Sources of Self-efficacy in Mathematics; A Validation Study

7/25/2019 Sources of Self-efficacy in Mathematics; A Validation Study

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Contemporary Educational Psychology 34 (2009) 89101

Contents lists available at ScienceDirect

Contemporary Educational Psychology

j o u r n a l h o m e p a g e :w w w . e l s e v ie r . c o m / l o c a t e / c e d p s y c h

Sources of selfefficacy in mathematics: ! validation study

Ellen ". #shera$%

$ &ran' Pajaresb

a#niversity of (entuc'y$ Educational and Counseling Psychology$ )*+ Dic'ey ,all$ "e-ington$ ( *0123$

#S!bEmory #niversity$ 234* 5orth Decatur 6oad$ Suite )*$ !tlanta$ 7! 88))$ #S!

a r t i c l e i n fo

(eywords:

Sources of selfefficacy

Selfefficacy beliefs

Social cognitivetheory

9otivation

9athematics

9iddle school

a b s t r a c t

he purpose of this study was to develop and validate items with which to assess

!. ;andura theori?ed sources of selfefficacy among middle school

mathematics students. 6esults from Phase 2 =5 @ 2222> were used to develop and

refine items for subseAuent use. Bn Phase ) of the study =5 @ 4)*>$ a 8+item$ four

factor e-ploratory model fit best. Btems were revised to strengthen psychometric

properties. Bn Phase 8 =5 @ 48>$ a )*item$ fourfactor confirmatory factor model fit

best. his final model was invariant across gender and ethnicity. Subscales

correlated with selfefficacy$ selfconcept$ mastery goals$ and optimism. 6esults

suggest that the sources scale is psychometrically sound and could be adapted for

use in other domains.

)4Elsevier Bnc.

!ll rightsreserved.

2. Bntroduction

!s a fundamental part of his social cognitive

theory$ ;andura =2+41> posited that unless people

believe they can produce desired outcomes they

have little incentive to act. !lthough ample research

attests to the predictive power of selfefficacythe

beliefs students hold about their academic

capabilitieson academic achievement$ there have

been fewer efforts to investigate the sources

underlying these selfbeliefs =Pajares #rdan$

)1>.

;eliefs about one


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actions$ students build their efficacy beliefs through

the vicarious e-perience of observing others. Bn

many academic endeavors$ there are no absolute

measures of proficiency. ,ence$ students can gauge

their capabilities in relation to the performance of

others. Students compare themselves to particular

individuals such as classmates$ peers$ and adults as

they ma'e judgments about their own academic

capabilities. hey are most li'ely to alter their

beliefs following a model


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+ E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22

success =;andura$ 2++3K and see ,attie

imperley$ )3>. Social persuasions may be

limited in their ability to create enduring increases

in selfefficacy$ however. Bt may actually be easier

to undermine an individual.

&inally$;andura =2++3> hypothesi?ed that self

efficacy beliefs are informed by emotional and

physiological states such as an-iety$ stress$

fatigue$ and mood. Students learn to interpret their

physiological arousal as an indicator of personal

competence by evaluating their own

performances under differing conditions. Strong

emotional reactions to schoolrelated tas's can

provide cues to e-pected success or failure. ,igh

an-iety can undermine selfefficacy. Students who

e-perience a feeling of dread when going to a

particular class each day li'ely interpret their

apprehension as evidence of lac' of s'ill in thatarea. Bn general$ increasing students< physical and

emotional wellbeing and reducing negative

emotional states strengthens selfefficacy.

Perhaps the greatest limitation of research that

has been conducted on the sources of self

efficacy is the manner in which the sources have

been operationali?ed and assessed. &or this

reason$ findings to date regarding the sources of

selfefficacy should be interpreted with caution.

;elow we provide a description of the measures

used to assess the sources$ and we discuss their

limitations.

2.2. 9easuring the sources of selfefficacy

6esearchers have not reached consensus on

how best to measure the sources of selfefficacy

in academic settings. 9ost have used adapted

versions of the Sources of 9athematics Self

Efficacy Scale =S9ES> developed by"ent$ "ope?$

;iesch'e$ 2++2. Lriginally designed to assess

the sources of mathematics selfefficacy of college

students$ the items have been adapted for use in

both academic and social settings =!nderson

;et?$ )2K ;ritner Paj ares$ )1K "ope?

"ent$ 2++)K Smith$ )2K #sher Pajares$

)1b>. 9atsui$ 9atsui$ and Lhnishi =2++> also

designed a scale to measure the sources of

college students< mathematics selfefficacy$ whichhas been adapted for use with younger students

=i.e.$ (lassen$ )*>. ,ampton =2++4> developed

the Sources of !cademic SelfEfficacy scale$

which was validated and subseAuently used with

high school and college students with learning

disabilities =,ampton 9ason$ )8>. Lther

researchers have relied on unpublished sources

items =;ates (hasawneh$ )3K Stevens$

LlivMre?$ Nr.$ ,amman$ )1> or have used

alternate measuresas pro-ies for one or more of

the sources =Chin (ameo'a$ ))K Nohnson$

)0>. ;elow we analy?e the measures used to

assess each source.

