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The development of the ability to process information
JOURNAL
The
OF EXPERIMENT.\L
Development
CHILD
PSYCHOLOGY
of the
Ability
6, 368-383 (1968)
to Process
Information’
LINDA S. SIEGEL Yale University’ The development of the ability to process information was studied in a series of three experiments involving fourth- and sixth-grade children. Experiment I examined the ability of children to process information as a function of the amount and rate of information reduction required by the task. Amount, not rate, of information reduction was found to be a significant determinant of task difficulty. Older children were better able to process information than younger children. There was an interaction between age and task difficulty such that processing of greater amounts of information was differentially more difficult for younger children. Experiment II studied the effect of redundancy on these tasks. Redundancy was found to result in a significant improvement in performance only when the stimuli were presented at a 5-second rate. Experiment III examined the effects of practice with filtering tasks on performance of the information-reduction tasks. The data indicated that practice with a filtering task improved performance. However, no differences were found between different types of filtering tasks.
Recent theoretical interpretations of cognition have stressed the information-processing characteristics of cognitive processes (e.g., Bruner, 1964; Miller, Galanter, and Pribram, 1960; Munsinger and Kcssen, 1964). These theorists assume that there are developmental changes in the ability to process information. The purpose of the present series of studies was to assess experimentally the developmental changes in the ability to process information using tasks in which the informational characteristics were known. The tasks that were used were drawn from a classification system developed by Posner (1962, 1964) as part of a general information-processing theory of thinking. Two types of tasks, ‘This report is based on a dissertation submitted to the Graduate School of Yale University in partial fulfillment of the requirements for a doctoral degree. The author is grateful to William Kessen, chairman of the dissertation committee, as well as the other members of the committee, Robert Crowder and Edward Johnson, for their suggestions and advice. The author also wishes to thank Mr. J. Rook of the Guilford Lakes School, Sister M. Stephanie of the Sacred Heart School, Sister M. Philomena of Our Lady of Lourdes School, Mr. Davis and Mrs. Asbury of the Jefferson Elementary School, and Mr. Marine and Mr. Pulliam of the Russell Boulevard School for their cooperation in providing subjects. ‘Now at the University of Missouri. 368
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information conservation and information reduction, were used. An information-conservation task is one in which the amount of information in the stimuli and responses is equivalent; that is, all the information in the stimulus is preserved in the response. Rote-learning tasks are examples of information-conservation tasks. In an information-reduction task the response contains less information than the stimulus; that is, there is more than one stimulus for each response. For example, conceptattainment tasks involve information reduction. The information tasks chosen for the present experiments were condensation ones, in which all the stimulus information is necessary to make the response, and filtering ones, in which some of the stimulus dimensions are irrelevant and can be ignored for the making of a response. Previous experimentation with adults has indicated that the difficulty of a task is directly related to the amount of information reduction required by it. This relationship has been demonstrated in tasks involving reaction time (Fitts and Biederman, 1965), classification of words (Pollack, 1963), paired associate learning (Metzger, 1958)) and the categorization of numbers (Posner and Rossman, 1965). Therefore, for any age group, it was predicted that an information-conservation task would be the easiest and that tasks would become progressively more difficult as more information reduction is required by them. Also, rate of information reduction has been found to be a significant factor in determining task difficulty (LaFond, Crowder, and Kessen, 1967). One aspect of the present research was to examine the generality of this finding. There is evidence that information processing capacity increases with development (e.g., Morin and Forrin, 1965; Munsinger and Kessen, 1964). On the basis of these data, it was expected that older children would be better able to process information than younger children. In addition, as tasks become more difficult and more complex cognitive structures are required, greater age differences in performance were expected. Thus, it was expected that there would be an interaction between age and task difficulty such that at the younger ages, a differential amount of difficulty would be experienced as the information required by the task increases. Therefore, there would be little difference on a conservation task between children of different ages, but as increasing amounts of reduction are required, there would be a greater discrepancy between age levels. EXPERIMENT
I
Experiment I was designed to test the following specific hypotheses: (a) the difficulty of a task increases as the amount of information reduction required by it increases ; (b) the difficulty of a task increases as the rate of information reduction required by it increases; (c) there is
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an increase in the ability to process information with development; and (d) a disproportionate amount of difficulty will be experienced by younger children as the information reduction required by the task increases. METHOD
Subjects The Ss were 32 fourth-grade and 32 sixth-grade ford Lakes School in Guilford, Connecticut.
children
from the Guil-
Stimuli The stimuli were 200 one- and two-digit numbers, selected at random from the population of the numbers from 1 to 33, excluding 17. The numbers were divided into four groups of 50 numbers each. A separate task was performed with each group of 50 numbers. The numbers were presented to S at either 5- or g-second intervals. Tasks The characteristics of the four information processing tasks (adapted from Posner, 1962) are summarized in Table 1. The t.asks in this study involved an information-condensation, rather than a filtering paradigm. The tasks were identical in stimulus information but varied in response information. The stimulus information was calculated on the basis of TBBLE -.
1
C!II.~~XYCRI~~I~S OF THE INFORMATIONPROCESSINGTASKS OF EXPERIMENT I0 Task
Record
Add
HELO
A/B
Stimulus information Response information Information reduced Information reduced per second (5 seconds) Information reduced per second (8 seconds) a All values
are iu bits.
the five bits of information in the 32 numbers that were used as stimuli. The response information, which varied for each task, was calculated on the basis of the number of possible response alternatives. The information reduced was equal to the amount of information in the stimuli minus the amount of information in the response. The four tasks used were as follows :
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Record. The S was required to write down the numbers as they were presented. Add. The S was required to write down the sum of the one or two digits of each number. HELO. The S was required to make two responses for each number. An 0 or E was circled depending on whether the number was odd or even; and H or L was circled depending on whether it was high (above 17) or low (below 17). A/B. The S was required to classify numbers according to the following system: A = High and odd or low and even, and B = High and even or low and odd. Design
The study was basically a 2 X 2 factorial with Grade Level (fourth or sixth) varied orthogonally to Presentation Rate between successive stimuli (5 or 8 seconds). There were 16 Ss in each of four groups; each S performed all four tasks. All S’s heard the 200 numbers in the same order. A different task was performed with each set of 50 numbers; thus, each S contributed 50 observations for each task. The order in which the tasks were performed was balanced such that each S received the tasks in one of four orders. The four orders were selected from a possible 24, such that each task immediately followed every other task once in one of the four orders. Four Ss in each group, two males and two females, received the same order of tasks. Procedure
The Ss were tested in groups of two; each pair was composed of one male and one female from the same grade. Before each task, S was instructed to read the instructions silently as E read them aloud. Five practice problems, similar to the test ones, were completed before the start of each task to insure that S understood what he was expected to do. The stimuli were presented by means of a tape recorder. Each S recorded his answers on an answer sheet; at the top of each answer sheet was a description of the response requirement relevant to the task on which S was working. RESULTS
The percentage of correct responses as a function of the amount of information reduction required by the task is plotted for each group in Fig. 1. Clearly, the HELO and A/B tasks were more difficult than the Record and Add tasks. So few errors were made in the Record and Add tasks that all statistical analyses were performed on the HELO and A/B
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tasks. The scores of the HELO and A/B tasks were corrected for chance according to the procedure developed by Posner (1962) .3 Task was a significant variable (F = 135.55, df = 1, 60, p < .OOl), indicating that the HELO task was significantly easier than the A/B task. Slower presentation rates made the processing of information easier, as indicated by the significant effect of Rate (F = 15.74, df = 1, 60, p < .OOl). The significant Task X Rate interaction (F = 11.94, df = 1, 60, p < .OOl) indicated that the more difficult tasks were differentially more difficult at the faster presentation rate.
