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Effects of two levels of stimulus complexity upon hypothesis sampling systems among second and sixth grade children
IOURNAL
OF
EXPERIMENTAL
CHILD
Effects Complexity
PSYCHOLOGY
20,
of Two Levels
upon among
of Stimulus
Hypothesis Sampling Second and Sixth Grade
College
Systems
Children
BARRY GHOLSON AND SHELDON Hunler
(1975)
105-118
of lhe City
University
DANZIGER of New
York
Groups of second and sixth grade children each solved a series of discrimination-learning problems involving four and eight dimensions that contained blanktrial probes for the S’s hypothesis (H). There were significant effects of grade level on three dependent measures (learning, generating consistent H patterns, sampling locally consistent Hs). Main effects of stimulus complexity were significant on five measures (the three above, rejecting disconfirmed Hs, maintaining confirmed Hs). There were no interactions involving any of these measures. The hypothesis sampling system (Sy) observed in each problem was also determined. Among sixth grade Ss this measure was unaffected by stimulus complexity level. Second grade Ss generated logically structured Sys in 65% of four-dimensional, but only 30% of eight-dimensional problems. They generated stereotyped behaviors or unsystematic sequences of Hs in 70% of eight-dimensional, but only about 35% of four-dimensional problems. Detailed analyses revealed that among second grade Ss good information processors (in terms of four component processes above) usually imposed a logical structure on four-dimensional, but generated unsystematic sequences of Hs in many of eight-dimensional problems. Poor processors generated stereotyped behaviors in both four- and eight-dimensional problems.
The purpose of this study was to examine, within the conceptual framework of hypothesis (H) theory, the effects of two levels of stimulus complexity upon the performances of second and sixth grade children. Stimulus complexity is known to affect measures of learning in a wide variety of tasks among children of this age range (e.g., Lubker, 1967; Lubker & Spiker, 1966; Osler & Kofsky, 1965, 1966; Schantz, 1967; Tighe & Tighe, 1968; Wolff, 1967) and some previous research in which both age and complexity were variables suggests that the two might interact. Osler and Kofsky (1966) for example, in a study of concept learning, reported such an interaction among third and sixth grade chilThis research was supported by Grants 01714 and 10098 from the Research Foundation of the City University of New York, awarded to Barry Gholson. The writers thank Kathleen McConville for her aid in conducting the experiment. Requests for reprints should be sent to Barry Gholson, Department of Psychology, Memphis State University, Memphis, TN 38152. 105 Copyright Q 1975 by Academic Press, Inc. All rights of reproduction m any form reserved.
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dren. Schonebaum (1973), in a study of H coding, presented summary data that suggested an age by stimulus complexity interaction among third, fifth, and seventh grade children (p. 149), but statistical tests were not reported. The specific focus of the investigation was upon systems dictating H selection (Gholson, Levine & Phillips, 1972) and several component processes assumed to underlie the use of Hs in solving discriminationlearning problems (Erickson, 1968; Gregg & Simon, 1967; Levine, 1966, 1969; Trabasso & Bower, 1968). It was anticipated that the relationship among the H selection systems and processing components might be systematically related to stimulus complexity level (Osler & Kofsky, 1965, 1966). Each child was presented with a series of four- and eightdimensional discrimination problems in which blank-trial probes (Levine, 1966) were inserted between feedback trials in order to determine how Hs were used by Ss in attempting to achieve solution. Although eight-dimensional problems with blank-trial probes have been previously used with adult Ss (Eimas, 1970; Levine, 1969), earlier research with children has used only four-dimensional problems (cf., Eimas, 1969, 1970; Gholson ef al., 1972; Gholson, Phillips & Levine, 1973; Ingalls & Dickerson, 1969; Nuessle, 1972). METHOD
Subjects. The Ss were 30 second grade (mean CA = 7: 10) and 30 sixth grade (mean CA = 11: IO) children. They were drawn from public schools serving lower-middle class neighborhoods in the New York metropolitan area. Each child solved problems at two levels of stimulus complexity. Stimulus materials. Each S was presented individually with a series of two-alternative simultaneous discrimination-learning problems. Stimuli for one condition involved eight dimensions: form (alphabetic letters such as X vs. T), color (black vs. white), size (large vs. small), box position (under vs. over the letter), box volume (full vs. empty), border shape (square vs. circle), border number (one vs. two), and border design (solid vs. dashed). Four-dimensional stimuli were used in the other condition. These were constructed from various combinations of four of the eight dimensions described above. Eight four-dimensional problems used in the main experiment were constructed so that each of the eight dimensions occurred four times and no two problems involved the same combination of dimensions. The letters were located 2 in. apart on 5 x 8 cards. The large and small letters were 1.5 and % in. high. The outer border had a 3 in. diam (circle) or side (square). The inner border had a 2.75 in. diam or side. The outer borders were .5 in. apart on the cards.
HYPOTHESIS
SAMPLING
SYSTEMS
107
Stimuli for all problems were arranged with special restrictions (see Levine, 1966, 1969). Each problem involving four bivalued dimensions was arranged into two sets of four stimulus-pairs each. In each set each level of every dimension was exactly counterbalanced (i.e., paired twice) with each level of all other dimensions (Levin’s orthogonality criterion, 1966). One set was used for feedback trials. These were so arranged that any three consecutive feedback trials logically defined the solution. The other set was used to construct blank-trial (i.e., no feedback) probes. The stimulus-pairs used in each probe (4 trials in length) were arranged so that each of the eight simple Hs would yield a unique 3-l pattern of responses, i.e., three responses to one side and one response to the other. This eliminated any correspondence between the eight response patterns corresponding to simple Hs and patterns dictated by response-sets such as position alternation or perseveration (i.e., 2-2 or 4-0 patterns). Stimuli used in eight-dimensional problems were constructed according to the same criteria. Two sets of eight different stimulus pairs per problem were used (one set for feedback trials the others for blanks). In each set each level of every dimension was paired exactly four times with each level of every other dimension (see Levine, 1969, for more complete description). Stimulus-pairs used for feedback trials were so arranged that any four consecutive trials logically defined the solution. Stimuli in each blank-trial probe (five trials in length, see below) were arranged so that each of the 16 simple Hs would yield a unique 4-1 or a 3-2 response pattern. The two position-alternation patterns were excluded from the latter. Pretraining. In order to introduce the simple Hs, blank trials, feedback, etc., six pretaining problems preceded the main experiment. The first pretaining problem was a four-dimensional that consisted of 16 feedback trials. On presentation of the first stimulus pair the simple Hs were described by dimension (this was done at the outset of all problems), then S was instructed to choose the one of the two “pictures” he thought was correct. If S pointed to the correct side, he was told “Yes, (pointing) this one was correct.” If he pointed to the incorrect side he was told “No, this one was correct” (pointing to the correct side). In either case, the experimenter continued to point to the correct stimulus for approximately three set before turning to the next card (this procedure was used for feedback trials throughout the experiment). After completing the 16 trials, S was asked to verbalize the solution. If correct he was told “very good” and went on to the next problem. If S was wrong the problem was re-presented following a hint: He was told to try the two values on the solution dimension (e.g., if the solution was black S was told to try black or white to see if either was the answer). If the
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problem was still not solved the solution was stated and the next problem immediately presented. This procedure was continued throughout pretraining only. Every S was required to solve at least two of the six pretraining problems prior to the hint, but none was lost fat failure to meet this criterion. The second problem, consisting of 20 feedback trials, was an eightdimensional. Problem three, a four-dimensional, introduced blank trials in sets of two. All the remaining problems involved blank trials. In five (four-dimensional), and six problems four (eight-dimensional), (eight-dimensional) blank trials were in sets of three, four, and five, respectively. The experimenter always turned the card immediately after S’s response on each blank trial. Experimental problems. Each S then received an alternating series of eight four-dimensional and eight eight-dimensional problems. The fourdimensional problems were 31 trials in length with feedback presented every fifth trial from trial one through 31. Thus, there were seven feedback trials and six sets of four blank trials. The eight-dimensional problems were 43 trials long with feedback presented every sixth trial beginning with the first. Here there were eight feedback trials and seven sets of five blank trials. The reasons for the procedural discrepancies between four- and eight-dimensional problems were the following (see Levine, 1969, for details): (a) The difference in the number of blank trials within probes was required to equate the probability that random responses during probes would correspond to simple Hs (50% in each case); (b) the difference in total number of feedback trials was due to the necessity for one more such trial to logically define the solution in eightdimensional than four-dimensional problems. For each S the sequence of problems was randomly ordered within the restriction that the presentation of four- and eight-dimensional problems alternated. Solutions for each problem for each S were randomly selected (but no two consecutive problems had solutions drawn from the same dimension). At the completion of each problem the S was told “very good.” Following this the first stimulus pair for the next problem was presented and described by E. Every S served in three daily sessions each about 45 min in length. The six pretraining problems were presented in the first session. Half the 16 experimental problems were presented in each of the two remaining sessions. Each S was tested on 3 consecutive days when possible. In no case did the three sessions require more than 1 week. RESULTS