9astery e-perience has been assessed in

various ways. 6esearchers who follow models

such as those put forth by "ent and his colleagues

have assessed mastery e-perience by as'ing

students to rate their past and current

performance in the academic subject of interest$

and items have shown strong internal consistency

=;ritner Pajares$ )1K "ent et al.$ 2++2>. Lne

problematic practice$ however$ has been the use

of students< objective performance as an indicator

of mastery e-perience. &or e-ample$ someresearchers have as'ed participants to selfreport

previous grades obtained =(lassen$ )*K 9atsui

et al.$ 2++> or have used actual test scores as a

measure of mastery e-perience =Chin

(ameo'a$ ))>. Such assessments do not reflect

the mastery e-periences described by ;andura

=2++3> as students< interpretations of e-perienced

events rather than as their objective performance.

his source of selfefficacy can be better obtained

through selfreport items that invite students to

rate the degree to which they have e-perienced

success rather than through con
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crete indicators of past performance such as

grades. Lne need only imagine how two students

with opposite academic histories might respond to

a grade of OO; in mathematics to understand how

such interpretations might differently alter their

selfefficacy =see Pajares$ )1>. Bn fact$ when

subjecting this contention to empirical scrutiny$

researchers have found that perceptions of one. Ihen they have

assessed social persuasions in this way$ most

investigators have reported moderate to strong

reliabilities for social persuasion items. Some

researchers have used measures inconsistent

with ;andura theori?ing about this

source. &or e-ample$ some have assessed social

persuasions with items tapping others. Lthers have assessed this

source by as'ing students to rate the e-tent to

which their instructors provide them with OOprompt

and regular feedbac' =;ates (hasaw neh$

)3$ p. 242>. Such items do not reflect social

persuasions asdefined and theori?ed by ;andura

=2++3>$ nor do they assess the e-tent to which

students receive evaluative feedbac' and

criticism.

;andura =2++3> contended that a number of

factors can influence physiological and affective

states$ including mood$ physical strength$ and

distress levels. ;ut physiological arousal has

typically been assessed as students< an-iety

toward a particular academic subject. "ent and his

colleagues used the &ennemaSherman 9ath

!n-iety Scale revised by ;et? =2+34> to measure

the physiological arousal of high school and

college students =7ainor "ent$ 2++4K"ent et al.$

2++2$ 2++1K "ope? "ent$ 2++)>. !n-iety items

havealso been used by other researchers =;ates

(hasawneh$ )3K ;ritner$ )4K ;ritner

Pajares$ )1K Pajares$ Nohnson$ #sher$)3KSmith$ )2K Stevens et al.$ )1K #sher

Pajares$ )1b>. Lthers have used additional

items used to measure this source such as as'ing

students to rate how much they li'e a particular

subject =9atsui et al.$ 2++>$ how thin'ing of a

subject ma'es them feel =(lassen$ )*>$ or how

school affects their physiological func
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E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22 +2

tioning =,ampton$ 2++4>. 6esearchers using

an-iety as a measure of physiological arousal

have reported strong reliability estimates.

!lthough one used factor analysis to

e-amine their 20 sources items. hey imposed a

threefactor solution representing vicarious

e-perience$ social persuasions$ and physiological

arousal that fit the model relatively well. he

authors provided little information on the factor

analytic methods employed$ however.

&urthermore$ because mastery e-perience was

eAuated with past performance$ construct validity

was established for only three sources. (lassen

=)*> later attempted to enhance the construct

validity of 9atsui et al..

E-ploratory factor analysis has been used to

assess the latent structure of sources items

adapted from "ent et al. =2++2> for use with

younger students. Some researchers found that a

fivefactor model in which vicarious e-perience

was separated into a peer and an adult factor bestfit the data$ but items representing the peers factor

demonstrated poor internal consistency =#sher

Paj ares$ )1b>. ;ritner and Pajares =)1>

foundthat a fourfactore-ploratory model best fit

the data in a sample of middle school science

students.

Stevens et al. =)1> used a confirmatory

factor analytic measurement model to determine

whether the parceled scores from sources

subscale items supported a single latent factor

representing the sources of mathematics self

efficacy. Due to poor fit$ the measurement model

was revised such that only the combination of

mastery e-perience$ vicarious e-perience$ and

social persuasions formed the sources factor.

Btems assessing an-iety factor analy?ed
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separately with negative valence mathematics

interest items to form a latent factor labeled

OOemotional feedbac' =p. 230>. Ihen the factor

structure of variables is un'nown$ particularly

when the factor structure may be

multidimensional$ parceling items may result in a

misspecified factor solution or in estimation bias

=;andalos$ ))>. Bt is also possible that the

negative wording in these items may li'ely have

led to what 9arsh =2++1> referred to asOOartifactors blurring conceptual and theoretical

distinctions in the variables.

he limitations noted above point to the need

for researchers to develop more thorough

measures that assess the multidimensionality of

the hypothesi?ed sources of selfefficacy. &actor

analytic results and the low reliability of the

vicarious e-perience subscales reported across

studies suggest that measures used to assess this

source have been inadeAuate. &urthermore$ in

many cases little information about the construct

validity of the sources items has been provided$

and there has been little correspondence between

the actual variables used and ;andura

theori?ed sources. &indings from such studies can

offer little insight about how academic self

efficacy develops.

2.8. Convergent validity

9astery e-perience has been shown to be the

most consistent predictor of students< selfefficacy

across academic domains and levels$ but reports

for the other three sources have been less con

sistent. hese inconsistent results are li'ely due to

methodological problems such as poor reliability$

aggregated scores that mas' information from any

one source$ or multicollinearity between thesources. Bt bears noting$ however$ that the

conte-tual factors present may have partly

determined how the sources have functioned in

diverse academic settings. Differences in the

predictive value of the sources on selfefficacy

vary according to the domain in which the

constructs are assessed$ and the magnitude and

strength of the relationship between the sources

and selfefficacy appear to be influenced by

students< gender$ ethnicity$ or academic ability

level =e.g.$ "ent et al.$ 2++1K #sher Pajares$

)1b>. hough it is too early to ma'e general

observations about the part played by these

conte-tual factors$ additional research should

e-amine whether students from different groupsinterpret information about their efficacy differently.

Ie view four primary reasons why establishing

a valid and reliable measure of the hypothesi?ed

sources of selfefficacy is warranted. &irst$ there

has been little consistency across studies as

regards the items used to assess the sources$

which has resulted in inconsistent findings.

Second$ low reliabilities have plagued vicarious

e-perience items. hird$ researchers have not yet

determined whether the measurement models

representing the sources scores are invariant

across student groups. &inally$ and perhaps most

important$ many of the items in the measures

used to date have not been consistent with

;andura original description of the

sources and thus offer little evidence for or against

the theori?ed influence of the sources.

