Role of Self-Efficacy and Self-Concept Beliefs in Mathematical Problem Solving- A Path Analysis-Pajares, Frank; Miller, M. David.-pajares

Journal of Educational Psychology1994, Vol. 86, No. 2, 193-203

Copyright 1994 by the American Psychological Association, Inc.0022-0663/94/$3.00

Role of Self-Efficacy and Self-Concept Beliefs in Mathematical ProblemSolving: A Path Analysis

Frank Pajares and M. David Miller

Path analysis was used to test the predictive and mediational role of self-efficacy beliefs inmathematical problem solving. Results revealed that math self-efficacy was more predictive ofproblem solving than was math self-concept, perceived usefulness of mathematics, prior experi-ence with mathematics, or gender (N = 350). Self-efficacy also mediated the effect of gender andprior experience on self-concept, perceived usefulness, and problem solving. Gender and priorexperience influenced self-concept, perceived usefulness, and problem solving largely through themediational role of self-efficacy. Men had higher performance, self-efficacy, and self-concept andlower anxiety, but these differences were due largely to the influence of self-efficacy, for genderhad a direct effect only on self-efficacy and a prior experience variable. Results support thehypothesized role of self-efficacy in A. Bandura's (1986) social cognitive theory.

Social cognitive theory suggests that self-efficacy, "peo-ple's judgments of their capabilities to organize and executecourses of action required to attain designated types ofperformances" (Bandura, 1986, p. 391), strongly influencesthe choices people make, the effort they expend, and howlong they persevere in the face of challenge. According toBandura (1986), how people behave can often be betterpredicted by their beliefs about their capabilities than bywhat they are actually capable of accomplishing, for thesebeliefs help determine what individuals do with the knowl-edge and skills they have.

Although researchers have established that self-efficacy isa strong predictor of behavior (Maddux, Norton, & Stolten-berg, 1986), research on the relationship between self-effi-cacy and academic performance in areas such as mathemat-ics is still limited (Bouffard-Bouchard, 1989). Studies ofmath self-efficacy have been largely correlational, and re-searchers have emphasized the need to construct causalmodels with which to conceptualize and test hypothesizedrelationships (Hackett & Betz, 1989; Meece, Wigfield, &Eccles, 1990). When causal modeling has been used, mostmodels have excluded key variables identified as influenc-ing math performance (most notably, self-concept), or thetheoretical framework used to hypothesize relationshipswas not based on social cognitive theory. Thus, resultshave added little to a better understanding of self-effica-cy's influence.

Bandura (1986) hypothesized that self-efficacy beliefsmediate the effect of other determinants of performancesuch as gender and prior experience on subsequent perfor-

Frank Pajares and M. David Miller, Department of Foundations,College of Education, University of Florida.

We thank the anonymous reviewers of this article for theircritical feedback and valuable suggestions.

Correspondence concerning this article should be addressed toFrank Pajares, Department of Foundations, College of Education,1403 Norman Hall, University of Florida, Gainesville, Florida32611.

mance; that is, when these determinants are controlled,self-efficacy judgments are better predictors of perfor-mance. Bandura also argued that constructs such as self-concept, perceived usefulness, and anxiety are "commonmechanisms" of personal agency in the sense that they, likeself-efficacy beliefs, also influence an outcome. However,these mechanisms are, to a great extent, the result of self-efficacy judgments—their influence is largely due to theconfidence with which individuals approach a task. Conse-quently, although strong correlational relationships are ob-served between these mechanisms and related outcomes, therelationships are mostly due to the influence of self-efficacyon the common mechanisms. Self-efficacy judgments alsomediate the effect of gender and prior experience on thecommon mechanisms; that is, when gender and prior expe-rience are controlled, self-efficacy is a stronger predictor notonly of a related outcome but of common mechanisms suchas anxiety, self-concept, and perceived usefulness.

The purpose of this study was to use path analysis tech-niques to test Bandura's (1986) hypotheses regarding thepredictive and mediational role of self-efficacy in the areaof mathematics. First, we sought to determine whether theconfidence with which students approach the solving ofmath problems had stronger direct effects on their problem-solving performance than did their math self-concept, mathanxiety, perceived usefulness of mathematics, prior experi-ence with mathematics, and gender. Second, we testedwhether self-efficacy mediated the effect of gender andprior experience on both the common mechanisms andproblem-solving performance.

Of special interest to us was the interplay between self-efficacy and self-concept. The conceptual differencebetween these two constructs is not always clear ininvestigations. Reyes (1984), for example, used the termsmath confidence and math self-concept synonymously,and Felson (1984) referred to academic self-concept asself-perceptions of ability, suggesting that one reason whythese self-percepts affect performance is because of theireffect on students' effort, persistence, and anxiety. Others

193

194 FRANK PAJARES AND M. DAVID MILLER

have written about self-concept "of ability" and haveoperationalized it as individuals' ratings of their ability inacademic areas, that is, basically as generalized academicself-efficacy (e.g., Bachman & O'Malley, 1986; Feather,1988).

Self-concept differs from self-efficacy in that self-effi-cacy is a context-specific assessment of competence toperform a specific task, a judgment of one's capabilities toexecute specific behaviors in specific situations. Self-con-cept is not measured at that level of specificity and includesbeliefs of self-worth associated with one's perceived com-petence. It is clear that beliefs regarding confidence are partof an individual's self-concept, but Bandura (1986) arguedthat self-concept and self-efficacy represent different phe-nomena and must not be mistaken for each other.

Shavelson, Hubner, and Stanton (1976) introduced a hi-erarchical model that differentiated between general, aca-demic, social, emotional, and physical self-concepts. Aca-demic self-concepts were further differentiated as English,history, science, or math self-concepts. This model is nowwidely accepted and researchers warn that using globalindexes instead of the more specific self-appraisals is oflimited value. Self-concept judgments in academic endeav-ors, however, may be subject or course specific, but they arenever item or task specific. They are not specific assess-ments of capability. Compared with self-efficacy judg-ments, self-concept judgments are more global and lesscontext dependent. The course-specific self-concept ques-tion, "Are you a good math student?" taps different cogni-tive and affective processes than the self-efficacy question,"Can you solve this specific problem?"