INFORMATION
REDUCED
(BITS)
FIQ. 1. Mean percentage of correct responses as a function of amount of information reduction (bits). &--0, Grade 4, 5 seconds; @---a (grade 4, 8 seconds; O-0, grade 6, 5 seconds; O---O) grade 6, 8 seconds.
The sixth-grade children performed significantly better than the fourth graders (F = 45.37, df = 1, 60, p < .OOl). Thus, the expected age differences in ability to process information were demonstrated. The significant Task X Grade interaction (F = 24.19, df = 1, 60, p < .OOl) indicated that information reduction became disproportionately easier with increasing age. The faster rate, however, was not differentially difficult for the younger children as opposed to the older ones, as shown by the absence of a significant Grade X Rate interaction (8’ = 1.67, df = 1, 60). To examine the relationship of task difliculty and rate of information reduction, the percentage of correct responses was plotted in Fig. 2 as a function of rate of information reduction (bits/second). For the sixthgrade group, a task became more difficult as the rate of information reduction required by it increased. A slight deviation from this trend occurred in the HELO task at 5 seconds. A more marked reversal is *The formula for correcting the HELO scores was: [(no. correct4/3 no. wrong)/ total no.) x 1001; the formula for correcting the A/B scores was: [(no. correct no. wrong)/total no.) X 1001.
ARLLITY TO PROCESS INFORMATION
RATE
OF
INFORMATION
373
REDUCTION
FIG. 2. Mean percentage of correct responses as a function of the rate of information reduction (bits/second). @-@, Grade 4; a- - -0) grade 6.
evidenced in the fourth-grade group. Thus, the A/l3 task at eight sec. is more difficult than the HELO task at 5 seconds, although the former requires a slower rate of information processing. DBXJSSION
Task difficulty was found to increase as the amount of information required by the task increased. However, the possibility exists that differences other than the amount of information reduction required by the tasks were responsible for the relative difficulty of the tasks. Differences in demands made on S’s memory can be eliminated since Ss were permitted to write down either the number or their decision about one of its dimensions when it was presented which minimized the retention requirements of the tasks. The HELO and A/B tasks were not different in the logical structure of the rule S had to employ, since they both involved complex exclusive disjunctions. In addition, no child tested had any difficulty classifying numbers on the dimensions of oddness or magnitude or with the addition of numbers; these responses are apparently well learned by children of the ages used in this study. Thus, it appears that the amount of information reduction is the most significant predictor of difficulty for these stimuli and tasks. However, task difficulty was not found to be a simple monotonic function of rate of information reduction as it had been with adults. The HELO task at 5 seconds required a faster rate of information processing than the A/B task at 8 seconds, but the latter was more difficult. Since the A/E! task was more difficult than the HELO task at the two presentation
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rates used in this experiment, it would appear that the task characteristics, rather than the rate of information reduction, determine task difficulty. The A/B task, unlike the HELO task, required an arbitrary association of attributes with categories which may have been responsible for its difficulty. The relationship of rate and task difficulty more closely resembled the adult findings for the sixth-grade children than for the fourth-grade children. With increasing development, the rate of information reduction appears to become a more accurate measure of task difficulty. EXPERIMENT
II
It has been assumed that the limits of human ability to process information can be partially overcome by coding the single bits of information in the environment into larger units (Miller, 1956; Munsinger and Kessen, 1964). Coding enables humans to construct categories and handle greater amounts of information than would be possible without it. One method of experimentally introducing the possibility for coding is through the use of redundancy or some form of regularity in the input stimulus information. Redundancy, defined in terms of symmetry, has increased the ability to process the information in random shapes (Munsinger and Kessen, unpublished results). Sequential redundancy, through the repetition of patterns, has improved the learning of series of lett,ers (Miller, 1958) and the prediction of probabilities associated with patt>ernsof flashing lights (Bruner, Wallach, and Galanter, 1959). The introduction of redundancy which reduces the amount of information that must be processed in each stimulus should be expected to improve performance on information-processing tasks. The type of redundancy used in the present experiment was sequential redundancy, which involved the alternation of the stimulus values of a particular dimension. This type of redundancy was expected to improve performance on all tasks. It has been found that older children are more responsive to the symmetrical redundancy in random figures than are younger children (Munsinger and Kessen, unpublished results). Thus, it was also hypothesized that older children would be more likely to respond to sequential redundancy and would show relatively greater improvement in performance as a result of the redundancy. METHOD
Subjects The Ss were 96 fourth- and 96 sixth-grade children from Our Lady of Lourdes School and the Sacred Heart School in Columbia, Missouri and the Jefferson Elementary School in Centralia, Missouri.
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Stimuli Nonredundant. The stimuli for the nonredundant condition were 200 one- and two-digit numbers, selected at random from the population of the numbers from 1 to 33, excluding 17. These were the same stimuli as those used in Exp. I. Redundant. The stimuli for the redundant condition were 200 one- and two-digit numbers, ranging from 1 to 33, excluding 17. For one redundant list, the numbers were alternately odd and even; for the other redundant list they were alternately high (above 17) and low (below 17). Tasks
Two of the tasks used in Exp. I, the HELO and A/B tasks, were used in the present experiment. The informational characteristics of each task are presented in Table 2. CHARACTERISTICS
TABLE 2 OF THE INFORMATION PROCESSING
TASKS
OF EXPERIMENT
HELO Task condition
Redundant
Stimulus information Response information Information reduced Information reduced per second (5 seconds) Information reduced per second (8 seconds) u All values
A/B
Nonredundant
4 1 3
IIn
5 2 3
Redundant 4 1 3
Nonredundant 5 1 4
.60
60
.60
.80
.38
3s
.3s
.50
are in bits.
Design
Six Ss were assigned at random to each of the 32 conditions of the experiment. Grade Level (fourth or sixth), Presentation Rate (5 or 8 seconds), Task (HELO or A/B), Redundancy (redundant or nonredundant), and Sex were the dimensions of the design. One-half of the Ss in the redundant condition received the high-low redundancy and the other half received the odd-even redundancy. These two types of redundancy were equally distributed among all the other variables. Procedure
In general, the procedure was the same as in Exp. I. Each S performed only one task for 200 trials. In addition, Ss were told that there would be a lo-second pause between each group of ten numbers, and they were told the range of numbers which they would hear.