2.*. Purpose of the study

Consistent with much of the research on self

efficacy in school settings$ most investigations of

the sources have been conducted in the domain

of mathematics. !nd most studies of the sources

have been underta'en with high school and

college students. his seems surprising given the

tendency for students< judgments about their

mathematics capabilities to decline when studentsencounter the more rigorous coursewor' of middle

school =!nderman 9aehr$ 2++*>. &or this

reason we elected to create a measure of sources

of selfefficacy for use in the domain of

mathematics and with middle school students.
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7/23

+) E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22

;ecause conclusions drawn from empirical

investigations of the sources are only as reliable

as are the items from instruments on which data

are gathered and results obtained$ items

developed directly from the tenets of social

cognitive theory are li'ely to produce results that

are able to e-pand and refine these tenets.

,ence$ the aim of this study was to develop andvalidate items with which to assess ;andura theori?ed four sources of selfefficacy in

the area of mathematics at the middle school

level.

here are two important reasons why a valid

and reliable measure of the sources of self

efficacy is needed. &irst$ selfefficacy beliefs play

a critical role in the academic and career choices

of students =,ac'ett$ 2++0>. 5aturally$ then$ it is

important for teachers and counselors to be

cogni?ant of the factors that help create and

nurture the selfefficacy beliefs of their students.

his information is invaluable in helping teacherstailor their instructional strategies and counseling

practices in ways most supportive both of their

students< selfefficacy and$ subseAuently$ of their

achievement. eachers and counselors can also

ma'e use of such assessments as they evaluate

the manner in which academic programs and

intervention strategies may influence the self

efficacy beliefs of the young people in their care.

!ll professional educators would readily agree that

identifying the ways in which students< unreal

istically low selfefficacy beliefs can be challenged

and altered is an essential and critical enterprise.

!nother important reason why a

psychometrically sound assessment of the

sources of selfefficacy is reAuired is that the te

nets of ;andura social cognitive theory

regarding the wor'ings of selfefficacy cannot

effectively be tested without such an assessment.

6esearchers who wish to understand the

formation of academic selfefficacy must obtain

that understanding using valid and reliable

measures that faithfully reflect the sources hypoth

esi?ed and their role within the broader structure

of social cognitive theory. his is especially

important in the field of academic motivation

where the sources of selfefficacy have often been

operationali?ed and measured in a manner that

bears little resemblance to how they were

hypothesi?ed by;andura =2+41$2++3>!

he overall validation process too' place in

three phases$ during which we followed the scale

validation protocol described by Spec tor =2++)>!

Ie first aimed to craft items to assess each

source bymatching them carefully to each source

as it has been described by;andura =2++3$ chap.

8>. Ie ne-t sought to establish a psycho

metrically sound model to measure the sources of

selfefficacy and to test whether the model is

invariant across gender$ ethnicity$ and

mathematics ability level. Ie e-amined evidence

for convergent and divergent validity by assessingthe relationship between the sources$ selfefficacy$

and other constructs typically included in studies

of academic motivation. Ie henceforth refer to

these respective phases as Phase 2$ Phase )$

and Phase 8 to render our procedures and

findings straightforward.

). Phase 2

).2. 9ethods

).2.2. Participants

Bn the fall of )0$ we invited a focus group of

7rade 1 students =n @ )8>$ a si-thgrade

mathematics teacher$ a parent of three middle

school students$ an eighthgrade teacher and

mathematics department chair$ and a middle

school principal to complete a survey and to

provide us with feedbac' on item wording and

clarity. Ie selected si-thgrade students for this

focus group because they represented the

youngest participants in the study and thus would

be most li'ely to point out unfamiliar or unclearwording.
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8/23

Several wee's later$ we conducted a large

scale investigation of the revised survey

instrument with 2222 students =00+ girls$ 00)

boys> in 7rades 1 =n @ 838>$ 7rade 3 =n @ 830>$

and 7rade 4 =n @ 818> enrolled in a public

suburban middle school in the Southeastern

#nited States. 9ost students in this sample were

of uppermiddle socioeconomic status.

Participants identified themselves as 1)R Ihite

=n @ 133>$ 23R !sian or !sian !merican =n @ 24+>$28R ;lac' or !frican !merican =n @ 283>$ 0R

,ispanic =n @ 04>$ and )R of mi-ed ethnic origin

=n @ )3>. wentythree students did not report

their ethnicity.

).2.). Data sources and collection procedures

Ie followed a number of steps when creating

the Sources of 9iddle School 9athematics Self

Efficacy Scale. Ie relied on the seminal

theoretical wor' in which the sources of self

efficacy are described =;andura$ 2++3> to create

items to assess each of the four sources. Btems

were written as firstperson statements$ and

students were as'ed to rate how true or falseeach statement was for them on a scale from 2

=definitely false> to 1 =definitely true>. Student

focus group participants were drawn from a si-th

grade language arts class. he first author was

present to debrief the focus group participants and

to discuss item wording. !dults provided feedbac'

on the telephone or via email correspondence.

!fter having first subjected the initial 4*item

sources instrument to focus group participants for

feedbac'$ we made slight revisions to item

wording. Ie did not at this point drop any items.

he revised items were then used with the larger

sample described above. he sources scale used

in Phase 2 comprised 4* items: )2 masterye-perience items$ )8 vicarious e-perience items$

) social persuasions items$ and ) physiological

and affective state items.

Ie also assessed mathematics selfefficacy

using four measures: mathematics grade self

efficacy and mathematics courses selfefficacy

=;andura$ )1K ,ac'ett ;et?$ 2+4+>K

mathematics s'ills selfefficacy =see 5C9$

)>K and selfefficacy for selfregulated learning

=;andura$ )1K #sher Pajares$ )4>. Students

responded to the selfefficacy measures on a si-

point "i'erttype scale ranging from 2 =not at all

confident>$ to 1 =completely confident>. !lpha

reliabilities for the selfefficacy measures were .+*$

.+*$ .+0$ and .40$ respectively.Bnstruments were administered to middle

school students during an e-tended homeroom

class monitored by the first author and trained

graduate students. Directions were read aloud to

all students via a closedcircuit video broadcast

prerecorded by the first author. Students

submitted their surveys in a sealed envelope to

ensure anonymity.

