infants based their searches at least in part on spatial factors, while consistent searching in a first-to-last or last-to-first order would clearly indicate some use of temporal information to structure searches. It is not possible to conclude from either kind of pattern that infants relied wholly on one kind of information to the exclusion of the other, however; evidence for spatial ordering does not rule out some degree of temporal ordering as well, or vice versa. Indeed, the occurrence of more ordered search in the linear displacement conditions than in the nonlinear ones suggests that both spatial and temporal information played a role in the ordering of infants’ searches. The kinds of ordering infants showed in the linear displacements conditions are summarized in Table 1. The only significant pattern at 16 months was a spatial pattern in the three-location condition. Here infants’ searches followed a right-to-left spatial ordering significantly more often than expected by chance
SEARCH
Mean
Proportions
FOR
INVISIBLY
DISPLACED
TABLE 1 of Infants’ Ordered-Search to Specific Spatial or Temporal
OBJECTS
21
Sequences Orderings Age
Problem/Type
of
Three-Location
Lineor
Ordering
f6-month-olds
that
Correspond
Group 24-month-olds
Displacement
Left-right
spotiol
ordering
.21
.65
Right-left
spotiol
ordering
.79
.35
Forword
temporal
ordering
.60
.00
Reverse
temporal
ordering
.32
.20
Five-Location
Linear
Displacement
Left-right
spatial
ordering
.53
.42
Right-left
spatial
ordering
.47
.50
Forward
temporal
ordering
.60
.79
Reverse
temporal
ordering
.40
.21
(.50), r(18)=3.28, p< .Ol. At 24 months, in contrast, there was evidence of temporal ordering in both conditions. Search sequences corresponding to the forward temporal ordering occurred significantly more often than expected by chance, 1~~3.27, ps< .Ol. The developmental increase in temporally ordered search suggested by these results was corroborated by an analysis of variance on the overall proportion of infants’ search sequences on linear displacement problems that corresponded to the forward temporal ordering of the displacement locations. On the average, .34 of 16-month-olds’ search sequences fit this ordering, compared with .57 of the 24-month-olds’, F( 1,48) = 5.44, p< .05. A final analysis on systematic ordering in infants’ searches looked for consistencies in the way individual infants ordered their search sequences on the linear displacement problems. Combining data from the three-location and five-location conditions, this analysis looked for subjects whose search sequences were consistent with any single one of the four possible ordered search patterns (spatial: left-to-right; spatial: right-to-left; temporal: forward ordering; temporal: reverse ordering) on problems where only a single search had been made as well as on problems where a sequence of at least two searches had been obtained. Infants were classified as using a given search pattern if their searches were compatible with that pattern on all or all but one of the four or more linear displacement problems they received. By this criterion, 4 of the 16-month-olds and 12 of the 24-month-olds showed search in the forward temporal order. Again, this result represents a significant increase with age, x2 (1) = 4.87, p< .05 (corrected for continuity). Seven additional infants showed other regular search patterns. Two 24-month-olds consistently searched in accordance with the reverse temporal order. One 24-month-old consistently searched from right-to-left. Two 16-month-olds and 2 24-month-olds consistently moved from one end of the displacement locations toward the other by
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searching adjacent locations (Bertenthal & Fischer, 1983) without adopting either a consistent spatial order (i.e., always left-to-right or always right-to-left) or a consistent temporal one (i.e., corresponding always to the forward displacement sequence or always to its reverse). The rest of the infants did not show any regular ordering in their searches. DISCUSSION
Two kinds of developmental changes were observed in the way infants ordered their searches among the displacement locations. First, there was an increase in ordered searches of any kind, suggesting that the older infants were generally more systematic than the younger infants in searching a set of possible locations. And second, the ordered searches that did occur were more likely to correspond to the temporal ordering of locations in the displacement sequence at 24 than at 16 months. Both of these trends may contribute to the increase in reverse-ordered search in late infancy reported in the Piagetian literature, although that particular search pattern occurred only infrequently in the present study, even among the 24-month-olds. Increases in ordered searching were evident both in the proportions of linear displacement problems on which infants searched from left-to-right or right-to-left, and so in either the forward or reverse displacement order, and also in the numbers of individual infants who showed consistent kinds of ordering across the four or more linear displacement problems they received. Even at 24 months, however, a full half of the infants tested still did not use any form of ordering consistently. Thus, there was clearly substantial variability in this aspect of performance. However, the unclassifiability of many infants’ search patterns is not surprising in light of the stringency of the classification criteria used. In most invisible displacements work, infants are simply categorized as “passing” or “failing” the task according to a dichotomous criterion that puts every possible response pattern into one category or the other. In contrast, the classification system used here is more like those popularized in rule assessment work with much older children (see, e.g., Siegler, 1976) in that it specifies several systematic patterns of responding of interest while leaving a large number of other possible patterns as too complex or inconsistent to be interpreted. Rule assessment methodology has proven difficult to apply to children below 4 or 5 years of age (Siegler, 1978), apparently because of the greater variability intrinsic to very young children’s performance (Sophian, Larkin, & Kadane, 1985). In this context, the identification of specific kinds of ordering in even a minority of infants’ searches is an important result. The increase in temporally ordered searches with age fits well with the Piagetian idea that Stage 6 infants base their searches on a representation of the movements of the object during the invisible displacement sequence. However, in the present study, temporally ordered searches nearly always corresponded to the forward order of the displacement sequence, rather than the reverse order as reported in the Piagetian literature. The low frequencies of
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FOR INVISIBLY
DISPLACED
OBJECTS
23
