Strategy modeling, age, and information-processing efficiency

JOURNAL

OF EXPERIMENTAL

CHILD

Strategy Modeling,

PSYCHOLOGY

26, 58-70 (1978)

Age, and Information-Processing Efficiency SHANNA

RICHMAN

University

of Georgia

AND BARRY Memphis

GHOLSON State

University

Second- and sixth-grade children were exposed to observational learning procedures prior to presentation of a series of discrimination problems that contained probes for hypotheses between consecutive feedback trials. One group at each age level observed a complex, perfect information-processing strategy called focusing that is rarely shown spontaneously by elementary school children. Another group saw no explicit strategy, but the component skills necessary to generate any strategy were demonstrated. In a third condition, children observed a strategy called dimension checking, which is the modal strategy shown spontaneously by children of this age range. Results indicated that sixth graders performed equally well under each tape exposure condition while second graders showed their best performance after observation of the dimension-checking tape and poorest after exposure to the focusing tape. Performance was intermediate when basic skills were demonstrated. Results were discussed in relation to developmental learning theory and Piagetian theory.

Problem-solving behavior may be conceived of as the systematic application of response rules that were previously learned or that emerge as a consequence of interaction with the elements of a problem. While such rules may be learned through selective reinforcement, rule learning is often accomplished through imitation or observational learning. In fact, Bandura (1971) argues that vicarious learning often results in faster acquisition than does selective reinforcement. A number of studies have demonstrated that observational procedures can lead children to abstract, apply, and generalize complex problem-solving rules in a variety of tasks (e.g., Henderson, Swanson, & Zimmerman, 1975; Liebert & Swenson, 1972; Rosenthal & Zimmerman, 1976; Zimmerman & Rosenthal, 1974). This paper is based on a Department of Psychology, The second author was the ShannaRichman, Department

doctoral dissertation completed by the first author City University of New York, New York, New principle advisor. Requests for reprints should be ofPsychology, Fordham University, Bronx, New York

0022-0695/78/0261-0058$02.00/O Copyright 0 1978 by Academic Press, Inc. All rights of reproduction in any form reserved.

58

in the York. sent to 10458.

STRATEGY

MODELING

59

Problem-solving strategies have been elicited from college students (e.g., Brunner, Goodnow, & Austin, 1956) and evidence is accumulating that strategies that are not manifest by children under standard conditions can be elicited through modeling (e.g., Denny, 1972; Mosher & Homsby, 1966). Within the context of hypothesis theory, Levine (1966, 1975) and his colleagues have delineated the kinds of strategies that adults and children of various ages use in conventional discrimination-learning problems. This research has established clear developmental differences in the efficiency and complexity of the problem-solving strategies that are spontaneously manifested. Related work has attempted to elucidate the conditions under which subjects of different ages employ the basic elements or component skills that underlie such strategies (e.g., Eimas, 1970; Gholson & Danziger, 1975; Gumer & Levine, 1971; Ingalls & Dickerson, 1969; Offenbach, 1974). The present study examined second- and sixth-grade children’s vicarious acquisition of complex problem-solving strategies, called hypothesissampling systems (see Gholson, Levine, & Phillips, 1972; Levine, 1975), and the component skills or “precursor” behaviors, such as correct use of feedback and locally consistent hypothesis sampling (Erickson, 1968), that underlie such systems. The traditional blank-trials methodology (Levine, 1966) was employed. The strategies of primary interest were called “focusing” and “dimension checking.” Focusing involves perfect information processing. The subject considers all possible hypotheses at the outset of a problem and eliminates from the set held all logically disconfirmed cues after each feedback trial. Dimension checking is less efficient. The subject appropriately categorizes the two cues in each dimension and systematically proceeds through the list manifesting one hypothesis from each of the dimensions. The subject recognizes that the complementary cue of that dimension is logically disconfirmed at the time of selection. Other systems include “hypothesis checking” and “stimulus preference.” The hypothesis checking strategy involves ordering the cues into pairs on each dimension and trying both hypotheses of each pair, one after the other. Stimulus preference involves manifestation of the same hypothesis following each feedback trial despite its repeated disconfirmation. The latter system is referred to as a srereotype because it will never, in principle, lead to solution. Previous research has established that elementary school children show little focusing during problem-solving, dimension checking in about half their problems, and both hypothesis checking and stimulus preference in 10% to 20% (cf. Gholson et al., 1972; Phillips & Levine, 1975). These percentages were obtained by grouping by experimental condition, all problems identified as exemplifying a given system (e.g., dimension checking). Corrrections for misclassifications are then applied to the tentatively cataloged systems (see Levine, 1975, Appendix for complete details). In

