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A i udes owa ds ma hema ics a seconda y
le el: De elopmen and s uc u al alida ion
o he Scale o Assessing A i udes owa ds
Ma hema ics in Seconda y Educa ion (SAT-
MAS)
La a Yáñez-Ma quina1, Lou des Villa dón-Gallego 1
1
Facul y o Psychology and Educa ion, Uni e si y o Deus o, Bilbao
Spain
Co espondence: La a Yáñez-Ma quina. Facul y o Psychology and Educa ion, Uni e si y o Deus o. A da. de
las Uni e sidades, 24. 48007 Bilbao (Spain). E-mail: la a.yannez@deus o.es
© Educa ion & Psychology I+D+i and Ilus e Colegio O icial de la Psicología de Andaluacía O ien al (Spain)
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Abs ac
In oduc ion. In seconda y educa ion, s uden s’ low achie emen and engagemen in ma he-
ma ics a e closely ela ed o hei a i udes owa ds he subjec . Despi e he in e na ional body
o esea ch, an exhaus i e li e a u e e iew o he exis ing ins umen s o measu ing i d aws
a en ion o he inconsis ency in he de ini ion and co esponding ac o s uc u e o he con-
s uc a i udes owa ds ma hema ics. The e o e, he aim o his pape is o de elop and ali-
da e an ins umen o measu ing seconda y s uden s’ a i udes owa ds ma hema ics based on
a p elimina y de ailed heo e ical amewo k.
Me hod. The sample comp ised 792 s uden s, wi h an a e age age o 13.96 (SD = 1.09)
yea s, om Biscay (Basque Coun y Au onomous Region, Spain). Con i ma o y ac o anal-
yses we e conduc ed o es he heo e ical p oposed non-hie a chical s uc u e, consis ing o
h ee i s -o de ac o s (s uden ’s ma h sel -concep , pe cei ed use ulness o ma hema ics and
in e es o ma hema ics).
Resul s. The esul s la gely con i med ha his model showed a good i o he da a. In e nal
consis ency, disc iminan alidi y and c i e ion- ela ed alidi y es s yielded good C onbach’s
alpha coe icien s, s ong co ela ions be ween he p oposed dimensions and mode a ely posi-
i e co ela ion sco es be ween a i udes owa ds ma hema ics and s uden s’ ma hema ical
pe o mance measu ed wi h a ma h achie emen es de eloped ad-hoc.
Discussion. The esul ing 19-i em scale may ep esen a psychome ically sound ins umen
bo h o esea ch pu poses and o educa ional in e en ions. To conclude, he con ibu ion o
he p esen s udy o he esea ch on a i udes owa ds ma hema ics is discussed, and some is-
sues a e sugges ed o u u e esea ch o add ess.
Keywo ds: A i udes owa ds ma hema ics, seconda y educa ion, ma hema ics educa ion,
con i ma o y ac o analysis.
Recep ion: 11.28.15 Ini ial accep ance: 12.14.15 Final accep ance: 10.16.16
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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Resumen
In oducción. El bajo log o y el escaso comp omiso en ma emá icas de los es udian es de
secunda ia es án es echamen e elacionados con sus ac i udes hacia la asigna u a. A pesa de
la amplia in es igación exis en e al espec o, una e isión exhaus i a de la li e a u a sob e
ins umen os pa a su medición concluye con la inconsis encia en la de inición de la concep-
ualización eó ica y co espondien e es uc u a ac o ial del cons uc o ac i udes hacia las
ma emá icas. Po an o, el obje i o de es e es udio es desa olla y alida un ins umen o pa a
la medición de las ac i udes hacia las ma emá icas de es udian es de secunda ia basado en un
de allado ma co eó ico p e io.
Mé odo. La mues a es u o compues a po 792 es udian es, con una edad media de 13.96 (DE
= 1.09) años, p oceden es de Bizkaia (Comunidad Au ónoma del País Vasco, España). Se
lle a on a cabo análisis ac o iales con i ma o ios pa a es a la es uc u a eó ica no je a qui-
zada p opues a, consis en e en es ac o es elacionados de p ime o den (au oconcep o ma-
emá ico del es udian e, u ilidad pe cibida de las ma emá icas e in e és hacia las ma emá icas).
Resul s. Los esul ados con i ma on que es e modelo p esen aba buenos índices de bondad de
ajus e. Los análisis co espondien es a consis encia in e na, alidez disc iminan e y alidez de
c i e io a oja on buenos coe icien es al a de C onbach, co elaciones signi ica i as en e las
dimensiones p opues as y co elaciones mode adas y posi i as en e las ac i udes hacia las
ma emá icas y el endimien o ma emá ico de los es udian es, que ue medido con un es ma-
emá ico desa ollado ad-hoc.
Discussion. La escala esul an e, de 19 í ems, ep esen a un ins umen o psicomé icamen e
obus o an o pa a ines de in es igación como pa a in e enciones educa i as. Pa a conclui ,
se discu e la con ibución del p esen e es udio al ámbi o de las ac i udes hacia las ma emá i-
cas, y se sugie en algunos aspec os pa a u u as líneas de in es igación.
Palab as Cla e: Ac i udes hacia las ma emá icas, educación secunda ia, educación ma emá-
ica, análisis ac o ial con i ma o io.
Recibido: 28.11.15 Acep ación Inicial: 14.12.15 Acep ación inal: 16.10.16
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In oduc ion
S uden s’ ma hema ical unde pe o mance has become wo isome in many coun ies
(Lipne ich, MacCann, K umm, Bu us, & Robe s, 2011). Despi e he g owing impo ance o
ma hema ical hinking and ma hema ics- ela ed skills o an indi idual’s ull de elopmen in
oday’s socie y, his subjec is pe cei ed by mos s uden s as abs ac , di icul , bo ing and
wi hou ela ion o asks o e e yday li e (Ignacio, Nie o, & Ba ona, 2006). In such a con ex ,
socio-cogni i e heo ies ha e sugges ed ha s uden s’ belie s and expec a ions a e a majo
de e minan o hei pu sui o and engagemen in ma hema ics cou ses (C ombie e al., 2005;
G oo enboe & Hemmings, 2007; Malmi ou i, 2007). Howe e , hose a i udes a e no inna e
bu o med o e ime by expe iences, declining much o e he ansi ion om uppe elemen-
a y school o junio high school (Wa , 2000).