Since the four- and eight-dimensional problems required three and four feedback trials respectively to provide enough information for solution, a natural measure of learning was the percentage of correct responses
HYPOTHESIS
SAMPLING
109
SYSTEMS
on the subsequent feedback trials (four in each case). In the fourand eight-dimensional conditions the younger Ss were correct on 65.6 and 56.6% of these trials, while the sixth grade Ss were correct on 72.8 and 64.1%. Analysis of variance performed on scores revealed significant effects of both age, F(1,58) = 7.86, p < .05, and stimulus complexity, F(1,58) = 9.67, p < .05. The interaction did not approach significance (F < 1). The data of blank-trial probes fall into two classes: In four-dimensional problems, the eight 3-1 patterns of response dictated by the eight simple Hs and the eight patterns not consistent with these Hs (2-2 and 4-O patterns); in eight-dimensional problems, the sixteen 4-l and 3-2 patterns dictated by simple Hs and the remaining 16 inconsistent patterns. Thus, if Ss were generating responses randomly during blank-trial probes, 50% of their response patterns would be expected to correspond to simple Ils in both conditions. The percentage of consistent H patterns (P C H) ranged from 80.1 (1345/1680) for second grade Ss in eight-dimensional problems to 90.5 (1303/1440) for the older Ss in four-dimensional. Each of these values differed significantly from chance (p < .05, in each case). These percentages were comparable to those reported in earlier research and were high enough to justify the use of blank trials to probe for 5s’ Hs. These data, further divided according to whether the probe was preceded by a negative (P c HI F = -) or positive (P c HF = +) feedback are presented in Table 1. A three-factor analysis of variance, performed on percentages normalized (Guilford, 1954) by an arcsin transformation (this was done in all remaining analyses of variance), yielded significant effects of preceding feedback, grade level, and stimulus complexity, F(1,116) > 5.71, p < .05, in each case. The information processing conception of H theory stipulates that S retains his H when it is followed by positive feedback but rejects his H and selects a new one after negative feedback (Gregg & Simon, 1967; Levine, 1966, 1969; Trabasso & Bower, 1968). These assumptions were examined in the present study by looking at all cases in which two con-
THE
PERCENTAGES BLANK-TRIAL
OF CONSISTENT PROBES WHEN (F =
+)
TABLE 1 H PATTERNS THE
PREVIOUS
OR INCORRECT
(P c H) FEEDBACK (F =
-)
Four-dimensions Grade
level
(P c HIF
Grade
two
88.9
Grade
six
92.1
= +)
OBSERVED DURING WAS CORRECT
Eight-dimensions (P CHIF
75.9 88.5
= -)
(P cHIF 84.5 88.4
= +)
(P C HIF 75.8 81.4
= -)
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secutive blank-trial probes revealed consistent H patterns. The probabilities that two consecutive Hs were identical, P(H = Hi-J, when intervening feedback was positive (Fi = +) and negative (Fi = -) may be seen in Table 2 (all scores in this table based on more than 290 observations). A two-factor analysis of variance performed on probabilities of maintaining confirmed Hs revealed that only the stimulus complexity effect was significant, F(1,58) = 21.02, p < .05. A similar analysis performed on probabilites of maintaining disconfirmed Hs also revealed only a significant effect of stimulus complexity, F(1,58) = 12.23, p < .05, but the age effect approached significance (p < . 10). Neither interaction was significant (F < 1, in both cases). Another measure of the effects of feedback concerns the pool of Hs from which Ss resampled following errors. Various assumptions concerning this pool have been proposed, ranging from random sampling with replacement or “zero memory” (Restle, 1962), to global consistency or “perfect processing” (Gregg & Simon, 1967). Zero memory predicates that the probability of maintaining a disconfirmed H is .125 in four-dimensional and .0625 in eight-dimensional problems. Since the observed probabilities were higher than these values in three of the four conditions (i.e., second grade both conditions, sixth grade eight-dimensional problems, see Table 2), a measure of resampling was derived from the data. Consider a trial on which S chooses a stimulus containing the cues (Hs) “large, black, T, single border” and receives negative feedback. All four of these Hs would be disconfirmed, not just the H that dictated the response. This would reduce the set of possible correct Hs to four. A locally consistent H (Erickson, 1968) is drawn from among only those that were consistent with the stimulus that was positive on the previous feedback trial. If the zero memory assumption held, however, the Hs observed following negative feedback would be locally consistent only 50% of the time. The proportions of Hs that were locally consistent in each condition may be seen in the right side of Table 2. TABLE THE PROBABILITIES WHEN INTERVENING
P(Hi
THAT Two FEEDBACK AND THE
= ff-,lFi
= +)
Dimensions
2
CONSECUTIVE Hs WERE IDENTICAL, P(H, = H,+,), WAS POSITIVE (F, = +) OR NEGATIVE (Fi = -) LOCAL CONSISTENCY DATA
P(H,
= H,-,IF,
= -)
Dimensions
Local
consistency
Dimensions
Grade
level
4
8
4
8
4
8
Grade Grade
two six
.89 .93
.81 .87
.13 .05
.23 .I1
.74 .87
67 .76
HYPOTHESIS
SAMPLING
SYSTEMS
111
Each of these values differed from the 50% implied by zero memory (p < .05, in each case). Analysis of variance revealed significant effects of age, F(1,58) = 8.10, p < .05, and stimulus complexity, F(1,58) = 8.25, p < .05. The interaction was not significant (F < 1). Two different measures of the effects of negative feedback lead, then, to contradictory conclusions: The probability that S maintained a disconfirmed H suggested (in three of the four conditions) that Restle’s zero memory assumption held. The local consistency data, however, indicated that in all four conditions Ss usually rejected several of the logically disconfirmed Hs following negative feedback. Gholson et al. (1972) suggested that this contradiction could be resolved by analysis of protocols of individual Ss. In that study a few Ss adopted a primitive style of responding in which they frequently maintained the same H for many trials despite disconfirmation. Most Ss, however, almost always immediately abandoned a disconfirmed H. Examination of protocols of individual Ss in the present study revealed that 14 Ss (nine second grade, five sixth grade) accounted for 83% of the cases in which a disconfirmed H was maintained in fourdimensional problems, while 36 of the 60 Ss never maintained a disconfirmed H and the remaining 10 did so only once. Similarly, 27 Ss (17 second grade, 10 sixth grade) accounted for 91% of the cases in which a disconfirmed H was maintained in eight-dimensional problems, while 21 Ss never did so and the remaining 12 did so only once. One further dependent measure was examined here. This concerned the effect of stimulus complexity upon the hypothesis sampling system (Sy) observed in each problem. This analysis assumes that when S approaches a discrimination problem he attempts solution by sampling and rejecting Hs according to some systematic plan. Six different Sys were delineated in previous research. Three of these were characterized as strategies because they would, if followed perfectly, eventually lead to solution. The remaining three, chacterized as stereotypes, entailed the repeated manifestation of the same H despite disconfirmation (and never lead to solution). Just as Hs were inferred from sequences of choice responses during blank-trial probes, Sys were inferred from sequences of Hs. The details and rationale of this analysis were reported elsewhere (Gholson et al., 1972), so the description here is brief. The three strategies were called “focusing,” “dimension checking,” and “hypothesis checking.” Only problems in which H sampling was locally consistent were considered for these categories. When S uses the focusing Sy he begins the problem by simultaneously considering all possible Hs (eight in 4-dimensional, 16 in g-dimensional problems), and processes information perfectly, eliminating all logically disconfirmed Hs from his set after each feedback trial. In a four-dimensional problem (with orthogonal stimuli), for example, the set of globally consistent Hs
