Journal of Educational Psychology1981, Vol. 73, No. 1,93-105

Copyright 1981 by the American Psychological Association, Inc.0022-0fifi3/81/7;i01-009:i$00,7,r)

Modeling and Attributional Effects on Children'sAchievement: A Self-Efficacy Analysis

Dale H. SchunkStanford University

Children showing low arithmetic achievement received either modeling of di-vision operations or didactic instruction, followed by a practice period. Dur-ing practice, half of the children in each instructional treatment received ef-fort attribution for success and difficulty. Both instructional treatments en-hanced division persistence, accuracy, and perceived efficacy, but cognitivemodeling produced greater gains in accuracy. In the context of competencydevelopment, effort attribution had no significant effect either on perceivedefficacy or on arithmetic performance. Perceived efficacy was an accuratepredictor of arithmetic performance across levels of task difficulty and modesof treatment. The treatment combining modeling with effort attribution pro-duced the highest congruence between efficacy judgment and performance.

The theory of self-efficacy postulatesthat different modes of influence changebehavior in part by creating and strength-ening self-percepts of efficacy (Bandura,1977, in press). Perceived self-efficacy isconcerned with judgments of one's capabilityto perform given activities. In this view,perceived self-efficacy affects behavioralfunctioning by influencing people's choice ofactivities, effort expenditure, and persistencein the face of difficulties. The higher theperceived efficacy, the greater is the sus-tained involvement in the activities andsubsequent achievement.

Achievement behavior has been analyzedhistorically in terms of level of aspiration and

This article is based on a doctoral dissertation sub-mitted to the School of Education, Stanford University.This research was supported in part by Public HealthResearch Grant M-5162 to Albert Bandura from theNational Institute of Mental Health and by the Dis-sertation Support Fund through the Stanford Univer-sity School of Education.

I would like to express my appreciation to AlbertBandura, John Gaa, and Elizabeth Ghatala for theirthoughtful comments on an earlier version of this articleand to Joseph Carbonari for his assistance with the dataanalysis. Thanks are also due to Denis Cronin, BillDwan, Judy Ekstrand, Teri Garza, Al Guzman, PatKyllonen, and Jane Padilla for their aid, and to theprincipals, teachers, and students of the participatingschools in the Palo Alto, California, Unified SchoolDistrict.

Requests for reprints should be sent to Dale H.Schunk, who is now at the Foundations of EducationDepartment, University of Houston, Houston, Texas77004.

outcome expectations. Although thesedifferent concepts involve an expectancyelement, they differ in important ways fromthe concept of self-efficacy. Level of aspi-ration is concerned with the goals people setfor themselves (Lewin, 1935; Lewin, Dembo,Festinger, & Sears, 1944). Aspirations differfrom judgments of what one can do in thehere and now. Outcome expectations referto subjective estimates that a given behaviorwill lead to certain outcomes (Rotter, 1954;Rotter, Chance, & Phares, 1972). Self-per-cepts of efficacy are concerned with judg-ments of one's capability to produce a givenpattern of behavior.

Results of a series of studies designed toalter phobic behavior provide support forself-efficacy theory (Bandura & Adams,1977; Bandura, Adams, & Beyer, 1977;Bandura, Adams, Hardy, & Howells, 1980).Self-efficacy is enhanced by informationconveyed through such different treatmentmodalities as actual performance, modeling,and systematic desensitization. Self-per-cepts of efficacy predict not only level ofbehavioral change resulting from differenttreatments but also variations in coping be-havior by persons receiving the same type oftreatment and even specific performanceattainments by individuals on differenttasks.

Because self-efficacy is postulated to havemotivational effects, it seems especiallyrelevant to children's achievement behavior.Children who have a strong sense of efficacy

94 DALE H. SCHUNK

in a given subject matter would be expectedto exhibit strong achievement strivings. Incontrast, children who perceive themselvesas inefficacious should tend to shunachievement tasks or to engage in themhalfheartedly and to give up readily in theface of obstacles. It follows from this theorythat experiences designed to raise self-effi-cacy should also enhance persistence andskillful performance.