An in e na ional body o esea ch has highligh ed he close ela ionship be ween s u-
den s’ d opou a es in ma hema ics and bo h hei p esen and u u e ma hema ical pe o -
mance (Bouchey & Ha e , 2005; Anjum, 2006; Skaal ik & Skaal ik, 2006; Samuelsson &
G ans om, 2007; Kadije ich, 2008; Williams & Williams, 2010; Lipne ich, MacCann,
K umm, Bu us, & Robe s, 2011). In his line, pa icula ly in e es ing is he me a-analysis
ca ied ou by Ma and Kisho (1997) wi h longi udinal modelling. The indings sugges ed ha
a i udes owa ds ma hema ics exe ed causal e ec s on ma hema ics achie emen . Howe e ,
he co esponding obse ed e ec sizes we e ound o be small, which was explained by he
au ho s as a consequence o ce ain psychome ic limi a ions in he ins umen s designed o
measu e a i udes owa ds ma hema ics. These limi s ha e been also acknowledged in mo e
ecen esea ch by Zan, B own, E ans and Hannula (2006) and Lim and Chapman (2013),
which asse ed ha he ac o s uc u e o a i udes owa ds ma hema ics emains ambiguous.
As seen in Table 1, a deep look on he psychological li e a u e p o ides a numbe o di e ing
concep ualiza ions o he cons uc a i udes owa ds ma hema ics, which has esul ed in many
ins umen s a ge ing o measu e i . These measu emen s o assessing a i udes owa ds
ma hema ics ha e been d awn om pee - e iewed a icles. Measu emen s o assessing a i-
udes owa ds science o s a is ics ha e no been conside ed in his li e a u e e iew because
ecen e idence sugges s ha a i udes owa ds hese h ee subjec s show di e en ajec o ies
o e adolescence, meaning ha each cons uc should be in es iga ed sepa a ely (Ba h e al.,
2011).
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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F om he exis ing ins umen s, he Fennema-She man Ma hema ics A i ude Scales
(FSMAS; Fennema & She man, 1976) ha e been he mos widely used ac oss all le els o he
ma hema ics cu iculum. Since i s de elopmen , his se o nine subscales has been ansla ed
in o se e al languages o i s use wi h samples om di e en sociodemog aphic backg ounds.
Ne e heless, O’Neal, E nes , McLean, and Temple on (1988) ha e yielded poo alidi y and
eliabili y sco es, concluding ha he o iginal subscales migh no p ope ly gauge he esea ch
cons uc . In line wi h his, Melancon, Thompson, and Becnel (1994) we e unable o ind a
sui able model i o he o iginal s uc u al p oposal by Fennema and She man (1976) and
yielded a mo e pa simonious s uc u e, consis ing o eigh ac o s. Likewise, Mulhe n and
Race (1998) p oposed a sho ened e sion o six sepa a e ac o s, which yielded be e in e -
nal consis ency on bo h he ull scale and unde lying subscales.
Ano he in e es ing ins umen is he A i udes Towa d Ma hema ics In en o y (ATMI;
Tapia & Ma sh, 2004), which has a mo e dis inc and cohesi e ac o s uc u e, assessed by
bo h explo a o y and con i ma o y analyses. Howe e , his 40-i em scale is oo ime demand-
ing. The e o e, in o de o educe he ime equi ed o i s adminis a ion, Lim and Chapman
(2013) de eloped a sho ened e sion. The con i ma o y analyses yielded sound p ope ies,
bu a high co ela ion coe icien was ound be ween he enjoymen and mo i a ion dimen-
sions ( = .96). This esul indica ed ha hese wo la en ac o s we e s a is ically isomo phic
and he e o e, a educ ion o he ac o s uc u e o h ee ac o s would p esumably yield a
be e model i o he da a.
On he o he hand, some ins umen s, al hough p ima ily de eloped o measu e a i udes
owa ds ma hema ics, ac ually comp ise in he same scale bo h a i udinal dimensions (e.g.,
mo i a ion, pe cei ed use ulness) and ma hema ics anxie y. Tha is he case o he Fennema-
She man Ma hema ics A i ude Scales (FSMAS; Fennema & She man, 1976), Ma hema ics
A i ude In en o y (MAI; Sandman, 1980), Escala de Ac i udes hacia las Ma emá icas (EAM;
Auzmendi, 1992), Escala de Ac i udes hacia la Ma emá ica-Uni e sidad (EAHM-U; Bazán,
1997) and Sho o m o Ma hema ics A i ude Scale (Yasa , 2014). Ne e heless, as E ans
(2006) claimed, a i udes owa ds ma hema ics and ma hema ics anxie y a e wo sepa a e sub-
domains o he mo e gene al domain ma hema ical a ec . This means ha he cons uc a i-
udes owa ds ma hema ics has i s own ac o s uc u e and i s assessmen s should be es ed
sepa a ely om ma hema ics anxie y.
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Mo eo e , esea ch on he subdomain a i udes owa ds ma hema ics has ex ensi ely
acknowledged i s mul idimensional na u e and has iden i ied s uden ’s con idence as a salien
unde lying a iable (Ru ell, Mason, & Allen, 1998; Gómez-Chacón, 2000; Hanulla, 2002; Di
Ma ino & Zan, 2010). In some cases, s uden ’s con idence is no included, such as in he
Ma h A i ude Scale (Aiken & D ege , 1961), he Du on Scale (DAS; Du on & Blum, 1968),
Enjoymen and Value scales (E and V scales; Aiken, 1974), Ins umen measu ing ce ain
a i udes owa d ma hema ics (Michaels & Fo sy h, 1977) and Cues iona io pa a medi las
ac i udes hacia las ma emá icas en alumnos de ESO (Muñoz & Ma o, 2006). In o he cases,
his a iable appea s di ided in o wo sub ac o s, such as in he scale o measu ing a i udes
owa d ma hema ics in Compulso y Seconda y Educa ion (Alemany-A ebola & La a, 2010)
and Escala de Ac i udes hacia las Ma emá icas (EAM; Palacios, A ias, & A ias, 2014). In he
o me , he au ho s dis inguished be ween posi i e and nega i e sel -concep ; in he la e , he
au ho s dis inguished be ween he pe cei ed ma hema ical incompe ence and sel -concep .
Howe e , due o hei na u e, in bo h cases, he wo sub ac o s conside ed by he au ho s
should be cons i uen o he same homogeneous dimension.