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AND GHOLSON

the present study the focusing strategy was modeled to investigate whether observational learning procedures could elicit a strategy that is infrequently shown spontaneously by either second- or sixth-grade children. In another condition no strategy was explicitly modeled, but the component skills necessary to generate any strategy were demonstrated. In a third condition each child observed dimension checking, the modal system shown spontaneously by children of this age range. METHOD

Subjects The subjects were 72 second-grade (mean age = 7.8, range = 7.049) and 72 sixth-grade children (mean age = 11.9, range = 11.2- 12.9) drawn from public schools serving middle class areas of New York City. Twenty four children (12 boys, 12 girls) were randomly assigned to each of three tape-exposure conditions at each grade level. There were no significant age differences among children in the three conditions at either grade level. Materials Each child was individually presented with a series of 11 bi-valued, fourdimensional discrimination problems that contained blank-trial probes (i.e., no feedback following responses) for hypotheses (see Gholson et al., 1972; Levine, 1966,1975). The four dimensions were alphabetic letter (e.g., X vs T), color (e.g., red vs blue), size (3.8 vs 1.9 cm in height), and line position (line over the top vs line under the bottom of the letter). Blank-trial probes, four trials in length, were inserted between consecutive feedback trials. Stimulus combinations presented on feedback trials were internally orthogonal so that any three consecutive trials logically specified the solution to the problem (Levine, 1966). Procedure Each child was first presented a series of four pretraining problems to familiarize him or her with the task requirements, that is, possible solutions, feedback delivery, blank-trials, etc. At the outset of each problem the eight possible solutions were described by dimension to the child. Following the child’s choice responses on feedback trials, the experimenter said either “Correct, the answer is in this picture” or “Wrong, the answer is in this picture” and pointed to the correct stimulus array for about three sec. On blank trials, the card was turned as soon as the child responded. Immediately following pretraining, the child and experimenter watched one of three IO-min videotapes. All three tapes contained exactly the same visual script. Stimulus cards and an experimenter’s and modeling subject’s hands were all that were visible to the subject. The model solved four

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61

different problems, each with a different set of stimuli, sequence of choice responses, feedback pattern, and a solution drawn from a different dimension. On the focusing tape, each of the four problems was solved by a model who explicitly stated the operations involved in the use of a focusing strategy and provided a summary rule. On the dimension-checking tape, the soundtrack provided a description of the operations and a summary rule for the dimension-checking strategy. The scripts for the tapes were pretested on second graders to insure comprehension of both vocabulary and syntax, On the component skills tape, verbalizations were limited to the same introduction and feedback sequences as on the other two tapes and the modeling subject stated her hypothesis before each blank-trial probe. She illustrated the other component skills by silently choosing the stimulus complex containing the stated hypothesis, choosing a new locally consistent hypothesis after disconfirmation, and maintaining a confirmed hypothesis. No strategy or summary rule was stated at any time. After the videotape was finished the child was presented with a series of seven experimental problems each 36 trials in length (eight feedback trials, seven blank-trial probes each four trials in length). The total time required for each child was about 50 min. RESULTS AND DISCUSSION

In order for any strategy to be shown in a problem, four precursor behaviors must obtain during the first three blank-trial probes and feedback trials. The child must (a) manifest a pattern of choice responses consistent with one of the eight cues (i.e., an hypothesis) during each blanktrial probe, (b) maintain an hypothesis when it is confirmed, (c) change the hypothesis when it is disconfirmed, and (d) following negative feedback choose his or her next hypothesis from among the cues in the positive stimulus array (local consistency). Thus, the consistency of these behaviors would be expected to provide an estimate of the children’s strategic approaches to the problems. Table 1 presents the mean percentages observed on all four precursor measures for the two age levels under each observational condition. These percentages are based upon all the data of each problem. Each of the four measures was analyzed by a fixed, age x tape x sex analysis of variance performed on percentages normalized by arcsin transformations (Guilford, 1954). No main effects of sex were significant. Several two- and three-way interactions involving sex were significant, but these will not be discussed, beyond giving theF values, since the interactions followed no interpretable pattern. Analysis of the percentages of consistent hypotheses manifested during probes showed significant main effects of tape [F(2,132) = 3.61, p < .05] and age [F(1,132) = 44.98, p < .05]. Two interactions were sig-