Self-concept theorists have argued that an individual'sself-concept mediates the influence of other determinants onsubsequent performance and is the stronger predictor of thatperformance when those determinants are controlled. Socialcognitive theorists propose that these are functions of self-efficacy. A substantive question of our study, then, iswhether individuals' beliefs of self-worth as math studentsare more predictive of solving math problems (and mediatethe effect of their gender and prior experience) than theirbeliefs of their capability to solve the specific problemsrequired to assess just what sort of students they are.

As regards anxiety, Bandura (1986) contended that it isonly when people cannot predict or exercise control overevents that they have reason to fear them. Anxiety is gen-erally determined by the confidence individuals bring to atask. Efficacy beliefs predict "how well people cope withthreats and how much fear arousal they experience" (p.321). Self-efficacy will retain predictiveness of perfor-mance even when the effects of anxiety are controlled,whereas the effect of anxiety should dissipate when self-efficacy percepts are controlled.

Overview of Research Findings

Math Self-Efficacy

Confidence in learning mathematics, conceptual forerun-ner to math self-efficacy, has consistently been found to

predict math-related performance (Hackett, 1985). Early on,confidence was globally assessed by asking students generalquestions about their perceived math abilities. Math self-efficacy has more recently been assessed as individuals'judgments of their capabilities to solve specific math prob-lems, perform math-related tasks, or succeed in math-related courses (see Betz & Hackett, 1983).

Most researchers investigating the relationship betweenmath self-efficacy and performance have reported a strongcorrespondence. Collins (1982) found that, when prior per-formance was controlled, children with high self-efficacyoutperformed children with low self-efficacy in the comple-tion of novel math problems, showed greater effort, andpersisted longer in reworking incorrect problems. Siegel,Galassi, and Ware (1985) found that a model that includedself-efficacy accounted for a larger portion of the variancein math performance than did a model with anxiety andaptitude as the independent measures.

Bandura (1986) cautioned that, because judgments ofself-efficacy are task specific, different ways of assessingconfidence will differently correspond to the assessed per-formance. Self-efficacy must be specifically rather thanglobally assessed, must correspond directly to the criterialperformance task, and must be measured as closely aspossible in time to that task. These guidelines are seldomfollowed, and so the mismeasurement of self-efficacy is arecurring theme in educational research, often producingpoorly defined constructs, confounded relationships, ambig-uous findings, and uninterpretable results.

For example, Benson (1989) found that the path fromwhat she called math self-efficacy to performance was notsignificant, whereas that between math self-concept andperformance was. However, self-efficacy was assessed withthree global items dealing with expected success in the class(e.g., "No matter how hard I study, I will not do well in thisclass"). Self-concept was assessed with seven items specificto feelings of math self-worth (e.g., "I feel insecure in amath class"). Performance was the mid-term exam grade ina statistics course. Benson concluded that additional studieswere required to verify the relationship between the twoconstructs and to explore why self-efficacy did not influ-ence performance or statistical test anxiety. One answermay be that comparing confidence to succeed in a class witha statistics mid-term grade is not likely to produce the sortof correspondence that social cognitive theory hypothesizes.The more appropriately assessed feelings of math-specificself-concept, on the other hand, should, and did, have astronger correspondence with a math-related measure.

Cooper and Robinson (1991) found that a regressionmodel with math anxiety, American College Test—Quan-titative (ACT-Q) scores, and prior math experience re-vealed that self-efficacy did not account for a significantportion of the variance in performance. However, the re-searchers compared self-efficacy to succeed in math courseswith scores on a performance measure that consisted ofsolving problems. Norwich (1987) reported that when theeffects of math self-concept were controlled, self-efficacydid not predict math performance. Only prior math perfor-mance and math self-concept contributed significant van-

MATH SELF-EFFICACY 195

ance. However, Norwich used hierarchical regression andentered variables according to their assumed causal influ-ences from a self-concept perspective, with self-conceptentered first and self-efficacy last. Results may have beendifferent if the order had been entered with causal assump-tions hypothesized by social cognitive theory.

Recently, Randhawa, Beamer, and Lundberg (1993)found that generalized math self-efficacy mediated theeffect of various math attitudes on math achievement.However, their generalized math self-efficacy was thecomposite score of the three subscales of the MathematicsSelf-Efficacy Scale (MSES)—judgments of capability tosolve math problems, complete math-related tasks, andsucceed in math-related courses. The criterial task was amixture of the composite of teacher-assigned grades in al-gebra and scores on an algebra achievement test. Theachievement test portion of the outcome measure wasconceptually related only to the problems scale, althoughproblems on the test differed markedly from those pre-sented on the self-efficacy assessment; the teacher-as-signed grades bore little relation to any of the self-effi-cacy judgments. Consequently, although the math attitudemeasures had a strong direct effect on self-efficacy, theyalso had a stronger direct effect on performance than didself-efficacy. Bandura (1986) wrote that "it is no more in-formative to speak of self-efficacy in global terms than tospeak of nonspecific social behavior" (p. 411). The choiceof a generalized math self-efficacy score by Randhawa etal. is theoretically at odds with Bandura's warning, aswas their hypothesis that math attitudes similar to self-concept and anxiety are causally predominant over self-efficacy judgments.

Math Self-Concept

Although sometimes confounded by imprecise definitionsand varying measurements, findings consistently show thatmath self-concept is related to math performance (seeMarsh, Walker, & Debus, 1991). However, few studies havecompared the effects of self-efficacy and self-concept onperformance. Marsh et al. (1991) compared the direct effectof achievement on the math self-concept and self-efficacyof fifth graders and reported a stronger direct effect onself-concept than on self-efficacy. Such a hypothesized re-lationship, however, begged the question of which self-belief had the stronger influence on achievement.

Few researchers have investigated the relationship be-tween math self-concept and math self-efficacy, and nonefrom the perspective of social cognitive theory. Relich(1983), cited in Marsh (1990), assessed math self-concept,math achievement, performance on a division task, andself-efficacy for the division task. Achievement correlatedequally strongly with self-efficacy (globally assessed) andself-concept. Specific performance on the division task,however, was more strongly correlated with specificallyassessed self-efficacy than with math self-concept. Theseresults provide support for the task-specific nature of self-efficacy measurement. Other findings are contradictory.

Norwich (1987) found that self-concept was not related toself-efficacy when students were either familiar or unfamil-iar with a task. Marsh et al. (1991) compared the mathself-concept and self-efficacy of elementary school studentsand reported correlations as low as .18.