The cu en s udy
D awing on he li e a u e e iew, he comp ehensi e analysis o he con en o Table 1
sugges s he i em edis ibu ion in h ee main ca ego ies: s uden ’s ma h sel -concep , pe -
cei ed use ulness o ma hema ics and in e es o ma hema ics.
Table 1. Measu emen s o assessing a i udes owa ds ma hema ics
Ins umen Dimensions/I ems Psychome ic e i-
dence
Ma h A i ude Scale
(Aiken & D ege , 1961) A unidimensional 20-i em scale consis ed o 10 i ems con-
no ing nega i e eelings and 10 i ems conno ing posi i e
eelings.
EFA
Tes - e es eliabil-
i y: .94
(N=127)
The Du on Scale (DAS;
Du on & Blum, 1968) A homogeneous scale consis ing o 27 i ems ha disc imi-
na e be ween posi i e and nega i e eelings abou a i hme-
ic.
Spea man-B own
eliabili y o he ull
scale: .84
(N=346)
Enjoymen and Value
Scales (E scale and V
scale; Aiken, 1974)
A se o wo scales, which can be used ei he sepa a ely o
join ly: Enjoymen scale (11) and Value scale (10) EFA
C onbach’s alpha o
E scale: .95
C onbach’s alpha o
V scale: .85
(N = 190)
Fennema-She man
Ma hema ics A i ude A se o nine subscales, which can be used ei he sepa a ely
o join ly: Ma hema ics anxie y scale (12), a i ude owa d EFA
Spli -hal eliabili y
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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Scales (FSMAS; Fenne-
ma & She man, 1976) success in Ma hema ics scale (12), con idence in lea ning
Ma hema ics scale (12), e ec ance mo i a ion in Ma hema -
ics scale (12), a he scale (12), mo he scale (12), Ma he-
ma ics as a male domain (12), eache scale (12), use ulness
o Ma hema ics scale (12).
( o he subscales):
.86-.93
(N=1,600)
Ins umen measu ing
ce ain a i udes owa d
ma hema ics (Michaels
& Fo sy h, 1977)
A se o ou subscales: enjoymen o wo d p oblems (1),
enjoymen o pic o ial p oblems (1), app ecia ion o he
u ili y o ma hema ics (10), secu i y wi h ma hema ics (10),
EFA
Spea man-B own
eliabili y ( o he
subscales): .51-.78
(N=299)
Ma hema ics A i ude
In en o y (MAI; Sand-
man, 1980)
A se o six subscales, esul ing in a o al o 48 i ems: pe -
cep ion o Ma hema ics eache s, alue o Ma hema ics,
sel -concep in Ma hema ics, ma h anxie y, enjoymen o
Ma hema ics, mo i a ion in Ma hema ics.
EFA
Reliabili y ( o he
subscales): .69-.89
(N=5,034)
Escala de ac i ud de
ca ác e e bal (Gai ín,
1990)
A 22-i em scale wi h h ee unde lying ac o s: liking, use-
ulness, and con idence-anxie y. EFA
Tes - e es eliabili y
( o he dimensions):
.77-.93
(N=3,637)
Escala de Ac i udes hacia
las Ma emá icas (EAM;
Auzmendi, 1992)
A 25-i em scale wi h i e unde lying ac o s: use ulness (5),
con idence (5), anxie y (5), liking (5), mo i a ion (5). EFA (PCA and VR)
C onbach’s alpha
( o he dimensions):
.50-.91
C onbach’s alpha o
he ull scale: .93
(N=1,221)
Escala de Ac i udes hacia
la Ma emá ica-
Uni e sidad (EAHM-U;
Bazán, 1997)
A 31-i em scale wi h ou unde lying ac o s: a ec i i y (8),
applicabili y (8), abili y (8) and anxie y (7). EFA
C onbach’s alpha
( o he dimensions):
.71-.91
A i udes owa d Ma he-
ma ics and Ma hema ics
Taugh wi h Compu e
(AMMEC; U sini,
Sánchez, & O endain,
2004)
A 29-i em scale comp ising h ee subscales: liking o ma h-
ema ics (11), liking o ma hema ics augh wi h compu e
(11), sel -con idence (7).
EFA
(PCA and VR)
C onbach’s alpha
( o he subscales):
.68-.81
C onbach’s alpha o
he ull scale: .80
Spli -hal eliabili y
o he ull scale: .71
(N=439)
A i udes owa d Ma he-
ma ics In en o y (ATMI;
Tapia & Ma sh, 2004)
A 40-i em scale wi h ou unde lying dimensions: sel -
con idence (15), alue (10), enjoymen (10), mo i a ion (5) EFA (ML and VR)
and CFA
C onbach’s alpha
( o he dimensions):
.88-.95
C onbach’s alpha o
he ull scale: .97
Tes - e es eliabili y
( o he dimensions):
.70-.80
Tes - e es eliabili y
o he ull scale: .89
(N=545)
Cues iona io pa a medi
las ac i udes hacia las
ma emá icas en alumnos
A 19-i em scale wi h wo unde lying ac o s: liking and
use ulness (9), eache ’s a i ude owa d ma hema ics pe -
cei ed by he s uden (10)
EFA (PCA and VR)
C onbach’s alpha o
he ull scale: .97
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de ESO (Muñoz & Ma o,
2006) (N=1,220)
Scale o measu ing
a i udes owa d ma he-
ma ics in compulso y
seconda y educa ion
(Alemany-A ebola &
La a, 2010)
A 35-i em scale wi h se en unde lying ac o s: beha iou al
componen (13), a ec i e componen (7), nega i e sel -
concep (5), posi i e sel -concep (3), cogni i e componen
(3), demo i a ion owa ds ma hema ics (2), expec ancy (2)
EFA and CFA
C onbach’s alpha
( o he dimensions):
.43-.89
C onbach’s alpha o
he ull scale: .92
(N=236)
Sho ened e sion o he
A i udes owa d Ma he-
ma ics In en o y (sho
ATMI; Lim & Chapman,
2013)
A 19-i em sho ened ATMI e sion wi h ou subscales:
enjoymen (5), mo i a ion (4), sel -con idence (5), pe -
cei ed alue (5).