The purpose of this study was to test hy-potheses from self-efficacy theory in the areaof children's arithmetic achievement. First,the theory predicts that providing subjectswith modeling, guided performance, cor-rective feedback, and self-directed masterywill foster development of skills and self-efficacy (Bandura, 1977). One group ofchildren therefore received cognitive mod-eling of problem-solving strategies withguided participation (Bandura, 1976; Mei-chenbaum, 1977). In this approach, chil-dren observed adult models verbalize aloudthe cognitive operations they were using asthey engaged in arithmetic problem-solvingactivities. The children then practicedapplying what they had learned with cor-rective modeling of any constituent opera-tions they failed to grasp. The comparisonapproach involved didactic instruction.Children received the same explanatorymaterial, the same amount of practiceapplying the knowledge they had gained, andthe same feedback of accuracy, but they didnot receive any modeling of cognitive oper-ations. Although it was expected thatdidactic instruction would also raise skillsand self-efficacy, there is evidence to suggestthat with young children, providing ex-planatory principles with exemplary mod-eling is more effective in developing cogni-tive skills than is providing explanatoryprinciples alone (Rosenthal & Zimmerman,1978).

The second set of hypotheses concernedthe effects on achievement of effort attri-bution for success and difficulty providedduring the process of competency develop-ment. According to attribution theory, as-cribing past achievement outcomes to effortis hypothesized to have motivational effects.To the extent that children come to believethat increased effort produces success, they

should persist longer in the face of difficul-ties and thereby increase the level of theirperformance (Weiner, 1977,1979; Weiner etal., 1971). Attribution training programs inthe area of achievement behavior oftenconcentrate on changing children's causalascriptions of failure from lack of ability tolack of effort. Results of such studies gen-erally show that attributing failure to a lackof effort increases persistence (Andrews &Debus, 1978; Chapin & Dyck, 1976; Dweck,1975).

Self-efficacy theory predicts that activeengagement in activities promotes devel-opment of skills and self-efficacy (Bandura,in press). Viewed from this perspective,effort attribution can affect self-efficacy andthe development of skills to the extent thatit results in more active efforts. But suchefforts require minimal skills to start with.In the present context, effort attributionmay have different effects in the two in-structional treatments. If children canapply operations more readily throughmodeling, then effort attribution could leadto more active engagement with further skilland self-efficacy gains. On the other hand,if skills develop slower with didactic in-struction, the validity of effort attribu-tionespecially for difficultymay be mit-igated in favor of other factors, such as taskdifficulty. Developmental evidence indi-cates an increasing ability to integrate in-formation from several sources in arriving atcausal attribution (Guttentag & Longfellow,1977).

A third set of hypotheses tested in thepresent study concerned the relationship ofself-efficacy to subsequent achievement. Ina series of studies with adult phobics, Ban-dura and his colleagues (Bandura & Adams,1977; Bandura, Adams, & Beyer, 1977) foundthat subjects accurately appraise theircapabilities to perform given activities, asrevealed by high agreement between self-efficacy judgment and subsequent perfor-mance at the level of individual tasks. Ac-curate appraisal is important, sincemisjudgments in either direction can havenegative consequences. Persons who over-estimate their capabilities are apt to becomedemoralized through repeated task failure,whereas those who underestimate their

MODELING AND ATTR1BUTIONAI, EFFECTS OF ACHIEVEMENT 95

capabilities may shun achievement contexts,thereby precluding opportunities for skilldevelopment.

Accuracy of self-percepts is affected by thevalidity of information on which they arebased. Modeling seems ideally suited forthis purpose because it focuses children'sattention on problem-solving strategies andcorrective operations. To the extent thatthe benefits of modeling are augmented byboosts in performance arising from the ef-fects of effort attribution on task engage-ment, attribution should also lead to moreaccurate appraisal. Conversely, with theless explicit information provided by adidactic mode of treatment, effort attribu-tion might offer no significant advantage inappraisal compared with no attribution.

In the present study, children who hadexperienced repeated failure at arithmeticreceived either a didactic or a cognitive-modeling treatment designed to increasetheir knowledge of arithmetic operations.For half of the children in each of thesetreatments, the experimenter periodicallyascribed the children's successes to sustainedeffort and their difficulties to insufficienteffort. The remaining children received thecompetency training without causal attri-bution for their performances. Arithmeticskill, persistence, and self-efficacy weremeasured before and after treatment.