Math Anxiety

As early as 1957, Dreger and Aiken suspected that indi-viduals suffered from "number anxiety," and various studieshave since demonstrated a negative correlation betweenmath anxiety and math performance (see Schwarzer, Seipp,& Schwarzer, 1989, for meta-analysis). In most cases, how-ever, math anxiety is not a powerful predictor when vari-ables such as self-efficacy, self-concept, prior experience,and perceived usefulness are controlled (Llabre & Suarez,1985; Meece et al., 1990).

Hackett (1985) investigated the effects of math self-effi-cacy on math anxiety using path analyses with relationshipshypothesized from social cognitive theory and found thatself-efficacy had a strong direct effect. Self-efficacy alsohad a stronger direct effect on choice of math-related ca-reers than did anxiety and an even stronger total effect.Math self-efficacy was also a stronger predictor of mathanxiety than either prior high school math experience orgender.

Perceived Usefulness of Mathematics

Fennema and Sherman (1976) incorporated perceivedusefulness into their Mathematics Attitude Scales, and re-searchers have used these and other scales to demonstratethat perceived usefulness is consistently related to mathperformance (e.g., Armstrong, 1985). As was the case withmath confidence, correlations were generally moderate. Asexpected, students' perceived usefulness of mathematics isalso related to the confidence they express in their ability(Hackett & Betz, 1989; Lent, Lopez, & Bieschke, 1991).

Gender

Literature on the relationship between gender and mathperformance is abundant. Early findings showed that chil-dren did not differ in their math performance during ele-mentary school but that differences began to appear inmiddle school and increased with time and schooling (seeFennema & Sherman, 1978). Data from the National As-sessment of Educational Progress, Differential AptitudeTest national norming groups, and Preliminary ScholasticAptitude Test—Mathematics show declines over the lasttwo decades in gender differences in quantitative tasks.Only at the highest levels of math achievement do mencontinue to outperform women (Feingold, 1988).

Some researchers have suggested that gender differencesin mathematics stem from sociocultural factors and urgeinvestigators to expand collection of data such as students'confidence (Ethington, 1989; Hart, 1990). Fennema and


Sherman (1978) found that when affective variables such asconfidence were included in a model, performance differ-ences disappeared. This led them to suspect that affectivevariables were the source of sex differences. Subsequentresearchers have reported that, when differences in prepa-ration and confidence are controlled, fewer differences onmath achievement are found (e.g., Lapan, Boggs, & Morrill,1989). Social cognitive theory suggests that self-efficacypercepts mediate the effect of gender on math performance.

The relationship between gender and math self-efficacyhas not been explored as thoroughly as that between genderand math performance. Early studies suggested that boyswere more confident in their math skills (Fennema &Sherman, 1978). Recent findings suggest that boys and girlsreport equal confidence during the elementary years but, bymiddle and high school, boys grown more confident(Pintrich & De Groot, 1990).

Prior Experience with Mathematics

Percepts of ability are formed as individuals attempt andcomplete tasks. However, Bandura (1986) argued that peo-ple are more influenced by how they interpret their experi-ence than by their attainments per se. For this reason,self-efficacy beliefs usually predict future behavior betterthan does past experience. Prior experience influences sub-sequent behavior largely through its effect on self-efficacybeliefs, and these can influence performance "independentof past behavior" (p. 424). The few studies on math perfor-mance to include math background report a relationship(e.g., Cooper & Robinson, 1991; Hackett, 1985). Supportfor Bandura's contention also comes from studies that ex-plore the role of these variables from an expectancy-valueorientation (Meece et al., 1990; Pokay & Blumenfeld,1990). Researchers who have explored the relationship be-tween prior experience and math self-efficacy have reportedboth significant correlations and direct effects (e.g., Cooper& Robinson, 1991; Hackett, 1985).

Method

Participants and Setting

Participants consisted of 350 undergraduates (229 women and121 men) from a large public university in the South, the majorityof whom were enrolled in classes in the College of Education.Participation was voluntary and no remuneration was provided, butmost instructors provided course credit. Of the total sample, 137were education majors, and 213 represented a variety of majorsthroughout the university.

Measures

Math self-efficacy. The problems scale of the MathematicsConfidence Scale (MCS) was created by Dowling (1978), whodeveloped the instrument to assess the math confidence of collegestudents. Problems on the MCS represent three components ofmathematics (arithmetic, algebra, and geometry), three levels ofcognitive demand (computation, comprehension, and application),

and two problem contexts (real and abstract). (Sample item:"There are three numbers. The second is twice the first and the firstis one-third of the other number. Their sum is 48. Find the largestnumber.") Dowling reported a correlation of .57 between the MCSand the confidence scale of Fennema and Sherman's (1976) Math-ematics Attitude Scales. Because the original 10-point Likert scalewas considered cumbersome and unnecessarily over-specific, Lan-genfeld and Pajares (1992) conducted a study with 145 undergrad-uates and using a 5-point scale. Coefficient alpha revealed that theinstrument had strong internal consistency (.91).

Perceived usefulness of mathematics. The measure of per-ceived usefulness was adapted from a 20-item instrument createdby Shell, Murphy, and Bruning (1989) in which students wereasked to rate the importance of reading or writing skills forachieving various life goals. The items include the domains ofemployment, social activities, family life, education, and citizen-ship. We replaced the words reading or writing with mathematics.(Sample item: "How important is skill in mathematics for gradu-ating from college?") Shell et al. (1989) reported Cronbach's alphaof .93 and positive and above .40 item/total correlations for allitems on the original instrument. Langenfeld and Pajares (1992)also obtained .93, with the instrument reworded to reflect per-ceived usefulness of mathematics.

Math anxiety. The Mathematics Anxiety Scale (MAS) wasadapted by Betz (1978) from the anxiety scale of the Fennema-Sherman Mathematics Attitudes Scales to create an instrumentmore appropriate to college students. The MAS consists of 10items—five positively worded and five negatively worded. (Sam-ple item: "I get really uptight during math tests.") Scoring of thenegative items is reversed so that a high score indicates lowanxiety. Betz reported a split-half reliability coefficient of .92.Correlations of about .70 have been reported between the MASand the 98-item Mathematics Anxiety Rating Scale (Cooper &Robinson, 1991). Dew, Galassi, and Galassi (1983) reported Cron-bach's alpha of .72 and 2-week test-retest reliability of .87. Hack-ett and Betz (1989) reported Cronbach's alpha values ranging from.86 to .90. Frary and Ling (1983) subjected the items to factoranalysis and found that they loaded highly (.89) on the factor theydefined as math anxiety.