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is reduced to four following the first feedback trial, two Hs following the second, and a single H (the solution) following the third feedback trial. Dimension checking is less efficient. It assumes that S imagines a list of the dimensions, categorizes the two Hs onto each appropriately, then proceeds through the list testing one dimension at a time. Only one H per dimension (locally consistent at the time of selection) is manifested, since S recognizes that its complement was logically disconfirmed at the time of selection, e.g., S samples a locally consistent H from the size dimension, then if it is disconfirmed he rejects the size dimension as containing the solution and tries a locally consistent H from the color dimension, etc. When hypothesis checking is observed it is assumed the Hs are ordered into pairs on each dimension. The S then goes through the dimensions, systematically testing the Hs of each pair, e.g., he tries “large,” then “small” before rejecting the size dimension, etc. The stereotypes included “stimulus preference,” “position alternation,” and “position perseveration.” When stimulus preference is manifested the same H follows each feedback trial despite its disconfirmation. The two position oriented stereotypes were not considered further here (they occurred in only two problems), since they occur frequently only among kindergarten-age Ss (see Gholson et al., 1972, 1973; Rieber, 1969). Figure 1 contains the relative frequencies of each of the Sy sequences for each age group and stimulus complexity level. Due to restrictions dictated by criteria for categorization of problems as Sys not all problems could be used.l These curves were based on about 22% (208/960) of the problems. This was comparable to the 1530% obtained in earlier research. There are some possible sequences of Hs that Ss could manifest that do not fit the four Sy categories of Fig. 1. Consider a four-dimensional ’ Among second grade Ss 46 and 47 problems were used in the four and eight-dimension conditions, respectively. Corresponding numbers for sixth grade were 63 and 52. Several qualifications had to be met before a problem was categorized: (a) Since Sys are inferred from sequences of Hs, only problems in which S received negative feedback at the third (four-dimensions) or fourth (eight-dimensions) feedback trial were used: (b) only problems in which consistent Hs were manifested during the first three (four-dimensions) or four (eight-dimensions) blank-trial probes could be used; (c) each feedback trial response was required to be consistent with the immediately preceding H and S was required to maintain his H when he received positive feedback. Of the 752 problems that were not used in Fig. 1, approximately 65% contained positive feedback at the third feedback trial, thus did not meet the first criterion. About 25% did not meet the second criterion. The remaining 10% contained a shift and did not meet the third criterion. Given the three restrictions statistical corrections could be applied to the strategy frequencies. These corrections were required because a less sophisticated Sy can produce an H sequence identical to a more sophisticated Sy and be misinterpreted (a supplementary appendix containing this analysis can be obtained from the first author).
HYPOTHESIS
SAMPLING
113
SYSTEMS A GRADE
50
TWO
-
4-D
-
8-D
C-
-
-D
13 .’
a 60
GRADE
-
FO
D-‘h
H-al
SIX
S-P
RANDOM
sr
FIG. 1. The relative checking (H-Ch), and dimensional (4-D) and reflects the frequency
frequency of focusing (Fo). dimension checking (D-Ch), stimulus preference (S-P) for second and sixth grade eight-dimensional (8-D) problems. The category labeled of occurrence of unsystematic H sequences (see text).
hypothesis Ss in four“Random”
problem in which S received negative feedback on each of the first three feedback trials. The H sequences “large, black, small,” or “large, large, small,” for example, do not correspond to any of the Sy categories described above. In fact, fewer than 50% of the possible sequences of Hs that could be manifested in four-dimensional problems and fewer than 20% of the possible H sequences that Ss could manifest in eightdimensional problems correspond to the four Sy categories described above (position Sys were not considered). The category on the righthand side of Fig. I labeled (for convenience) “Random” reflects the frequencies of occurrence of these unsystematic H sequences. In previous research with elementary-school children about 15% of the problems involved such unsystematic sequences. This was comparable to the data of the present study in three of the four conditions. Among second grade Ss in the eight-dimension condition, however, 38% of the problems involved such sequences of Hs. Tests of independence performed on the data of Fig. 1 indicated a significant difference between
114 the two complexity
GHOLSON
AND
conditions
DANZIGER
among
second grade (x2(4) = 12.82,
p < .OS), but not sixth grade Ss (x2(4) = 1.63, p> .25). Further analyses
revealed significant differences between second and sixth grade Ss in eight-dimensional (x2(4) = 18.22, p < .05), but not four-dimensional problems (x2(4) = 4.53, p > .25). DISCUSSION
Results revealed significant main effects of grade level upon three dependent measures (learning, generating consistent H patterns, sampling locally consistent Hs). The findings were not expected, since two previous studies that compared elementary-school children (grades two, four, and six) using this methodology reported essentially identical performances across grades: Eimas (1969) found differences on only one of five dependent measures he examined (global consistency) and Gholson et al. (1972) on only one of six they examined (maintaining a confirmed H). There were two procedural discrepancies, however, that could account for these differences. First, each S in the present study was presented with problems involving two levels of stimulus complexity, while earlier research used only four-dimensional problems. Second, Ss in the present study were lower-middle class and attended urban schools. Earlier research used middle and upper-middle class children attending suburban schools. There were significant main effects of stimulus complexity level upon five dependent measures (learning, generating consistent Hs, rejecting disconfirmed Hs, sampling locally consistent Hs, maintaining confirmed Hs). In each case performance decreased when complexity increased. The effects on the learning measure were not unexpected, since others have reported similar results (e.g., Lubker, 1967; Osler & Kofsky, 1966; Shantz, 1967; Tighe & Tighe, 1966). Previous findings bearing on the remaining measures are tenuous, since data relevant to children of this age range have not been previously reported. Comparison of two separate studies using adult Ss that were reported by Levine (1969, 3A, 3B) revealed a 1% difference in favor of four-dimensional problems on two measures, but this (1%) difference was reversed on a third. Comparison of (adult) groups taken from two of Eimas’ studies (1969, Adult group; 1970, Expt 2, CON group) showed a small difference (4%) in favor of eightdimensional problems on the only comparable measure. It should be noted, however, that these measures were similarly affected in children, but not adults when the temporal relationship between stimulus information and feedback was altered (Gholson et al., 1973). The fact there was no age by stimulus complexity interaction involving any of the above measures was surprising in view of the Sy analysis. The Sys observed among sixth grade Ss were totally unaffected by
HYPOTHESIS
SAMPLING
SYSTEMS
115
stimulus complexity level (but fewer problems met the criteria for categorization in eight-dimensional problems, see footnote 2). Results of both complexity levels were essentially identical to those reported earlier for four-dimensional problems (Gholson et ul., 1972). Among second grade Ss, however, the analysis revealed striking differences. While the relative frequencies of the Sys generated by these Ss in four-dimensional problems were very similar to those obtained previously under similar conditions (Gholson et al., 1972, 1973), in eight-dimensional problems there was a dramatic shift. These Ss generated strategy Sys (focusing, dimension checking, hypothesis checking) in 65% of their four-dimensional, but only 30% in eight-dimensional problems. The stimulus preference stereotype was observed in 17% of their four-dimensional, but 32% of their eight-dimensional problems. Finally, in their four-dimensional problems these Ss generated unsystematic sequences of Hs at about the same level (15%) observed in previous studies and among sixth grade Ss here. But such “random” sequences of Ns occurred in 38% of their eight-dimensional problems. Several points should be considered in examining possible implications of these findings: Stimulus complexity level affected all dependent measures except Sys among sixth grade Ss, but included Sy effects also among the younger children. The absolute difference between performances in four-dimensional and eight-dimensional problems was very similar for both age levels on each dependent measure (except Sys). Performances of second grade Ss in four-dimensional problems were essentially identical to those of sixth grade Ss in eight-dimensional problems on every dependent measure examined. These considerations suggested two initial interpretations that might account for the patterns of results obtained. The first related to the patterns of differences among the two age groups in the four and eightdimensional problems. Reduced efficiency of such cognitive components of information processing as rejecting disconfirmed Hs, sampling locally consistent Hs, etc., does not affect the logical structure (Sy here) imposed to the task by sixth grade Ss. Among second grade children, however, an equivalent (absolute) reduction in efficiency of these same component processes might disorganize the logical structure imposed, leading to stereotyped responding or unsystematic H sequences. The second possibility was suggested by the similarities in performances of the younger Ss in four-dimensional to the older Ss in eightdimensional problems. It was possible that in order for S to impose a logical structure on the problem-solving task each component process must operate at some critical level, probably similar to that observed here among second grade Ss in four-dimensional problems (or sixth grade in eight-dimensional).
