ORIGINAL RESEARCH
published: 17 Augus 2021
doi: 10.3389/ psyg.2021.703580
F on ie s in Psychology | www. on ie sin.o g 1Augus 2021 | Volume 12 | A icle 703580
Edi ed by:
Pie o Cip esso,
Uni e si y o Tu in, I aly
Re iewed by:
Isabel Rami ez,
Na ional Uni e si y o Dis ance
Educa ion (UNED), Spain
Begoña Delgado,
Na ional Uni e si y o Dis ance
Educa ion (UNED), Spain
*Co espondence:
Viole a Pina
iole apina@ug .es
Diana Ma ella
[email p o ec ed]
Special y sec ion:
This a icle was submi ed o
Quan i a i e Psychology and
Measu emen ,
a sec ion o he jou nal
F on ie s in Psychology
Recei ed: 30 Ap il 2021
Accep ed: 08 July 2021
Published: 17 Augus 2021
Ci a ion:
Pina V, Ma ella D,
Chacón-Moscoso S, Sa acos i M and
Fenolla -Co és J (2021)
Gende -Based Pe o mance in
Ma hema ical Fac s and Calcula ions
in Two Elemen a y School Samples
F om Chile and Spain: An Explo a o y
S udy. F on . Psychol. 12:703580.
doi: 10.3389/ psyg.2021.703580
Gende -Based Pe o mance in
Ma hema ical Fac s and Calcula ions
in Two Elemen a y School Samples
F om Chile and Spain: An Explo a o y
S udy
Viole a Pina1
*, Diana Ma ella2
*, Sal ado Chacón-Moscoso 3,4, Mahia Sa acos i 5,6 and
Ja ie Fenolla -Co és7
1Depa amen o de Psicología E olu i a y de la Educación, Facul ad de Educación, Economía y Tecnología de Ceu a,
Uni e sidad de G anada, Ceu a, Spain, 2Ins i u o de Es udios Sociales y Humanís icos, Facul ad de Ciencias Sociales y
Humanidades, Uni e sidad Au ónoma de Chile, Región Me opoli ana, Chile, 3Depa amen o de Psicología Expe imen al,
Uni e sidad de Se illa, Se illa, Spain, 4Depa amen o de Psicología, Uni e sidad Au ónoma de Chile, San iago, Chile,
5Núcleo Cien í ico y Tecnológico en Ciencias Sociales y Humanidades, Uni e sidad de la F on e a, Temuco, Chile, 6Escuela
de T abajo Social, Facul ad de Ciencias Sociales, Uni e sidad de Valpa aíso, Valpa aíso, Chile, 7Depa amen o de
Psicología, Uni e sidad Loyola Andalucía, Se illa, Spain
Gende di e ences in ma hema ical pe o mance a e no conclusi e acco ding o
he scien i ic li e a u e, al hough such di e ences a e suppo ed by in e na ional
s udies such as he T ends in In e na ional Ma hema ics and Science S udy (TIMSS).
Acco ding o TIMSS 2019, ou h-g ade male s uden s ou pe o med emale s uden s
in Spanish-speaking coun ies, among o he s. This wo k app oaches he s udy on
gende di e ence by examining he basic calcula ion skills needed o handle mo e
complex p oblems. Two in e na ional samples o second and hi d g ade s om Chile and
Spain we e selec ed o his explo a o y s udy. Tes s on basic ma hema ical knowledge
(symbolic and non-symbolic magni ude compa isons, luency, and calcula ion) we e
adminis e ed. The es s did no show signi ican di e ence o size e ec be ween gende s
o mean pe o mance, a iance in he dis ibu ion o pe o mance, o pe cen iles. As
no ed in he exis ing li e a u e on his opic and ei e a ed by hese indings, g ea ca e
should be exe cised when epo ing on possible gende di e ences in ma hema ical
pe o mance, as hese can con ibu e o low sel -concep among emale s uden s.
Keywo ds: gende di e ences, p ima y educa ion, ma hema ical luency, calcula ion, child en
INTRODUCTION
As echnology g ows by leaps and bounds, new ields o s udy and analysis ools a e also expanding:
Big Da a, a i icial in elligence, modeling enginee ing, so wa e a chi ec u e, e c. This has inc eased
he demand o p o essionals, bo h men and women, wi h he solid knowledge o ma hema ics
needed o such oles (Belloum e al., 2019). Howe e , women con inue o be unde ep esen ed
in his kind o p o essional oles bu o e ep esen ed in lowe paying jobs (Adams e al., 2019).
De e mining he o igin o hese di e ences is challenging as cogni i e, social, and cul u al ac o s
o e he cou se o one’s li e may all con ibu e, making i di icul o connec ma hema ical abili ies
du ing childhood o gende di e ences on he job ma ke . Howe e , i his gende gap we e
Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
in insic, i could appea du ing childhood, making i essen ial o
de e mine whe he his is he case and, hus, in e ene o a oid
u u e unde ep esen a ion o women.
The educed p esence o women in ma hema ical ields
is no hing new. As indica ed by Kane and Me z (2012, p.