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RESULTS
The percentage of correct responses for each of the groups is shown in Table 3. As in Exp. I, the scores of both tasks were corrected for chance. An analysis of variance performed on these data indicated that the significant Grade, Task, and Rate differences of the previous experiment were replicated (F = 53.84, df = 1, 160, p < .OOl; F = 103.55, df = 1, TABLE MEAN
PERCENTAGE
3
OF CORRECT RESPONSES USED IN EXPERIMENT II
ON THE TASKS
Grade 4 HELO
Redundant Nonredundant
A/B
5 seconds
8 seconds
5 seconds
8 seconds
93.11 82.89
93.23 95.12
35.92 12.83
48.92 44.17
Grade 6 HELO
Redundant Nonredundant
A/B
5 seconds
8 seconds
5 seconds
8 seconds
96.28 84.98
98.19 98.50
81.08 55.33
95.75 93.92
160, p < .OOl; F = 22.16, df = 1, 160, p < .OOl; respectively). As in Exp. I, there were significant interactions of Grade x Task (F = 40.07, df = 1, 160, p < .OOl) and Task X Rate (F = 6.71, df = 1, 160, p < .025). Once again, the interaction of Grade and Rate was not significant (F < 1, df = 1, 160). The introduction of redundancy increased the number of correct responses on both tasks as indicated by the significance of Redundancy (F = 7.68, df = 1, 160, p < .Ol). However, redundancy was effective only at the 5-second rate. The Rate X Redundancy interaction was significant (F = 5.99, df = 1, 160, p < .025). The predicted Task X Redundancy interaction was not significant (F = 1.79, df = 1, 160). The expected differential effects of redundancy on the younger children failed to appear; there was no significant Grade X Redundancy interaction (F < 1, df = 1, 160). The absence of a significant effect of sex (F < 1, df = 1, 160) indicated that there were no substantial differences between males and females on
ABILITY
TO PROCESS
INFORMATION
these tasks. None of the higher order interactions significance.
377 approached statistical
DISCUSSION
The data of Exp. II indicated that sequential redundancy increased the ease with which information could be processed when stimuli were presented at a 5-second rate. No effects of redundancy were found with a longer interval between successive stimuli. The differential effects of redundancy as a function of rate may be attributed to the lower probability that S attended to the preceding stimulus in the longer presentation intervals. Thus, the type of redundancy which depends on the previous stimulus may be more difficult for the S to perceive with longer intervals between the stimuli. Although redundancy resulted in a significant improvement in performance as a result of its introduction, it is interesting to note that only a few of the Ss were able to notice and verbalize the stimulus alternation. An examination of Table 2 suggests that the introduction of redundancy should not be expected to affect the HELO task and should make the performance on the A/B task equivalent to the HELO one, since the redundancy decreased the amount of information reduction required by the A/B task. Table 3 indicates that the expected equivalence of the HELO and A/B redundant tasks did not occur. Thus, task difficulty in this situation was not a simple function of the amount of information reduction required by the task and depends to some extent on the type of coding mechanisms available to S. EXPERIMENT
III
The tasks with which the preceding experiments have been concerned involved a type of information reduction which is referred to as condensation, in which all the stimulus attributes are simultaneously relevant for the choice of correct response. In condensation tasks, of which the A/B task is an example, the response categories are not systematically related to one stimulus dimension. A particular category is composed of a number of attributes of each dimension. Shepard, Hovland, and Jenkins (1961) and Garner (1966) have found that a classification task in which the stimuli could be categorixed on the basis of one dimension was easier to learn than when several dimensions were simultaneously relevant. The arbitrary association of attributes with categories may contribute to the difficulty of the condensation task. If the difficulty in an information condensation task is a result of the greater demands placed on the information processing capacities of S due to the relevance of many dimensions, practice on a filtering type of information-reduction task with a single relevant dimension should im-
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prove the performance in a subsequent condensation task involving that dimension. Furthermore, if S is exposed to redundancy in a filtering task, it is expected that redundancy will more easily be perceived in a subsequent condensation task and performance will be better than for an S who had received a nonredundant series of stimuli in a preceding filtering task. Since only one dimension is relevant in a filtering task, redundancy in this dimension is more likely to be perceived. It is also expected that experience with redundancy on a particular dimension in a filtering task would make redundancy on this dimension more salient in a subsequent condensation task. Thus, redundancy on the same dimension in a filtering and condensation task which are presented sequentially should result in a better performance than if the redundancy was in a different dimension in each task. The hypotheses to be tested in Exp. III are as follows: (a) filtering on one dimension improves performance in a condensation task involving this dimension; (b) if S was exposed to redundant stimuli in a filtering task, he would be more likely to respond to redundancy on the A/B task than if he was exposed to the nonredundant stimuli; and (c) The Ss exposed to redundancy on a particular dimension would be more likely to respond to redundancy on this dimension than on a different dimension. METHOD
Subjects The Xs were 48 fourth-grade and 48 sixth-grade Russell Boulevard School in Columbia, Missouri.
children
from
the
Stimuli The stimuli were the same redundant and nonredundant and two-digit numbers that were used in Exp. II.
series of one-
Tasks Two types of tasks were used-filtering and A/B tasks. The filtering tasks consisted of the categorization of numbers on either odd-even or the high-low dimension. Only one dimension was relevant in a particular filtering task. In the high-low filtering task, S was asked to circle H if the number was high and L if it was low. In the odd-even filtering task, S was asked to circle 0 if the number was odd and E if it was even. The filtering tasks were performed on either redundant or nonredundant stimuli. The odd-even dimension was the only one relevant for the odd-even redundant stimuli; and only the high-low dimension was relevant for the high-low redundant stimuli.
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The A/B task was the same as the one used in the previous experiments. Design
For both the filtering and the A/B tasks the numbers were presented at 5-second rate. Eight Ss (four males and four females) were randomly assigned to one of 12 groups. There were two Grade Levels (fourth or sixth), two Types of Filtering tasks (redundant or nonredundant stimuli), and three Test Conditions (redundancy on the same dimension, redundancy on a different dimension, and nonredundant stimuli). This latter variable refers to the similarity between the filtering and test stimuli; that is, whether the same dimension that was relevant in the filtering task was the redundant dimension in the test with the A/B task. Appropriate counterbalancing of the odd-even and high-low dimensions was employed. Procedure
In general, the procedure was the same as in Exps. I and II. The Ss were run in groups of four; two males and two females from the same grade were in each group. Each S received 100 trials on the filtering task which was immediately followed by 100 trials on the A/B task. RESULTS
The data from Exp. III indicated that all the groups from both grades demonstrated perfect or near perfect performance on the filtering tasks. To test the hypothesis that practice on a filtering task with a single relevant dimension would improve performance on a condensation task involving this dimension, the scores of the Ss of Exp. III and the relevant groups from Exp. II were compared. Since S received 100 trials on the A/B task in Exp. III, the data for this comparison used the scores of the first 100 trials on the A/B task of the 8s in Exp. II. These results are presented in Table 4. Eight groups are presented in this comparison. Four of these are from Exp. II and represent performance on the A/B task at 5 seconds without any filtering experience. The two grade levels (fourth and sixth) and the two types of A/B tests (with redundant or nonredundant stimuli) are shown separately. There were 12 Xs in each of these groups. The other four groups are from Exp. III and represent performance on the A/B task at 5 seconds after filtering experience. There were 32 Ss in each grade who were tested on redundant stimuli after various types of filtering tasks. (All the various types of filtering tasks described in the Method section are grouped together for the purposes of this comparison.) There were 16 8s in each grade who were tested with nonredundant stimuli after filtering experience. Analyses of these data were performed in the following manner because of the unequal numbers of subjects in the groups: the four groups from
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Exp. II had 12 Ss in each of them so 12 Ss were randomly selected from the appropriate groups of Exp. III for one “replication.” An analysis of variance was performed on these data. There were two levels of Grade (fourth and sixth), two levels of Redundancy (redundant or nonredundant stimuli in the A/B task), and two levels of Filter (absence or presence of prior filtering experience). A second “replication” involved 12 additional Ss randomly selected from each of the groups with 16 Ss. The scores of the 12 Ss from each of the four groups from Exp. II were used again in this analysis. The two “replications” yielded almost1 identical results.