Math self-concept. The Self Description Questionnaires (SDQ)comprise academic and course-specific self-concept items. Weused the math scale of the SDQIII, a 180-item self-concept mea-sure consisting of 13 scales and developed specifically to assessself-concept of older adolescents and college students (Marsh,1992). (Sample item: "Mathematics makes me feel inadequate.")Marsh and O'Neill (1984) conducted two validation studies of theSDQIII and reported high reliabilities for the 13 factors. Factorloadings for the math scale items ranged from .74 to .91. In twostudies, they reported coefficient alphas of .93 and .95 for the mathscale. They also reported that the scale correlated strongly withcriterion measures such as school certificate (achievement) scoresin mathematics (.58), students' self-descriptions (.74), and ratingsby others (.77).

Prior experience. Frary and Ling (1983) defined prior highschool math experience as the maximum math level attained inhigh school courses, whereas other researchers have asked studentsto self-report the number of years during which they had takenhigh school mathematics (e.g., Hackett & Betz, 1989). However,some students can take 4 years of mathematics and never progressbeyond geometry; others can take more than one math course in 1year. It is logically more likely for a student who has progressedthrough Advanced Placement Calculus in 4 years of high school tohave developed stronger self-efficacy and prior knowledge thananother student who only progressed through Algebra I in those


same 4 years. Consequently, we operationalized prior high schoolmath experience as did Frary and Ling.

College math experience has been operationalized as (a) thenumber of semesters in which mathematics was taken, (b) thenumber of math courses taken, or (c) the number of semestercredits obtained. The first is shortsighted—students may take oneor more courses during a semester. The number of college mathcourses is so varied, however, that assessing college math experi-ence the way one might assess high school experience is notfeasible. Thus, earned semester credits makes the most sense.

Math performance. The Mathematics Problems PerformanceScale (MPPS), like the math self-efficacy scale, was developed byDowling (1978). Consistent with Bandura's (1986) guidelines, theproblems on which performance was assessed were the same asthose on which confidence was measured. The MPPS is an 18-item, multiple-choice instrument constructed with mid-range dif-ficulty items from the National Longitudinal Study of Mathemat-ical Abilities (NLSMA), developed specifically for use withcollege students, and composed of three nonorthogonal subscalesconsisting of math components, cognitive demand, and problemcontext (see Romberg & Wilson, 1969). Dowling (1978) reportedKR 20 coefficient of reliability of .788 and mean item difficulty of.291. For an item to be included in the final instrument, thefollowing criteria had to be met: (a) percentage correct between .30and .70, (b) point-biserial correlation coefficient greater than .50,(c) discrimination index greater than .40, and (d) significant cor-rected phi coefficient (p < .01).

Procedure and Data Collection

The instruments were group administered in individualclasses. Students were first asked to complete the self-efficacy,perceived usefulness, self-concept, and anxiety measures. Theywere informed they would be asked to solve the problems onwhich their confidence was being assessed. After these formswere collected, the performance measure was administered. Ban-dura (1986) suggested that efficacy and performance be assessedwithin as close a time period as possible and that efficacy as-sessment precede performance assessment. All instruments wereadministered during one class period. This also ensured that ab-sences would not create a situation whereby some students com-pleted one measure but not another. Pilot testing had demon-strated that the class periods provided ample time in which tocomplete all measures.

Data Analysis

Path analysis techniques are used to examine the direct andindirect effects between variables, although they are not without

their critics (see Freedman, 1987). Cook and Campbell (1979)suggested that they are especially appropriate when "theoretical,empirical, and commonsense knowledge of a problem" (p. 307)provides a defensible mapping of the latent variables present andtheir probable causal links. Path analysis is, therefore, especiallyappropriate in an investigation in which the tenets of social cog-nitive theory and previous findings are such that hypothesizedrelationships have strong theoretical and empirical support.

The path model tested was as follows: Gender was hypothe-sized to influence all variables; level of high school mathematicswould mediate the influence of gender and influence the remain-ing variables; math experience in college would mediate the in-fluence of gender and high school math experience and influ-ence the remaining variables; math self-efficacy would mediatethese prior influences on both the performance task and thethree common mechanisms—math self-concept, math anxiety,and perceived usefulness; the common mechanisms were hy-pothesized to influence performance directly.

Results

Table 1 presents the means, standard deviations, andPearson product-moment correlations for all variables in thestudy. Students averaged a high school math level close toanalytical geometry and trigonometry (or pre-calculus), ahigh level explained by the fact that the sample consisted ofuniversity students. Participants had completed an averageof 10.3 college credits in math courses. The importance ofthese variables rested on the fact that social cognitive theorypredicts that, although an individual's self-efficacy beliefsare partly based on such prior experience, these beliefs aremore strongly predictive of subsequent performance.

Math self-efficacy scores ranged from 36 to 90. Possiblescores ranged from 18 to 90; hence, although some studentsexpressed maximum confidence in their problem-solvingability, even the least confident averaged 2 on the 5-pointLikert scale. A mean score of 4.09 (much confidence) peritem suggested that students were largely confident abouttheir ability to solve the problems. The phenomenon ofscoring above the midpoint of the Likert scale was not aspronounced with math self-concept or anxiety and did notoccur with perceived usefulness. Self-concept scores rangedfrom 10 to 80 (the minimum and maximum possible), witha mean of 5.0 on the 8-point Likert scale, indicating that apositive self-concept statement is more true than false.

Table 1Means, Standard Deviations, and Zero-Order Correlations of Variables in the Path Analysis

Variable M SD Gender HSL CC USE MSC MAS MSE PERF

HSLCCUSEMSCMASMSEPERF

4.910.350.949.731.873.614.1

1.26.0

15.216.610.910.52.8

.11*- .07

.05

.13*

.15**

.24***

.17***

—.15**.12*.48***.44***.47***.44***

—.06.25***20***.23***.23***

—.40***.32***.19***.14***

—.87***.61***.54***

.56***

.51*** .70**Note. HSL = high school level; CC = college credits earned; USE = perceived usefulness of mathematics; MSC = math self-concept;MAS = math anxiety; MSE = math self-efficacy; PERF = math performance.*p < .05. ** p < .01. ***p< .0001 .