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In an attempt to evaluate these possibilities the second grade Ss were divided into two groups on the basis of their scores on four component measures in eight-dimensional problems. The criteria used to separate them were taken from mean scores on these component measures in four-dimensional problems. The component measures that were included were the probabilities of generating consistent Hs during probes, rejecting disconfirmed Hs, maintaining confirmed Hs, and local consistency (the learning measure was not used, since it is directly related to Sys). Those Ss whose scores in eight-dimensional problems were better than the mean performances of all second grade Ss in four-dimensional problems on at least three of the four component measures were considered “good” processors (12 Ss). Those Ss who showed scores lower than the criterion values on at least three of the four measures were considered “poor” processors (16 Ss). Two Ss did not fit the criteria and were not considered further. The Sys (or H sequences) of “good” and “poor” processors are presented in Table 3. The three categories on the right side of the table were the following: The column labeled “Strategies” included focusing, dimension checking, and hypothesis checking; “Stereotypes” refers to stimulus preference; the “Random” category refers to all sequences of Hs that did not correspond to any Sy (see above). The performances of good and poor processors shown in the right side of Table 3 suggest that neither of the interpretations considered above was in line with the data. Those (second grade) Ss who generally showed good performances in terms of the underlying components of information processing (in eight-dimensional problems) imposed a logical structure on the task involving four-dimensions. But even though these same TABLE THE
H
SEQUENCES
OF SECOND
DIMENSIONAL
GRADERS
PROBLEMS “GOOD” AND
Criteria: Mean scores of all second grade Ss in four-dimensional problems
WITH “POOR”
3 IN
FOUR-DIMENSIONAL Ss SEPARATED PROCESSORS
The Ss whose performantes in eight-dimensional problems were better and worse than criteria
P(H, P(H,
(P CH) = .83 = Hi_llFi = -) = .13 = HCIIFi = +) = .88 Local consistency = .74
(%)
SS
Better = 12 Ss (“good” processors) Worse = 16 Ss (“poor” processors)
4-D 8-D 4-D 8-D
EIGHT-
The H sequences observed in four-dimensional (4-D) and eight-dimensional (8-D) problems Strategies
Means
AND INTO
76 50 35 16
Stereotypes m 8 0 50 63
Random (%) 16 50 15 21
HYPOTHESIS
SAMPLING
SYSTEMS
117
component processes operated at high efficiency in eight-dimensional problems, the logical structure was frequently lost, resulting in Hs being generated in unsystematic (or random) sequences in half of these problems. The remaining Ss, among whom the underlying component processes were not efficiently used (in eight-dimensional problems), manifested mostly stereotyped behaviors in all problems. The reasons for the differential effects of stimulus complexity upon the H sequences observed among the two age groups and among the “good” and “poor” processors in the second grade children are not obvious and remain a problem for future research. The large proportion of unsystematic H sequences (labeled “random” above) among the younger children in eight-dimensional problems was also puzzling. While such sequences undoubtedly represent a more sophisticated approach to the task than stereotypic (stimulus preference) responding, how these unsystematic H sequences should be considered in relation to the strategy categories is unclear. This is, of course, a problem for future research and theory, but related literature suggests at least two possible interpretations of these sequences. Some important component of information processing, such as memory, that was not measured here might itself be related both to other component processes and Sys. Some Ss, for example, might have remembered (or sampled) only a small subset of the cues specified by E as possible solutions (Ingalls & Dickerson, 1969), or might have forgotten which Hs (or dimensions) had been previously tried and disconhrmed (Eimas, 1970; Neimark, Slotnick, & Ulrich, 1971). Another possibility is that our “Random” category reflected some imperfectly formed strategy or a strategy other than those considered here. Wandersman and Wandersman (1973) have provided some evidence that the latter might be the case (see also Bruner, Goodnow, & Austin, 1956). Some of their Ss, for example, apparently began each problem with a small subset of the possible Hs and attempted to focus. If this subset was exhausted prior to solution the S took a new subset and tried again, etc. Other Ss manifested H sequences that similarly approximated dimension checking and hypothesis checking. REFERENCES Bruner, J. S., Goodnow. J. J.. & Austin, G. A. A study of thinking. New York: Wiley, 1956. Eimas, P. D. A developmental study of hypothesis behavior and focusing. Journal of Experimental Child Psychology, 1969. 8, 160-172. Eimas, P. D. Effects of memory aids on hypothesis behavior and focusing in young children and adults. Journal of E.yperinzental Child Psychology, 1970. 10, 319-336. Erickson, J. R. Hypothesis sampling in concept identification. Journal of Experimental Psychology, 1968, 76, 12-18. Gholson, B., Levine, M., & Phillips. S. Hypothesis, strategies, and stereotypes in discrimination learning. Journal of Experimental Child Psychology, 1972. 13, 423446.
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Gholson, B., Phillips, S., & Levine, M. Effects of the temporal relationship of feedback and stimulus information upon discrimination-learning strategies. Journal of Experimental
Child
Psychology,
1973, 15, 425441.
Gregg, L. W., & Simon, H. A. Process models and stochastic theories of simple concept formation. Journal of Mathematical Psychology, 1967, 4, 246-276. Guilford, J. P. Psychometric methods. New York: McGraw-Hill, 1954. Ingalls, R. P., & Dickerson, D. J. Development of hypothesis behavior in human concept identification. Developmental Psychology, 1969, 1, 707-716. Levine, M. Hypothesis behavior by humans during discrimination learning. Journal of Experimental Psychology, 1966, 71, 331-338. Levine, M. Neo-noncontinuity theory. In G. Bower & J. T. Spence (Eds.), The psychology of learning and motivation. Vol. 3, New York: Academic, 1969. Lubker. B. J. Irrelevant stimulus dimensions and children’s performance on simultaneous discrimination problems. Child Development, 1967, 38, 119-125. Lubker, B. .I., & Spiker, C. C. The effects of irrelevant stimulus dimensions on children’s oddity-problem learning. Journal of Experimental Child Psychology, 1966,3, 207-215. Neimark, E., Slotnick, N. S., & Ulrich, T. Development of memorization strategies. Developmental Psychology, 1971, 5, 427432. Nuessle, W. Reflectivity as an influence on focusing behavior of children. Journal of Experimental Child Psychology, 1972, 14, 265-276. Osler, S. F., & Kofsky, E. Stimulus uncertainly as a variable in the development of conceptual ability. Journal of Experimental Child Psychology, 1965, 2, 264279. Osler, S. F., & Kofsky, E. Structure and strategy in concept learning. Journal of Experimental Child Psychology, 1966, 4, 198-209. Restle, F. The selection of strategies in cue learning. Psychological Review, 1962, 69, 329-343. Rieber, M. Hypothesis testing in children as a function of age. Developmental Psychology, 1969, 1, 389-395. Schonebaum, R. M. A developmental study of differences in initial coding and recoding of hypothesis information. Journal of Experimental Child Psychology, 1973, 16,413-423. Shantz, C. U. Effects of redundant and irrelevant information on children’s seriation ability. Journal of Experimental Child Psychology, 1967, 5, 208-222. Tighe, L. S., L Tighe, T. J. Discrimination learning: Two views in historical perspective. Psychological Bulletin, 1966, 66, 353-370. Tighe, T. J., & Tighe, L. S. Perceptual learning in the discrimination processes of children: An analysis of five variables in perceptual pretraining. Journal of Experimental Psychology, 1968, 77, 125-134. Trabasso, T., & Bower, G. Attention in learning. New York: Wiley, 1968. Wandersman, L. P., & Wandersman, A. H. Range of information processing and strategy selection in discrimination learning: A comparison of seventh grade and college students under conditions varying cognitive load. Paper presented at Eastern Psychological Association Meetings, Washington, D. C., 1973. Wolff, J. L. Concept attainment, intelligence, and stimulus complexity: An attempt to replicate Osler and Trautman (19611. Journal of Experimental Psychology, 1967, 73, 488-490. RECEIVED:
March 22, 1974;
REVISED:
July 1, 1974
OF
EXPERIMENTAL
CHILD
Effects Complexity
PSYCHOLOGY
20,
of Two Levels
upon among
of Stimulus
Hypothesis Sampling Second and Sixth Grade
College
Systems
Children
BARRY GHOLSON AND SHELDON Hunler
(1975)
105-118
of lhe City
University
DANZIGER of New
York
Groups of second and sixth grade children each solved a series of discrimination-learning problems involving four and eight dimensions that contained blanktrial probes for the S’s hypothesis (H). There were significant effects of grade level on three dependent measures (learning, generating consistent H patterns, sampling locally consistent Hs). Main effects of stimulus complexity were significant on five measures (the three above, rejecting disconfirmed Hs, maintaining confirmed Hs). There were no interactions involving any of these measures. The hypothesis sampling system (Sy) observed in each problem was also determined. Among sixth grade Ss this measure was unaffected by stimulus complexity level. Second grade Ss generated logically structured Sys in 65% of four-dimensional, but only 30% of eight-dimensional problems. They generated stereotyped behaviors or unsystematic sequences of Hs in 70% of eight-dimensional, but only about 35% of four-dimensional problems. Detailed analyses revealed that among second grade Ss good information processors (in terms of four component processes above) usually imposed a logical structure on four-dimensional, but generated unsystematic sequences of Hs in many of eight-dimensional problems. Poor processors generated stereotyped behaviors in both four- and eight-dimensional problems.