MEAN
PERCENTAGE OF CORRECT RESPONSES ON THE A/B PRESENTATION RATE) 7Jsm IN EXPERNENTS II Grade Redundant
Filtering experience (Exp. III) No filtering experience (Exp. II)
TASKS (5-SECONT) AND III Grade
4
Eonredundant
Redundant,
6 JSonredundant
57.13
33.50
79.56
85.00
35.92
12.83
x7 .04
55.33
The significant Grade and Redundancy differences of the previous study were replicated (for Grade, Replication 1, F = 48.87, df = 1, 88, p < .OOl, Replication 2, F = 40.38, o?f = 1, 88, p < .OOl; for Redundancy, Replication 1, F = 6.31, df = 1, 88, p < .OOl; Replication 2, F = 7.62, df = 1, 88, p < .Ol). Prior practice on a filtering task significantly improved performance on a subsequent condensation task as evidenced by the significance of this variable (for Replication 1, F = 12.61, df = 1, 88, p < .OOl; for Replication 2, F = 15.70, df = 1, 88, p < .OOl‘, . There were no developmental differences in the effects of either the Redundancy or the Filtering variable as evidenced by the lack of significant Grade x Redundancy or Grade X Filter interactions. The condensation task (A/B) performance of the groups from Experiment III with various types of filtering experience is presented in Table 5. An analysis of the data summarized in Table 5 revealed a significant main effect of Grade (F = 20.37, df = 1, 84, p < .OOl), indicating that the overall performance of the fourth-grade Ss was less than that of the sixth-grade Ss. Neither the main effects of Type of Filtering nor Test were significant (F = 1.80, df = 1, 84; F < 1, df = 2, 84, respectively). There was, however, a significant Grade X Test interaction (F = 4.09, df = 2, 84, p < .025). Because of the significance of this interaction, separate analyses of the Type of Filtering and Test factors for each grade were performed. For the sixth grade, the main effects of Type of Filtering
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or Test and the interaction between them were not significant (F < 1, df = 1, 44; F = 3.89, df = 1, 44; F = 1.55, df = 1, 44, respectively). However, there was a significant effect of Test (F = 11.73, cZf= 1, 44, p < .OOl) and a significant Type of Filtering X Test interaction (F = 5.61, df = 1, 44, p < .025) only in the fourth grade. Type of filtering was not a significant variable (F = 3.62, df = 1, 44). Because of the significant interaction between Type of Filtering and Test, individual comparisons were made between the various groups in the fourth grade. TABLE MEAN
PERCENTAGE
5
OF CORRECT RESPONSES USED IN EXPERIMENT III
FOR THE TASKS
Grade 4 Test
Redundant filtering
Redundant Same Different Nonredundant
63.25 63.00 46.00
Grade 6
Nonredundant iiltering 27.50 74.75 21.00
Redundant filtering
Nonredundant filtering
84.75 71.75 91.75
87.75 74.00 78.25
Redundant filtering was more effective than nonredundant filtering only for the group in which the same dimension was redundant in both the filtering and A/B tasks (t = 2.17, p < .05). In comparisons of the Test variable of the redundant filtering groups, no groups were significantly different from one another. In comparisons of the Test variable in the nonredundant filtering groups, the group that practiced with different dimensions than were redundant on the A/B task performed significantly better than the same and nonredundant groups (t = 3.61, p < .Ol ; t = 3.28, p < .Ol, respectively). DISCUSSION
The hypothesis that Ss exposed to redundant stimuli in a filtering task would be more likely to respond to redundancy on the A/B task than Ss exposed to nonredundant stimuli was confirmed only in the fourth-grade group who filtered the same dimension that was redundant in the A/B task. It was also apparent that Ss who received redundancy on a particular dimension were not more likely to respond to redundancy on this dimension than they were to redundancy on a different dimension. The performance of both age groups on the filtering tasks indicated that the dimensions of odd-even and high-low were well learned and suggests that the HELO and A/B tasks were particularly difficult because of the requirement to process two dimensions simultaneously. Practice on a
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filtering task improved performance on the A/B task. Thus, it was found that training with the processing of a dimension facilitated the performance of a task which involved that dimension, among others. The relative failure of the various redundant filtering tasks to transfer to redundancy in the test and the failure of redundancy to show greater transfer within the same dimension is surprising because the majority of Ss were able to verbalize the concept of alternation in the stimuli of the filtering task. The explanation probably lies in the fact that redundancy is extremely difficult for the children to perceive in the A/B task. The inflated performance of the fourth-grade group that performed a nonredundant filtering task and were tested on an A/B task with a different redundant dimension that they had filtered is difficult to account for and probably represents a sampling error. CONCLUSIONS
The results of the three experiments lend support to the theories of cognitive development which emphasize increased ability to process information as a function of age (e.g., Munsinger and Kessen, 1964). The findings are in accord with previous research (e.g., Munsinger and Kessen, 1964, unpublished results) which has shown developmental differences in the ability to process information in visual stimuli. The present experiments have demonstrated age related changes in the ability to process the information in numbers and thus have increased the range of situations about which developmental differences in information-processing ability are known. The information-processing analysis appears to be most applicable in tasks where the categories or stimulus attributes are well learned. If stimuli are used with which S is relatively unfamiliar, the characteristics of the stimuli must be coded before the information can be processed. The necessity of learning the characteristics of the stimuli may make an information-conservation task relatively difficult and less different from information-reduction tasks. The present series of studies also indicates that an information-reduction analysis is insufficient by itself to explain cognitive development; an understanding of the mechanisms of coding is also necessary. For example, the introduction of redundancy in the HELO task did not alter its information-reduction characteristics but did affect performance on it. It is assumed that the coding which occurred in the processing of redundant stimulation reduced the unpredictability of the sequence of stimuli. Coding appears to depend on, at least in part, finding patterns and regularity in incoming stimulation and grouping similar stimuli in categories. In addition, the effects of filtering on information condensation could
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not be directly predicted from an information theory analysis but required an understanding of the characteristics of the tasks. Most information analyses have a tendency to ignore the effects of prior experience with the stimuli (e.g., Posner, 1964). Theoretical recognition of the transfer effects of relevant previous experience, which presumably results in increased ability to code information, is necessary. REFERENCES BRUNER, BRUNER,
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1965, 69, 4OkS-412. GARNER, W. To perceive is to know. American Psychologist, 1966, 21, LAFOND, R. Q., CROWDER, R. G., AND KESSEN, W. Preference and rate reduction. Journal of Experimental Psychology, 1967, in press.
R. A comparison Experimental Psychology, MILLER, G. A. The magical capacity for processing MILLER, G. A. Free recall
METZGER,
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11-19.
of information
and concept formation.
Journal
of
56, 226-231.
number seven, plus or minus two: some limits on our information. Psychological Review, 1956, 63, 81-97. of redundant strings of letters. Journal of Experimental
Psychology, 1958, 56, 48%491. MILLER, G. A., GALANTER, E., AND PRIBRAM, havior. New York: Holt, 1960. MORIN, R. E., AND FORRIN, B. Information
Ii.