reverse-ordered searching observed here converge with similar findings in several other recent studies (Bertenthal & Fischer, 1983; Corrigan, 1981) in questioning the generality of the Piagetian observations. Several important limitations on those classic observations emerge from these nonreplications. First, a factor that has been implicated by several lines of work is the accumulation of learning or practice effects over trials. Corrigan (1981) showed that infants are more likely to begin their searches at the last displacement location if the object is in fact repeatedly hidden there; and Bertenthal and Fischer (1981) similarly demonstrated that the Piagetian patterns are more likely to occur when the displacement problems are presented in the context of a whole series of simpler problems, as they often have been in Piagetian studies designed to assess the ordinality of object permanence tasks. The present results fit with these findings insofar as they again show little evidence of reverseordered search on a task that is quite similar to the traditional Piagetian one (especially in the three-location linear displacement condition) except that it does not provide these kinds of opportunities for learning. A different sort of factor that is evident in the present study is the kind of displacement sequence that is used in hiding the object. Infants show much less systematicity in ordering their searches when the displacement sequence does not correspond to the spatial ordering of the locations than when the traditional spatially ordered displacements are used. These results suggest that spatial relationships among the locations play at least a facilitative role in infants’ ordered searches. A more profound role of spatial factors may be as an alternative basis for search patterns that have traditionally been interpreted in relation to the displacement sequence (i.e., as either forward or reverse searches). The evidence that 16-month-olds’ ordered searches in the three-location linear displacement condition tended to fit a right-to-left spatial pattern rather than either a forward or a reverse temporal one underscores the possibility that some studies may have overestimated the prevalence of temporally based searches because they did not distinguish spatially ordered searches from them. While the only infant who consistently searched from right-to-left was a 24-monthold, the patterns in the group data for the 16-month-olds suggest that spatial influences nevertheless contributed to their ordered searches and indeed had more impact, for the sample as a whole, than did the temporal ordering of locations in the displacement sequence. In summary, the present results point to changes in infants’ comprehensive search skills, particularly in skills for ordering a sequence of searches, that could help to explain the developmental changes in infants’ search for invisibly displaced objects that have been reported in the Piagetian literature. At the same time, they call into question the generality of the search patterns that have been reported. These findings strengthen the argument that invisible displacements problems are not a good index of infants’ representational abilities by providing an alternative explanation for the developmental changes in in-
24
SOPHIAN
visible displacements performance. At the same time, because infants’ invisible displacement performance has been the primary source of evidence for Piaget’s theory of the development of representation, the present results have an indirect bearing on that theory. By undermining the strength of the evidence Piaget cited to support his claim that representation emerges only at the end of infancy, the present results lend support to other lines of work indicating that infants may have some representational abilities substantially earlier. Piaget’s interpretation of infants’ search patterns on invisible displacement problems focused on their ability to infer the trajectory the object followed while it was concealed from view. He maintained that the reverse-ordered search he observed in late infancy was based on the inferred trajectory of the object, and correspondingly that the emergence of that search pattern reflected the acquisition of the representational abilities needed to infer the object’s unseen movements. This analysis has led to the widespread use of infants’ search patterns on the invisible displacement task to assess their level of cognitive development (e.g., Uzgiris & Hunt, 1975). However, it rests on two complementary premises, both of which are problematic: first, that infants who show the specified search patterns must be inferring the object’s movements, and second, that infants who do not search in those ways cannot yet infer the object’s movements. Corrigan (1981) and Bertenthal and Fischer (1983) have criticized the first of these premises, arguing that infants can arrive at the specified search patterns on a sensorimotor basis. This argument is supported by evidence from their work and also from the present study that the prevalence of the key search patterns in Piaget’s analysis depends on such task characteristics as regularities in the object’s hiding place across trials and spatial features of the displacement sequence. Sophian and Sage (1983) criticized the second premise of the Piagetian account of invisible displacement performance, noting that there is no logical reason why infants should show any particular search pattern even if they can infer the object’s movements, since the object could in theory end up in any of the displacement locations. The evidence of selective search in their study supports their claim that infants may understand the object’s movements well before they show the search patterns that have been the focus of Piagetian invisible displacement research. In recent years, the Piagetian tradition of looking at infants’ search for evidence of basic concepts like object permanence has increasingly given way to a newer tradition, which focuses on the search process itself as an early form of problem solving. The present work analyses the developmental patterns Piaget observed in infants’ invisible displacement performance within the framework provided by this newer problem-solving tradition. In shifting focus from the specific search patterns Piagetian work has emphasized to more general changes in comprehensive search skills, it connects the age differences in infants’ invisible displacement performance with developmental trends that extend across a wide range of age and search problems.
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FOR INVISIBLY
DISPLACED
25
OBJECTS
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I. C., & Hunt, J. M. (1975). Assessment in infancy. Urbana: University of Illinois Press. H. M., Somerville, S. C., Revelle, C., Haake, R. J., & Sophian, C. (1984). The development of comprehensive search skills. Child Development, 55, 472-481. 3 December
1984;
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n