10), di e ences be ween males and emales ha e been ound
in he ma hema ics pa icipa ion a e, mean and high-end
pe o mance, and a iance in he dis ibu ion o pe o mance,
making gende di e ence he subjec o ex ensi e deba e.
Ha elock Ellis (1894) was he i s o in end o empi ically
jus i y he di e ences be ween men and women wi h his
a iabili y hypo hesis. Acco ding o his hypo hesis, men could
be expec ed o show g ea e a iabili y han women in physical
and in ellec ual abili ies. This would explain he p edominance
o men in highe academic and scien i ic posi ions, bu also
hei p e alence in c ime. This hypo hesis coincided wi h he
expanded p esence o women in highe educa ion and hei
demands o ecogni ion (Shields, 1982) and con inued o be
de ended, wi h mino modi ica ions, un il he 21s cen u y, when
he ocus u ned o ex eme sco es and pe cen iles. In pa icula ,
some s udies ound mo e emales in he lowe pe cen iles
and mo e males in he highe pe cen iles o di e en ma h
assignmen s (Ba ba esi e al., 2005; Reigosa-C espo e al., 2012;
Anaya e al., 2017).
Ne e heless, in a wide s udy ca ied ou by Bake and Jones
(1993) wi h 77,602 s uden s om 19 coun ies, ma hema ical
pe o mance be ween gende s was ound o a y by coun y
and he ype o educa ion s uden s ecei ed; addi ionally, he
di e ences we e no ed o be dec easing o e ime. The au ho s
also la gely debunked he hypo hesis o a iabili y when hey
poin ed ou ha gende di e ences in pe o mance dec ease
when women ha e mo e equi able access o highe educa ion and
quali ied wo k. Indeed, se e al s udies ( o ins ance, Kane and
Me z, 2012) ha e mo ed away om he de e minis ic hypo hesis
o a iabili y, p o iding empi ical e idence o a hypo hesis o
sociocul u al ac o s.
Coinciding wi h he a gumen ha sociocul u al ac o s ha e
he g ea es bea ing on ma hema ical pe o mance, di e ences
be ween gende s should g adually disappea as socie y becomes
mo e p og essi e and inclusi e. Lindbe g e al. (2010) suppo
his hypo hesis in a b oad me a-analysis. Based on 242 s udies
published be ween 1999 and 2007 (a o al sample o 1,286,350
indi iduals bo h males and emales), he au ho s concluded ha
ma hema ical pe o mance is simila o bo h gende s, no ing
ha any gende di e ence can be a ibu ed o un ela ed ac o s.
The au ho s conclude ha i is c ucial o dissemina e hese
esul s o coun e ac s e eo ypes abou [alleged] emale ma h
in e io i y (Lindbe g e al., 2010, p. 1134). Mo e ecen s udies
ha e eplica ed hese esul s ( o ins ance, Voye and Voye ,
2014; Scheibe e al., 2015; Ke sey and Can lon, 2018), and o he s
ha e limi ed he di e ences o a mino i y o asks (Hu chison
e al., 2019).
Gi en he empi ical e idence epo ed in he li e a u e,
males and emales would be expec ed o pe o m simila ly on
in e na ional s udies such as he TIMSS (Ins i u o Nacional de
E aluación Educa i a [INEE], 2016, 2020). Un o una ely, his
is no he case. Acco ding o he TIMSS, he gende gap in
ma hema ical pe o mance is p esen as ea ly as ou h g ade
and, acco ding o he las edi ion (2019), has e en inc eased
in coun ies such as Spain. Gende di e ences a he ou h
g ade le el can also be no ed, al hough o a lesse ex en , in
o he Spanish-speaking coun ies ha pa icipa ed in TIMSS
2019. Chile, o example, wen om ha ing no signi ican
gende di e ences in ma hema ics in he 2015 epo o ha ing
signi ican ones in he 2019 epo (Ins i u o Nacional de
E aluación Educa i a [INEE], 2016, 2020). In ac , samples
om Spanish-speaking coun ies show a la ge gende gap in
in e na ional epo s, bu ew s udies include hem in hei
analysis (e.g., he me a-analysis by Voye and Voye , 2014).
This explo a o y s udy conside s wo Spanish-speaking
samples om Chile and Spain, bo h o which a e
unde ep esen ed in he li e a u e. Fi s , i is impo an o
analyze po en ial gende di e ences o hese coun ies. Second,
by looking in o he samples om hese wo coun ies, common
pa e ns may be ound ha could allow an ea ly in e en ion o
be designed.
Bo h Spain and Chile ha e simila ma h cu icula a he
elemen a y school le el. In bo h Chile (MINEDUC, 2018) and
Spain (e.g., Dec e o n.◦, 198/2014), s uden s a e doing single-
digi addi ion and sub ac ion a he end o he i s g ade (a
a ound age se en). In second g ade, hey lea n mul iplica ion
and begin adding and sub ac ing beyond single digi s. In hi d
g ade, hey begin using mul iplica ion and di ision o sol e ma h
p oblems. Al hough bo h samples a e socially and cul u ally
dis inc , he objec i e o his s udy was o in es iga e whe he
gende di e ences exis and, i so, whe he he pa e n is he
same o he wo Spanish-speaking coun ies. Since bo h Chile
and Spain ha e simila ma h cu icula, i his was he case, he
gende gap could be conside ed in insic.