H. Plans
and
the
structure
of be-
processing: choice reaction times of first- and third-grade students for two types of association. Child Development, 1965, 36, 7X3-720. MUNSINGER, H., AND KESSEN, W. Uncertainty, structure and preference. Psychological Monographs: General and Applied, 1964, 78, No. 9 (Whole No. 586). POLLACK, I. Speed of classification of words into super-ordinate categories. Journal of Verbal Learning and Verbal Behavior, 1963, 2, 159-165. POSNER, M. I. An informational approach to thinking. Tech. Rep., Office of Research Administration, Ann Arbor, April, 1962. POSNER, M. I. Information reduction in the analysis of sequential tasks. Psychological Review, 1964, 71, 491-504. Pos~zs, M. I., AND ROSSMAN, E. The effect of size and location of informational transforms upon short term retention. Journal of Experimental Psychology, 1965, 70, 496509. SHEPARD, R. N., HOVLAND, C. J., AND JENKINS, H. M. Learning and memorization of General and Applied, 1961, 75, 13 classification. Psychological Monograph,s: (Whole No. 517).
The
OF EXPERIMENT.\L
Development
CHILD
PSYCHOLOGY
of the
Ability
6, 368-383 (1968)
to Process
Information’
LINDA S. SIEGEL Yale University’ The development of the ability to process information was studied in a series of three experiments involving fourth- and sixth-grade children. Experiment I examined the ability of children to process information as a function of the amount and rate of information reduction required by the task. Amount, not rate, of information reduction was found to be a significant determinant of task difficulty. Older children were better able to process information than younger children. There was an interaction between age and task difficulty such that processing of greater amounts of information was differentially more difficult for younger children. Experiment II studied the effect of redundancy on these tasks. Redundancy was found to result in a significant improvement in performance only when the stimuli were presented at a 5-second rate. Experiment III examined the effects of practice with filtering tasks on performance of the information-reduction tasks. The data indicated that practice with a filtering task improved performance. However, no differences were found between different types of filtering tasks.
Recent theoretical interpretations of cognition have stressed the information-processing characteristics of cognitive processes (e.g., Bruner, 1964; Miller, Galanter, and Pribram, 1960; Munsinger and Kcssen, 1964). These theorists assume that there are developmental changes in the ability to process information. The purpose of the present series of studies was to assess experimentally the developmental changes in the ability to process information using tasks in which the informational characteristics were known. The tasks that were used were drawn from a classification system developed by Posner (1962, 1964) as part of a general information-processing theory of thinking. Two types of tasks, ‘This report is based on a dissertation submitted to the Graduate School of Yale University in partial fulfillment of the requirements for a doctoral degree. The author is grateful to William Kessen, chairman of the dissertation committee, as well as the other members of the committee, Robert Crowder and Edward Johnson, for their suggestions and advice. The author also wishes to thank Mr. J. Rook of the Guilford Lakes School, Sister M. Stephanie of the Sacred Heart School, Sister M. Philomena of Our Lady of Lourdes School, Mr. Davis and Mrs. Asbury of the Jefferson Elementary School, and Mr. Marine and Mr. Pulliam of the Russell Boulevard School for their cooperation in providing subjects. ‘Now at the University of Missouri. 368
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369
information conservation and information reduction, were used. An information-conservation task is one in which the amount of information in the stimuli and responses is equivalent; that is, all the information in the stimulus is preserved in the response. Rote-learning tasks are examples of information-conservation tasks. In an information-reduction task the response contains less information than the stimulus; that is, there is more than one stimulus for each response. For example, conceptattainment tasks involve information reduction. The information tasks chosen for the present experiments were condensation ones, in which all the stimulus information is necessary to make the response, and filtering ones, in which some of the stimulus dimensions are irrelevant and can be ignored for the making of a response. Previous experimentation with adults has indicated that the difficulty of a task is directly related to the amount of information reduction required by it. This relationship has been demonstrated in tasks involving reaction time (Fitts and Biederman, 1965), classification of words (Pollack, 1963), paired associate learning (Metzger, 1958)) and the categorization of numbers (Posner and Rossman, 1965). Therefore, for any age group, it was predicted that an information-conservation task would be the easiest and that tasks would become progressively more difficult as more information reduction is required by them. Also, rate of information reduction has been found to be a significant factor in determining task difficulty (LaFond, Crowder, and Kessen, 1967). One aspect of the present research was to examine the generality of this finding. There is evidence that information processing capacity increases with development (e.g., Morin and Forrin, 1965; Munsinger and Kessen, 1964). On the basis of these data, it was expected that older children would be better able to process information than younger children. In addition, as tasks become more difficult and more complex cognitive structures are required, greater age differences in performance were expected. Thus, it was expected that there would be an interaction between age and task difficulty such that at the younger ages, a differential amount of difficulty would be experienced as the information required by the task increases. Therefore, there would be little difference on a conservation task between children of different ages, but as increasing amounts of reduction are required, there would be a greater discrepancy between age levels. EXPERIMENT
I
Experiment I was designed to test the following specific hypotheses: (a) the difficulty of a task increases as the amount of information reduction required by it increases ; (b) the difficulty of a task increases as the rate of information reduction required by it increases; (c) there is
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an increase in the ability to process information with development; and (d) a disproportionate amount of difficulty will be experienced by younger children as the information reduction required by the task increases. METHOD
Subjects The Ss were 32 fourth-grade and 32 sixth-grade ford Lakes School in Guilford, Connecticut.
children
from the Guil-
Stimuli The stimuli were 200 one- and two-digit numbers, selected at random from the population of the numbers from 1 to 33, excluding 17. The numbers were divided into four groups of 50 numbers each. A separate task was performed with each group of 50 numbers. The numbers were presented to S at either 5- or g-second intervals. Tasks The characteristics of the four information processing tasks (adapted from Posner, 1962) are summarized in Table 1. The t.asks in this study involved an information-condensation, rather than a filtering paradigm. The tasks were identical in stimulus information but varied in response information. The stimulus information was calculated on the basis of TBBLE -.
1
C!II.~~XYCRI~~I~S OF THE INFORMATIONPROCESSINGTASKS OF EXPERIMENT I0 Task
Record
Add
HELO
A/B
Stimulus information Response information Information reduced Information reduced per second (5 seconds) Information reduced per second (8 seconds) a All values
are iu bits.
the five bits of information in the 32 numbers that were used as stimuli. The response information, which varied for each task, was calculated on the basis of the number of possible response alternatives. The information reduced was equal to the amount of information in the stimuli minus the amount of information in the response. The four tasks used were as follows :
ABILITY
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INFORMATION
371
Record. The S was required to write down the numbers as they were presented. Add. The S was required to write down the sum of the one or two digits of each number. HELO. The S was required to make two responses for each number. An 0 or E was circled depending on whether the number was odd or even; and H or L was circled depending on whether it was high (above 17) or low (below 17). A/B. The S was required to classify numbers according to the following system: A = High and odd or low and even, and B = High and even or low and odd. Design
The study was basically a 2 X 2 factorial with Grade Level (fourth or sixth) varied orthogonally to Presentation Rate between successive stimuli (5 or 8 seconds). There were 16 Ss in each of four groups; each S performed all four tasks. All S’s heard the 200 numbers in the same order. A different task was performed with each set of 50 numbers; thus, each S contributed 50 observations for each task. The order in which the tasks were performed was balanced such that each S received the tasks in one of four orders. The four orders were selected from a possible 24, such that each task immediately followed every other task once in one of the four orders. Four Ss in each group, two males and two females, received the same order of tasks. Procedure
The Ss were tested in groups of two; each pair was composed of one male and one female from the same grade. Before each task, S was instructed to read the instructions silently as E read them aloud. Five practice problems, similar to the test ones, were completed before the start of each task to insure that S understood what he was expected to do. The stimuli were presented by means of a tape recorder. Each S recorded his answers on an answer sheet; at the top of each answer sheet was a description of the response requirement relevant to the task on which S was working. RESULTS
The percentage of correct responses as a function of the amount of information reduction required by the task is plotted for each group in Fig. 1. Clearly, the HELO and A/B tasks were more difficult than the Record and Add tasks. So few errors were made in the Record and Add tasks that all statistical analyses were performed on the HELO and A/B
372
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SIEGEL
tasks. The scores of the HELO and A/B tasks were corrected for chance according to the procedure developed by Posner (1962) .3 Task was a significant variable (F = 135.55, df = 1, 60, p < .OOl), indicating that the HELO task was significantly easier than the A/B task. Slower presentation rates made the processing of information easier, as indicated by the significant effect of Rate (F = 15.74, df = 1, 60, p < .OOl). The significant Task X Rate interaction (F = 11.94, df = 1, 60, p < .OOl) indicated that the more difficult tasks were differentially more difficult at the faster presentation rate.