Anxiety scores also ranged from the minimum of 10 to themaximum of 50, with a mean of 3.2 on the 5-point Likertscale. Recall that the anxiety measure scored higher for lowanxiety, hence 3.2 represents anxiety slightly lower thanundecided. Perceived usefulness scores ranged from 21(minimum possible = 20) to 97 (maximum possible =100), with a mean of 2.5 on the 5-point Likert scale.Students found mathematics more than a little important butless than moderately important.

Correlations between all independent variables and bothself-efficacy and performance were significant. Magnitudeswere consistent with those of previous investigations. The.87 correlation between self-concept and anxiety, however,created a problem of multicollinearity. Although the MASand the math scale of the SDQIII have been used exten-sively and purport to measure different constructs, they havenot previously been used in the same study. Because effectsfrom the common mechanisms would in part be a functionof multicollinearity, we decided to remove anxiety from thepath analysis, a choice guided by our primary interest in theinterplay between self-concept and self-efficacy. Anxietywas included, however, in subsequent analyses of genderdifferences. Further analyses showed that no other correla-tion was high enough to create an instability in the param-eter estimates of the path analysis. Consequently, all othercommon mechanisms were maintained in the model.

Table 2 provides a decomposition of effects from the pathanalysis. The independent variables accounted for 52% of

the variability in problem-solving performance, F(6, 343) =61.80, p < .OOOL Each of the regression models was alsosignificant. Figure 1 illustrates the path analysis model withnonsignificant paths removed. Note that this is the fullmodel and not a reduced model recomputed with nonsig-nificant relationships removed. Figure 1 is provided for easeof interpretation and to show the residual path coefficients(R). These coefficients represent factors that affect a spe-cific variable but that are not measured or accounted for inthe model—the square root of the unexplained variation inthe dependent variable.

Of all path coefficients from the independent variables toperformance, only those from math self-efficacy (/3 = .545,t = 10.87, p < .0001), math self-concept (/3 = .163, t =3.07, p < .005), and high school level (/3 = .099, t = 2.22,p < .05) were significant. The magnitude of the self-efficacy/performance path coefficient is such, however, thatthe answer to the substantive question of the study is readilyapparent. The effects of gender, high school level, andcollege credits on math self-efficacy were all positive andsignificant, as hypothesized. Table 3 provides an overviewof direct and indirect effects on math performance and mathself-efficacy.

As hypothesized, self-efficacy had stronger direct effectson performance than did any of the variables in the study.Moreover, both its direct and total effects were significantlystronger than those of the other variables. Math self-conceptand high school level each had modest direct effects. Re-

Table 2Decomposition of Effects From the Path Analysis

Effect

On high-school levelof gender

On college creditsof genderof high school level

On math self-efficacyof genderof high school levelof college credits

On perceived usefulnessof genderof high school levelof college creditsof math self-efficacy

On math self-conceptof genderof high school levelof college creditsof math self-efficacy

On math performanceof genderof high school levelof college creditsof math self-efficacyof perceived usefulnessof math self-concept

Note. N = 350.* p < .05. ** p < .01. *** p

(Intercept)Parameterestimate

(4.85)0.29

(6.82)-1.06

0.79(51.05)

4.603.570.32

(30.59)0.340.570.050.23

(-24.47)-0.35

3.400.290.74

(1.16)0.070.220.020.14

-0.010.03

< .0001.

Standardizedestimate

.114

-.089.159

.209

.419

.185

.011

.046

.019

.158

-.010.251.106.466

.011

.099

.052

.545-.042

.163

t

2.14*

-1.583.00**

4.57***9.07***4.03***

0.200.770.342.51**

-0.245.44***2.50**9.65***

0.292.22*1.33

10.87***-1.02

3.07**

R2

.01

.03

.29

.04

.43

.52


R=.99 R=.76

Math High SchoolExperience

Gender

1 9

-.099—,

-.251-

.419—•

.209—•

.185—•

MathematicsSelf-concept

HatheSelf-

I 1—

ticsEfficacy

College HathExperience

Rs.98

-.545-

-.158—• PerceivedUsefulness

MathematicsPerformance

R=.84 R=.98 R=.69

Figure 1. Significant path coefficients between all variables in the study. Dotted lines indicatepath coefficients for residuals (R).

suits from the path analysis suggest that the relationshipbetween performance and both self-concept and perceivedusefulness was largely a result of noncausal covariation,largely due to the effect of problems self-efficacy. It is clearthat self-efficacy affected performance almost exclusivelydirectly rather than indirectly through the mediated vari-ables. Moreover, prior experience and gender affected per-formance largely through their influence on self-efficacy.Their indirect effects on performance were strong, as weretheir direct effects on self-efficacy. The indirect effects ofthese variables on performance were, in fact, also largely aresult of self-efficacy. The interactive effects of gender weretested and found nonsignificant.

Gender Differences

Had the data been examined by looking only at correla-tional relationships and mean differences, past findings re-porting gender differences in math-related constructs wouldhave been supported. Results of independent samples t tests,adjusted using the Dunn procedure (a = .005), are pre-sented in Table 4.

Men reported higher math self-efficacy than did women.Consistent with prior findings, women expressed higherlevels of math anxiety. Men also had a higher average scoreon the performance measure. These differences are note-worthy, considering that men and women did not differ in

Table 3Direct and Indirect Effects on Math Self-Efficacy and MathematicsProblem-Solving Performance

Effect

On math performanceof math self-conceptof perceived usefulnessof math self-efficacyof college creditsof high school levelof gender

On math self-efficacyof college creditsof high school levelof gender

r

.540*

.140*

.697*

.232*

.438*

.171*

.234*

.470*

.245*

Directeffect

.163*-.042

.545*

.052

.099*

.011

.185*

.419*

.209*

Indirecteffect

.000

.000

.083

.115*

.276*

.121*

.000

.029

.031

Totaleffect

.163*-.042

.625*

.167*

.375*

.132*

.185*

.448*

.240*

Noncausalcovariation

.377

.182

.072

.065

.063

.039

.049

.022

.005

* p < .05.