In e na ional e alua ions and e en ma h es s adminis e ed
a schools o en do no conside he skills and basic knowledge
o acqui ing ma hema ical abili ies, and a e ins ead ocused
on complex calcula ion o p oblem sol ing (Noswo hy e al.,
2013). Hence, when gende di e ences a e obse ed in such
es s, i is ha d o de e mine whe he such di e ences a e also
p esen o mo e basic ma h skills. A logical hypo hesis is ha
he basic abili ies needed o complex asks would also show a
gende gap. In ecen yea s, di e en s udies ha e explo ed wha
basic nume ical skills necessa y o ma hema ical achie emen
a e esponsible o gende di e ences ( o ins ance, Ke sey and
Can lon, 2018; Hu chison e al., 2019).
In his ega d, he li e a u e has widely epo ed on he basic
skills equi ed o ma hema ical achie emen . On one hand, non-
symbolic magni ude compa ison (e.g., he abili y o look a wo
g oups o objec s and de e mine which is g ea e in numbe ), is
conside ed a s epping s one o lea ning numbe s (see Lande l,
2019). Fo non-symbolic compa ison, isuospa ial pe cep ion,
no he abili y o coun , is equi ed (Ke sey and Can lon, 2018).
Once i is acqui ed, boys and gi ls can ela e quan i ies wi h
symbolic numbe s ( o ins ance, ela ing he numbe ou wi h
ou objec s) and lea n he meaning o he A abic nume al. On
he o he hand, symbolic magni ude compa ison ( he abili y o
choose which o wo numbe s is la ge ) equi es pa icipan s
o e icien ly access he analog magni ude ep esen a ions ha
F on ie s in Psychology | www. on ie sin.o g 2Augus 2021 | Volume 12 | A icle 703580
Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
co espond o he A abic nume als in o de o de e mine which
numbe is g ea e (Lande l, 2019). Two asks a e widely used
o e alua e hese abili ies: he symbolic magni ude compa ison
ask and he non-symbolic magni ude compa ison ask. A ecen
me a-analysis has con i med ha bo h asks co ela e wi h
subsequen ma hema ical pe o mance, al hough he co ela ion
is highe o he symbolic compa ison ask (Schneide e al.,
2016).
Once child en unde s and he meaning o he A abic
nume als, hey s a o coun . The i s ope a ions a e simple
single-digi addi ion and sub ac ion wi h a sum o <10.
Depending on one’s knowledge o a i hme ic ac s, wo s a egies
a e mainly used. In he beginning, he child will ha e o coun o
sol e he ope a ion; and h ough epe i ion, he answe s become
lodged in hei memo y (De Smed e al., 2019). The au oma ion
o hese ope a ions has been conside ed c i ical o de eloping
obus complex calcula ions (Roye e al., 1999).
Calcula ion and ma hema ical p oblems a e conside ed mo e
complex a eas o ma hema ical pe o mance. Ma hema ical
p oblems also equi e o he abili ies such as eading
comp ehension (Abedi and Lo d, 2001; Donlan e al., 2007).
Calcula ion usually includes he ou basic ma hema ical
ope a ions (addi ion, sub ac ion, mul iplica ion, and di ision)
and gene ally canno be sol ed om memo y, since i usually
in ol es double digi s o mo e. Child en can use a wide
a ie y o s a egies o app oaching hese ope a ions, such
as decomposi ion o sequencing (Hickendo e al., 2019).
Calcula ion also equi es execu i e unc ions, such as wo king
memo y. The s a egy child en use depends no only on hei
indi idual skills bu also on he ins uc ion hey ha e ecei ed.
Gende di e ences ha e been ound (e.g., Diaman opoulou
e al., 2012) o hese complex asks. Winkelmann e al.
(2008) p oposed ha dispa i ies in di e en s udies on
gende di e ences can be a ibu ed o wha is conside ed
“basic abili y” in a pa icula s udy and on he cogni i e
esou ces equi ed o each ask. The b eakdown o asks
by gende di e ences allows o he design o lea ning and
suppo s a egies in speci ic a eas o g adually educe he
gende gap.