).2.8. !nalyses

Singer and Iillett =)8> observed that OOwise

researchers conduct descriptive e-ploratory

analyses of their data before fitting statistical

models =p. 21>. Bt was in this spirit that we

undertoo' data analyses at this and each

subseAuent phase of the validation study. Ie first

closely e-amined item means$ standard

deviations$ freAuency distributions$ s'ewness$ and

'urtosis. Ie assessed evidence for construct

validity by e-amining each item


9/23


s'ewness or 'urtosis$ low itemtotal or item

outcome correlations> was deleted or revised.

).2.*. 6esults and discussion

Lf the 4* sources items used in Phase 2$ )8

items =28 of which were vicarious e-perience

items> were identified as having low itemtotalcorrelations. ;ecause previous findings have

suggested that i tems tapping vicarious

e-periences from peers or from adults may

represent two distinct factors =e.g.$ "ent et al.$

2++1K #sher Pajares$ )1b>$ we recalculated

itemtotal correlations for thevicarious e-perience

items after separating them into three categories

representing vicarious e-perience from peers$

from adults$ and from self. 6esults still revealed

ten problematic itemtotal correlations among the

vicarious e-perience items. hese findings mir

rored the difficulties other researchers have had in

creating internally consistent items to assess this

source$ particularly as it pertains to vicarious

influences in mathematics.

Ie ne-t e-amined correlations between each

item and the four selfefficacy measures.

Coefficients below T.8T were observed for 3 of the

4* mastery e-perience correlations$ 00 of the +)

vicarious e-perience correlations$ 2+ of the 4

social persuasions correlations$ and 21 of the 4

physiological state correlations. &inally$ we loo'ed

across all criteria and flagged items that were

subpar on multiple indicators. Poorlyperforming

items were removed and used to generate new

items for use in Phase ).

8. Phase )

8.2. 9ethods

8.2.2. Participants

Participants in Phase ) were 4)* students

=*80 girls$ 84+ boys> in 7rade 1 =n @ )*4>$ 7rade

3 =n @ )0+>$ and 7rade 4 =n @ 823> enrolled at a

public suburban middle school in the

Southeastern #nited States. School records

identified these participants as 11R Ihite =n @

0*1>$ )2R ;lac' or !frican !merican =n @ 232>$

1R ,ispanic =n @ 0>$ *R !sian or !sian

!merican =n @ 8>$ and 8R of mi-ed ethnic origin

=n @ )3>. !lthough most students in this samplewere of uppermiddle socioeconomic status$ )2R

=n @ 23)> were registered to receive free or

reducedprice lunch. Students were grouped by

ability in mathematics and received instruction that

was either below grade level$ on grade level$ or

above grade level. he school had identified 234

students as OOtalented and gifted in mathematics.

8.2.). Data sources and collection procedures

;ased on findings of Phase 2$ we made

modifications and additions to the Sources of

9iddle School 9athematics SelfEfficacy Scale

items$ particularly those tapping vicarious

e-perience and social persuasions$ which

demonstrated some psychometric wea'nesses in

Phase 2. Lnce again$ we too' care to craft and

retain items that represented as many facets of

each source as possible as described by ;andura

=2++3>.Ie began Phase ) with 41 sources items:

2) assessing mastery e-perience$ 8 assessing

vicarious e-perience$ )4 assessing social

persuasions$ and 21 assessing physiological

state. Ie used the same selfefficacy measures inPhase ) as were used in Phase 2. Bnternal

consistency for the selfefficacy measures ranged

from .4+ to .+*. Bnstruments in Phase ) were

administered in individual mathematics classes by

the first author in &ebruary of )1.

8.2.8. !nalyses

Ie used the same cutoff criteria described in

Phase 2 for determining the psychometric fitness

of the items. hese criteria incorporated s'ew

and 'urtosis cutoffs recommended by(line =)0>
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10/23

for analyses using ma-imum li'elihood =9">

estimation. Ie then conducted e-ploratory factor

analysis =E&!> with 9" estimation to determine

whether four distinct sources underlay students and

2 items on &actor 8 =loadings from

.* to .30>. hese factors were respectivelylabeled physiological state and vicarious

e-perience. Si- items loaded on &actor *$ labeled

mastery e-perience =loadings from .** to .11>.

he four factors accounted for a combined +4R

of the variance$ and the interfactor correlations

ranged from .)+ between mastery e-perience

and vicarious e-perience to .1 between mastery

e-perience and social persuasions. he items

composing each of the four factors also

demonstrated good internal consistency =a range

from

.40 to .+)>.

*. Phase 8

*.2. 9ethods

*.2.2. Participants

Participants in Phase 8 were 48 students

=*4 girls$ 8+0 boys> in 7rade 1 =n @ )4)>$ 7rade

3 =n @ )00>$ and 7rade 4 =n @ )11> enrolled at a

public suburban middle school in the

Southeastern #nited States. School records

identified these participants as 13R Ihite =n @

0*2>$ 2+R ;lac' or !frican !merican =n @ 20>$

1R ,ispanic =n @ 02>$ *R !sian or !sian

!merican =n @ )4>$ and *R of mi-ed ethnic origin

=n @ 88>. Lnce again$ most students were of

uppermiddle socioeconomic status$ but 2+R =n @208> were registered to receive free or reduced

price lunch. Students receiving selfcontained

special education mathematics instruction were

not included in the studyK however$ special

education students receiving inclusion instruction

=n @ *2> were invited to participate. Students were

grouped by ability in mathematics and received

instruction that was either below grade level =n @

32$ +R>$ on grade level =n @ *3+$ 1R>$ or above

grade level =n @ )08$ 82R>.