The purpose of this study was to examine, within the conceptual framework of hypothesis (H) theory, the effects of two levels of stimulus complexity upon the performances of second and sixth grade children. Stimulus complexity is known to affect measures of learning in a wide variety of tasks among children of this age range (e.g., Lubker, 1967; Lubker & Spiker, 1966; Osler & Kofsky, 1965, 1966; Schantz, 1967; Tighe & Tighe, 1968; Wolff, 1967) and some previous research in which both age and complexity were variables suggests that the two might interact. Osler and Kofsky (1966) for example, in a study of concept learning, reported such an interaction among third and sixth grade chilThis research was supported by Grants 01714 and 10098 from the Research Foundation of the City University of New York, awarded to Barry Gholson. The writers thank Kathleen McConville for her aid in conducting the experiment. Requests for reprints should be sent to Barry Gholson, Department of Psychology, Memphis State University, Memphis, TN 38152. 105 Copyright Q 1975 by Academic Press, Inc. All rights of reproduction m any form reserved.
106
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dren. Schonebaum (1973), in a study of H coding, presented summary data that suggested an age by stimulus complexity interaction among third, fifth, and seventh grade children (p. 149), but statistical tests were not reported. The specific focus of the investigation was upon systems dictating H selection (Gholson, Levine & Phillips, 1972) and several component processes assumed to underlie the use of Hs in solving discriminationlearning problems (Erickson, 1968; Gregg & Simon, 1967; Levine, 1966, 1969; Trabasso & Bower, 1968). It was anticipated that the relationship among the H selection systems and processing components might be systematically related to stimulus complexity level (Osler & Kofsky, 1965, 1966). Each child was presented with a series of four- and eightdimensional discrimination problems in which blank-trial probes (Levine, 1966) were inserted between feedback trials in order to determine how Hs were used by Ss in attempting to achieve solution. Although eight-dimensional problems with blank-trial probes have been previously used with adult Ss (Eimas, 1970; Levine, 1969), earlier research with children has used only four-dimensional problems (cf., Eimas, 1969, 1970; Gholson ef al., 1972; Gholson, Phillips & Levine, 1973; Ingalls & Dickerson, 1969; Nuessle, 1972). METHOD
Subjects. The Ss were 30 second grade (mean CA = 7: 10) and 30 sixth grade (mean CA = 11: IO) children. They were drawn from public schools serving lower-middle class neighborhoods in the New York metropolitan area. Each child solved problems at two levels of stimulus complexity. Stimulus materials. Each S was presented individually with a series of two-alternative simultaneous discrimination-learning problems. Stimuli for one condition involved eight dimensions: form (alphabetic letters such as X vs. T), color (black vs. white), size (large vs. small), box position (under vs. over the letter), box volume (full vs. empty), border shape (square vs. circle), border number (one vs. two), and border design (solid vs. dashed). Four-dimensional stimuli were used in the other condition. These were constructed from various combinations of four of the eight dimensions described above. Eight four-dimensional problems used in the main experiment were constructed so that each of the eight dimensions occurred four times and no two problems involved the same combination of dimensions. The letters were located 2 in. apart on 5 x 8 cards. The large and small letters were 1.5 and % in. high. The outer border had a 3 in. diam (circle) or side (square). The inner border had a 2.75 in. diam or side. The outer borders were .5 in. apart on the cards.
HYPOTHESIS
SAMPLING
SYSTEMS
107
Stimuli for all problems were arranged with special restrictions (see Levine, 1966, 1969). Each problem involving four bivalued dimensions was arranged into two sets of four stimulus-pairs each. In each set each level of every dimension was exactly counterbalanced (i.e., paired twice) with each level of all other dimensions (Levin’s orthogonality criterion, 1966). One set was used for feedback trials. These were so arranged that any three consecutive feedback trials logically defined the solution. The other set was used to construct blank-trial (i.e., no feedback) probes. The stimulus-pairs used in each probe (4 trials in length) were arranged so that each of the eight simple Hs would yield a unique 3-l pattern of responses, i.e., three responses to one side and one response to the other. This eliminated any correspondence between the eight response patterns corresponding to simple Hs and patterns dictated by response-sets such as position alternation or perseveration (i.e., 2-2 or 4-0 patterns). Stimuli used in eight-dimensional problems were constructed according to the same criteria. Two sets of eight different stimulus pairs per problem were used (one set for feedback trials the others for blanks). In each set each level of every dimension was paired exactly four times with each level of every other dimension (see Levine, 1969, for more complete description). Stimulus-pairs used for feedback trials were so arranged that any four consecutive trials logically defined the solution. Stimuli in each blank-trial probe (five trials in length, see below) were arranged so that each of the 16 simple Hs would yield a unique 4-1 or a 3-2 response pattern. The two position-alternation patterns were excluded from the latter. Pretraining. In order to introduce the simple Hs, blank trials, feedback, etc., six pretaining problems preceded the main experiment. The first pretaining problem was a four-dimensional that consisted of 16 feedback trials. On presentation of the first stimulus pair the simple Hs were described by dimension (this was done at the outset of all problems), then S was instructed to choose the one of the two “pictures” he thought was correct. If S pointed to the correct side, he was told “Yes, (pointing) this one was correct.” If he pointed to the incorrect side he was told “No, this one was correct” (pointing to the correct side). In either case, the experimenter continued to point to the correct stimulus for approximately three set before turning to the next card (this procedure was used for feedback trials throughout the experiment). After completing the 16 trials, S was asked to verbalize the solution. If correct he was told “very good” and went on to the next problem. If S was wrong the problem was re-presented following a hint: He was told to try the two values on the solution dimension (e.g., if the solution was black S was told to try black or white to see if either was the answer). If the
108
GHOLSON
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DANZIGER
problem was still not solved the solution was stated and the next problem immediately presented. This procedure was continued throughout pretraining only. Every S was required to solve at least two of the six pretraining problems prior to the hint, but none was lost fat failure to meet this criterion. The second problem, consisting of 20 feedback trials, was an eightdimensional. Problem three, a four-dimensional, introduced blank trials in sets of two. All the remaining problems involved blank trials. In five (four-dimensional), and six problems four (eight-dimensional), (eight-dimensional) blank trials were in sets of three, four, and five, respectively. The experimenter always turned the card immediately after S’s response on each blank trial. Experimental problems. Each S then received an alternating series of eight four-dimensional and eight eight-dimensional problems. The fourdimensional problems were 31 trials in length with feedback presented every fifth trial from trial one through 31. Thus, there were seven feedback trials and six sets of four blank trials. The eight-dimensional problems were 43 trials long with feedback presented every sixth trial beginning with the first. Here there were eight feedback trials and seven sets of five blank trials. The reasons for the procedural discrepancies between four- and eight-dimensional problems were the following (see Levine, 1969, for details): (a) The difference in the number of blank trials within probes was required to equate the probability that random responses during probes would correspond to simple Hs (50% in each case); (b) the difference in total number of feedback trials was due to the necessity for one more such trial to logically define the solution in eightdimensional than four-dimensional problems. For each S the sequence of problems was randomly ordered within the restriction that the presentation of four- and eight-dimensional problems alternated. Solutions for each problem for each S were randomly selected (but no two consecutive problems had solutions drawn from the same dimension). At the completion of each problem the S was told “very good.” Following this the first stimulus pair for the next problem was presented and described by E. Every S served in three daily sessions each about 45 min in length. The six pretraining problems were presented in the first session. Half the 16 experimental problems were presented in each of the two remaining sessions. Each S was tested on 3 consecutive days when possible. In no case did the three sessions require more than 1 week. RESULTS