EFA and CFA
C onbach’s alpha
( o he subscales):
.85-.90
C onbach’s alpha o
he ull scale:.93
Tes - e es eliabili y
o he ull scale: .75
(N=1,601)
Sho o m o Ma hema -
ics A i ude Scale (Yasa ,
2014)
A 19-i em scale wi h ou unde lying dimensions: enjoy-
men (6), ea , anxie y and bo edom (5), place o ma hema -
ics in li e (4), pe cei ed ma hema ics success (4).
EFA (BCA) and
CFA
C onbach’s alpha
( o he dimensions):
.82-.89
C onbach’s alpha o
he ull scale: .96
(N=1,801)
Escala de Ac i udes hacia
las Ma emá icas (EAM;
Palacios, A ias, & A ias,
2014)
A 32-i em scale unde lying ou dimensions: pe cep ion o
ma hema ical incompe ence (12), liking (12), pe cep ion o
use ulness (4), ma hema ical sel -concep (4)
EFA (PAF, ML and
PR) and CFA
C onbach’s alpha
( o he dimen-
sions):.68-.93
C onbach’s alpha o
he ull scale: .95
(N=4,807)
No e. BCA=Basic Componen Analysis, CFA=Con i ma o y Fac o Analysis, EFA=Explo a o y Fac o Analy-
sis, ML=Maximum Likelihood, PCA=P incipal Componen Analysis, PR=P omax Ro a ion, VR=Va imax Ro a-
ion.
Using his ca ego iza ion as a basis o he p esen s udy, he heo e ical model p oposed
o be es ed is i-dimensional and non-hie a chized, wi h he ollowing de ini ions o he
h ee ela ed i s -o de la en ac o s:
S uden ’s ma h sel -concep : encompasses a b oad ange o s uden ’s esponses abou
he o his abili y o lea n and do ma hema ics (e.g., “I am unable o sol e ma h p oblems”). A
s uden who sco es high in his dimension belie es ha she o he has he abili y o unde s and
and sol e ma h- ela ed asks. On he o he hand, a s uden sco ing low in his dimension does
no belie e ha she o he has he abili y o unde s and and do ma hema ics.
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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Pe cei ed use ulness o ma hema ics: measu es he s uden s’ ex insic u ili y alue o
ma hema ics. This dimension, as de ined by Eccles and Wig ield (2002), measu es s uden s’
belie s abou he applicabili y o ma hema ics o hei cu en and u u e goals and in ela ion
o school, ca ee and e e yday li e (e.g., “Lea ning ma h will inc ease my u u e job oppo u-
ni ies”). The e o e, a s uden who sco es high in his dimension inds ma hema ics e y use ul
o bo h hei cu en and u u e goals; whe eas a s uden sco ing low inds i useless o bo h
hei cu en and u u e goals.
In e es o ma hema ics: e e s o he amoun o in e es s uden s ha e in lea ning and
doing ma hema ics (e.g., “Time jus lies by when I am sol ing ma h p oblems”). A s uden
who sco es high in his dimension has high in e es in lea ning and doing ma hema ics. On he
o he hand, a s uden sco ing low dislikes ma hema ics, inds i bo ing and does no ake
pleasu e om lea ning and doing ma hema ics.
Me hod
Pa icipan s
The sample consis ed o 792 seconda y s uden s, which we e selec ed ia a clus e -
sampling me hod om 36 classes om he p o ince o Biscay (Basque Coun y Au onomous
Region, Spain). This sample was hen di ided in o wo subg oups acco ding o he language
in which hey lea n ma hema ics (see Table 2).
Table 2. Sociodemog aphic p o ile o he sample
2nd g ade 4 h g ade To al
Females
Males
Females
Males
Subsample 1
45 72 88 138 343
Subsample 2
137 138 88 86 449
To al 182 210 176 224 792
Ins umen s
Scale o assessing a i udes owa ds ma hema ics in seconda y educa ion (SATMAS)
A pool o i ems was collec ed om all he examined ins umen s (see Table 1) and e-
dis ibu ed in he a o emen ioned h ee dimensions. A e emo ing edundan i ems, ewo d-
ing some o he s and adding a ew newly w i en ones, a inal pool o 36 i ems was ob ained
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he bes s uc u e o explain he cons uc a i udes owa d ma hema ics, as i showed a sim-
ple s uc u e compa ed o ha o M1a.
Table 6. Goodness-o - i indices o he e ised s uc u es
Model
Subsample
χ
2
S-B
/d
NNFI
CFI
IFI
SMSR
RMSEA (90% CI)
AIC
M1 S1 3.56 .90 .91 .91
.071 .068 [.062, .072] 354.52
S2 2.06 .90 .91 .91
.079 .068 [.059, .077] 13.683
M1a S1 2.78 .94 .95 .95
.053 .056 [.050, .062] 128.803
S2 1.62 .95 .96 .96
.058 .052 [.040, .063] -63.335
M1b S1 3.28 .93 .94 .94
.056 .064 [.057, .070] 190.994
S2 1.77 .94 .95 .95
.060 .058 [.046, .069] -34.504
M1c S1 2.88 .94 .95 .95
.053 .058 [.051, .064] 130.788
S2 1.54 .96 .96 .96
.057 .049 [.036, .061] -68.206
Final model
In addi ion, all s anda dized ac o loadings and in e - ac o co ela ions we e s a is ical-
ly signi ican (p < .05), wi h alues anging om .49 o .92 o ac o loadings and om .21 o
.73 o in e - ac o co ela ions (see Figu e 1). These esul s unde sco ed he disc iminan
alidi y o he scale be ween he h ee unde lying la en ac o s.
Figu e 1. Con i ma o y ac o analysis o SATMAS wi h subsample 1 (N = 563) and subsam-
ple 2 (N = 229)
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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No e. MSC=Ma h Sel -Concep , PUM=Pe cei ed Use ulness o Ma hema ics, IM=In e es o Ma hema ics.
Addi ional p ope ies o he las 19-i em SATMAS we e assessed wi h he composi e
eliabili y (CR) and C onbach’s coe icien (
α
) o each dimension. The eliabili y analyses
showed good in e nal consis ency o he s uden ’s ma h sel -concep (CR
s1
= .93,
α
s1
= .93;
CR
s2
= .89,
α
s2
= .89), pe cei ed use ulness o ma hema ics (CR
s1
= .78,
α
s1
= .78; CR
s2
=
.80,
α
s2
= .80) and in e es o ma hema ics (CR
s1
= .90, α
s1
= .91; CR
s2
= .90, α
s2
= .91). Re-
ga ding he ull scales, eliabili ies we e α
1
= .93 and α
2
= .91 o Subsample 1 and Subsam-
ple 2, espec i ely. The eliabili y sco es we e ound o be good based on he Nunnally’s c i-
e ion (Nunnally, 1978). The e o e, he esul s sugges ed ha he i ems we e in e nally con-
sis en in ep esen ing he co esponding ac o .