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AND

GHOLSON

nificant: age by tape [F(2,132) = 3.32, p < .05] and age by tape by sex [F(2,132) = 3.32, p < .05]. Scheffe tests indicated that there were no differences among the sixth graders associated with tape-exposure condition. Second graders manifested significantly fewer hypotheses than sixth graders after exposure to the focusing and component-skills tapes, but they did not differ from the sixth graders after exposure to the dimensionchecking tape. Second-grade children who viewed the dimension-checking tape produced significantly more hypotheses than those exposed to the focusing tape. Performance of those exposed to the component-skills tape was intermediate and did not differ significantly from either of the others. Since previous research indicates that dimension-checking is the modal strategy produced by elementary school children of all ages (about half their problems) when no opportunity for observational learning is provided, facilitation of performance following exposure to the dimensionchecking tape was not surprising. It was surprising, however, that second graders showed relative decrements in performance after exposure to the component skills and focusing tapes, while the sixth graders performed equally well in all three conditions. As will be seen below, this pattern was seen on all dependent measures examined. Analysis of the percentages of hypotheses that were maintained when confirmed showed significant main effects of tape [F(2,132) = 5.84, p < .05] and age [F(1,132) = 26.84, p < .05]. The significant interactions included tape by sex [F(2,132) = 4.101 and tape by age by sex [F(2,132) = 5.521. Similarly, analysis of the percentages of hypotheses that were maintained following disconfirmation revealed a main effect of age [F(1,132) = 9.88, p < .05] and a tape by sex interaction [F(2,132) = 3.641. Inspection of Table 1 reveals, however, that the sixth graders in the three conditions performed equally well on both measures; while second graders exposed to the dimension-checking tape showed considerably better performance than those who viewed the focusing tape in both cases. The local consistency data revealed two significant main effects and one significant interaction: tape [F(2,132) = 3.24, p < .05], age [F(1,132) = 36.081, and age by tape [F(2,132) = 5.24,~ < .05]. Scheffe tests indicated that second graders exposed to the focusing tape showed significantly less local consistency when compared to those shown the dimension-checking tape. Again, there were no differences due to tape-exposure condition among the sixth graders. In summary, then, statistical treatment of the precursor data revealed a fairly consistent pattern of findings. Among the sixth graders, performance of children in the three conditions was nearly identical on each of the four measures and there were no significant differences. Among the second graders, performance was markedly lower after exposure to the focusing tape than after exposure to the dimension-checking tape, and

STRATEGY

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MODELING

TABLE

1

MEAN PERCENTAGES OF HYPOTHESES, MAINTAINED CONFIRMED AND DISCONFIRMED HYPOTHESES, AND LOCALLY CONSISTENT SAMPLING FOR SECOND AND SIXTH GRADERS AFTER EXPOSURE TO EACH MODELING TAPE

Tape exposure condition 2nd Grade

6th Grade

Percent hypotheses

Focusing Dimension checking Component skills

77.29 92.48 82.22

Focusing Dimension checking Component skills

96.55 96.04 95.93

Percent maintained confirmed hypotheses

Focusing Dimension checking Component skills

73.65 92.93 79.04

Focusing Dimension checking Component skills

93.69 96.80 96.40

Percent maintained disconfirmed hypotheses

Focusing Dimension checking Component skills

13.39 4.26 6.73

Focusing Dimension checking Component skills

1.42 2.03 0.92

Percent locally consistent hypotheses

Focusing Dimension checking Component skills

76.15 89.71 93.61

Focusing Dimension checking Component skills

97.30 97.63 96.10

the differences reached significance on two of the four measures. Performance was generally intermediate following exposure to the component-skills tape. With the exception of the second-grade children exposed to the focusing tape, the findings here are in close agreement with data previously reported in research involving elementary school children that involved no opportunity for observational learning (e.g., Eimas, 1970; Ingalls & Dickerson, 1969; Offenbach, 1974). This comparability indicates that with regard to precursor behaviors, the observational procedures did little more than reinforce and consolidate those that already existed. That such skills might be fragile among the younger children, however, is suggested by the finding that exposure to the complex focusing strategy promoted contusion rather than consolidation. TABLE THE