*.2.). Data sources and collection procedures

!lthough we were pleased with the 8+ items

retained in Phase )$ there were several reasonswhy we felt it important to include more rather

than fewer items in the final phase of the

validation study. &irst$ many items that survived

Phase ) were redundant and could be improved

by slight modification. Ie also made


11/23

+* E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22

changes to some of the items that did not survive

empirical scrutiny in Phase ) in hopes of retaining

them in Phase 8. Second$ adding or modifying

items once again helped us in our Auest to

develop items reflective of the multidimensionality

of the sources described by ;andura =2++3>.

hird$ we began the final phase of the study by

submitting items to e-perts in social cognitivetheory for their feedbac' on content validity of the

final items =!. ;andura$ personal communication$

5ovember )$ )1K ;. N. Vimmerman$ personal

communication$ Lctober )*$ )1K D. ,. Schun'$

personal communication$ 5ovember 2$ )1>.

hese e-perts were as'ed whether items were

theoretically sound$ and they were given space to

comment on each of the items. ;ased on the

observations and recommendations of these

scholars$ we rejected four items =e.g.$ OOB.

Cronbach$ as was reported use of selfhandicapping strategies =e.g.$ OOSome students fool

around the night before a math test. hen if they

don. Cronbach drawn from the "ife Lrientation est

6evised ="L6K Scheier Carver$ 2+40> =a @ .

40>.
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12/23

he instrument used in Phase 8 was

administered to students in their mathematics

classes by the first author during 5ovember and

December of the )1J)3 school year.

Students< responses to all motivation statements

were assessed using a "i'erttype scale ranging

from 2 =definitely false> to 1 =definitely true>.

o further test the convergent validity of the

sources of mathematics selfefficacy$ we obtained

two measures of students< achievement inmathematics: students< semester grades in mathe

matics as well as their mathematics teacher. Ie e-pected that

students with higher ratings in their mathematics

competence would tend to report more mastery

e-perience and social persuasions and lower

negative arousal than those with lower

mathematics competence.

*.2.8. !nalyses

he primary aim of Phase 8 was to ascertain

the model that best represented the simple

structure of the sources of selfefficacy. Ie made

our initial decisions for item elimination by

invo'ing cutoff criteria for the descriptive and

correlational statistics described in Phase 2. Ie

then imposed a more stringent psychometric

cutoff to eliminate items with s'ewness or 'urtosis

e-ceeding one standard deviation from the mean

=(line$ )0>. Ie ne-t e-amined the itemtotal

correlations$ flagging items whose correlations

with subscale totals were less than or eAual to .00.

his higher threshold provided a more stringent

criterion for item selection$ but$ bearing in mind

that itemtotal correlations are inherentlydependent on items that may themselves be

problematic$ we used this criterion as only one

indication of an item.his enabled us to arrive at a final sources

scale that was parsimonious$ practical$ and

conceptually and psychometrically strong.

Ie used confirmatory factor analysis =C&!> to

test a measurement model of scores on the

remaining sources items. #nli'e E&! in which thenumber of factors is un'nown$ C&! reAuires that

researchers have a strong hypothesis regarding

the number of latent variables in a model

=hompson$ )*>. Bn 'eeping with findings from

Phase )$ our measurement model included four

latent variables: mastery e-perience$ vicarious

e-perience$ social persuasions$ and physiological

states. he factors were permitted to covary =see

"ent et al.$ 2++1>. Error terms were hypothesi?ed

to be uncorrelated. Bn each model the first item

loading was constrained to 2. to set the scale of

measurement$ and no items were allowed to

double load.

Ie relied on four commonlyused inde-es todetermine the fit of each C&! model: the SatorraJ

;entler =S;> v)test statistic$ used when data are

nonnormally distributed$ which was the case withour data =;entler$ )0>K the comparative fit inde-=C&B>K the root mean sAuare error of appro-imation =69SE!>K and the standardi?edroot mean sAuare residual =S696>. Statisticianssuch as ;yrne =)1> freAuently remindresearchers that fit inde-es can only describe amodel and ;yrne =)1> changes to the modelwere made only if and when in the service ofcreating a stronger
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13/23


model both conceptually and theoretically and

always with an eye toward model parsimony.

Ie conducted tests for multigroup

measurement invariance by e-amining two

increasinglyrestrictive hierarchical C&! measure

ment models. hese models were based on

analysis of covariance structures and were runseparately by gender$ ethnicity$ and ability level for

all subgroups with more than 2 participants.

he baseline model tested for eAuivalent factor

structure$ not ta'ing into account the factor

pattern loadings. Bn the second model$ factor

loadings were constrained to be invariant across

groups. Ie compared the fit of the two models to

determine whether the factor loadings in each

model were invariant. ! nonsignificant change in

chisAuare =see &rench &inch$ )1> and a

change in C&B of less than .2 =Cheung

6ensvold$ ))> were indicative of model

invariance.

Ie e-amined evidence for the e-ternal validity

of the sources items by calculating descriptive

statistics and Pearson correlations between the

final sources subscales$ selfefficacy outcomes$

and the motivation variables of interest. o

establish construct validity$ we conducted four

multiple regression analyses in which we

e-amined$ simultaneously$ the independent

contribution of the four sources of selfefficacy to

the prediction of each selfefficacy measure.

;ecause previous results =#sher Pajares$

)1b>and theoretical guidance =;andura$ 2++3>

suggest that the relationship between

physiological state and selfefficacy is potentially

curvilinear$ we included the Auadratic term ofphysiological state in each initial model. Bf the term

was nonsignificant$ it was removed from the final

model. Ie supplemented these analyses with

commonality analysis and regression structure

coefficients =Courville hompson$ )2>.