INFORMATION
REDUCED
(BITS)
FIQ. 1. Mean percentage of correct responses as a function of amount of information reduction (bits). &--0, Grade 4, 5 seconds; @---a (grade 4, 8 seconds; O-0, grade 6, 5 seconds; O---O) grade 6, 8 seconds.
The sixth-grade children performed significantly better than the fourth graders (F = 45.37, df = 1, 60, p < .OOl). Thus, the expected age differences in ability to process information were demonstrated. The significant Task X Grade interaction (F = 24.19, df = 1, 60, p < .OOl) indicated that information reduction became disproportionately easier with increasing age. The faster rate, however, was not differentially difficult for the younger children as opposed to the older ones, as shown by the absence of a significant Grade X Rate interaction (8’ = 1.67, df = 1, 60). To examine the relationship of task difliculty and rate of information reduction, the percentage of correct responses was plotted in Fig. 2 as a function of rate of information reduction (bits/second). For the sixthgrade group, a task became more difficult as the rate of information reduction required by it increased. A slight deviation from this trend occurred in the HELO task at 5 seconds. A more marked reversal is *The formula for correcting the HELO scores was: [(no. correct4/3 no. wrong)/ total no.) x 1001; the formula for correcting the A/B scores was: [(no. correct no. wrong)/total no.) X 1001.
ARLLITY TO PROCESS INFORMATION
RATE
OF
INFORMATION
373
REDUCTION
FIG. 2. Mean percentage of correct responses as a function of the rate of information reduction (bits/second). @-@, Grade 4; a- - -0) grade 6.
evidenced in the fourth-grade group. Thus, the A/l3 task at eight sec. is more difficult than the HELO task at 5 seconds, although the former requires a slower rate of information processing. DBXJSSION
Task difficulty was found to increase as the amount of information required by the task increased. However, the possibility exists that differences other than the amount of information reduction required by the tasks were responsible for the relative difficulty of the tasks. Differences in demands made on S’s memory can be eliminated since Ss were permitted to write down either the number or their decision about one of its dimensions when it was presented which minimized the retention requirements of the tasks. The HELO and A/B tasks were not different in the logical structure of the rule S had to employ, since they both involved complex exclusive disjunctions. In addition, no child tested had any difficulty classifying numbers on the dimensions of oddness or magnitude or with the addition of numbers; these responses are apparently well learned by children of the ages used in this study. Thus, it appears that the amount of information reduction is the most significant predictor of difficulty for these stimuli and tasks. However, task difficulty was not found to be a simple monotonic function of rate of information reduction as it had been with adults. The HELO task at 5 seconds required a faster rate of information processing than the A/B task at 8 seconds, but the latter was more difficult. Since the A/E! task was more difficult than the HELO task at the two presentation
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rates used in this experiment, it would appear that the task characteristics, rather than the rate of information reduction, determine task difficulty. The A/B task, unlike the HELO task, required an arbitrary association of attributes with categories which may have been responsible for its difficulty. The relationship of rate and task difficulty more closely resembled the adult findings for the sixth-grade children than for the fourth-grade children. With increasing development, the rate of information reduction appears to become a more accurate measure of task difficulty. EXPERIMENT
II
It has been assumed that the limits of human ability to process information can be partially overcome by coding the single bits of information in the environment into larger units (Miller, 1956; Munsinger and Kessen, 1964). Coding enables humans to construct categories and handle greater amounts of information than would be possible without it. One method of experimentally introducing the possibility for coding is through the use of redundancy or some form of regularity in the input stimulus information. Redundancy, defined in terms of symmetry, has increased the ability to process the information in random shapes (Munsinger and Kessen, unpublished results). Sequential redundancy, through the repetition of patterns, has improved the learning of series of lett,ers (Miller, 1958) and the prediction of probabilities associated with patt>ernsof flashing lights (Bruner, Wallach, and Galanter, 1959). The introduction of redundancy which reduces the amount of information that must be processed in each stimulus should be expected to improve performance on information-processing tasks. The type of redundancy used in the present experiment was sequential redundancy, which involved the alternation of the stimulus values of a particular dimension. This type of redundancy was expected to improve performance on all tasks. It has been found that older children are more responsive to the symmetrical redundancy in random figures than are younger children (Munsinger and Kessen, unpublished results). Thus, it was also hypothesized that older children would be more likely to respond to sequential redundancy and would show relatively greater improvement in performance as a result of the redundancy. METHOD
Subjects The Ss were 96 fourth- and 96 sixth-grade children from Our Lady of Lourdes School and the Sacred Heart School in Columbia, Missouri and the Jefferson Elementary School in Centralia, Missouri.
ABILITY
TO
PROCESS
375
INFORMATION
Stimuli Nonredundant. The stimuli for the nonredundant condition were 200 one- and two-digit numbers, selected at random from the population of the numbers from 1 to 33, excluding 17. These were the same stimuli as those used in Exp. I. Redundant. The stimuli for the redundant condition were 200 one- and two-digit numbers, ranging from 1 to 33, excluding 17. For one redundant list, the numbers were alternately odd and even; for the other redundant list they were alternately high (above 17) and low (below 17). Tasks
Two of the tasks used in Exp. I, the HELO and A/B tasks, were used in the present experiment. The informational characteristics of each task are presented in Table 2. CHARACTERISTICS
TABLE 2 OF THE INFORMATION PROCESSING
TASKS
OF EXPERIMENT
HELO Task condition
Redundant
Stimulus information Response information Information reduced Information reduced per second (5 seconds) Information reduced per second (8 seconds) u All values
A/B
Nonredundant
4 1 3
IIn
5 2 3
Redundant 4 1 3
Nonredundant 5 1 4
.60
60
.60
.80
.38
3s
.3s
.50
are in bits.
Design
Six Ss were assigned at random to each of the 32 conditions of the experiment. Grade Level (fourth or sixth), Presentation Rate (5 or 8 seconds), Task (HELO or A/B), Redundancy (redundant or nonredundant), and Sex were the dimensions of the design. One-half of the Ss in the redundant condition received the high-low redundancy and the other half received the odd-even redundancy. These two types of redundancy were equally distributed among all the other variables. Procedure
In general, the procedure was the same as in Exp. I. Each S performed only one task for 200 trials. In addition, Ss were told that there would be a lo-second pause between each group of ten numbers, and they were told the range of numbers which they would hear.