PERCENTAGE

AFTER

2

OF PROBLEMS SOLVED BY SECOND AND SIXTH EXPOSURE TO EACH OF THE MODELING TAPES

GRADERS

Tape exposure condition Grade

Focusing

Dimension checking

Component skills

Second Sixth

23.16 76.37

45.14 69.45

22.72 71.86

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AND GHOLSON

One would predict, of course, that performances on the precursor measures would be closely correlated with the probabilities that the children achieved solution in their problems. The solution criterion adopted was correct feedback-trial response on trials five through eight and manifestation of the correct hypothesis in each of the intervening probes. The sixth graders solved 72% of their problems and the second graders 30%. Table 2 presents the mean percentages of problems solved by each group. Analysis of variance showed a significant effect of age [F(1,132) = 90.93, p < .05] and an age by tape interaction [F(2,132) = 5.23, p < .05]. Scheffe tests revealed that sixth graders solved significantly more problems than second graders in each condition. There were no significant differences among the sixth graders, but the younger children exposed to the dimension-checking tape solved significantly more problems than those in either of the remaining groups (which did not differ from each other). Thus, the pattern of results obtained on this measure was consistent with the pattern in the precursor data. The final dependent measures involved the systems data. Since a system is inferred from the child’s responses on each of the first three feedback trials and the blank-trial probe that follows each (a total of 1.5 trials), various kinds of information-processing errors result in behaviors that do not fit any such category (see above). Sixth graders generated the necessary precursor behaviors during these first 15 trials in many more problems (80%) than did the second graders (56%). The percentages of categorizable problems for each age group after exposure to the different tapes may be seen in Table 3. Analysis of variance showed significant effects ofage [F(1,132) = 37.32,~ < .05], tape [F(2,132) = 7.53,~ < .05], and their interaction [F(2,132) = 7.57,~ < .05]. Scheffe tests indicated that sixth graders did not differ as a function of tape-exposure condition. The percentage of problems in which second graders avoided processing errors was significantly greater after exposure to the dimension-checking tape than either the focusing or component-skills tape. The latter two groups did not differ from each other. Here again, only those second graders who viewed the dimension-checking tape performed at about the same level (73%) as the sixth graders (78% to 83%). TABLE PERCENTAGE SIXTH

3

OF CATEGORIZEABLE PROBLEMS FOR SECOND GRADERS AFTER EXPOSURE TO EACH TAPE

AND

Tape exposure condition Grade

Focusing

Dimension checking

Second Sixth

43.16 78.19

73.47 83.73

Component skills 53.33 78.04

STRATEGY

65

MODELING

Figs. 1 and 2 present the distributions of hypothesis-sampling systems observed among second and sixth graders, respectively, after exposure to each of the observational learning conditions. In addition to the systems previously defined, children sometimes show appropriate performances on each of the precursor measures; but their sequence of hypotheses does not fit any discernable system category (e.g., red, large, blue). This sequence would be classified unsystematic in that it does not fit any system category. As may be seen in Fig. 1, little focusing was shown by the second graders of any condition. Dimension-checking occurred more frequently than any other system among all three groups. Since the component-skills tape demonstrated the precursor behaviors but presented no specific strategy, children in this condition were expected to impose their own cognitive organization on the problem-solving task. The 50% dimension checking obtained among these children was remarkably consistent with previous research involving second graders given no opportunity for observational learning (e.g., Gholson & Danziger, 1975; Gholson et al., 1972; Phillips & Levine, 1975). Exposure to the dimension-checking tape was not, however, completely redundant, since children in this condition showed 17% more dimension-checking than did those exposed to the component-skills tape. They also avoided processing errors in 20% more problems (Table 3), solved 23% more problems (Table 2), and generally showed better performances on the precursor measures. These

n

FOGUSINGTAPE D”ENSlON-O+EOlONG TAPE

0

CGMFGNEWTSGILLS TAPf

HYPOTHESIS -SAMPLING

SYSTEMS

FIG. 1. The relative frequency of occurrence of each hypothesis among second graders after exposure to the modeling tapes.

sampling

system

RICNMAN

AND GHOLSON

TAPE n FOOUNYO OIYWSION-C4EOKNQ TAPE q CSNPOUENT SKlllS TKPE

0

FOCUSING

STEREOTYPES HYPOTHESIS -SAMPLGtG

UNSYGYEYATIC

SYSTEMS

FIG. 2. The relative frequency of occurrence of each hypothesis among sixth graders after exposure to the modeling tapes.