Since the four- and eight-dimensional problems required three and four feedback trials respectively to provide enough information for solution, a natural measure of learning was the percentage of correct responses
HYPOTHESIS
SAMPLING
109
SYSTEMS
on the subsequent feedback trials (four in each case). In the fourand eight-dimensional conditions the younger Ss were correct on 65.6 and 56.6% of these trials, while the sixth grade Ss were correct on 72.8 and 64.1%. Analysis of variance performed on scores revealed significant effects of both age, F(1,58) = 7.86, p < .05, and stimulus complexity, F(1,58) = 9.67, p < .05. The interaction did not approach significance (F < 1). The data of blank-trial probes fall into two classes: In four-dimensional problems, the eight 3-1 patterns of response dictated by the eight simple Hs and the eight patterns not consistent with these Hs (2-2 and 4-O patterns); in eight-dimensional problems, the sixteen 4-l and 3-2 patterns dictated by simple Hs and the remaining 16 inconsistent patterns. Thus, if Ss were generating responses randomly during blank-trial probes, 50% of their response patterns would be expected to correspond to simple Ils in both conditions. The percentage of consistent H patterns (P C H) ranged from 80.1 (1345/1680) for second grade Ss in eight-dimensional problems to 90.5 (1303/1440) for the older Ss in four-dimensional. Each of these values differed significantly from chance (p < .05, in each case). These percentages were comparable to those reported in earlier research and were high enough to justify the use of blank trials to probe for 5s’ Hs. These data, further divided according to whether the probe was preceded by a negative (P c HI F = -) or positive (P c HF = +) feedback are presented in Table 1. A three-factor analysis of variance, performed on percentages normalized (Guilford, 1954) by an arcsin transformation (this was done in all remaining analyses of variance), yielded significant effects of preceding feedback, grade level, and stimulus complexity, F(1,116) > 5.71, p < .05, in each case. The information processing conception of H theory stipulates that S retains his H when it is followed by positive feedback but rejects his H and selects a new one after negative feedback (Gregg & Simon, 1967; Levine, 1966, 1969; Trabasso & Bower, 1968). These assumptions were examined in the present study by looking at all cases in which two con-
THE
PERCENTAGES BLANK-TRIAL
OF CONSISTENT PROBES WHEN (F =
+)
TABLE 1 H PATTERNS THE
PREVIOUS
OR INCORRECT
(P c H) FEEDBACK (F =
-)
Four-dimensions Grade
level
(P c HIF
Grade
two
88.9
Grade
six
92.1
= +)
OBSERVED DURING WAS CORRECT
Eight-dimensions (P CHIF
75.9 88.5
= -)
(P cHIF 84.5 88.4
= +)
(P C HIF 75.8 81.4
= -)
110
GHOLSON
AND
DANZIGER
secutive blank-trial probes revealed consistent H patterns. The probabilities that two consecutive Hs were identical, P(H = Hi-J, when intervening feedback was positive (Fi = +) and negative (Fi = -) may be seen in Table 2 (all scores in this table based on more than 290 observations). A two-factor analysis of variance performed on probabilities of maintaining confirmed Hs revealed that only the stimulus complexity effect was significant, F(1,58) = 21.02, p < .05. A similar analysis performed on probabilites of maintaining disconfirmed Hs also revealed only a significant effect of stimulus complexity, F(1,58) = 12.23, p < .05, but the age effect approached significance (p < . 10). Neither interaction was significant (F < 1, in both cases). Another measure of the effects of feedback concerns the pool of Hs from which Ss resampled following errors. Various assumptions concerning this pool have been proposed, ranging from random sampling with replacement or “zero memory” (Restle, 1962), to global consistency or “perfect processing” (Gregg & Simon, 1967). Zero memory predicates that the probability of maintaining a disconfirmed H is .125 in four-dimensional and .0625 in eight-dimensional problems. Since the observed probabilities were higher than these values in three of the four conditions (i.e., second grade both conditions, sixth grade eight-dimensional problems, see Table 2), a measure of resampling was derived from the data. Consider a trial on which S chooses a stimulus containing the cues (Hs) “large, black, T, single border” and receives negative feedback. All four of these Hs would be disconfirmed, not just the H that dictated the response. This would reduce the set of possible correct Hs to four. A locally consistent H (Erickson, 1968) is drawn from among only those that were consistent with the stimulus that was positive on the previous feedback trial. If the zero memory assumption held, however, the Hs observed following negative feedback would be locally consistent only 50% of the time. The proportions of Hs that were locally consistent in each condition may be seen in the right side of Table 2. TABLE THE PROBABILITIES WHEN INTERVENING
P(Hi
THAT Two FEEDBACK AND THE
= ff-,lFi
= +)
Dimensions
2
CONSECUTIVE Hs WERE IDENTICAL, P(H, = H,+,), WAS POSITIVE (F, = +) OR NEGATIVE (Fi = -) LOCAL CONSISTENCY DATA
P(H,
= H,-,IF,
= -)
Dimensions
Local
consistency
Dimensions
Grade
level
4
8
4
8
4
8
Grade Grade
two six
.89 .93
.81 .87
.13 .05
.23 .I1
.74 .87
67 .76
HYPOTHESIS
SAMPLING
SYSTEMS
111
Each of these values differed from the 50% implied by zero memory (p < .05, in each case). Analysis of variance revealed significant effects of age, F(1,58) = 8.10, p < .05, and stimulus complexity, F(1,58) = 8.25, p < .05. The interaction was not significant (F < 1). Two different measures of the effects of negative feedback lead, then, to contradictory conclusions: The probability that S maintained a disconfirmed H suggested (in three of the four conditions) that Restle’s zero memory assumption held. The local consistency data, however, indicated that in all four conditions Ss usually rejected several of the logically disconfirmed Hs following negative feedback. Gholson et al. (1972) suggested that this contradiction could be resolved by analysis of protocols of individual Ss. In that study a few Ss adopted a primitive style of responding in which they frequently maintained the same H for many trials despite disconfirmation. Most Ss, however, almost always immediately abandoned a disconfirmed H. Examination of protocols of individual Ss in the present study revealed that 14 Ss (nine second grade, five sixth grade) accounted for 83% of the cases in which a disconfirmed H was maintained in fourdimensional problems, while 36 of the 60 Ss never maintained a disconfirmed H and the remaining 10 did so only once. Similarly, 27 Ss (17 second grade, 10 sixth grade) accounted for 91% of the cases in which a disconfirmed H was maintained in eight-dimensional problems, while 21 Ss never did so and the remaining 12 did so only once. One further dependent measure was examined here. This concerned the effect of stimulus complexity upon the hypothesis sampling system (Sy) observed in each problem. This analysis assumes that when S approaches a discrimination problem he attempts solution by sampling and rejecting Hs according to some systematic plan. Six different Sys were delineated in previous research. Three of these were characterized as strategies because they would, if followed perfectly, eventually lead to solution. The remaining three, chacterized as stereotypes, entailed the repeated manifestation of the same H despite disconfirmation (and never lead to solution). Just as Hs were inferred from sequences of choice responses during blank-trial probes, Sys were inferred from sequences of Hs. The details and rationale of this analysis were reported elsewhere (Gholson et al., 1972), so the description here is brief. The three strategies were called “focusing,” “dimension checking,” and “hypothesis checking.” Only problems in which H sampling was locally consistent were considered for these categories. When S uses the focusing Sy he begins the problem by simultaneously considering all possible Hs (eight in 4-dimensional, 16 in g-dimensional problems), and processes information perfectly, eliminating all logically disconfirmed Hs from his set after each feedback trial. In a four-dimensional problem (with orthogonal stimuli), for example, the set of globally consistent Hs
112
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DANZIGER