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RESULTS
The percentage of correct responses for each of the groups is shown in Table 3. As in Exp. I, the scores of both tasks were corrected for chance. An analysis of variance performed on these data indicated that the significant Grade, Task, and Rate differences of the previous experiment were replicated (F = 53.84, df = 1, 160, p < .OOl; F = 103.55, df = 1, TABLE MEAN
PERCENTAGE
3
OF CORRECT RESPONSES USED IN EXPERIMENT II
ON THE TASKS
Grade 4 HELO
Redundant Nonredundant
A/B
5 seconds
8 seconds
5 seconds
8 seconds
93.11 82.89
93.23 95.12
35.92 12.83
48.92 44.17
Grade 6 HELO
Redundant Nonredundant
A/B
5 seconds
8 seconds
5 seconds
8 seconds
96.28 84.98
98.19 98.50
81.08 55.33
95.75 93.92
160, p < .OOl; F = 22.16, df = 1, 160, p < .OOl; respectively). As in Exp. I, there were significant interactions of Grade x Task (F = 40.07, df = 1, 160, p < .OOl) and Task X Rate (F = 6.71, df = 1, 160, p < .025). Once again, the interaction of Grade and Rate was not significant (F < 1, df = 1, 160). The introduction of redundancy increased the number of correct responses on both tasks as indicated by the significance of Redundancy (F = 7.68, df = 1, 160, p < .Ol). However, redundancy was effective only at the 5-second rate. The Rate X Redundancy interaction was significant (F = 5.99, df = 1, 160, p < .025). The predicted Task X Redundancy interaction was not significant (F = 1.79, df = 1, 160). The expected differential effects of redundancy on the younger children failed to appear; there was no significant Grade X Redundancy interaction (F < 1, df = 1, 160). The absence of a significant effect of sex (F < 1, df = 1, 160) indicated that there were no substantial differences between males and females on
ABILITY
TO PROCESS
INFORMATION
these tasks. None of the higher order interactions significance.
377 approached statistical
DISCUSSION
The data of Exp. II indicated that sequential redundancy increased the ease with which information could be processed when stimuli were presented at a 5-second rate. No effects of redundancy were found with a longer interval between successive stimuli. The differential effects of redundancy as a function of rate may be attributed to the lower probability that S attended to the preceding stimulus in the longer presentation intervals. Thus, the type of redundancy which depends on the previous stimulus may be more difficult for the S to perceive with longer intervals between the stimuli. Although redundancy resulted in a significant improvement in performance as a result of its introduction, it is interesting to note that only a few of the Ss were able to notice and verbalize the stimulus alternation. An examination of Table 2 suggests that the introduction of redundancy should not be expected to affect the HELO task and should make the performance on the A/B task equivalent to the HELO one, since the redundancy decreased the amount of information reduction required by the A/B task. Table 3 indicates that the expected equivalence of the HELO and A/B redundant tasks did not occur. Thus, task difficulty in this situation was not a simple function of the amount of information reduction required by the task and depends to some extent on the type of coding mechanisms available to S. EXPERIMENT
III
The tasks with which the preceding experiments have been concerned involved a type of information reduction which is referred to as condensation, in which all the stimulus attributes are simultaneously relevant for the choice of correct response. In condensation tasks, of which the A/B task is an example, the response categories are not systematically related to one stimulus dimension. A particular category is composed of a number of attributes of each dimension. Shepard, Hovland, and Jenkins (1961) and Garner (1966) have found that a classification task in which the stimuli could be categorixed on the basis of one dimension was easier to learn than when several dimensions were simultaneously relevant. The arbitrary association of attributes with categories may contribute to the difficulty of the condensation task. If the difficulty in an information condensation task is a result of the greater demands placed on the information processing capacities of S due to the relevance of many dimensions, practice on a filtering type of information-reduction task with a single relevant dimension should im-
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prove the performance in a subsequent condensation task involving that dimension. Furthermore, if S is exposed to redundancy in a filtering task, it is expected that redundancy will more easily be perceived in a subsequent condensation task and performance will be better than for an S who had received a nonredundant series of stimuli in a preceding filtering task. Since only one dimension is relevant in a filtering task, redundancy in this dimension is more likely to be perceived. It is also expected that experience with redundancy on a particular dimension in a filtering task would make redundancy on this dimension more salient in a subsequent condensation task. Thus, redundancy on the same dimension in a filtering and condensation task which are presented sequentially should result in a better performance than if the redundancy was in a different dimension in each task. The hypotheses to be tested in Exp. III are as follows: (a) filtering on one dimension improves performance in a condensation task involving this dimension; (b) if S was exposed to redundant stimuli in a filtering task, he would be more likely to respond to redundancy on the A/B task than if he was exposed to the nonredundant stimuli; and (c) The Ss exposed to redundancy on a particular dimension would be more likely to respond to redundancy on this dimension than on a different dimension. METHOD
Subjects The Xs were 48 fourth-grade and 48 sixth-grade Russell Boulevard School in Columbia, Missouri.
children
from
the
Stimuli The stimuli were the same redundant and nonredundant and two-digit numbers that were used in Exp. II.
series of one-
Tasks Two types of tasks were used-filtering and A/B tasks. The filtering tasks consisted of the categorization of numbers on either odd-even or the high-low dimension. Only one dimension was relevant in a particular filtering task. In the high-low filtering task, S was asked to circle H if the number was high and L if it was low. In the odd-even filtering task, S was asked to circle 0 if the number was odd and E if it was even. The filtering tasks were performed on either redundant or nonredundant stimuli. The odd-even dimension was the only one relevant for the odd-even redundant stimuli; and only the high-low dimension was relevant for the high-low redundant stimuli.
ABILITY
TO PROCESS INFORMATION
379
The A/B task was the same as the one used in the previous experiments. Design
For both the filtering and the A/B tasks the numbers were presented at 5-second rate. Eight Ss (four males and four females) were randomly assigned to one of 12 groups. There were two Grade Levels (fourth or sixth), two Types of Filtering tasks (redundant or nonredundant stimuli), and three Test Conditions (redundancy on the same dimension, redundancy on a different dimension, and nonredundant stimuli). This latter variable refers to the similarity between the filtering and test stimuli; that is, whether the same dimension that was relevant in the filtering task was the redundant dimension in the test with the A/B task. Appropriate counterbalancing of the odd-even and high-low dimensions was employed. Procedure
In general, the procedure was the same as in Exps. I and II. The Ss were run in groups of four; two males and two females from the same grade were in each group. Each S received 100 trials on the filtering task which was immediately followed by 100 trials on the A/B task. RESULTS
The data from Exp. III indicated that all the groups from both grades demonstrated perfect or near perfect performance on the filtering tasks. To test the hypothesis that practice on a filtering task with a single relevant dimension would improve performance on a condensation task involving this dimension, the scores of the Ss of Exp. III and the relevant groups from Exp. II were compared. Since S received 100 trials on the A/B task in Exp. III, the data for this comparison used the scores of the first 100 trials on the A/B task of the 8s in Exp. II. These results are presented in Table 4. Eight groups are presented in this comparison. Four of these are from Exp. II and represent performance on the A/B task at 5 seconds without any filtering experience. The two grade levels (fourth and sixth) and the two types of A/B tests (with redundant or nonredundant stimuli) are shown separately. There were 12 Xs in each of these groups. The other four groups are from Exp. III and represent performance on the A/B task at 5 seconds after filtering experience. There were 32 Ss in each grade who were tested on redundant stimuli after various types of filtering tasks. (All the various types of filtering tasks described in the Method section are grouped together for the purposes of this comparison.) There were 16 8s in each grade who were tested with nonredundant stimuli after filtering experience. Analyses of these data were performed in the following manner because of the unequal numbers of subjects in the groups: the four groups from
380
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Exp. II had 12 Ss in each of them so 12 Ss were randomly selected from the appropriate groups of Exp. III for one “replication.” An analysis of variance was performed on these data. There were two levels of Grade (fourth and sixth), two levels of Redundancy (redundant or nonredundant stimuli in the A/B task), and two levels of Filter (absence or presence of prior filtering experience). A second “replication” involved 12 additional Ss randomly selected from each of the groups with 16 Ss. The scores of the 12 Ss from each of the four groups from Exp. II were used again in this analysis. The two “replications” yielded almost1 identical results.