sampling

system

findings suggest that exposure to the dimension-checking tape served to consolidate existing organization of both the precursor processes and the strategy. The data of Fig. 2 shows that sixth graders manifested some focusing in each observational learning condition, and maximally after exposure to the focusing tape (57%). Performance of this latter group was approximately the same as has been observed previously among college students, but dramatically higher than that shown spontaneously by sixth graders (cf. Gholson et al., 1972; Levine, 1975; Phillips & Levine, 1975). Children exposed to the component-skills tape showed dimensionchecking in almost half of their problems (47%); but, unexpectedly, they also showed a considerable amount of focusing (41%). A possible explanation for this latter finding is that observation of the model suggested to some children a plan which was available, but would not otherwise have been considered. The sixth graders exposed to the dimension-checking tape showed 67% dimension-checking and 22% focusing. In general, sixth graders showed either focusing or dimension checking in about 90% of their problems. The amount of focusing decreased and dimension-checking increased in going from the focusing to the component-skills to the dimension-checking tape. A few unsystematic hypothesis sequences were observed in each condition (about 8%), but considerably fewer than were manifested by the second graders (about 18%).

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A strategy manifest by a subject cannot, by definition, contain an information-processing error. For any of the three strategies to be inferred, the child must perform perfectly on the four precursor measures, at least until after the third hypothesis. Additionally, a child who manifests strategies is more likely to solve the problem, precisely because he or she responds correctly on the precursors. The four precursor measures and the percentage of solved problems can together be considered measures of information-processing efficiency. The number of strategies (focusing, dimension-checking, and hypothesis-checking) that a given child manifests should then be largely predictable from performance on the efficiency variables. Table 4 shows the intercorrelation matrix between the number of strategies shown by each of the children and their performance on the five information-processing efficiency measures. The percentage of problems solved produced the highest correlation with the number of strategies manifest (.719). Stepwise multiple regression analyses revealed that the percentage of hypotheses generated during blank-trial probes was the second most important predictor. The multiple correlation coefficient for these two taken together is .782. The remaining three variables did not significantly increase the multiple correlation coefficient and therefore were not stepped in. GENERAL

DISCUSSION

AND CONCLUSIONS

The striking finding was the differential effects of the three observational learning conditions upon children of the two age groups. Among the sixth graders, tape-exposure condition had no effect on either the precursor measures, the number of problems solved, or the number of problems in which strategies were manifested. The systems analysis revealed, however, that the proportion of problems in which the most efficient and complex strategy (focusing) was manifested was closely related to observational condition. Sixth graders exposed to the focusing tape showed 57% focusing; those who viewed the component-skills tape showed 47%; and the dimension-checking tape produced only 22%. The younger children, on the other hand, showed an exactly opposite pattern of performances. Those exposed to the dimensionchecking tape manifested many more problems involving strategies (mostly dimension-checking) than did those in either of the other groups. Children in the component-skills condition showed intermediate performance and those who observed the focusing tape showed the poorest performance of all. Unambiguous interpretation of these findings will have to await future research and theory, since previous work with second- and sixth-grade children in hypothesis-testing tasks of the type used here has

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RICHMAN

AND GHOLSON TABLE

INTERCORRELATION

4

MATRIX BETWEEN NUMBER OF STRATEGIES MANIFEST MEASURES OF INFORMATION-PROCESSING EFFICIENCY

AND FIVE

Independent variables

Independent variables 1 2 36 4 5

Dependent variable” (1) Number of Hypotheses strategies manifest .666 .554 - ,433 .476 .719

,655 -.398 .507 .577

(2) Maintained confirmed hypotheses

(3) Maintainedb disconfirmed hypotheses

(4) Locally consistent hypotheses

(5) Problems solved

-.232 ,310 ,563

-.595 -.367

.356

1.080

Note. The correlation matrices for each age/tape-exposure condition show the same general pattern as the overall matrix but there are moderate differences. The individual matrices are available on request from the senior author. n The maximum number of strategies = seven for any one child. b The negatives correlations for variable three are expected because an efficient processer will choose a new hypothesis after disconfirmation.

indicated that their performances are very similar in terms of both precursor measures and systems data (e.g., Gholson et al., 1972; Eimas, 1969; Phillips & Levine, 1975). Current developmental learning theory postulates that the child is an active force directing his or her attention, coding, memory, and inference processes. The child’s thinking and information-processing capacities are seen as continuously expanding and differentiating with time and experience. The present findings are not inconsistent with such a view; but we tentatively suggest an interpretation more congenial to Piaget’s stage-dependent cognitive theory (e.g., Inhelder & Piaget, 1958, 1964; Piaget, 1952, 1968). It has been shown elsewhere (Gholson, O’Connor, & Stem, 1976) that Piaget’s theory implies that concrete operational children (average age range about 6 to 11 years) have acquired the cognitive capabilities necessary to generate dimension-checking (or hypothesis-checking) strategies, but lack the requisite cognitive organization to focus. Focusing, according to this theory, requires formal operational thought, which is usually not achieved until age 11 or 12. The second graders exposed to the focusing tape may have attempted to understand and implement this strategy; but if, as Piaget’s theory suggests, they lacked the cognitive capabilities necessary to perform all the operations involved, confusion and disorganization would have resulted (see Beilin, 1971 for discussion of this issue) and led to generally poorer performance. Many of the sixth graders, on the other hand, might have