Table 4Mean Gender Differences in Math-Related Constructs

Construct

High schoolCollege creditsSelf-efficacySelf-conceptMath anxietyPerceived usefulnessPerformance

Women

5.110.671.848.230.650.313.7

Men

4.89.8

77.152.634.152.014.7

Difference

0.30.8

-5.3-4.4-3.5-1.7-1.0

t

-2.121.19

-4.89*-2.55-3.10*-1.02-3.29*

Prob > 1t 1

.0348

.2366

.0001

.0113

.0021

.3102

.0011Note. Ns: women = 229; men = 121. For the analysis, women were entered as 0 and men wereentered as 1.* p < .005.

prior experience. According to the path analysis, differencesin performance were due to a difference in math self-efficacy. Differences in math self-concept and perceivedusefulness did not reach significance.

tween gender and level of confidence, critical x2 (2, N =350) = 5.99, a = .05; observed / (2, N = 350) = .74.These results are similar to those reported by Hackett andBetz (1989).

The Question of Overconfidence

Past findings suggest that students generally overestimatetheir math performance capability (see Hackett & Betz,1989). We defined overestimation as marking an item 4 or5 on the self-efficacy Likert scale (much confidence orcomplete confidence) and then incorrectly answering thatitem; underestimation was defined as marking an item 1 or2 (no confidence at all or very little confidence) and gettingthe item correct. An answer of 3 was considered as uncer-tain and did not play a role in this assessment. Two types ofcongruence were possible. Congruence—no errors occurredwhen the student correctly predicted each subsequent re-sponse. Congruence—equal errors took place when thestudent overestimated and underestimated equally; that is,the student made one or more errors of overestimation andan equal number of errors of underestimation (see Table 5).

Note that 57% of the students overestimated their perfor-mance and 20% underestimated it. Of 350 students, only 25correctly predicted their responses to all 18 math problems.The magnitude of overconfidence was also greater than thatof underconfidence. Students overestimated by an averageof 1.91 problems; they underestimated by an average of1.06. Students in the overestimation and underestimationgroups, however, erred equally; that is, the 57% that over-estimated did so on 2.7 problems, whereas the 20% thatunderestimated did so on 2.67 problems. A chi-square testdemonstrated that there was no significant relationship be-

Table 5Overestimation, Underestimation, and Congruence

Women Men Total

Measure n nOverestimationUnderestimationCongruence—total

Congruence—no errorsCongruence—equal errors

130 57 70 58 200 5748 21 21 17 69 2051 21 30 25 81 2313 6 12 10 25 738 17 18 15 56 16

Discussion

The purpose of this study was to discover whether self-efficacy beliefs play the mediational role ascribed to themby Bandura (1986) and social cognitive theory, and whetherthese beliefs are stronger predictors of performance than areother presumed determinants and common mechanisms. Wefocused on the influence of self-efficacy on mathematicsbecause our interest in self-efficacy was founded on abroader interest in education and the academic performanceof students. In this context, the solving of math problemsafforded a clearer and more reliable assessment than waspossible in other academic contexts, but results would nev-ertheless inform social cognitive theory and its claims aboutself-efficacy in general.

The important finding to emerge was that students' judg-ments about their capability to solve math problems weremore predictive of their ability to solve those problems thanwere other variables found by previous research also to bestrongly related to math performance. Self-efficacy alsomediated the effect of gender and prior experience on mathself-concept, perceived usefulness of mathematics, andmath problem-solving performance. Tests of mean differ-ences showed that men and women differed in perfor-mance, self-efficacy, and self-concept, but results of thepath analysis suggest that these differences were mediatedby differences in the students' self-efficacy perceptions,for only between gender and self-efficacy was there a sig-nificant path coefficient. The effects of gender on self-concept and performance were largely indirect and medi-ated by self-efficacy. That is, the poorer performance andlower self-concept of the female students were largelydue to lower judgments of their capability. A similar phe-nomenon occurred with prior experience, both in highschool and college.

It should come as no surprise that what people believethey can do predicts what they can actually do and affectshow they feel about themselves as does of that task. Howcould it be otherwise? And yet, as we noted earlier, re-


searchers with other theoretical perspectives have long ar-gued that academic performance is better explained byfactors such as prior experience or beliefs of self-worth. Theclear implication to emerge from our findings is that re-searchers and school practitioners should be looking tostudents' beliefs about their capabilities as important medi-ators and predictors of performance. It is not within thescope of this investigation to outline the ways throughwhich social cognitive theorists suggest that both self-effi-cacy and academic performance can be enhanced. Instead,the reader is directed to the work of Schunk and associates,who provide insights as to how this can best be accom-plished (see Schunk, 1989, 1991).

Hackett and Betz (1989) suggested that "mathematicsteachers should pay as much attention to [students'] self-evaluations of competence as to actual performance" (p.271). We dare not go so far, but it seems clear that assessingstudents' self-efficacy can provide classroom teachers withadditional insights about their students' subsequent perfor-mance—insights beyond those obtainable by simply assess-ing prior knowledge. If self-efficacy is an important predic-tor of performance and is a primary cause of feelings ofself-worth and perceived usefulness, then efforts to identify,understand, and alter inaccurate judgments should provebeneficial. Moreover, if self-efficacy beliefs are major me-diators of behavior and behavior change, then counselinginterventions designed to change behavior are useful to thedegree that they increase the self-efficacy beliefs related tothe behavior in question. The math competence of manyundergraduates, for example, may tell us very little abouttheir math self-efficacy, and it is the latter factor that will becritical in their choice of math-related decisions such aspursuing math courses, majors, or careers. Avoidance ofmath courses has its roots in elementary or middle schooland generally begins in high school. It is likely that chil-dren's judgments of their competence and potential arelargely responsible for this avoidance (see Dweck & Leg-gett, 1988; Pintrich & De Groot, 1990). If self-efficacyassessments were to begin early in a student's academiccareer, inaccurate perceptions could also be identified earlyand appropriate interventions undertaken.

As social cognitive theory predicts, most students in thisstudy overestimated their performance. Bandura argued thatsome overestimation of capability is useful—it providesneeded effort and persistence. Many of the students, how-ever, underestimated their capability, and this is seldom adesirable state of affairs. Students who lack confidence inskills they possess are not likely to engage in tasks in whichthose skills are required, and they will exert less effort andpersistence in the face of difficulty. In the area of mathe-matics, researchers have demonstrated that self-efficacystrongly influences the choice of majors and career deci-sions of college students (see Lent & Hackett, 1987). Inmany cases, inaccurate perceptions of mathematics capabil-ity, and not poor preparation or lack of skill, are responsiblefor avoidance of math-related courses and careers.