It was hypothesized that compared withdidactic instruction, cognitive modelingwould result in higher arithmetic achieve-ment, persistence, self-efficacy, and accuracyof self-appraisal. Effort attribution wasexpected to lead to higher achievement,persistence, self-efficacy, and accuracy ofself-appraisal in the modeling treatment butnot in the didactic treatment.

Method

SubjectsThe sample consisted of 56 children ranging in age

from 9 years 2 months to 11 years 3 months, with a meanof 9 years 10 months. There were 33 males and 23 fe-males. Although varied socioeconomic backgroundswere represented, children were predominantlymiddle-class.

Children were drawn from five elementary schools.As an initial screening procedure, teachers identified

children who displayed low arithmetic achievement,persistence, and self-confidence. Those children werethen administered the formal preassessment individ-ually by an adult tester. Different adults administeredthe assessment and treatment procedures.

Pretreatment Assessment

Arithmetic performance test. The pretest consistedof 18 division problems graded in level of difficulty.They included 6 problems with one-digit divisors, 6 withtwo-digit divisors, 3 with three-digit divisors, and 3 withfour-digit divisors. The latter two groups of problemswere included to test the generalized effects of treat-ment, which included only problems with 1- and 2-digitdivisors. Thus, the performance test contained 12training problems and 6 generalization problems. Thearithmetic tasks were also graded in difficulty withincommon divisor level by having progressively moredigits in the dividends. The problems were presentedindividually in order of least-to-most difficult withincommon divisor level, except that four-digit divisorproblems occurred in positions 6, 12, and 18. Sincethese were very difficult problems, they were inter-spersed with less taxing ones; had they been grouped atthe end, cumulative fatigue might have exercised undueinfluence.

Each division problem was presented on a single page.Children were instructed to examine each problem andto place the page on a completed stack when they werethrough solving the problem or had chosen not to workit any longer. The tester recorded the time childrenspent with each problem.

Efficacy judgment. Children's pretest level of effi-cacy was measured after the division performance testto insure familiarity with the different types of prob-lems. The efficacy scale ranged from 10 to 100 in in-tervals of 10, with verbal descriptors occurring at thefollowing points: 10 = not sure, 40 = maybe, 70 =pretty sure, 100 = real sure. At the outset, childrenwere given practice with the efficacy assessment pro-cedure by judging their capability to jump progressivelylonger distances. A wide variety of distances rangingfrom a few inches to several yards was included to insurethat children understood both the scale direction andthe general meaning of each of the 10 points. Followingthis practice, children were shown for 2 sec each 18 pairsof division problems in increasing level of difficulty.This brief exposure was sufficient to portray the natureof the tasks but too short to attempt any solutions. Foreach of the samples, children privately judged on sep-arate efficacy scales their capability to solve that typeof problem, according to the following directions:

Circle the number on the line that matches howsure you are that you could work problems likethose shown and get the right answers. Rememberthat the higher the number the more sure you arewhile the lower the number the less sure you are.Please be honest and mark how you really feel rightnow.

Each sample pair corresponded in form and diffi-culty to one problem on the preceding test. However,

96 DALE H. SCHUNK

the problems in the efficacy set were not the same asthose on the performance test. Since the self-efficacymeasures tapped new applications of the cognitive skill,children had to rely on generali/able perceptions of theircapabilities in making the judgments.

Experimental AssignmentsSince the study was aimed at children who exhibited

gross deficits in arithmetic skills, children who solvedat least four problems were eliminated. Those meetingthis criterion were randomly assigned to one of fourconditions of 12 subjects each (modeling-attribution,modeling-no attribution, didactic-attribution, didac-tic-no attribution) or to a nontreated control group of8 subjects.

Training SessionsOn separate days, children received three 55-minute

training sessions, each of which contained three phases.The first phase (10 minutes) provided instruction ondivision strategies. The second phase (35 minutes)provided children with opportunities to practice thestrategies they had learned. During the third self-directed mastery phase (10 minutes), children solvedproblems on their own. Training was administeredindividually; trainer and child were seated side-by-sideduring the instruction and practice phases. The trainermoved out of the child's sight at the end of the practicephase and the child worked alone during the self-di-rected mastery phase.