Gende di e ences end o be mo e e iden in uppe
elemen a y. Some s udies do p esen e idence o a gende gap
o lowe elemen a y (Jo dan e al., 2006; Scheibe e al., 2015),
bu o he s do no (Lachance and Mazzocco, 2006). Thi d g ade
seems o be a c i ical yea o he de ec ion o gende di e ences
in ma hema ical pe o mance, al hough he s udies a his le el
a e sca ce. As an example, Ge many p esen s gende di e ences
s a ing in hi d g ade (Winkelmann e al., 2008). In Spain, he
TIMSS (2015 and 2019) epo s a la ge gende gap in ou h
g ade, hus sugges ing a possible gende gap in hi d g ade
as well. Ano he in e na ional s udy, TERCE 2015 (UNESCO,
2016), shows ha he numbe o La in Ame ican coun ies whe e
males ha e an ad an age o e emales inc eases be ween hi d
and six h g ade. The e o e, second and hi d g ade a e conside ed
c ucial. The aim o his s udy is no o de e mine he age a
which gende di e ences, i hey exis , appea , bu o obse e
whe he hese di e ences a e de ec ed in lowe elemen a y in
Spanish-speaking coun ies.
This s udy del es in o hese di e ences o de e mine i
hey a e p esen in he i s yea s o school o basic ma h
skills. A e con olling o eading p o iciency, ma hema ical
pe o mance by Spanish-speaking second and hi d g ade s in
Chile and Spain will be compa ed o non-symbolic compa ison,
symbolic compa ison, luency, and calcula ion. As pa o his
s udy, any di e ences in mean pe o mance, a iance in he
dis ibu ion o pe o mance, and pe cen iles will be assessed.
Acco ding o he li e a u e, di e ences a e no expec ed in
basic ma hema ical asks such as symbolic and non-symbolic
compa ison bu could appea o asks ha equi e ma hema ical
luency and calcula ion. We hypo hesize ha a g ea e numbe o
males will be in he highe pe cen iles and a g ea e numbe o
emales will be in he lowe pe cen iles.
METHODOLOGY
Pa icipan s
The pa icipan s we e second and hi d g ade s a ou schools
in he O’Higgins egion (Chile) and se en schools in Mu cia
(Spain). These child en we e o ganized in o wo sepa a e
samples, one o each coun y, wi h a mean age o 7.75 o he
second g ade s (M=7.68, SD =0.31 o he Spanish child en,
and M=7.88, SD =0.48 o he Chilean child en) and 8.77
o he hi d g ade s (M=8.7, SD =0.33 o he Spanish
child en, and M=8.89, SD =0.39 o he Chilean child en).
The sample was o med by 201 Spanish school child en (107
second g ade s and 94 hi d g ade s; 55.2% male and 44.8%
emale) and 184 Chilean school child en (90 second g ade s and
94 hi d g ade s; 48.9% male and 51.1% emale) and was collec ed
h ough inciden al sampling. The ollowing exclusion c i e ia
we e es ablished: ision di icul ies, diagnosis o au ism spec um
diso de o cogni i e impai men , insu icien knowledge o he
Spanish language, and, in he case o he hi d g ade s, signi ican
di icul ies eading. Table 1 de ails he numbe o males and
emales by g ade and coun y. Possible di e ences ega ding age
(Mann–Whi ney U) and gende p opo ion by g ade and coun y
(χ2) we e examined.
This s udy was ca ied ou ollowing he ecommenda ions
o he Chilean Commission o Scien i ic and Technological
In es iga ion (CONICYT in i s Spanish ac onym). The p o ocol
was app o ed by he E hics Commi ee o Uni e sidad de
la F on e a (Ac 066-2017, on Shee 036-17). The s udy
complied wi h he s anda ds o he e hical commi ee o
Uni e sidad Au ónoma de Chile and wi h he ag eemen
be ween he Depa men o Educa ion and Uni e si ies o he
au onomous communi y o Region o Mu cia and Uni e sidad
de Mu cia. In o med consen was eques ed o pa icipa e in
his s udy.
Ins umen s
The ollowing pape -and-pencil es s we e adminis e ed o
measu e ma hema ical pe o mance and eading luency.
Nume ical magni ude compa isons (Noswo hy e al., 2013).
This ask includes wo di e en pa s:
F on ie s in Psychology | www. on ie sin.o g 3Augus 2021 | Volume 12 | A icle 703580
Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
TABLE 1 | Dis ibu ion in he Spanish language sample o second and hi d g ade s: sco ing on symbolic es by gende .