*.2.*. 6esults and discussion

he final sources of selfefficacy items were

administered to this new sample of students and

the more stringent psychometric cutoff criteria

described above were imposed. hrough this

process we identified 8* problematic items that

were removed from further analysis. &ivesimilarlyworded items were also removed$

leaving us with 8* items. Ie used psychometric

and conceptual =theoretically driven>

considerations when selecting the )* best items to

retain for the confirmatory factor analysis. Lf the

items retained in the final model$ seven were

used in Phase 2$ si- were modified from Phase 2

for use in Phase )$ seven were used in Phase )$

one was modified from Phase ) for use in Phase8$ and three were new items designed for Phase

8. able 2 presents the correlation matri- and

itemtotal correlations for the dependent =ob

served> variables in the model. Bnteritem

correlations among the si- items designed to

measure each source ranged from .* to

.14. he si- items in each of the four subscales

showed adeAuate internal consistency$ with

Cronbach .44 for

mastery e-perience$ .4* for vicarious e-perience$

.44 for social persuasions$ and

.43 for physiological state.

he final measurement model$ illustrated in

&ig. 2$ showed acceptable fit$ S; v)=)*1> @

12.)2$ p .2$ C&B @ .+1$ 69SE! @.*$ S696 @ .*. !ll standardi?ed factor loadingsin the model were significant at the a@ .0 leveland ranged in magnitude from.12 to .48. !s described above$ rarely do

individuals rely on only one informational source

when ma'ing judgments of their efficacy to

perform academic tas's =;andura$ 2++3>. ,ence$

the sources of selfefficacy are theoretically

interrelated$ which the findings of this study

maintain. he four sources factors showed

intercorrelations ranging in magnitude from .*0

=between vicarious e-perience and physiological

state> to .48 =between social persuasions andmastery e-perience>. he strong correlation be

tween mastery e-perience items and social

persuasions is not surprising$ given that these two

sources tend to operate in tandem in this conte-t.

Students who perceive their past performances in

mathematics as successful are li'ely to receive

freAuent praise on those very performances.

Conversely$ students who interpret their efforts in

mathematics as futile are li'ely to receive =or to

perceive> messages from others that they are not

capable. Bn the absence of an e-periential base$

social persuasions often become hollow platitudes

that do little to influence efficacy judgments

=;andura$ 2++3>.

able 2

9eans$ standard deviations$ and correlations for final sources of selfefficacy items
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5 @ 48.

5ote. Btemtotal correlations between each item and its subscale counterparts appear on diagonal. Btems within each givensubscale appear in grayscale.


15/23

+1 E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22

&ig. 2. 9easurement 9odel for the )*Btem Sources of 9iddle School 9athematics SelfEfficacy Scale. 5ote. S; v)=)*1> @ 12.)2$ C&B @ .+1$ 696 @ .*$ 69SE! @ .*$ 69SE!

+R CB: =.84$ .*3> Parameters without asteris's were fi-ed to 2. !ll path coefficients were statistically significant$ p .0.

able )

Summary of 7oodnessof&it Statistics for the &inal Sources of SelfEfficacy 9easure

ment 9odel by Subgroup

Subgroup 9odel S;v)

df C&B S696 69SE!

7irls **.08 )*1 .+1 .0 .*

;oys **8.*2 )*1 .+0 .0 .0

!frican !merican students 8).30 )*1 .+0 .1 .0

Ihite students *+0.23 )*1 .+0 .0 .0

Ln"evel students *83.+3 )*1 .+1 .* .*

!bovelevel students 8+1.2 )*1 .+* .0 .1

5ote. 6obust statistics are reported. 9odels were specified for each subgroup as

illustrated in &ig. 2. 7irls =n @ *4>$ ;oys =n @ 8+0>K !frican !merican =n @ 20>$ Ihite

=n @ 0*2>K Ln "evel =n @ *3+>$ !bove "evel =n @ )08>.


16/23

*.2.0. ests for measurement invariance

6ecall that we conducted confirmatory factor analyses on two

increasinglyrestrictive hierarchical measurement models for each of

the three subgroups of interest: gender$ ethnicity$ and mathematics

ability level. ;ecause the measurement model showed adeAuate

model fit for girls$ boys$ !frican !merican students$ Ihite students$ on

level students$ and abovelevel students =see results in able )>$ we

specified the same model for each subgroup when testing for factorial

invariance.

he measurement model was invariant for girls and boys$ with an

adjusted D S; v)=)> @ )3.0) =see able 8>. he nonsignificant chi

sAuare statistic provides evidence against rejecting the nullhypothesis$ which states that the model postulated does not differ
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17/23


able 8

ests for Bnvariance of &inal Sources of SelfEfficacy 9easurement 9odel !cross 7ender$ Ethnicity$ and !bility "evel

7roup: 9odel S;v)

df C&B S696 69SE! 69SE! +R CB 9odel Comparison D S;v)

D df D C&B

7ender: 9odel 2Configural =no constraints> 448.+* *+) .+01 .*3 .*0 .*$ .*+

7ender: 9odel )&actor loadings invariant +84.+3 00) .+00 .0) .** .*$ .*+ ) versus 2 )3.0) ) .2

Ethnicity: 9odel 2Configural =no constraints> 430.03 *+) .+0) .0* .*4 .*)$ .08

Ethnicity: 9odel )&actor loadings invariant 4+4.88 02) .+0) .1 .*3 .*)$ .0) ) versus 2 23.1 ) !000

9ath !bility: 9odel 2Configural =no constraints> 488.+0 *+) .+01 .0 .** .84$ .*+ 9ath !bility: 9odel )&actor loadings invariant 401.0) 02) .+01 .00 .*8 .84$ .*4 ) versus 2 2+.0) ) !000

5ote. 6obust statistics are reported. he D S;v)represents a corrected value =see Satorra ;entler$ )2>. he D S;v

) statistics are not statistically significant$ indicating

eAuivalence in the two measurement models for each subgroup.

7irls =n @ *4>$ ;oys =n @ 8+0>K !frican !merican =n @ 20>$ Ihite =n @ 0*2>K Ln "evel =n @ *3+>$ !bove "evel =n @ )08>.

from the population model =;yrne$ )1K hompson$ )*>. heanalysis by ethnicity also revealed that the sources items wereinvariant for Ihite and !frican !merican students. he twogroupmodel with constrained loadings also showed an adeAuate fit to the

data$ DS; v)=)> @ 23.1. &inally$ the sources items were invariant

for students on and above level in mathematics$ showing an

acceptable fit in the invariance model$ adjusted DS; v)=)> @ 2+.0).

able * listseach item in the final Sources of 9iddle School 9athematics

SelfEfficacy Scale along with its standardi?ed loading estimate and errorterm for each of the seven measurement models. Bn all analyses$ the

standardi?ed factor loadings were significant at the a @ .0 level and

ranged in magnitude from .*2 to .3+.