Finally, c i e ion- ela ed alidi y o he scale was assessed by he Pea son co ela ion
coe icien s be ween a i udes owa ds ma hema ics and he sco es ob ained in ma hema ics
achie emen es s. Posi i e signi ican co ela ions we e ound, as expec ed, be ween s u-
den ’s ma h sel -concep and ma h achie emen (
s1
= .23, p < .001;
s2
= .22, p < .001), pe -
cei ed use ulness o ma hema ics and ma h achie emen (
s1
= .22, p < .001;
s2
= .23, p <
.001) and in e es o ma hema ics and ma h achie emen (
s1
= .20, p < .001;
s2
= .21, p <
.001). The ull scale is included in Table 7.
Table 7. Las e sion o he 19-i em SATMAS
S uden ’s ma h sel -concep
IT01
I eel mo e oolish han my classma es when sol ing
ma h p oblems and exe cises
IT02
In spi e o my e o , I canno unde s and ma h
IT03
I ha e di icul ies wi h ma h
IT04
I was no a bo n ma h lea ne
IT05
I am unable o sol e ma h p oblems
IT06
Wha e e I do, I ge low g ades in ma h
IT07
I will be always ha d o me o lea n ma h
Pe cei ed use ulness o
ma hema ics
IT08
Ma h is e y use ul
IT09
E e ybody needs o lea n ma h
IT12
Ma h is necessa y o li e
IT13
Ma h is impo an o socie y de elopmen
IT15
Lea ning ma h is impo an o my u u e job
In e es o ma hema ics IT17
I like s udying ma h
IT18
I like ma h
IT19
Time jus lies by when I am s udying ma h
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IT20
S udying ma h is un
IT21
Time jus lies by when I am sol ing ma h p oblems /
exe cises
IT22
Ma h is en e aining
IT23
Ma h is a d ag
Discussion
O e he pas yea s, he e has been a g owing in e es in s udying he s uden s’ a i udes
owa ds ma hema ics because o hei impo an ole in he engagemen in and mas e y o
ma hema ics (e.g., McLeod, 1992; Goldin, 2002; G oo enboe & Hemmings, 2007;
Malmi ou i, 2007). Ne e heless, co ela ional esea ch on a i udinal a iables and ma he-
ma ical pe o mance has been con ingen on he psychome ic p ope ies o he measu emen s
o measu ing he cons uc a i udes owa ds ma hema ics. Th ee conclusions may be d awn
om a comp ehensi e li e a u e e iew on he exis ing ins umen s. Fi s ly, he mos widely
ci ed ins umen s a e he FSMAS (Fennema & She man, 1976) and he ATMI (Tapia &
Ma sh, 2004), which ha e also been ansla ed in o se e al languages o hei use in back-
g ounds wi h di e en socio-cul u al cha ac e is ics. Howe e , subsequen eplica ion s udies
o hese ins umen s (e.g., O’Neal, E nes , McLean, & Temple on, 1988; Melancon, Thomp-
son, & Becnel, 1994; Mulhe n & Race, 1998) ha e ob ained e idence ha ebuilding some o
hei la en ac o s and sho ening he scales o ewe subdomains would yield a be e i o
da a. Secondly, he e a e some ins umen s (i.e., MAI, Sandman, 1980; EAM, Auzmendi,
1992; EAHM-U, Bazán, 1997; Sho Fo m o Ma hema ics A i ude Scale, Yasa , 2014) ha ,
al hough p ima ily se o measu e a i udes owa ds ma hema ics, ac ually mix bo h a i udinal
ac o s and ma hema ics anxie y. Ne e heless, a i udes owa ds ma hema ics and ma hema -
ics anxie y a e claimed o be conside ed as wo sepa a e subdomains o he mo e gene al do-
main ma hema ical a ec (E ans, 2006). This means ha a i udes owa ds ma hema ics has
i s own ac o s uc u e and i s assessmen s should be es ed sepa a ely om ma hema ics anx-
ie y. Thi dly, hey a e o he measu emen s ha do no include s uden ’s sel -con idence as an
unde lying ac o (i.e., in he Ma h A i ude Scale, Aiken & D ege , 1961; DAS, Du on &
Blum, 1968; E and V Scales, Aiken, 1974; Ins umen measu ing ce ain a i udes owa d
ma hema ics, Michaels & Fo sy h, 1977; and Cues iona io pa a medi las ac i udes hacia las
ma emá icas en alumnos de ESO, Muñoz & Ma o, 2006) o ha include i in such a way ha
emains ambiguous (i.e., in he scale o measu ing a i udes owa ds ma hema ics in Compul-
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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so y Seconda y Educa ion, Alemany-A ebola & La a, 2010; and EAM, Palacios, A ias, &
A ias, 2014). As a esul o his lack o consis ency in de ining he heo e ical concep ualiza-
ion o he cons uc a i udes owa ds ma hema ics, his pape aims o de elop and alida e,
by means o con i ma o y echniques, a s uc u al model o his cons uc .
D awing on he comp ehensi e analysis o he exis ing ins umen s, h ee la en ac o s
a e es ed as i s -o de cons i uen s o he a i udes owa ds ma hema ics, conside ing his as a
non-hie a chized s uc u e: a) s uden s’ ma h sel -concep , b) pe cei ed use ulness o ma he-
ma ics, and c) in e es o ma hema ics. The sample, consis ing o 792 compulso y seconda y
s uden s, was di ided in o wo subg oups acco ding o he language in which hey lea ned
ma hema ics (Spanish o Basque). Goodness-o - i indices we e calcula ed o he heo e ical
model and u he imp o emen s we e made a e examining s anda dized ac o loadings,
modi ica ion co a iance indices and s anda dized esidual co a iance sco es. The las e sion,
ob ained a e elimina ing ou o iginal i ems and o cing o co a ia e o ano he wo pai s o
i ems, yielded a be e model i . The goodness-o - i indices we e ound o be e y simila in
bo h s uden subg oups. In e nal consis ency, measu ed by C onbach’s coe icien , had an
a e age alue o .92, which was e e ed o as excellen acco ding o Nunally’s c i e ion
(Nunnally, 1978). Disc iminan and c i e ion- ela ed alidi ies we e also assessed. On he one
hand, in e - ac o co ela ion sco es we e posi i e and anged om .21 o .73, meaning ha
he la en ac o s we e no s a is ically isomo phic. On he o he hand, bi a ia e co ela ion
analyses yielded signi ican posi i e co ela ion sco es be ween each a i udinal dimension
and he sco e ob ained in he ma hema ical achie emen es , de eloped ad-hoc. Al hough
s a is ically signi ican , hese co ela ion sco es we e ound o be small, which was explained
by he e ec ha o he a iables, no conside ed in his pape , had on s uden s’ ma hema ical
achie emen . In ac , a li e a u e e iew d aws a en ion o he ac ha ma hema ics achie e-
men is a ec ed no only by cogni i e and a i udinal ac o s, bu also by school en i onmen
(C eeme s & Reezig , 2006) o ins uc ional s a egies (Van de G i & Hou een, 2006).