Instructional MaterialsAlthough different packets were used for each session,

their format was identical. The first two pages of eachpacket explained the solution strategies and providedexemplars that showed application of the strategiesstep-by-step. The solution strategies were based on thedistributive algorithm, which requires a separate divi-sion to arrive at each digit in the quotient and "bringingdown" numbers one at a time from the dividend. Oneach of the next several pages was one division problem;children worked these pages one at a time during thepractice phase and enough pages were included so thatno child finished all of them. Children were informedof the correctness of their solutions; for small compu-tational errors trainers asked children to check theirwork. Several self-directed mastery problems appearedon the last two pages.

Treatment ConditionsTreatments were distinguished by the mode of in-

struction given during the instruction phases, the for-mat of corrective feedback for conceptual errors oc-curring during the practice phases, and whe.ther effortattribution was provided for successes and difficultiesduring the practice phases.

Cognitive-modeling treatment. During the in-struction phase children observed an adult model solvedivision problems contained in the explanatory pages

of the training packet and verbalize aloud the solutionstrategies used to arrive at the correct solutions. Duringthe practice phase corrective modeling was providedwhen children encountered conceptual difficulties. Onthese occasions, the trainer modeled the relevantstrategy while referring to the appropriate explanatorypage.

Didactic treatment. Children in this condition ini-tially studied the same explanatory pages on their own,after which they worked the practice problems. Whenchildren experienced conceptual difficulty duringpractice, the trainer referred them to the relevant sec-tion of the explanatory pages and told them to reviewit. If children were still baffled after a referral, theywere asked to read the section aloud.

This condition represented as complete a treatmentas cognitive modeling except that modeling was notprovided during instruction or practice. The explan-atory pages were pilot tested to insure that the vocab-ulary was understandable by children low in arithmeticachievement.

Attribution treatment. For children assigned to themodeling- and didactic-attribution conditions, thetrainer attributed their successes to high effort and theirdifficulties to low effort on the average of once every 5-6minutes during the practice phase of each of the threetraining sessions. Children received each type of at-tribution about 20 times during training so as to makethe effort attributions salient. To insure credibility,attributions were given when it seemed most appro-priate. For example, success was attributed to higheffort when children succeeded on a task after ex-pending a great deal of effort ("You worked really hardon that one"). Conversely, difficulty was attributed toinsufficient effort when children seemed less diligentin their efforts or after they had performed some oper-ation carelessly ("You need to work harder"). Effortattribution was never verbalized in conjunction withcorrective feedback to avoid confusing the two.

Posttreatment A.s.ses.vmeni

The posttreatment assessment was conducted withina week after completion of training. The procedureswere identical to those used in the pretreatment as-sessment except that efficacy judgments were collectedbefore the division performance test. The self-efficacyscores obtained prior to this test provided the measurefor testing their predictive value.

The division performance test was similar in form anddifficulty to that used in the pretreatment assessment,but it included different problems. A parallel form wasused to eliminate any possible effects due to increasedfamiliarity with the problems. Both forms were ad-ministered to 13 fourth graders not participating in thestudy. Their scores on these alternate forms werehighly correlated (r = .92).

Children's scores were obtained from the school dis-trict on the mathematical portion of the MetropolitanAchievement Tests (MAT; Durost, Bixlcr, Wrightstone,Prescott, & Balow, 1970) to determine whether math-ematical ability was related to children's response totreatment. The MAT score obtained for each child,expressed as a percentile rank, represented a compositeof three subtests that tapped mathematical computa-

MODELING AND ATTRIBUTIONAL EFFECTS OF ACHIEVEMENT 97

tion, concepts, and problem solving. The MAT com-posite scores were low (M = 32.4, SD = 20.7), whichsupported the teachers' nominations.