Spanish sample Chilean sample
M(DT) Male Female U p aMale Female U p
Second g ade
N 107 90
Gende n(%) 56(52.3) 51(47.7) 49(54.4) 41(45.6)
Magni ude compa ison
Symbolic 29.3(9.3) 33.0(6.8) 1055.0 0.020 −0.26 29.9(10.1) 30.9(10.6) 961.0 0.727
Num. e o s 0.1(0.4) 0.1(0.9) 1572.2 0.060 0.6(1.3) 0.7(1.2) 931.5 0.850
Non-symbolic 29.1(7.6) 31.6(5.7) 1103.5 0.042 −0.23 28.8(13.8) 33.9(12.0) 796.5 0.092
Num. e o s 0.3(1.0) 0.6(0.1) 1419.5 0.932 1.4(2.7) 2.2(2.9) 826.0 0.110
Thi d g ade
N 94 94
Gende n(%) 55(58.5) 39(41.5) 55(58.5) 39(41.5)
Magni ude compa ison
Symbolic 37.7(7.0) 39.8(6.2) 837.0 0.069 39.3(10.2) 37.4(11.2) 1158.0 0.513
Num. e o s 0.2(0.6) 0.1(0.4) 1126.5 0.443 0.6(1.1) 0.6(1.1) 1051.5 0.847
Non-symbolic 32.3(7.3) 31.7(4.8) 1196.0 0.344 37.0(11.3) 35.5(11.4) 1193.5 0.355
Num. e o s 0.5(1.0) 0.3(0.6) 1135.5 0.412 1.7(2.7) 1.1(1.6) 1133.5 0.618
P eDisCal
Sen ences 13.6(14.7) 14.7(2.9) 905.5 0.199 13.2(6.9) 12.8(6.2) 1090.0 0.896
Num. e o s 2.2(1.9) 1.6(1.2) 1237.0 0.193 6.5(9.3) 3.2(2.4) 1252.5 0.163
Ma hema ical luency 17.7(6.8) 17.1(4.5) 1079.5 0.960 12.9(5.5) 10.7(5.1) 1369.5 0.023 0.27
Num. e o s 1.5(2.5) 1.1(1.7) 1127.0 0.652 1.8(2.6) 1.3(1.4) 1050.5 0.864
Calcula ion 11.6(4.2) 11.0(3.4) 1143.0 0.589 9.0(4.3) 9.0(4.3) 1126.0 0.683
Num. e o s 0.2(0.6) 0.3(0.6) 1202.0 0.313 4.1(8.0) 1.9(8.0) 1294.5 0.083
Sco es a e shown in e ms o mean and s anda d de ia ion (no mean sco es) o acili a e unde s anding.
aE ec size co esponding o he bise ial co ela ion be ween anges. Only alues co esponding o signi ican di e ences be ween he g oups a e p o ided.
- Symbolic ask (56-digi pai s), whe e he pa icipan s we e
asked o compa e nume ical pai s (numbe s one h ough nine)
and indica e which numbe was highe .
- Non-symbolic ask (56 do a ays), whe e do a ays o a ying
quan i ies a e p esen and he pa icipan s we e asked o
indica e which side had mo e do s.
Each es had a ime limi o 1 min, and he dependen a iable
was he numbe o co ec answe s.
P eDisCal (Pina e al., 2020). This is a se o h ee es s ha
measu e eading luency, ma hema ical luency, and calcula ion,
in ha o de . Al hough he P eDisCal scale was de eloped in
Spain, a c oss- alida ion p ocess was ca ied ou in se e al La in
Ame ican coun ies. Some o he i ems we e modi ied because
o in e p e a ion issues ( ela ed o sociocul u al ac o s) in La in
Ame ican coun ies. The es included he ollowing asks:
- Sen ences. This ask consis s o 47 sen ences ha assess eading
luency. Each sen ence has a missing wo d, o ins ance: “The
s awbe ies a e .. .” ollowed by i e answe op ions (one is
co ec ). The inco ec al e na i es a e close g amma ically o
seman ically. All he sen ences a e easy o unde s and. The es
had a ime limi o 3 min. The dependen a iable is he numbe
o co ec answe s. I is a alida ed es wi h adequa e es - e es
eliabili y [ (169) =0.8, p<0.001].
- Ma hema ical luency. The a i hme ic ac s a e es ed h ough
63 single-digi addi ion and sub ac ion ope a ions. All sums
a e <10. The maximum ime is 1 min in his es , and he
dependen a iable is he numbe o co ec answe s. The
eliabili y o he es is adequa e [ (169) =0.85, p<0.001].
- Calcula ion. This es comp ises 45 i ems o inc easing
di icul y and assesses complex calcula ion. Pa icipan s ha e
o de e mine wha numbe o symbol, o i bo h a e missing in
a compa ison o wo ope a ions (e.g., “3 +_=5+1”). The
es had a ime limi o 3 min, and he dependen a iable was
he numbe o co ec answe s. The es - e es eliabili y o he
alida ed scale was accep able [ (169) =0.75, p<0.001].
P ocedu e
The asks we e adminis e ed in Feb ua y o Spain and in
Sep embe o he same yea o Chile in o de o e lec he same
momen o he academic calenda in bo h coun ies. T ained
e alua o s collec i ely adminis e ed he es du ing he school
day. Gi en ha P eDisCal equi ed a ce ain deg ee o eading
p o iciency and complex calcula ion abili y, i was adminis e ed
only o he hi d g ade s, while he magni udes compa ison
es s we e adminis e ed o bo h he second and hi d g ade
samples. In he case o he magni ude compa isons, he symbolic
es was adminis e ed i s , ollowed by he non-symbolic es .
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Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
The P eDisCal was adminis e ed in keeping wi h he o de
es ablished o ha es , e.g., sen ences, ma hema ical luency,
and calcula ion.