Despi e he p omising indings, he e a e also some me hodological limi a ions ha wa -
an cau ious conside a ions in gene alizing he esul s. Fi s , da a we e collec ed solely om
Biscay (Basque Coun y Au onomous Region, Spain), meaning ha he esul s a e no en i ely
gene alizable ou side o a Basque popula ion. Ne e heless, he e a e some pieces o e idence
sugges ing ha i is possible o ely on he quali y o he da a. On he one hand, he s uden
La a Yáñez-Ma quina & Lou des Villa dón-Gallego
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sample was selec ed ia a clus e -sampling me hod, and he desc ip i e s a is ics o he esul -
ing g oup we e e y simila o ha o he e e ence popula ion, acco ding o he o icial en-
olmen da a o he Educa ion Depa men o Basque Go e nmen o he school yea in
which he s udy was ca ied ou . As a esul , he sample g oup was ep esen a i e and la ge
enough o he esea ch pu poses, al hough no comple ely p obabilis ic in case o gene aliz-
ing he indings ou side Biscay. In his line, u u e esea ch using la ge samples om di e -
en sociodemog aphic con ex s would be necessa y o u he assess he in a iance o he ac-
o s uc u e. On he o he hand, his s udy p o ides s ong eliabili y and alidi y e idence o
he ins umen (i.e., cons uc alidi y, disc iminan alidi y, c i e ion- ela ed alidi y and in-
e nal consis ency), bu i would be in e es ing o assess he s uc u al s abili y h ough es -
e es eliabili y analyses.
Gi en he eliabili y and alidi y e idence ga he ed in he p esen s udy, he 19-i em
SATMAS p o es o be a p omising ins umen o assessing seconda y s uden s’ a i udes
owa ds ma hema ics. On he one hand, he esul s la gely suppo ed he heo e ical concep u-
aliza ion acco ding o which a i udes owa ds ma hema ics is a mul idimensional cons uc
wi h a non-hie a chized s uc u e consis ing o he h ee a o emen ioned i s -o de ac o s
(namely, s uden ’s ma h sel -concep , pe cei ed use ulness o ma hema ics and in e es o
ma hema ics). This was ound o be a g ea con ibu ion o he esea ch on a i udes owa ds
ma hema ics. On he o he hand, he de eloped scale is easy o adminis e and no ime-
demanding, as his sho o m akes seconda y s uden s 15 minu es o comple e. The e o e,
ei he school counselo s o educa o s migh use i o measu e s uden s’ a i udes owa ds
ma hema ics and p o ide ea ly a en ion measu es in case he le els o ma hema ical sel -
concep and mo i a ion we e low. This migh be o g ea in e es pa icula ly o hose s u-
den s showing s ong ma hema ical skills bu s uggling wi h low expec a ions and in e es ,
which pu hem a isk o disengagemen in ma hema ics and ma hema ics- ela ed pa hways.
In ac , since a i udes owa ds he subjec ha e been shown o decline om uppe elemen a y
school o junio high school, de eloping and alida ing a measu emen a ge ing seconda y
s uden s would u nish insigh s wi hin he ield o ma hema ics educa ion and may well be-
come a s a ing poin o iden i y and p e en hose d opou isky si ua ions a ma hema ics
class ooms. On o he hand, esea che s migh use i as he s a ing poin o iden i y he key
domains o a i udes owa ds ma hema ics a ec ing he ma hema ical achie emen and u he
in es iga e he a iables which a ec hei p e alence. In ac , assessing he dimensions un-
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
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de lying a i udes owa ds ma hema ics is c i ical o gain knowledge abou he plausible ac-
o s ha a ec ma hema ical achie emen .
Acknowledgemen s
This esea ch was unded by he Uni e si y o Deus o Resea ch T aining G an s P o-
g amme 2013-2016 (Uni e si y o Deus o, Bilbao).
Re e ences
Aiken, L.R. (1974). Two scales o a i ude owa d ma hema ics. Jou nal o Resea ch in
Ma hema ics Educa ion, 5, 67-71. doi: 10.2307/748616
Aiken, L.R., & D ege , R.M. (1961). The e ec o a i udes on pe o mance in lea ning ma h-
ema ics. Jou nal o Educa ional Psychology, 52(1), 19-24.
Alemany-A ebola, I., & La a, A.I. (2010). Las ac i udes hacia las ma emá icas en el alumna-
do de ESO: un ins umen o pa a su medición. Publicaciones, 40, 49-71.
Anjum, R. (2006). The ole o sel -concep in ma hema ics achie emen o p ima y school
child en. Pakis an Jou nal o Social and Clinical Psychology, 4, 21-38.
Auzmendi, E. (1992). Las ac i udes hacia la ma emá ica-es adís ica en las enseñanzas medias
y uni e si a ia: Ca ac e ís icas y medición. Bilbao: Mensaje o.
Ba h, J.M., Todd, B., McCallum, D.M., Golds on, M., Guadagno, R.E., Roskos, B., &
Bu khal e , C. (2011). E ec s o engaging class oom s a egies and eache suppo
on s uden ou comes o e school ansi ions. P oceedings o he Ame ican Socie y o
Enginee ing Educa ion.
Bazán, J.L. (1997). Me odología es adís ica de cons ucción de p uebas. Una aplicación al
es udio de ac i udes hacia las ma emá icas en la UNALM. UNALM: Lima ( esis).