MEAN
PERCENTAGE OF CORRECT RESPONSES ON THE A/B PRESENTATION RATE) 7Jsm IN EXPERNENTS II Grade Redundant
Filtering experience (Exp. III) No filtering experience (Exp. II)
TASKS (5-SECONT) AND III Grade
4
Eonredundant
Redundant,
6 JSonredundant
57.13
33.50
79.56
85.00
35.92
12.83
x7 .04
55.33
The significant Grade and Redundancy differences of the previous study were replicated (for Grade, Replication 1, F = 48.87, df = 1, 88, p < .OOl, Replication 2, F = 40.38, o?f = 1, 88, p < .OOl; for Redundancy, Replication 1, F = 6.31, df = 1, 88, p < .OOl; Replication 2, F = 7.62, df = 1, 88, p < .Ol). Prior practice on a filtering task significantly improved performance on a subsequent condensation task as evidenced by the significance of this variable (for Replication 1, F = 12.61, df = 1, 88, p < .OOl; for Replication 2, F = 15.70, df = 1, 88, p < .OOl‘, . There were no developmental differences in the effects of either the Redundancy or the Filtering variable as evidenced by the lack of significant Grade x Redundancy or Grade X Filter interactions. The condensation task (A/B) performance of the groups from Experiment III with various types of filtering experience is presented in Table 5. An analysis of the data summarized in Table 5 revealed a significant main effect of Grade (F = 20.37, df = 1, 84, p < .OOl), indicating that the overall performance of the fourth-grade Ss was less than that of the sixth-grade Ss. Neither the main effects of Type of Filtering nor Test were significant (F = 1.80, df = 1, 84; F < 1, df = 2, 84, respectively). There was, however, a significant Grade X Test interaction (F = 4.09, df = 2, 84, p < .025). Because of the significance of this interaction, separate analyses of the Type of Filtering and Test factors for each grade were performed. For the sixth grade, the main effects of Type of Filtering
ABILITY
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or Test and the interaction between them were not significant (F < 1, df = 1, 44; F = 3.89, df = 1, 44; F = 1.55, df = 1, 44, respectively). However, there was a significant effect of Test (F = 11.73, cZf= 1, 44, p < .OOl) and a significant Type of Filtering X Test interaction (F = 5.61, df = 1, 44, p < .025) only in the fourth grade. Type of filtering was not a significant variable (F = 3.62, df = 1, 44). Because of the significant interaction between Type of Filtering and Test, individual comparisons were made between the various groups in the fourth grade. TABLE MEAN
PERCENTAGE
5
OF CORRECT RESPONSES USED IN EXPERIMENT III
FOR THE TASKS
Grade 4 Test
Redundant filtering
Redundant Same Different Nonredundant
63.25 63.00 46.00
Grade 6
Nonredundant iiltering 27.50 74.75 21.00
Redundant filtering
Nonredundant filtering
84.75 71.75 91.75
87.75 74.00 78.25
Redundant filtering was more effective than nonredundant filtering only for the group in which the same dimension was redundant in both the filtering and A/B tasks (t = 2.17, p < .05). In comparisons of the Test variable of the redundant filtering groups, no groups were significantly different from one another. In comparisons of the Test variable in the nonredundant filtering groups, the group that practiced with different dimensions than were redundant on the A/B task performed significantly better than the same and nonredundant groups (t = 3.61, p < .Ol ; t = 3.28, p < .Ol, respectively). DISCUSSION
The hypothesis that Ss exposed to redundant stimuli in a filtering task would be more likely to respond to redundancy on the A/B task than Ss exposed to nonredundant stimuli was confirmed only in the fourth-grade group who filtered the same dimension that was redundant in the A/B task. It was also apparent that Ss who received redundancy on a particular dimension were not more likely to respond to redundancy on this dimension than they were to redundancy on a different dimension. The performance of both age groups on the filtering tasks indicated that the dimensions of odd-even and high-low were well learned and suggests that the HELO and A/B tasks were particularly difficult because of the requirement to process two dimensions simultaneously. Practice on a
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LINDA S. SIEGEL
filtering task improved performance on the A/B task. Thus, it was found that training with the processing of a dimension facilitated the performance of a task which involved that dimension, among others. The relative failure of the various redundant filtering tasks to transfer to redundancy in the test and the failure of redundancy to show greater transfer within the same dimension is surprising because the majority of Ss were able to verbalize the concept of alternation in the stimuli of the filtering task. The explanation probably lies in the fact that redundancy is extremely difficult for the children to perceive in the A/B task. The inflated performance of the fourth-grade group that performed a nonredundant filtering task and were tested on an A/B task with a different redundant dimension that they had filtered is difficult to account for and probably represents a sampling error. CONCLUSIONS
The results of the three experiments lend support to the theories of cognitive development which emphasize increased ability to process information as a function of age (e.g., Munsinger and Kessen, 1964). The findings are in accord with previous research (e.g., Munsinger and Kessen, 1964, unpublished results) which has shown developmental differences in the ability to process information in visual stimuli. The present experiments have demonstrated age related changes in the ability to process the information in numbers and thus have increased the range of situations about which developmental differences in information-processing ability are known. The information-processing analysis appears to be most applicable in tasks where the categories or stimulus attributes are well learned. If stimuli are used with which S is relatively unfamiliar, the characteristics of the stimuli must be coded before the information can be processed. The necessity of learning the characteristics of the stimuli may make an information-conservation task relatively difficult and less different from information-reduction tasks. The present series of studies also indicates that an information-reduction analysis is insufficient by itself to explain cognitive development; an understanding of the mechanisms of coding is also necessary. For example, the introduction of redundancy in the HELO task did not alter its information-reduction characteristics but did affect performance on it. It is assumed that the coding which occurred in the processing of redundant stimulation reduced the unpredictability of the sequence of stimuli. Coding appears to depend on, at least in part, finding patterns and regularity in incoming stimulation and grouping similar stimuli in categories. In addition, the effects of filtering on information condensation could
ABILITY
TO
PROCESS
383
INFORMATION
not be directly predicted from an information theory analysis but required an understanding of the characteristics of the tasks. Most information analyses have a tendency to ignore the effects of prior experience with the stimuli (e.g., Posner, 1964). Theoretical recognition of the transfer effects of relevant previous experience, which presumably results in increased ability to code information, is necessary. REFERENCES BRUNER, BRUNER,
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