Da a Analysis
Fi s , he compa abili y o he g oups was e i ied by assessing
age and gende di e ences by g ade and coun y (χ2), and mean
pe o mance in he sen ences es be ween coun ies (S uden
). Second, basic pa ame ic assump ions o da a analysis
we e e i ied (no mali y using he Kolmogo o –Smi no es ,
homoscedas ici y using he Le ene es ). Non-pa ame ic es s
we e ca ied ou using he Mann–Whi ney U and s a is ical
bise ial co ela ions ( =0.1 as low; =0.3 as medium, and =
0.5 as high e ec ; Cohen, 1988); and χ2 o compa e gende and
pe cen ile pe o mance dis ibu ion in hi d g ade.
RESULTS
Bo h samples showed a simila gende dis ibu ion o pa icipan s
(χ2=0.09, p=0.768 o second g ade; χ2=0, p=1 o second
g ade). The e was no signi ican e idence be ween coun ies in
ela ion o he mean pe o mance in he sen ences es ( =1.35; p
=0.178). Howe e , signi ican di e ences we e de ec ed be ween
coun ies ega ding he mean age o s uden s ( = −5.04, p<
0.001, d= −0.52 o he hi d g ade; = −4.18, p<0.001,
d= −0.86 o he second g ade), wi h mode a e o high e ec
sizes (Cohen, 1988). Ne e heless, hese di e ences in age a e
no ele an o his s udy, since he analysis be ween coun ies
is ca ied ou compa ing gende , a a iable o which he e a e no
signi ican di e ences in he samples o bo h coun ies.
The dis ibu ion o da a was examined o each dependen
a iable acco ding o coun y and cou se. Excep o he
ma hema ical luency and calcula ion es s in he Chilean
hi d g ade sample, he emaining a iables ollowed a non-
no mal dis ibu ion (K-S <0.05); hus, non-pa ame ic analyses
we e applied.
The Le ene es showed signi ican di e ence in a iance
be ween gende s in he symbolic es o he Spanish sample o
second g ade s (F=3.97, p=0.049). The sco es o boys showed
highe a iabili y (σ2=86.5) wi h skewness o 0.18, (SE =0.32)
and ku osis o −0.19 (SE =0.63), compa ed wi h hose o he
gi ls (σ2=46.3) wi h skewness o 0.1 (SE =0.33), and ku osis
o 0.27 (SE =0.66), as shown in Figu e 1. Di e ences in a iance
we e no ound o he o he es s o ei he sample.
Spea man’s co ela ion was ca ied ou be ween es s o
each coun y (Table 2). The co ela ion be ween sco es on he
symbolic and non-symbolic es s was c ucially posi i e and
high in he second g ade sample. As o he hi d g ade s,
ma hema ical luency posi i ely co ela ed o calcula ion and
wi h sen ences; hese las wo subscales co ela ed posi i ely. The
symbolic es also co ela ed posi i ely wi h he non-symbolic
one ( s=0.46, p <0.001).
Mean Pe o mance by Gende and G ade
I di e en ia ed by gende , he Mann–Whi ney es s indica ed
ha he gi ls sco ed signi ican ly highe (See Table 2) in he
symbolic es o he Spanish second g ade s (U=1,055, p=0.02,
= −0.26), bu his was no he case o he Chilean sample (p
=0.727). Howe e , he e ec size o he signi ican di e ences
anged om low o mode a e. Rega ding he non-symbolic es ,
he esul s we e simila , wi h gi ls ou pe o ming he boys in he
Spanish sample (U=1,103, p=0.42, = −0.23), bu no in he
Chilean sample (p=0.092). In his case, he e ec size was lowe
han in he symbolic es . The di e ences de ec ed in he sample
disappea in he hi d g ade. In e ms o he numbe o mis akes
made on bo h es s, no signi ican di e ences we e ound be ween
gende s in ei he coun y.
In he hi d-g ade sample, signi ican di e ences we e only
ound be ween gende s o he ma hema ical luency es in he
Chilean sample (U=1,369, p=0.023, =0.27). He e, he gi ls
had lowe sco es (Md =9) han he boys (Md =13). In e ms
o he numbe o mis akes made on bo h es s, no signi ican
di e ences we e ound be ween gende s in ei he coun y a he
hi d g ade le el.
Ra io o Boys o Gi ls a Va ious Pe cen iles
Fou g oups o each sample we e o med acco ding o he sco es
hey ob ained and hei co esponding pe cen iles. G oup 1
sco ed in he 1–25 h pe cen ile; g oup 2 in he 26–50 h pe cen ile;
g oup 3 in he 51–75 h pe cen ile; and g oup 4 in he 76 h
pe cen ile o highe . χ2and i s signi icance we e calcula ed o
examine signi ican di e ences in he a io o males and emales
in he di e en pe cen ile g oups. As no signi ican di e ences
we e ound in e ms o pe o mance o boys and gi ls in he
hi d-g ade es s (excep o ma hema ical luency, which had a
low e ec size), he g oups we e o med by s uden s om bo h
coun ies. In he case o he second g ade s, he calcula ions
a ied by coun y.