Ben le , P.M. (2005). EQS S uc u al equa ions p og am manual. Encino, CA: Mul i a ia e
So wa e. Inc.
Bouchey, H.A., & Ha e , S. (2005). Re lec ed app aisals, academic pe cep ions, and
ma h/science pe o mance du ing ea ly adolescence. Jou nal o Educa ional Psychol-
ogy, 97(4), 673-686. doi: 10.1037/0022-0663.97.4.673
B own, T. (2006). Con i ma o y ac o analysis o applied esea ch. New Yo k, NY: Guil-
o d P ess.
La a Yáñez-Ma quina & Lou des Villa dón-Gallego
- 578 - Elec onic Jou nal o Resea ch in Educa ional Psychology, 14(3), 557-581.
ISSN: 1696-2095. 2016. no. 40
h p://dx.doi.o g/10.14204/ej ep.40.15163
C eeme s, B.P.M., & Reezig , G.J. (2005). Linking school e ec i eness and school imp o e-
men : The backg ound and ou line o he p ojec . School e ec i eness and school im-
p o emen , 16(4), 359-371. doi: 10.1080/09243450500234484
C ombie, G., Sinclai , N., Sil e ho n, N., By ne, B.M., Dubois, D.I., & T innee , A. (2005).
P edic o s o young adolescen s’ ma h g ades and cou se en ollmen in en ions: Gen-
de simila i ies and di e ences. Sex Roles, 52(5-6), 351-367. doi: 10.1007/s11199-
005-2678-1
Di Ma ino, P., & Zan, R. (2010). ‘Me and ma hs’: Towa ds a de ini ion o a i ude g ounded
on s uden s’ na a i es. Jou nal o Ma hema ics Teache Educa ion, 13, 27-48. doi:
10.1007/s10857-009-9134-z
Du on, W.H., & Blum, M.P. (1968). The measu emen o a i udes owa d a i hme ic wi h a
Like - ype es . Elemen a y School Jou nal, 68, 259-264. doi: 10.1086/460443
Eccles, J.S., & Wig ield, A. (2002).Mo i a ional belie s, alues, and goals.Annual Re iew o
Psychology, 53, 109-132. doi: 10.1146/annu e .psych.53.100901.135153
Fennema, E., & She man, J.A. (1976). Fennema-She man Ma hema ics A i udes Scales: In-
s umen s designed o measu e a i udes owa d he lea ning o ma hema ics by e-
males and males. Jou nal o Resea ch in Ma hema ics Educa ion, 7, 324-336.
doi:10.2307/748467
Fo nell, C., & La cke , D.F. (1981). E alua ing s uc u al equa ion models wi h unobse able
a iables and measu emen e o . Jou nal o Ma ke ing Resea ch, 18(1), 39-50.
doi: 10.2307/3151312
Gai ín, J. (1990). Las ac i udes en educación. Un es udio sob e la educación ma emá ica. Ba -
celona: Boixa eu Uni e si a ia.
Goldin, G. (2002). A ec , me a-a ec , and ma hema ical belie s uc u es. In G. Lede , E.
Pehkonen & G. Tö ne (Eds.). Belie s: A hidden a iable in ma hema ics educa ion?
Do d ech : Kluwe .
Gómez-Chacón, I.M. (2000). A ec i e in luences in he knowledge o ma hema ics. Educa-
ional S udies in Ma hema ics, 43(2), 149-168. doi: 10.1023/A:1017518812079
G oo enboe , P., & Hemmings, B. (2007). Ma hema ics pe o mance and he ole played by
a ec i e and backg ound ac o s. Ma hema ics Educa ion Resea ch Jou nal, 19(3), 3-
10. doi: 10.1007/BF03217459
Hai , J.F., Black, W.C., Babib, B.J., & Ande son, R.E. (2010). Mul i a ia e da a analysis
(7
h
ed.). Uppe Saddke Ri e , NJ: P en ice Hall.
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
Elec onic Jou nal o Resea ch in Educa ional Psychology, 14(3), 557-581.
ISSN: 1696-2095. 2016. no. 40
-
579 -
h p://dx.doi.o g/10.14204/ej ep.40.15163
Helmke, A. (1989). Incen i e alue o success and ailu e in school. De elopmen al ends
and impac on academic achie emen . In F. Halisch & J.J.L. Van den Be chen (Eds.),
In e na ional pe spec i es on achie emen and ask mo i a ion (225-237). Lisse:
Swe s & Zei linge .
Hoyle, R.H., & Pan e , A.T. (1995). W i ing abou s uc u al equa ion models in s uc u al
equa ion modeling. In R.H. Hoyle (Ed.). S uc u al Equa ion Modeling: Concep s. Is-
sues and Applica ions (158-176). Thousand Oaks, CA: Sage.
Hu, L.T., & Ben le , P.M. (1999). Cu o c i e ia o i indices in co a iance s uc u e analy-
sis: Con en ional c i e ia e sus new al e na i es. S uc u al Quo a ion Modeling, 6,
1-55. doi: 10.1080/10705519909540118
Ignacio, N.T., Nie o, L.J., & Ba ona, E.G. (2006). The a ec i e domain in ma hema ics lea n-
ing. In e na ional Elec onic Jou nal o Ma hema ics Educa ion, 1(1), 16-32.
Kadije ich, D. (2008). TIMSS 2003: Rela ing dimensions o ma hema ics a i ude o ma he-
ma ics achie emen (MA). Zbo nik Ins i u a za pedagoska is azi anja, 40(2), 327-
346. doi: 10.2298/ZIPI0802327K
Lei, M., & Lomax, R.G. (2005). The e ec o a ying deg ees o nonno mali y in s uc u al
equa ion modeling. S uc u al Equa ion Modeling: A Mul idisciplina y Jou nal, 12, 1-
27. doi: 10.1207/s15328007sem1201_1
Lim, S.Y., & Chapman, E. (2013). De elopmen o a sho o m o he a i udes owa d ma h-
ema ics in en o y. Educa ional S udies in Ma hema ics, 83, 145-164. doi:
10.1007/s10649-012-9414-x
Lipne ich, A.A., MacCann, C., K umm, S., Bu us, J., & Robe s, R.D. (2011). Ma hema ics
a i udes and ma hema ics ou comes o U.S. and Bela usian Middle School S uden s.