*.2.1. Evidence of construct validity

he items$ both individually and combined$ were correlated with the

four selfefficacy measures. he magnitude of the ?eroorder

correlations between the sources subscales and the four selfefficacy

outcomes offers compelling evidence for the criterion validity of the

sources subscales. Correlations between the sources and selfefficacy

were all statistically significant =p .2> and ranged from an absolutevalue of .8) to .33. Consistent with past research$ the highest

correlation was that obtained between mastery e-perience and self

efficacy =see #sher Pajares$ in press>. Comparing the correlation

between the sources measures and selfefficacy outcomes to those

obtained in previous research studies of the sources reveals that the

measures created in this study are not only sound$ but demonstrate

greater predictive utility than have past measures.

Convergent validity was supported by the strong association

between the sources$ selfefficacy$ related motivation constructs$ and

achievement =see able 0>. Bn fact$ each source was related to

mathematics selfconcept$ invitations of self and others$ tas' goals$

selfhandicapping$ optimism$ and semester grades in mathematics.

hese associations were especially strong between the sources andmathematics selfconcept beliefs and invitations. 7iven the well

established relationship between selfefficacy and selfconcept$ there

is li'ely little distance between the pathways that nourish these two

selfbeliefs. Bndeed$ selfconcept theorists have contended that

students rely on factors such as mastery e-periences$ social

comparative information$ and praise when forming their self

perceptions =;ong S'aalvi'$ )8K S'aalvi'$ 2++3>. 9oreover$ there

is evidence to show that these sources have a more pronounced effect

on selfconcept when selfconcept is assessed at the domainspecific

level$ such as mathematics$ than at a more global level =L.

he strong correlations between the sources and students< ten

dency to be inviting of self and others also confirms past research

findings. 6esearchers have contended that the invitational =or

disinvitational> messages that students send themselves and others

act as a sieve through which their observations of themselves and the

world necessarily pass =#sher Pajares$ )1aK Qaliante Paj ares$

2+++>. Bndeed$ the sources of selfefficacy and invitationsshare some

features. &or e-ample$ Pur'ey =)> has suggested that OOas'ing

students to describe what significant others say about them reveals

much about what students say to themselves =p. )1>. !s have other

researchers =Pajares Veldin$ 2+++K #sher Pajares$ )1a>$ we

found that all four sources were related to students< invitations of selfand others.

he sources subscales were also able to discriminate between

unrelated constructs. &or e-ample$ selfefficacy researchers have

noted that performance approach goals and selfefficacy are rarely

correlated =e.g.$ Pajares$ ;ritner$ Qaliante$ )>. Lur own results

corroborate this finding by showing low or nonsignificant correlations

between the sources of selfefficacy and students< performance

approach goal orientation. Correlations between vicarious e-perience

and achievement were also low$ whereas those between the other

three sources and achievement were not$ which would also be

e-pected.

Ie ne-t sought to ascertain the independent contribution made by

each of the four hypothesi?ed sources to the prediction of middle

school students< mathematics selfefficacy. Ie regressed the four selfefficacy outcome variablesgrade selfefficacy$ mathematics s'ills

selfefficacy$ courses selfefficacy$ and selfefficacy for selfregulated

learningon the four sources of selfefficacy in four simultaneous

multiple regression analyses =see able 1>. 6egression results

revealed that$ consistent with past research$ mastery e-perience was

a strong and consistent predictor of selfefficacy. Bn fact$ mastery

e-perience e-plained over )R of the variance in grade selfefficacy

and in mathematics s'ills selfefficacy$ minimi?ing the variance

e-plained by each of the other sources to )R or less. Qicarious

e-perience was a strong predictor of selfefficacy for selfregulated

learning$ e-plaining 21R of the variance in that outcome. Social

persuasions contributed modestly to the prediction of grade and

courses selfefficacy. Physiological state was Auadratically related to

selfefficacy for selfregulated learning.

hese findings offer support for ;andura theori?ing that

mastery e-perience is the most powerful source of selfefficacy and

that the three other sources also influence$ if to a lesser degree$

students< beliefs in their mathematics efficacy. !s our results also

indicate$ the relative predictive power of the sources of selfefficacy

depends on the outcome measure being used. Bt is easy to

understand$ for e-ample$ that students< perceptions of their mastery

e-perience are strongly related to their selfefficacy for obtaining a high

grade in mathematics. 9oreover$ our findings support ;andura


18/23

able *

Standardi?ed factor pattern loadings for final sources of selfefficacy items by subgroup

Btem &ull Sample 7irls ;oys

2. B ma'e e-cellent grades on math tests =9E2>)

.348 =.1))> .3+2 =.122> .33) =.180>

). B have always been successful with math =9E8>)

.3* =.13)> .3*8 =.11+> .381 =.133>

8. Even when B study very hard$ B do poorly in math =9E1>%2

.133 =.381> .1+4 =.321> .10) =.30+>

*. B got good grades in math on my last report card =9E4>2

.114 =.3**> .11* =.3*4> .13+ =.38*>

0. B do well on math assignments =9E+>29

.4)3 =.01)> .42 =.041> .40* =.0)>

1. B do well on even the most difficult math assignments =9E2)>8

.3+8 =.12> .42) =.04*> .311 =.1*8>

3. Seeing adults do well in math pushes me to do better =Q!*>)

.1++ =.321> .3) =.1+*> .148 =.382>

4. Ihen B see how my math teacher solves a problem$ B can picture myself solving the problem in the same way =Q!1>)

.3*0 =.113> .301 =.10*> .383 =.131>

+. Seeing 'ids do better than me in math pushes me to do better =QP2>2

.1)3 =.33+> .0+1 =.48> .103 =.308>

2. Ihen B see how another student solves a math problem$ B can see myself solving the problem in the same way =QP+>)

.142 =.38)> .18+ =.33> .324 =.1+1>

22. B imagine myself wor'ing through challenging math problems successfully =QS*>2

.32* =.3> .312 =.1*+> .13 =.3*)>

2). B compete with myself in math =QS0>8 .182 =.331> .018 =.4)3> .3 =.32*>

28. 9y math teachers have told that B am good at learning math =P*>29

.3* =.32> .14 =.388> .3)4 =.141>

2*. People have told me that B have a talent for math =P0>8

.3*2 =.13)> .3* =.138> .38+ =.138>

20. !dults in my family have told me what a good math student B am =P3>)