is reduced to four following the first feedback trial, two Hs following the second, and a single H (the solution) following the third feedback trial. Dimension checking is less efficient. It assumes that S imagines a list of the dimensions, categorizes the two Hs onto each appropriately, then proceeds through the list testing one dimension at a time. Only one H per dimension (locally consistent at the time of selection) is manifested, since S recognizes that its complement was logically disconfirmed at the time of selection, e.g., S samples a locally consistent H from the size dimension, then if it is disconfirmed he rejects the size dimension as containing the solution and tries a locally consistent H from the color dimension, etc. When hypothesis checking is observed it is assumed the Hs are ordered into pairs on each dimension. The S then goes through the dimensions, systematically testing the Hs of each pair, e.g., he tries “large,” then “small” before rejecting the size dimension, etc. The stereotypes included “stimulus preference,” “position alternation,” and “position perseveration.” When stimulus preference is manifested the same H follows each feedback trial despite its disconfirmation. The two position oriented stereotypes were not considered further here (they occurred in only two problems), since they occur frequently only among kindergarten-age Ss (see Gholson et al., 1972, 1973; Rieber, 1969). Figure 1 contains the relative frequencies of each of the Sy sequences for each age group and stimulus complexity level. Due to restrictions dictated by criteria for categorization of problems as Sys not all problems could be used.l These curves were based on about 22% (208/960) of the problems. This was comparable to the 1530% obtained in earlier research. There are some possible sequences of Hs that Ss could manifest that do not fit the four Sy categories of Fig. 1. Consider a four-dimensional ’ Among second grade Ss 46 and 47 problems were used in the four and eight-dimension conditions, respectively. Corresponding numbers for sixth grade were 63 and 52. Several qualifications had to be met before a problem was categorized: (a) Since Sys are inferred from sequences of Hs, only problems in which S received negative feedback at the third (four-dimensions) or fourth (eight-dimensions) feedback trial were used: (b) only problems in which consistent Hs were manifested during the first three (four-dimensions) or four (eight-dimensions) blank-trial probes could be used; (c) each feedback trial response was required to be consistent with the immediately preceding H and S was required to maintain his H when he received positive feedback. Of the 752 problems that were not used in Fig. 1, approximately 65% contained positive feedback at the third feedback trial, thus did not meet the first criterion. About 25% did not meet the second criterion. The remaining 10% contained a shift and did not meet the third criterion. Given the three restrictions statistical corrections could be applied to the strategy frequencies. These corrections were required because a less sophisticated Sy can produce an H sequence identical to a more sophisticated Sy and be misinterpreted (a supplementary appendix containing this analysis can be obtained from the first author).
HYPOTHESIS
SAMPLING
113
SYSTEMS A GRADE
50
TWO
-
4-D
-
8-D
C-
-
-D
13 .’
a 60
GRADE
-
FO
D-‘h
H-al
SIX
S-P
RANDOM
sr
FIG. 1. The relative checking (H-Ch), and dimensional (4-D) and reflects the frequency
frequency of focusing (Fo). dimension checking (D-Ch), stimulus preference (S-P) for second and sixth grade eight-dimensional (8-D) problems. The category labeled of occurrence of unsystematic H sequences (see text).
hypothesis Ss in four“Random”
problem in which S received negative feedback on each of the first three feedback trials. The H sequences “large, black, small,” or “large, large, small,” for example, do not correspond to any of the Sy categories described above. In fact, fewer than 50% of the possible sequences of Hs that could be manifested in four-dimensional problems and fewer than 20% of the possible H sequences that Ss could manifest in eightdimensional problems correspond to the four Sy categories described above (position Sys were not considered). The category on the righthand side of Fig. I labeled (for convenience) “Random” reflects the frequencies of occurrence of these unsystematic H sequences. In previous research with elementary-school children about 15% of the problems involved such unsystematic sequences. This was comparable to the data of the present study in three of the four conditions. Among second grade Ss in the eight-dimension condition, however, 38% of the problems involved such sequences of Hs. Tests of independence performed on the data of Fig. 1 indicated a significant difference between
114 the two complexity
GHOLSON
AND
conditions
DANZIGER
among
second grade (x2(4) = 12.82,
p < .OS), but not sixth grade Ss (x2(4) = 1.63, p> .25). Further analyses
revealed significant differences between second and sixth grade Ss in eight-dimensional (x2(4) = 18.22, p < .05), but not four-dimensional problems (x2(4) = 4.53, p > .25). DISCUSSION
Results revealed significant main effects of grade level upon three dependent measures (learning, generating consistent H patterns, sampling locally consistent Hs). The findings were not expected, since two previous studies that compared elementary-school children (grades two, four, and six) using this methodology reported essentially identical performances across grades: Eimas (1969) found differences on only one of five dependent measures he examined (global consistency) and Gholson et al. (1972) on only one of six they examined (maintaining a confirmed H). There were two procedural discrepancies, however, that could account for these differences. First, each S in the present study was presented with problems involving two levels of stimulus complexity, while earlier research used only four-dimensional problems. Second, Ss in the present study were lower-middle class and attended urban schools. Earlier research used middle and upper-middle class children attending suburban schools. There were significant main effects of stimulus complexity level upon five dependent measures (learning, generating consistent Hs, rejecting disconfirmed Hs, sampling locally consistent Hs, maintaining confirmed Hs). In each case performance decreased when complexity increased. The effects on the learning measure were not unexpected, since others have reported similar results (e.g., Lubker, 1967; Osler & Kofsky, 1966; Shantz, 1967; Tighe & Tighe, 1966). Previous findings bearing on the remaining measures are tenuous, since data relevant to children of this age range have not been previously reported. Comparison of two separate studies using adult Ss that were reported by Levine (1969, 3A, 3B) revealed a 1% difference in favor of four-dimensional problems on two measures, but this (1%) difference was reversed on a third. Comparison of (adult) groups taken from two of Eimas’ studies (1969, Adult group; 1970, Expt 2, CON group) showed a small difference (4%) in favor of eightdimensional problems on the only comparable measure. It should be noted, however, that these measures were similarly affected in children, but not adults when the temporal relationship between stimulus information and feedback was altered (Gholson et al., 1973). The fact there was no age by stimulus complexity interaction involving any of the above measures was surprising in view of the Sy analysis. The Sys observed among sixth grade Ss were totally unaffected by
HYPOTHESIS
SAMPLING
SYSTEMS
115
stimulus complexity level (but fewer problems met the criteria for categorization in eight-dimensional problems, see footnote 2). Results of both complexity levels were essentially identical to those reported earlier for four-dimensional problems (Gholson et ul., 1972). Among second grade Ss, however, the analysis revealed striking differences. While the relative frequencies of the Sys generated by these Ss in four-dimensional problems were very similar to those obtained previously under similar conditions (Gholson et al., 1972, 1973), in eight-dimensional problems there was a dramatic shift. These Ss generated strategy Sys (focusing, dimension checking, hypothesis checking) in 65% of their four-dimensional, but only 30% in eight-dimensional problems. The stimulus preference stereotype was observed in 17% of their four-dimensional, but 32% of their eight-dimensional problems. Finally, in their four-dimensional problems these Ss generated unsystematic sequences of Hs at about the same level (15%) observed in previous studies and among sixth grade Ss here. But such “random” sequences of Ns occurred in 38% of their eight-dimensional problems. Several points should be considered in examining possible implications of these findings: Stimulus complexity level affected all dependent measures except Sys among sixth grade Ss, but included Sy effects also among the younger children. The absolute difference between performances in four-dimensional and eight-dimensional problems was very similar for both age levels on each dependent measure (except Sys). Performances of second grade Ss in four-dimensional problems were essentially identical to those of sixth grade Ss in eight-dimensional problems on every dependent measure examined. These considerations suggested two initial interpretations that might account for the patterns of results obtained. The first related to the patterns of differences among the two age groups in the four and eightdimensional problems. Reduced efficiency of such cognitive components of information processing as rejecting disconfirmed Hs, sampling locally consistent Hs, etc., does not affect the logical structure (Sy here) imposed to the task by sixth grade Ss. Among second grade children, however, an equivalent (absolute) reduction in efficiency of these same component processes might disorganize the logical structure imposed, leading to stereotyped responding or unsystematic H sequences. The second possibility was suggested by the similarities in performances of the younger Ss in four-dimensional to the older Ss in eightdimensional problems. It was possible that in order for S to impose a logical structure on the problem-solving task each component process must operate at some critical level, probably similar to that observed here among second grade Ss in four-dimensional problems (or sixth grade in eight-dimensional).