Fo he hi d g oup, he e we e no signi ican gende
di e ences in e ms o he a io o boys o gi ls, he di e en
pe cen ile g oups, o o any o he es s (see Table 3). Howe e ,
signi ican di e ences we e ound in he symbolic es o he
Spanish sample o second g ade s (χ2=9.65, p=0.022). The
pe cen ages we e di e en o he i s g oup (sco ings be ween
he 1–25 h pe cen ile; χ2=6.54, p=0.011), wi h a la ge
quan i y o boys (30.4%) han gi ls (9.8%). Signi ican di e ences
we e no ound in he Chilean sample o second g ade s.
DISCUSSION
This s udy se ou o compa e he basic ma hema ical abili ies
o boys and gi ls, which p o e essen ial o he acquisi ion
o complex ma h skills. The sample was composed o boys
and gi ls om wo Spanish-speaking ye cul u ally di e en
coun ies in he second and hi d g ade, ages a which he
gende gap s a s o appea . The esul s allow us o conclude,
in keeping wi h he scien i ic li e a u e on he opic, ha in
e ms o basic ma hema ical knowledge, boys and gi ls show no
signi ican di e ences in ma hema ical pe o mance. P e ious
in es iga ions, including a ious me a-analyses (Lachance and
Mazzocco, 2006; Hyde e al., 2008; Lindbe g e al., 2010;
Voye and Voye , 2014; Scheibe e al., 2015), ha e no ed as
much. Simila ly, Hu chison e al. (2019) ound no di e ences
in nume ical and magni ude compa ison, nume ical o de ing,
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Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
FIGURE 1 | Dis ibu ion in he Spanish language sample o hi d g ade sco es on he symbolic es by gende .
TABLE 2 | Spea man’s co ela ions be ween he P eDisCal and magni ude compa ison ( hi d g ade es s).
P eDisCal Magni ude compa ison
Sen ences Ma hema ical luency Calcula ion Symbolic
P eDisCal
Ma hema ical luency 0.194
Calcula ion 0.253* 0.451***
Compa ison o magni ude
Symbolic 0.054 0.389*** 0.065
Non-symbolic 0.025 0.271** 0.314** 0.318**
*p<0.05; **p<0.01; ***p<0.001.
magni ude es ima ion, mul iplica ion, and di ision, al hough he
popula ion analyzed o hei s udy hailed om he Ne he lands,
meaning ha esul s could be di e en in coun ies wi h a
highe gende gap. The esul s o his s udy, howe e , e eal no
signi ican di e ences in mos o he asks conside ed o wo
Spanish-speaking samples om Chile and Spain, despi e he high
gende gap de ec ed in in e na ional es s o he wo coun ies
(such as TIMSS 2019).
The main di e ences a e ound in he symbolic es
(compa ison o wo numbe s o de e mine which one is highe )
in he Spanish sample o second g ade s. In pa icula , he gi ls
pe o med be e and he boys showed a g ea e a iabili y.
Addi ionally, emales had a highe mean pe o mance, and a
g ea e a io o males ell below he 25 h pe cen ile. Howe e ,
he e ec size is small in second g ade, and no such esul s
we e ound in he hi d g ade sample. Fo he non-symbolic
compa ison es , he gi ls pe o med be e once again, al hough
his di e ence disappea ed in hi d g ade. The di ec ion o
hese gende di e ences goes agains he hypo hesis o highe
pe o mance in males. In line wi h hese esul s, p e ious s udies
ha e shown gende di e ences in a o o emales in basic
abili ies ( o ins ance, Halpe n and W igh , 1996).
The only di e ence in a o o males was ound in he Chilean
sample in a e age pe o mance o ma hema ical luency in he
hi d g ade. Di e ences in addi ion and sub ac ion ha e been
ound p e iously, al hough he e has no always been e idence o
hese di e ences (Hu chison e al., 2019). In his case, he e ec
size was small and no di e ences we e ound o calcula ion,
meaning ha cau ion is c i ical when in e p e ing he esul s.
In he case o he Chilean hi d g ade s, es abili ies we e
ecen ly acqui ed, and he di e ences would likely disappea wi h
p ac ice. Impo an ly, ma hema ical luency is decisi e o he
obus de elopmen o complex calcula ion and is an abili y ha
can be p ac iced un il i is lea ned (Roye e al., 1999).
P io s udies ha e indica ed ha di e ences in ma hema ical
pe o mance ely on he kind o ask s uden s a e asked
o comple e. These s udies ha e ound ha emales pe o m
be e in a i hme ic and calculus, while males pe o m be e
in ma hema ical p oblem sol ing (By nes and Takahi a, 1993).
Howe e , he e ha e also been con lic ing esul s in he esea ch.
Fo ins ance, Roye e al. (1999) iden i ied ha males pe o m
be e in ma h- ac e ie al han emales. In ano he s udy,
Winkelmann e al. (2008) showed ha emales had poo e
basic skills, while males had a sligh ad an age in ma hema ical
p oblems, such as equa ions con aining a missing numbe . The
au ho s explained ha he esul s depended on basic elemen a y
skills and on how ma h p oblems a e de ined, i.e., on he cogni i e
esou ce ha each ask demanded.