.3*2=.132> .383 =.131> .3*1 =.111>

21. B have been praised for my ability in math =P28>29

.42) =.04*> .48 =.003> .3+ =.128>23. Lther students have told me that B)9 .3+) =.12> .4)+ =.00+> .310 =.1**>

24. 9y classmates li'e to wor' with me in math because they thin' B29

.320 =.3> .31) =.1*3> .113 =.3*0>

2+. Nust being in math class ma'es feel stressed and nervous =P,)>%29

.33+ =.1)1> .4)3 =.01)> .3)) =.1+2>

). Doing math wor' ta'es all of my energy =P,8>%)

.12) =.3+2> .123 =.343> .13 =.3+0>

)2. B start to feel stressedout as soon as B begin my math wor' =P,0>%2

.4)8 =.014> .4*8 =.084> .3+3 =.1*>

)). 9y mind goes blan' and B am unable to thin' clearly when doing math wor' =P,3>%2

.1+8 =.3)2> .320=.1++> .114 =.3**>

)8. B get depressed when B thin' about learning math =P,+>%29

.1+* =.3)> .3)* =.1+> .11 =.302>

)*. 9y whole body becomes tense when B have to do math =P,2)>%2

.333 =.18> .340 =.1)> .313 =.1*)>

5ote: !ll item loadings are statistically significant. Error variances are presented in parentheses to the right of each standardi?ed estimate. 5umeric superscripts denote the

study phase in which each item was first introduced. Btems that were modified in subseAuent phases are followed by the superscript OO9.

9E$ 9astery E-perienceK Q!$ Qicarious E-perience from !dults$ QP$ Qicarious E-perience from PeersK QS$ Qicarious E-perience

from SelfK P$ Social PersuasionsK P,$ Physiological State.%

6eversescored item.

+4
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19/23

E.".#sher$&.Pajares/Contempora

ryEducationalPsychology8*=)+>4+J22

E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22 ++

0. 7eneral discussion

Lur goal in this investigation was to develop and validate items that

assess the four theori?ed sources of selfefficacy =;andura$2++3>in the

area of middle school mathematics. Ie also aimed to e-amine the

relationship between these sources and selfefficacy$ other motivation

constructs$ and achievement. o this end$ we carefully crafted items to

assess the sources of selfefficacy as ;andura hypothesi?ed$ as'ed

e-pert selfefficacy theorists to provide feedbac' on the validity of the

items$ administered the items to middle school students$ and too' into

account the theoretical and statistical merits of the items when choosing

those best suited for investigating the sources. he final$ )*item

Sources of 9iddle School 9athematics SelfEfficacy Scale developednot only reflects the four sources hypothesi?ed by ;andura but also

displays strong psychometric properties and invariance across gender$

ethnicity$ and mathematics ability level. !nalyses of items in each of the

four sources subscales provided evidence for strong content validity$

internal consistency$ and criterion validity. Bndeed$ results of the factor

and reliability analyses reveal that the sources scale is psychometrically

sound and can be reliably used to assess the antecedents of

mathematics selfefficacy with students in 7rades 1J4.

Bt bears noting that$ even though the items designed to assess

vicarious e-perience in this study were internally consistent and

reflected the multidimensional nature of this source =i.e.$ tapped

vicarious e-perience from adults$ peers$ self>$ vicarious e-perience

remains a construct difficult to capture using traditional selfreport$

Auantitative measures. he same vicarious e-perience may boost the

mathematics efficacy beliefs of one study while lowering those of

another. his is no doubt why ;andura =2++3> asserted that OOa

distinction must be drawn between information conveyed by

e-perienced events and information as selected$ weighted$ and

integrated into selfefficacy judgments. ! host of personal$ social$ and

situational factors affect how direct and socially mediated e-periences

are cognitively interpreted =p. 3+>. Empirical assessments that Auantify

the sources will continue to reAuire scales particularly welltuned to the

cognitive appraisals students ma'e of efficacybuilding information$ and

researchers will need to be mindful of how the relationship between

vicarious e-perience and selfefficacy may be affected by such

appraisals.

Bnvestigators who Auantify the sources should also consider the role

played by item wording$ which can lead to different results =e.g.$ in factor

analysis> that may reflect artifacts rather than conceptual differences inunderlying constructs =9arsh$ 2++1>. Some researchers have contended

that the response patterns students use when answering certain

positively and negatively worded items may reflect a substantial

and meaningful personal bias =DiStefano 9otl$ )1K ,oran$

DiStefano$ 9otl$ )8>. Iith the e-ception of the items designed

to assess physiological state and one mastery e-perience item$

the items used in this study were positively worded. Bt is of course

possible that negativelyworded items would have elicited different

responses. Bn fact$ in crafting items the researcher becomes

Auic'ly aware that valence is only one piece of the semantic

pu??le. Compare an item from the final sources scale$ OO!dults in

my family have told me what a good math student B am$ to its

reverse$ OO!dults in my family have not told me what a good math

student B am. he two items assess Auite different e-periences$

and neither can be said to evaluate the degree to which an

individual receives negative persuasions. &or such an

assessment$ the researcher would need to include yet another

item such as: OO!dults in my family have told me what a bad math

student B am. his latter item would li'ely ma'e 'nown a new

dimension of social persuasions$ one untapped by positively

worded items such as those included in this and most other

studies of the sources. Bnvestigating the influence of such wording
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Documents

Sources of Self-efficacy in Mathematics; A Validation Study