Sources of Self-efficacy in Mathematics; A Validation Study
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Transcript of Sources of Self-efficacy in Mathematics; A Validation Study
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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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+) 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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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
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E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22 +8
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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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
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+* 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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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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E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22 +0
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.
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+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>.
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*.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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E. ". #sher$ &. Pajares / Contemporary Educational Psychology 8* =)+> 4+J22 +3
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
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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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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
http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page12http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13http://var/www/apps/conversion/tmp/scratch_7/HYPERLINK%23page13 -
7/25/2019 Sources of Self-efficacy in Mathematics; A Validation Study
20/23
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