It is important to know more about how students developinaccurate self-efficacy beliefs in the first place. How is itthat, in spite of success experiences and clearly demonstra-

ble skills, some students develop a profound lack of confi-dence in their abilities? Lent and Hackett (1987) suggestedthat this phenomenon is responsible for women failing topursue math courses, math-related majors, and careers. Re-search is needed on the process whereby children developthese beliefs. Dweck and Leggett (1988) were rightly con-cerned that fixed entity views of ability are developed earlyand tend to last in the absence of intervention techniques. Itwould be useful to know more about how these beliefs areacquired, why they persevere, and how they can be altered.

Because interventions designed to alter self-efficacy areoften desirable and beneficial, the nature of these interven-tions should be further explored. Classroom teachers maywell be impressed by the force of theory arguing thatself-efficacy beliefs are important determinants of perfor-mance, but they are apt to be more interested in ways to alterthese beliefs when they are inaccurate and debilitating tochildren. More research is also needed on the effect of theseinterventions on subsequent performance and self-efficacyas well as on anxiety and other self-beliefs such as attribu-tions and self-concept.

The reader will note that ability was not used as a controlvariable in the path model. Several researchers discouragethe inclusion of an ability measure in path analytic modelsof math performance. Dew, Galassi, and Galassi (1984)warned that ability assessments such as the SAT-Q areconfounded by attitudinal and anxiety elements. Thus, vari-ance accounted for by such measures could well includeself-efficacy and anxiety components. This confounding hasespecially plagued math anxiety research (Llabre & Suarez,1985). Lent et al. (1991) found that ability did not contributesignificant incremental variance to the prediction of mathcourse interest after controlling for self-efficacy. Hackettand Betz (1989) reported a significant relationship betweenglobally assessed math confidence and ACT-Q scores butfound that only self-efficacy was a significant predictor ofchoice of math-related major. They concluded that "thecognitive information tapped by the assessment of mathself-efficacy should, theoretically, encompass the informa-tion an individual has derived from his or her own pastperformance, making such achievement information asACT scores redundant if one possesses information aboutself-efficacy" (p. 270). Recent similar investigations haveexcluded an ability measure (e.g., Randhawa et al., 1993),and it was not used in our study. We would be remiss,however, if we did not acknowledge that its exclusion mayhave influenced the effects found, and we recommend thata future model include an ability measure with an eye totesting our findings.

The academic success associated with reported highschool level or number of credits earned in mathematics wasalso not part of the assessment. Our research focus wasexposure to course content rather than success. Level ofhigh school mathematics and number of credits earnedprovide strong and defensible measures of students' priorexperience with mathematics, and our operationalization ofthis variable is consistent with previous research in the field(Frary & Ling, 1983; Hackett & Betz, 1989). Success vari-ables such as grade point average would shift the emphasis


from course content exposure to previous performance at-tainments. Future studies, however, might be designed toexplore the influence of academic experience controlling forsome measure of success.

In addition, researchers might also explore the roles thatprerequisite prior knowledge and knowledge of strategies tosolve problems play in self-efficacy judgments as well ashow these judgments influence variables such as goal set-ting and attainment. The high average score also suggeststhat, in spite of Dowling's (1978) efforts, a more challeng-ing performance measure may be more appropriate in aca-demic settings similar to ours. Results of this investigationalso demonstrate that analyses such as path analyses orstructural equation modeling are required if substantivequestions are to be more clearly answered. Had we usedsimpler correlational or multiple regression analyses, theplethora of significant relationships may have led to con-clusions that would have been both unclear and misleading.

Our findings strengthen Bandura's (1986) claim that self-efficacy beliefs are key arbiters of human agency and alsolend support to researchers who contend that student moti-vation may be better explained by these beliefs than byother cognitive or affective processes (see Schunk, 1989,1991). Social cognitive theory offers a promising avenuethrough which to better understand this motivation, an av-enue that can help researchers and school practitioners notonly to understand the process itself but to inform themabout how they might pursue the important work of buildingcompetence and confidence.

References

Armstrong, J. M. (1985). A national assessment of participationand achievement in women in mathematics. In S. Chipman, L.Brush, & D. Wilson (Eds.), Women and mathematics: Balancingthe equation (pp. 59-94). Hillsdale, NJ: Erlbaum.

Bachman, J. G., & O'Malley, P. M. (1986). Self-concepts, self-esteem, and educational experiences: The frog pond revisited(again). Journal of Personality and Social Psychology, 50, 35-46.

Bandura, A. (1986). Social foundations of thought and action: Asocial cognitive theory. Englewood Cliffs, NJ: Prentice Hall.

Benson, J. (1989). Structural components of statistical test anxietyin adults: An exploratory study. Journal of Experimental Edu-cation, 57, 247-261.

Betz, N. E. (1978). Prevalence, distribution, and correlates of mathanxiety in college students. Journal of Counseling Psychology,25, 441-448.

Betz, N. E., & Hackett, G. (1983). The relationship of mathematicsself-efficacy expectations to the selection of science-based col-lege majors. Journal of Vocational Behavior, 23, 329-345.

Bouffard-Bouchard, T. (1989). Influence of self-efficacy on per-formance in a cognitive task. Journal of Social Psychology, 130,353-363.

Collins, J. L. (1982, March). Self-efficacy and ability in achieve-ment behavior. Paper presented at the meeting of the AmericanEducational Research Association, New York.

Cook, T. D., & Campbell, D. T. (1979). Quasi-experimentation:Design & analysis issues for field settings. Boston: HoughtonMifflin.

Cooper, S. E., & Robinson, D. A. G. (1991). The relationship of

mathematics self-efficacy beliefs to mathematics anxiety andperformance. Measurement and Evaluation in Counseling andDevelopment, 24(April), 4-11.

Dew, K. M. H., Galassi, J. P., & Galassi, M. D. (1983). Mathe-matics anxiety: Some basic issues. Journal of Counseling Psy-chology, 30, 443-446.

Dew, K. M. H., Galassi, J. P., & Galassi, M. D. (1984). Mathanxiety: Relations with situational test anxiety, performance,physiological arousal, and math avoidance behavior. Journal ofCounseling Psychology, 31, 580-583.

Dowling, D. M. (1978). The development of a mathematics confi-dence scale and its application in the study of confidence inwomen college students. Unpublished doctoral dissertation,Ohio State University, Columbus.

Dreger, R. M., & Aiken, L. R. (1957). The identification of num-ber anxiety in a college population. Journal of EducationalPsychology, 48, 344-351.