Results

The self-efficacy scores were analyzedusing a median split; judgments higher than55, which indicated at least moderate as-surance, were scored as efficacious, whereasthose lower than 55 were scored as ineffica-cious. Persistence was defined as thenumber of seconds children worked eachproblem. Performance-test problems werescored as correct if children correctly appliedthe division operations at each solution stageor made a small computational error butotherwise used the correct operations.1

There were no reliable differences due tosex or experimenter on any of the pretreat-ment or posttreatment measures; the datawere therefore pooled for subsequent anal-yses. Although there also were no reliabledifferences between treatment groups on anypretest measure, I decided to use pretestscores as predictors in the analyses of post-test measures to remove this extraneousvariability from the posttest scores. Re-moving pretest variation from posttest scoresin this fashion results in a more reliable scorethan using change scores (posttest minuspretest), which are often more unreliablethan either of the component variables(Cohen & Cohen, 1975). The use of pretestscores necessitated demonstration of ho-mogeneity of regression coefficients acrosstreatment groups (Kerlinger & Pedhazur,1973). Tests of slope differences for eachvariable were made by comparing a linearmodel that allowed separate slopes for thefour treatment groups against one that hadonly one slope parameter for estimating thepre-post relationship pooled across the fourtreatments. These analyses found the as-sumption of homogeneity of variance acrosstreatment groups to be tenable.

The posttest measures (accuracy, persis-tence, self-efficacy) were analyzed usingmultiple-regression procedures (Kerlinger& Pedhazur, 1973). The appropriate pretestscore was entered first in each of theseanalyses to derive a clearer picture of theinfluence of other factors. To check for in-tergroup differences, three categorical vari-ables were introduced as predictors for each

measure (Nie, Hull, Jenkins, Steinbrenner,& Bent, 1975). These three variables wereinstructional treatment (modeling-didactic),attribution within modeling (yes-no), andattribution within didactic (yes-no).

The decision to use multiple regressionwas based on the idea that factors other thantreatment might account for some variationin the posttest measures. For each of thethree measures, 1 felt that treatments, theappropriate pretest score, and the MATscore would account for some of the posttestvariability; in addition, self-efficacy theorypredicts that persistence should be in-fluenced by self-efficacy and that accuracyshould be influenced by both self-efficacyand persistence. The use of multiple re-gression in the present context, with a smalltotal sample size and a large number of pre-dictors, is not without problems. In suchinstances the regression coefficients tend tobe unstable from one sample to another,especially when the independent variablesare intercorrelated (Kerlinger & Pedhazur,1973). Although the present use of multipleregression seems justified, the reader shouldbear in mind this caution. As a safeguard,adjusted R2 results are also reported.

Pre- and posttreatment means are shownby condition in Table 1. The measures areclassified according to whether the problemsresembled those presented during training(training problems) or whether they requiredskill application to problems more complexthan those presented during training (gen-eralization problems). As the results ofthese two problem classes followed a similarpattern, only the results for training prob-lems will be reported to simplify the dis-cussion. Posttest scores were pooled acrossthe four treatments and compared withpretest scores using the t test for correlatedscores (Winer, 1971) to assess the overall

1 This scoring method provides a more sensitive

measure of children's division capabilities than a morestringent method requiring perfect accuracy on allcounts. By this latter method a child who performedthe correct operations but who made a small error insubtraction and therefore arrived at an incorrect answerwould be penalized as much as a child who failed to workthe problem. Performance-test data were analyzedusing both scoring methods. Their results were similar,so to avoid duplication the perfect-accuracy results arenot reported.

98 DALE H. SCHUNK

Table 1Pre- and Pastiest Achievemenl-Outcome Meant; and Standard Deviations by 1'roblcm Clans andExperimental Condition

Experimental condition

Problemclass

Modeling-attribution

M SO

Modeling noattribution

M SI)

Didactic-attribution

M SI)

Didactic -noattribution

M SI)

Control

M SI)

Accuracy"Training

PretestPosttest

GeneralizationPretestPosttest

2.2 1.68.3 3.6

.0 .01 .6 1 .6

2.7 2.57.8 3.0

.3 .61.2 1.6

2.4 1.76.3 2.7

.2 .3

.3 A

2.3 1.47.0 3.1

.2 .5

.5 .6

l . f i1.8

.0

.0

1.62.1

.0

.0

Persistence1'

TrainingPretestPosttest

GeneralizationPretestPosttest

36.0 3,5.699.7 53.3

3,5. 1 72. 1102.2 116.7

53.3 53.379.5 41.6

27.5 47.259.9 81.0

45.9 34.1100.1 57.8

27.0 32.647.8 64.2

65,0 6 1 .897.0 56.6

36.7 65.473.3 101.1

28.91 3.6

1 9.65.0

23.410.6

19.13.9

Self-efficacy1'Training

PretestPosttest

GeneralizationPretestPosttest

2.0 1.77.5 4.7

.0 .0

.9 1.2

2.3 2.17.2 5.0

.3 .61.5 1.6

2.2 1.97.4 4.2

.0 .01.2 1.5

3.2 2.76.3 4.4

.0 .01.7 1.7

1.82.8

.5

.0

2.44.1

.4

.0a Number of accurate solutions: maximum of 12 training, 6 generalization. '' Average number of sec/problem.