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been formal operational or transitional to formal thought (Inhelder & Piaget, 1958), and thus able to both understand and implement the more complex stratgey. REFERENCES processes. In A. Bandura (Ed.), Psychological Chicago: Aldine-Atherton, 1971. Beilin, H. The training and acquisition of logical operations. In M. F. Rosskopf, L. P. Steffe, & S. Taback (Eds.), Piagetian cognitive-development research and mathematical education. Washington: National Council of Teachers of Mathematics, 197 1. Bruner, J. S., Goodnow, J. J., & Austin, G. A. A Study of thinking. New York: John Wiley, 1956. Denny, D. Modeling and eliciting effects upon conceptual strategies. Child Development, 1972,43, 810-823. Eimas, P. D. A developmental study of hypothesis behavior and focusing. Journal of Experimental Child Psychology, 1969, 8, 160-172. Erickson, J. R. Hypothesis sampling in concept identification. Journal of Experimental Psychology, 1968, 76, 12-18. Gholson, B., & Danzinger, S. Effects of two levels of stimulus complexity upon hypothesis sampling systems among second- and sixth-grade children. Journal of Experimental Child Psychology, 1975, 20, 105- 118. Gholson, B., Levine, M., & Phillips, S. Hypotheses, strategies, and stereotypes in discrimination learning. Journal of Experimental Child Psychology, 1972, 13, 423-446. Gholson, B., & McConville, K. Effects of stimulus differentiation training upon hypotheses, strategies, and stereotypes in discrimination learning among kindergarten children. Journal of Experimental Child Psychology, 1974, 18, 81-97. Gholson, B., O’Connor, J., & Stem, I. Hypothesis sampling systems among preoperational and concrete operational kindergarten children. Journal of Experimental Child Psychology, 1976, 21, 61-76. Guilford, J. P. Psychometric methods. New York: McGraw-Hill, 1954. Gumer, E., & Levine, M. The missing dimension in concept learning. Journal of Experimental Psychology, 1971, 90, 39-44. Henderson, R. W., Swanson, R., & Zimmerman, B. J. Training seriation responses in young children through televised modeling of hierarchically sequenced rule components. American Educational Research Journal, 1975, 12, 479-489. Ingalls, R. P., & Dickerson, D. S. Development of hypothesis behavior in human concept formation. Developmental Psychology, 1969, 1, 707-716. Inhelder, B., & Piaget, J. The growth of logical thinking from childhood to adolescence. New York: Basic Books, 1958. Inhelder, B., & Piaget, J. The early growth of logic in the child. New York: Norton, 1964. Levine, M. Hypothesis behavior by humans during discrimination learning. Journal of Experimental Psychology, 1966, 71, 331-338. Levine, M. A cognitive theory of learning: research on hypothesis testing. Hillsdale, N. J.: Lawrence Erlbaum Associates, 1975. Liebert, R., & Swenson, S. A. Abstraction, inference, and the process of imitative learning. Developmental Psychology, 1972, 5, 500-504. Mosher, F., & Homsby, J. R. On asking questions. In J. Bruner (Ed.), Studies in cognitive growth. New York: John Wiley, 1966. Bandura,

A. Analysis

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Offenbach, S. I. A developmental study of hypothesis testing and cue selection strategies. Developmental Psychology, 1974, 10, 484-490. Phillips, S., & Levine, M. Probing for hypotheses with adults and children: Blank trials and introtacts. Journal of Experimental Psychology: General, 1975, 104, 327-354. Piaget, J. The child’s conception of number. New York: Humanities, 1952. Piaget, J. Six psychological studies. New York: Vintage, 1968. Rosenthal, T. L., & Zimmerman, B. J. Organization and stability of transfer in vicarious concept attainment. Child Development, 1976,47, 110-117. Zimmerman, B. J., & Rosenthal, T. L. Observational learning of rule-governed behavior by children. Psychological Bulletin, 1974, 81, 29-42. RECEIVED: November 29, 1976; REVISED: August 24, 1977.