Dweck, C. S., & Leggett, E. L. (1988). A social-cognitive ap-proach to motivation and personality. Psychological Review, 95,256-272.

Ethington, C. A. (1989). Gender differences in mathematics: Aninternational perspective. Journal of Research in MathematicsEducation, 20, 74-80.

Feather, N. T. (1988). Values, valences, and course enrollment:Testing the role of personal values within an expectancy-valenceframework. Journal of Educational Psychology, 80, 381-391.

Feingold, A. (1988). Cognitive gender differences are disappear-ing. American Psychologist, 43, 95-103.

Felson, R. B. (1984). The effect of self-appraisals of ability onacademic performance. Journal of Personality and Social Psy-chology, 47, 944-952.

Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman Math-ematics Attitude Scales: Instruments designed to measure atti-tudes toward the learning of mathematics by females and males.JSAS Catalog of Selected Documents in Psychology (Ms. No.1225), 6, 31.

Fennema, E., & Sherman, J. A. (1978). Sex-related differences inmathematics achievement and related factors: A further study.Journal for Research in Mathematics Education, 9, 189-203.

Frary, R. B., & Ling, J. L. (1983). A factor-analytic study ofmathematics anxiety. Educational and Psychological Measure-ment, 43, 985-993.

Freedman, D. A. (1987). As others see us: A case study of pathanalysis. Journal of Educational Statistics, 12, 101-128.

Hackett, G. (1985). The role of mathematics self-efficacy in thechoice of math-related majors of college women and men: Apath analysis. Journal of Counseling Psychology, 32, 47-56.

Hackett, G., & Betz, N. E. (1989). An exploration of the mathe-matics self-efficacy/mathematics performance correspondence.Journal for Research in Mathematics Education, 20, 261-273.

Hart, L. E. (1990). Two generations of feminist thinking. Journalfor Research on Mathematics Education, 21, 79-83.

Langenfeld, T. E., & Pajares, M. F. (1992). [Relationship of mathself-efficacy to math-related constructs and internal consistencyof MSES with 5-point Likert scale]. Unpublished raw data.

Lapan, R. T., Boggs, K. R., & Morrill, W. H. (1989). Self-efficacyas a mediator of investigative and realistic general occupationalthemes on the Strong-Campbell Interest Inventory. Journal ofCounseling Psychology, 36, 176-182.

Lent, R. W., & Hackett, G. (1987). Career self-efficacy: Empiricalstatus and future directions. Journal of Vocational Behavior, 30,347-382.

Lent, R. W., Lopez, F. G., & Bieschke, K. J. (1991). Mathematics


self-efficacy: Sources and relation to science-based careerchoice. Journal of Counseling Psychology, 38, 424-430.

Llabre, M. M., & Suarez, E. (1985). Predicting math anxiety andcourse performance in college women and men. Journal ofCounseling Psychology, 32, 283-287.

Maddux, J. E., Norton, L. W., & Stoltenberg, C. D. (1986). Self-efficacy expectancy, outcome expectancy, and outcome value:Relative effects on behavioral intentions. Journal of Personalityand Social Psychology, 51, 783-789.

Marsh, H. W. (1990). Influences of internal and external frames ofreference on the formation of math and English self-concepts.Journal of Educational Psychology, 82, 107-116.

Marsh, H. W. (1992). SDQ III. Campbelltown, New South Wales,Australia: University of Western Sydney, Publication Unit.

Marsh, H. W., & O'Neill, R. (1984). Self Description Question-naire III: The construct validity of multidimensional self-con-cept ratings by late adolescents. Journal of Educational Mea-surement, 21, 153-174.

Marsh, H. W., Walker, R., & Debus, R. (1991). Subject-specificcomponents of academic self-concept and self-efficacy. Contem-porary Educational Psychology, 16, 331-345.

Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors ofmath anxiety and its influence on young adolescents' courseenrollment and performance in mathematics. Journal of Educa-tional Psychology, 82, 60-70.

Norwich, B. (1987). Self-efficacy and mathematics achievement:A study of their relation. Journal of Educational Psychology, 79,384-387.

Pintrich, P. R., & De Groot, E. V. (1990). Motivational and self-regulated learning components of classroom academic perfor-mance. Journal of Educational Psychology, 82, 33-40.

Pokay, P., & Blumenfeld, P. C. (1990). Predicting achievementearly and late in the semester: The role of motivation and use oflearning strategies. Journal of Educational Psychology, 82,41-50.

Randhawa, B. S., Beamer, J. E., & Lundberg, I. (1993). Role ofmathematics self-efficacy in the structural model of mathematicsachievement. Journal of Educational Psychology, 85, 41-48.

Relich, J. D. (1983). Attribution and its relation to other affectivevariables in predicting and inducing arithmetic achievement: Anattributional approach to increased self-efficacy and achieve-ment in arithmetic. Unpublished doctoral dissertation, Univer-sity of Sydney.

Reyes, L. H. (1984). Affective variables and mathematics educa-tion. The Elementary School Journal, 84, 558-581.

Romberg, T. A., & Wilson, J. W. (1969). The development oftests. NLSMA Reports No. 7. Stanford, CA: SMSG.

Schunk, D. H. (1989). Self-efficacy and achievement behaviors.Educational Psychology Review, 1, 173-208.

Schunk, D. H. (1991). Self-efficacy and academic motivation.Educational Psychologist, 26, 207-231.

Schwarzer, R., Seipp, B., & Schwarzer, C. (1989). Mathematicsperformance and anxiety: A meta-analysis. In R. Schwarzer,H. M. Van Der Ploeg, & C. D. Spielberger (Eds.), Advances intest anxiety research (Vol. 6, pp. 105-119). Berwyn, PA: SwetsNorth America.

Shavelson, R. J., Hubner, J. J., & Stanton, G. C. (1976). Self-concept: Validation of construct interpretations. Review of Ed-ucational Research, 46, 407-441.

Shell, D. F., Murphy, C. C , & Bruning, R. H. (1989). Self-efficacyand outcome expectancy mechanisms in reading and writingachievement. Journal of Educational Psychology, 81, 91-100.

Siegel, R. G., Galassi, J. P., & Ware, W. B. (1985). A comparisonof two models for predicting mathematics performance: Sociallearning versus math aptitude-anxiety. Journal of CounselingPsychology, 32, 531-538.

Received February 17, 1993Revision received November 11, 1993

Accepted November 18, 1993 •