1: Number of efficacious judgments: maximum of 12 training, 6 generalization.

effects of treatment. All differences werepositive and reliable: (47) = 11.64, p < .01,for division accuracy; (47) = 5.95, p < .01,for persistence; and (47) = 7.68, p < .01, forself-efficacy. As expected, therefore, chil-dren who received treatment judged them-selves more efficacious, persisted longer, andsolved more problems. In contrast, thecontrols showed no reliable differences ex-cept for less persistence, (7) = 2.98,p < .03.

Self-KfficacyThe predictors entered to account for the

variation in treatment subjects' (N = 48)posttest self-efficacy judgments were pretestself-efficacy, MAT score, and the three cat-egorical variables. Only the effect due topretest self-efficacy was reliable, F(\, 42) =

8.77, p < .01. Although this effect indicatesthat the more efficacious children at theoutset tended to remain so, pretest self-ef-ficacy accounted for only 16% (14% adjusted)of the total variation in posttest self-efficacy;together, the five predictors accounted foronly 22% (18% adjusted) of the total varia-tion. Although it is clear that treatmentsdid not differentially affect self-efficacy, itis not clear what factor or factors weregreater influences. Possibly some compo-nents of the training that cut across treat-ments, such as children's perceptions of theirsuccesses and difficulties, were more im-portant than the components distinguishingthe treatments.

Persistence

The same five predictors were entered in

MODELING AND ATTRIBUTIONS, EFFECTS OF ACHIEVEMENT 99

the same order as in the preceding analysisexcept that pretest persistence was substi-tuted for pretest self-efficacy. In addition,posttest self-efficacy was entered last, sinceself-efficacy is hypothesized to influence taskpersistence.

Pretest persistence accounted for 22%(20% adjusted) and posttest self-efficacyaccounted for 11% (10% adjusted) of the totalvariation in posttest persistence. Theseincrements were statistically significant: forpretest persistence, F(l, 41) = 13.82, p < .01,and for posttest self-efficacy, F(lt 41) = 7.04,p < .05. Together, the six predictors ac-counted for 36% (31% adjusted) of the vari-ation in posttest persistence. Again, theseresults speak for the importance of factorsnot assessed in the present study as influ-ences on persistence.

Although the hypotheses that modelingand attribution within modeling would in-crease persistence were not supported, theexpected relationship between self-efficacyand persistence was found; children whojudged they could solve more problemssubsequently persisted longer on the prob-lems. But the heavy contribution of pretestpersistence indicates that children whopersisted longer on the pretest also did so onthe posttest. This may be a reflection ofwork-rate preference; for example, somechildren may have chosen to work theproblems slowly hoping to insure accuracy,whereas others may have been more con-cerned with completing the task morequickly.

Accuracy

Seven predictors were entered in a re-

gression equation to account for the varia-tion in posttest accuracy: accuracy pretestscore, MAT score, the three categoricalvariables as a group, and posttest self-effi-cacy and persistence as a group. Persistenceand self-efficacy were entered, since self-efficacy theory predicts that both shouldinfluence achievement. Results are shownin Table 2.

Self-efficacy, persistence, pretest accu-racy, the modeling-didactic variable, and theMAT score each accounted for a significantincrement in the explained portion of vari-ability in posttest accuracy. In contrast, thecontributions of the attribution variableswere nonsignificant. Thus, children whojudged themselves more efficacious andthose who persisted longer also solved moreproblems. Consistent with prediction,modeling children outperformed didacticchildren. The significant contribution ofpretest accuracy may seem puzzling, sincechildren were selected on the basis of lowaccuracy; nonetheless, pretest accuracyscores ranged from 0 to 3. The contributionof the MAT score suggests that regardless oftreatment, children with greater mathe-matical ability responded better to thetraining.