116
GHOLSON
AND
DANZIGER
In an attempt to evaluate these possibilities the second grade Ss were divided into two groups on the basis of their scores on four component measures in eight-dimensional problems. The criteria used to separate them were taken from mean scores on these component measures in four-dimensional problems. The component measures that were included were the probabilities of generating consistent Hs during probes, rejecting disconfirmed Hs, maintaining confirmed Hs, and local consistency (the learning measure was not used, since it is directly related to Sys). Those Ss whose scores in eight-dimensional problems were better than the mean performances of all second grade Ss in four-dimensional problems on at least three of the four component measures were considered “good” processors (12 Ss). Those Ss who showed scores lower than the criterion values on at least three of the four measures were considered “poor” processors (16 Ss). Two Ss did not fit the criteria and were not considered further. The Sys (or H sequences) of “good” and “poor” processors are presented in Table 3. The three categories on the right side of the table were the following: The column labeled “Strategies” included focusing, dimension checking, and hypothesis checking; “Stereotypes” refers to stimulus preference; the “Random” category refers to all sequences of Hs that did not correspond to any Sy (see above). The performances of good and poor processors shown in the right side of Table 3 suggest that neither of the interpretations considered above was in line with the data. Those (second grade) Ss who generally showed good performances in terms of the underlying components of information processing (in eight-dimensional problems) imposed a logical structure on the task involving four-dimensions. But even though these same TABLE THE
H
SEQUENCES
OF SECOND
DIMENSIONAL
GRADERS
PROBLEMS “GOOD” AND
Criteria: Mean scores of all second grade Ss in four-dimensional problems
WITH “POOR”
3 IN
FOUR-DIMENSIONAL Ss SEPARATED PROCESSORS
The Ss whose performantes in eight-dimensional problems were better and worse than criteria
P(H, P(H,
(P CH) = .83 = Hi_llFi = -) = .13 = HCIIFi = +) = .88 Local consistency = .74
(%)
SS
Better = 12 Ss (“good” processors) Worse = 16 Ss (“poor” processors)
4-D 8-D 4-D 8-D
EIGHT-
The H sequences observed in four-dimensional (4-D) and eight-dimensional (8-D) problems Strategies
Means
AND INTO
76 50 35 16
Stereotypes m 8 0 50 63
Random (%) 16 50 15 21
HYPOTHESIS
SAMPLING
SYSTEMS
117
component processes operated at high efficiency in eight-dimensional problems, the logical structure was frequently lost, resulting in Hs being generated in unsystematic (or random) sequences in half of these problems. The remaining Ss, among whom the underlying component processes were not efficiently used (in eight-dimensional problems), manifested mostly stereotyped behaviors in all problems. The reasons for the differential effects of stimulus complexity upon the H sequences observed among the two age groups and among the “good” and “poor” processors in the second grade children are not obvious and remain a problem for future research. The large proportion of unsystematic H sequences (labeled “random” above) among the younger children in eight-dimensional problems was also puzzling. While such sequences undoubtedly represent a more sophisticated approach to the task than stereotypic (stimulus preference) responding, how these unsystematic H sequences should be considered in relation to the strategy categories is unclear. This is, of course, a problem for future research and theory, but related literature suggests at least two possible interpretations of these sequences. Some important component of information processing, such as memory, that was not measured here might itself be related both to other component processes and Sys. Some Ss, for example, might have remembered (or sampled) only a small subset of the cues specified by E as possible solutions (Ingalls & Dickerson, 1969), or might have forgotten which Hs (or dimensions) had been previously tried and disconhrmed (Eimas, 1970; Neimark, Slotnick, & Ulrich, 1971). Another possibility is that our “Random” category reflected some imperfectly formed strategy or a strategy other than those considered here. Wandersman and Wandersman (1973) have provided some evidence that the latter might be the case (see also Bruner, Goodnow, & Austin, 1956). Some of their Ss, for example, apparently began each problem with a small subset of the possible Hs and attempted to focus. If this subset was exhausted prior to solution the S took a new subset and tried again, etc. Other Ss manifested H sequences that similarly approximated dimension checking and hypothesis checking. REFERENCES Bruner, J. S., Goodnow. J. J.. & Austin, G. A. A study of thinking. New York: Wiley, 1956. Eimas, P. D. A developmental study of hypothesis behavior and focusing. Journal of Experimental Child Psychology, 1969. 8, 160-172. Eimas, P. D. Effects of memory aids on hypothesis behavior and focusing in young children and adults. Journal of E.yperinzental Child Psychology, 1970. 10, 319-336. Erickson, J. R. Hypothesis sampling in concept identification. Journal of Experimental Psychology, 1968, 76, 12-18. Gholson, B., Levine, M., & Phillips. S. Hypothesis, strategies, and stereotypes in discrimination learning. Journal of Experimental Child Psychology, 1972. 13, 423446.
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Gholson, B., Phillips, S., & Levine, M. Effects of the temporal relationship of feedback and stimulus information upon discrimination-learning strategies. Journal of Experimental
Child
Psychology,
1973, 15, 425441.
Gregg, L. W., & Simon, H. A. Process models and stochastic theories of simple concept formation. Journal of Mathematical Psychology, 1967, 4, 246-276. Guilford, J. P. Psychometric methods. New York: McGraw-Hill, 1954. Ingalls, R. P., & Dickerson, D. J. Development of hypothesis behavior in human concept identification. Developmental Psychology, 1969, 1, 707-716. Levine, M. Hypothesis behavior by humans during discrimination learning. Journal of Experimental Psychology, 1966, 71, 331-338. Levine, M. Neo-noncontinuity theory. In G. Bower & J. T. Spence (Eds.), The psychology of learning and motivation. Vol. 3, New York: Academic, 1969. Lubker. B. J. Irrelevant stimulus dimensions and children’s performance on simultaneous discrimination problems. Child Development, 1967, 38, 119-125. Lubker, B. .I., & Spiker, C. C. The effects of irrelevant stimulus dimensions on children’s oddity-problem learning. Journal of Experimental Child Psychology, 1966,3, 207-215. Neimark, E., Slotnick, N. S., & Ulrich, T. Development of memorization strategies. Developmental Psychology, 1971, 5, 427432. Nuessle, W. Reflectivity as an influence on focusing behavior of children. Journal of Experimental Child Psychology, 1972, 14, 265-276. Osler, S. F., & Kofsky, E. Stimulus uncertainly as a variable in the development of conceptual ability. Journal of Experimental Child Psychology, 1965, 2, 264279. Osler, S. F., & Kofsky, E. Structure and strategy in concept learning. Journal of Experimental Child Psychology, 1966, 4, 198-209. Restle, F. The selection of strategies in cue learning. Psychological Review, 1962, 69, 329-343. Rieber, M. Hypothesis testing in children as a function of age. Developmental Psychology, 1969, 1, 389-395. Schonebaum, R. M. A developmental study of differences in initial coding and recoding of hypothesis information. Journal of Experimental Child Psychology, 1973, 16,413-423. Shantz, C. U. Effects of redundant and irrelevant information on children’s seriation ability. Journal of Experimental Child Psychology, 1967, 5, 208-222. Tighe, L. S., L Tighe, T. J. Discrimination learning: Two views in historical perspective. Psychological Bulletin, 1966, 66, 353-370. Tighe, T. J., & Tighe, L. S. Perceptual learning in the discrimination processes of children: An analysis of five variables in perceptual pretraining. Journal of Experimental Psychology, 1968, 77, 125-134. Trabasso, T., & Bower, G. Attention in learning. New York: Wiley, 1968. Wandersman, L. P., & Wandersman, A. H. Range of information processing and strategy selection in discrimination learning: A comparison of seventh grade and college students under conditions varying cognitive load. Paper presented at Eastern Psychological Association Meetings, Washington, D. C., 1973. Wolff, J. L. Concept attainment, intelligence, and stimulus complexity: An attempt to replicate Osler and Trautman (19611. Journal of Experimental Psychology, 1967, 73, 488-490. RECEIVED:
March 22, 1974;
REVISED:
July 1, 1974