Jou nal o Educa ional Psychology, 103(1), 105-118. doi: 10.1037/a0021949
Ma, X., & Kisho , N. (1997). Assessing he ela ionship be ween a i udes owa ds ma hema -
ics and achie emen in ma hema ics: A me a-analysis. Jou nal o Resea ch in Ma h-
ema ics Educa ion, 28(1), 26-47. doi: 10.2307/749662
Mahoney, C.A., Thombs, D.L., & Howe, C.Z. (1995). The a and science o scale de elop-
men in heal h educa ion esea ch. Heal h Educa ion Resea ch,10, 1-10. doi:
10.1093/he /10.1.1-a
McLeod, D.B. (1992). Resea ch on a ec in ma hema ics educa ion: A econcep ualisa ion. In
D.A. G ouws (Ed.), Handbook o esea ch on ma hema ics eaching and lea ning
(575-596). New Yo k, NY: McMillan.
La a Yáñez-Ma quina & Lou des Villa dón-Gallego
- 580 - Elec onic Jou nal o Resea ch in Educa ional Psychology, 14(3), 557-581.
ISSN: 1696-2095. 2016. no. 40
h p://dx.doi.o g/10.14204/ej ep.40.15163
Melancon, J.G., Thomson, B., & Becnel, S. (1994). Measu emen in eg i y o sco es om he
Fennema-She man Ma hema ics A i udes Scales: The a i udes o public school
eache s. Educa ional and Psychological Measu emen , 54, 187-192. doi:
10.1177/0013164494054001024
Michaels, L.A., & Fo sy h, R.A. (1977). Cons uc ion and alida ion o an ins umen measu -
ing ce ain a i udes owa d ma hema ics. Educa ional and Psychological Measu e-
men , 37(4), 1043-1049. doi: 10.1177/001316447703700429
Mulhe n, F., & Race, G. (1998). De elopmen o a sho ened o m o he Fennema-She man
Ma hema ics A i udes Scales. Educa ional and Psychological Measu emen , 58, 295-
306. doi: 10.1177/0013164498058002012
Muñoz, J.M., & Ma o, M.D. (2006). Diseño y alidación de un cues iona io pa a medi las
ac i udes hacia las ma emá icas en alumnos de ESO. Re is a galego-po uguesa de
psicoloxía e educación, 13, 413-424.
Nunnally, J.C. (1978). Psychome ic heo y (2
nd
ed.). New Yo k, NY: McG aw-Hill.
O’Neal, M.R., E nes , P.S., McLean, J.E., & Temple on, S.M. (1988, No embe ). Fac o ial
alidi y o he Fennema-She man Ma hema ics A i ude Scales. Pape p esen ed a he
annual mee ing o he Mid-Sou h Educa ional Resea ch Associa ion, Louis ille, KY.
Palacios, A., A ias, V., & A ias, B. (2014). A i udes Towa ds Ma hema ics: Cons uc ion and
Valida ion o a Measu emen Ins umen . Jou nal o Psicodidac ics, 19(1), 67-91. doi:
10.1387/Re Psicodidac .8961
Ru ell, M., Mason, J., & Allen, B. (1988). S udying a i ude o ma hema ics. Educa ional
S udies in Ma hema ics, 35, 1-18.
Samuelsson, J., & G ans om, K. (2007). Impo an p e equisi e o s uden s’ ma hema ical
achie emen . Jou nal o Theo y and P ac ice in Educa ion, 3(2), 150-170.
Sandman, R.S. (1980). The ma hema ics a i ude in en o y: Ins umen and use ’s manual.
Jou nal o Resea ch in Ma hema ics Educa ion, 11(2), 148-149. doi: 10.2307/748906
Sa o a, A. (2003). Powe o chi-squa e Goodness-o - i es in s uc u al equa ion models: he
case o non-no mal da a. In H. Yanai, A. Okada, K. Shigemasu, Y. Kano & J. J.
Meulman (Eds.). New de elopmen s o psychome ics (57-68). Tokio: Sp inge Ve lag.
Tabachnick, B.G., & Fidell, L.S. (2007). Using mul i a ia e s a is ics (5
h
ed.). Bos on, MA:
Allyn & Bacon.
Tapia, M. & Ma sh, G. E. (2004). An Ins umen o Measu e Ma hema ics A i udes. Academ-
ic Exchange Qua e ly, 8(2), 16-21.
A i udes owa ds ma hema ics a seconda y le el: De elopmen and s uc u al alida ion o he Scale o Assessing A i udes
owa ds Ma hema ics in Seconda y Educa ion (SATMAS)
Elec onic Jou nal o Resea ch in Educa ional Psychology, 14(3), 557-581.
ISSN: 1696-2095. 2016. no. 40
-
581 -
h p://dx.doi.o g/10.14204/ej ep.40.15163
Ullman, J.B. (2006). S uc u al equa ion modeling. In B.G. Tabachnick & L.S. Fidell (Eds.).
Using mul i a ia e s a is ics (5
h
ed), (653-771). Bos on, MA: Allyn & Bacon.
U sini, S., Sánchez, G., & O endain, M. (2004). Validación y con iabilidad de una escala de
Ac i udes hacia las Ma emá icas y hacia las Ma emá icas Enseñadas con Compu ado-
a. Educación Ma emá ica, 16(3), 59-78.
Van de G i , W., & Hou een, T. (2006). Unde pe o mance in p ima y schools. School E -
ec i eness and School Imp o emen , 17, 1-19. doi: 10.1080/09243450600697317
Wa , H.M.G. (2000). Measu ing a i udinal change in ma hema ics and English o e he i s
yea o junio high school: A mul idimensional analysis. Jou nal o Expe imen al Ed-
uca ion, 68, 331-361. doi: 10.1080/00220970009600642
Williams, T., & Williams, K. (2010). Sel -e icacy and pe o mance in ma hema ics: Recip o-
cal de e minism in 33 na ions. Jou nal o Educa ional Psychology, 102, 453-466. doi:
10.1037/a0017271
Yasa , M. (2014). Sho o m o Ma hema ics A i ude Scale: I s psychome ic p ope ies.
Pakis an Jou nal o S a is ics, 30(6), 1267-1277
Zan, R., B own, L., E ans, J., & Hannula, M.S. (2006). A ec in ma hema ics educa ion: An
in oduc ion. Educa ional S udies in Ma hema ics, 63(2), 113-
121.doi: 10.1007/s10649-006-9028-2