Path AnalysisThe finding that the variability in posttest

accuracy is a function of multiple influencesis interesting in its own right, but it would bemore meaningful to relate these data to acausal model. Such a model could then betested using path analysis (Kerlinger &Pedhazur, 1973; Nie et al., 1975) to deter-mine how well the model reproduces the

Table 2Regression Analysis of Hypothesized Predictors on Division Accuracy

Source ft2 cum R2 adjusted R'2 change dfSelf-efficacyPersistenceAccuracy pretestModeling-didacticMAT scoreAttribution (didactic)Attribution (modeling)Residual

.2419

.4335

.5683

.6190

.6621

.6726

.6729

.3271

.2388

.4237

.5474

.5749

.5979

.6072

.6074

.3926

.2419

.1916

.1348

.0507

.043 1

.0105

.0003

1I11111

40

29.57**23.42**16.48**6.19*5.27*1.28.04

Note, cum = cumulative; MAT = Metropolitan Achievement Tests.* p < .05. ** p < .01.

100 DALE H. SCHUNK

Table 3Original and Reproduced Correlations for theSelf-Efficacy Model (N = 48)

Variable 1 2 3 4

1.2.3.4.

TreatmentSelf-efficacyPersistenceAccuracy

.115

.034

.229

.115

.295

.565

.018

.295

.435

.234

.565

.438

Note. Original correlations are in the upper half of thetable; reproduced correlations are in the lower half.

original correlation matrix. Although pathanalysis cannot "prove" a theory to be cor-rect, it is useful in rejecting causal modelsthat demonstrate a poor fit to the original(full-model) correlations.

In its strictest form, self-efficacy theorypostulates that treatments promote changesin behavior through changes in self-perceptsof efficacy (Bandura, 1977). In this four-variable model, there are direct causal linksbetween treatment and self-efficacy, self-efficacy and persistence, self-efficacy andaccuracy, and persistence and accuracy.There are no direct paths from treatment topersistence or from treatment to accuracybecause treatment has no direct effect onthese measures. Rather, treatment influ-ences persistence through its effects onself-efficacy, and treatment also influencesaccuracy through its effects on self-efficacy,which in turn influences accuracy directlyand indirectly through persistence.

To test this parsimonious model, the cor-relations between the four variables werecomputed and are shown in the top half ofTable 3. Treatment is represented as acategorical variable (modeling-didactic).The attributional variable was dropped as itfailed to show any effects in the precedinganalyses. Self-efficacy, persistence, andaccuracy are represented as change scores(posttest minus pretest) for training prob-lems. Change scores were used to removepretest variability without adding extrapaths from pretest scores. This approachfits self-efficacy theory, which emphasizesbehavioral change as a function of changesin self-efficacy and persistence. However,the reader should interpret these results withcaution owing to the earlier warning aboutthe unreliability of change scores (Cohen &Cohen, 1975).

The results using this model reproducedthe original correlation matrix except for thecorrelation between treatment and accuracy:reproduced r = .05; original r = .23. Sincethis discrepancy is not small (

MODELING AND ATTRIBUTIONAL EFFECTS OF ACHIEVEMENT 101

solving that type of problem and subse-quently failing the exemplar. Self-efficacyjudgments higher than 55 were defined asindicating efficacy. Separate congruencepercentages were computed for training andgeneralization problems, although as beforethe results from the problem classes followeda similar pattern, so only the former will bediscussed.

Two measures of incongruence werecomputed to gain better insight into the ef-fects of the treatments on children's ap-praisals of their arithmetic efficacy. Thefirst was overestimation, defined as childrenjudging they could solve a certain class ofproblem but subsequently failing to solve theexemplar. The second was underestima-tion, defined as children judging they couldnot solve a particular type of problem butsubsequently solving the exemplar. Table4 shows the mean posttest percentages bytreatment. Comparison of these percent-ages with pretest percentages by treatmentcondition revealed no significant changes forthe modeling groups. However, didactic-attributional children showed less con-gruence on the posttest (70%) than on thepretest (90%), (11) = -3.24, p < .01, andoverestimated more on the posttest (19%)than on the pretest (4%), (11) = 2.73, p