One hypo hesis is ha gende di e ences can be ound in
complex a eas o ma hema ics ha demand mo e cogni i e
esou ces. In his sense, o example, he li e a u e sugges s
a ela ionship be ween spa ial abili ies and gende di e ences
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Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
TABLE 3 | Pe cen age and compa ison o hi d g ade boys and gi ls by g oups co esponding o he 25 h, 50 h, 75 h, and 100 h pe cen ile.
G oup 1(P25) G oup 2 (P50) G oup 3 (P75) G oup 4 (P100) Di e ences be ween g oups
χ2P
P eDisCal
Sen ences
Male 30,0 20,9 29,1 20,0 3.80 0.284
Female 21,8 29,5 23,1 25,6
N61 44 39 44
Calcula ion
Male 32,7 20,0 23,6 23,6 2.39 0.495
Female 32,1 28,2 16,7 23,1
N61 44 39 44
Ma hema ical luency
Male 24,5 29,1 22,7 23,6 1.60 0.659
Female 32,1 29,5 19,2 19,2
N52 55 40 41
Magni ude compa ison
Symbolic
Male 27,3 32,7 17,3 22,7 7.10 0.069
Female 24,4 21,8 33,3 20,5
N61 44 39 44
Non-symbolic
Male 27,3 18,2 30,9 23,6 5.65 0.130
Female 26,9 32,1 25,6 15,4
N61 44 39 44
G oups a e o ganized by pe cen iles: 1–25 h pe cen ile (G oup 1), 26–50 h pe cen ile (G oup 2), 51–75 h pe cen ile (G oup 3), and 76–100 h pe cen ile (G oup 4).
in ma hema ical pe o mance. Howe e , a ecen s udy did
no con i m hese esul s and ins ead concluded ha gende
di e ences may depend on he es and he s a egy used o
sol e each i em (Ramí ez-Uclés and Ramí ez-Uclés, 2020). The
esul s suppo his hypo hesis. In pa icula , he calcula ion
is he ask ha in ol es he highes cogni i e demand, bu
no gende di e ences we e ound. Ano he possibili y is ha
gende di e ences in ma hema ical pe o mance eme ge la e
in mo e complex ma hema ical asks o a e in luenced by
cul u al o social s e eo ypes, al hough he esul s show ha
a leas lowe elemen a y school child en do no exhibi
such di e ences.
Ano he hypo hesis o gende di e ences in ma hema ical
pe o mance is ela ed o he way in which he answe op ions
a e p esen ed on es s. Fo ins ance, in a s udy wi h PISA 2000
da a, La on aine and Monseu (2009) ound ha in all he
coun ies analyzed, open-ended (as opposed o mul iple choice)
answe s o eading asks a o ed emales. Fo ma hema ics,
Rou i sky and Tu ne suppo ed hese conclusions using PISA
2003 da a bu poin ed ou ha his di e ence disappea ed as
he complexi y o i ems inc eased (Rou i sky and Tu ne , 2003).
Fu u e in es iga ions should assess how he ques ions and ype o
answe op ions in luence he gende gap.
P e ious s udies ha e e ealed ha he lea ning ou ine
shows no di e ences be ween gende s, al hough boys and
gi ls do exp ess di e en a i udes owa d ma hema ics
(Ba be o-Ga cía e al., 2007). This could explain why di e ences
can be ound in highe g ades despi e being absen when basic
ma h skills a e e alua ed. Impo an ly, gende di e ences may
well be ela ed o he wo ding o asks o ins uc ions, o social
beha io s ha in luence how pa en s, eache s, and e en emale
s uden s iew hei own ma hema ical abili y, no by any in insic
ma h di icul ies (see Lindbe g e al., 2010).
This s udy p esen s se e al limi a ions. All he asks
conside ed had a ime limi , which can in luence he esul s.
P ocessing speed is essen ial o school pe o mance (Dodono a
and Dodono , 2012), and i is impo an o he diagnosis o
lea ning disabili ies, since child en wi h a diagnosis a e iden ical
o hose wi h mean pe o mance i we p o ide hem su icien
ime (Jo dan and Mon ani, 1997). The second cons ain o his
s udy is ha no in o ma ion was ob ained on he socioeconomic
le el o he child en. Howe e , bo h samples a ended public
schools, and none we e disad an aged. Las ly, his s udy is
explo a o y, and despi e ha ing a la ge sample, i canno be
deemed ep esen a i e o he o al popula ion o bo h coun ies.
Gende di e ences in ma hema ical pe o mance ha e been
less s udied in Spanish-speaking coun ies. This s udy was
laid ou as an ini ial app oach o esea ching his popula ion.
Based on exis ing li e a u e and he esul s, gende di e ences
a y by ask, s a egies used o sol e p oblems, coho , age,
and ins uc ions p o ided. Fo u u e esea ch, he sample
should be expanded geog aphically o highe ep esen a i eness
F on ie s in Psychology | www. on ie sin.o g 7Augus 2021 | Volume 12 | A icle 703580
Pina e al. Gende -Based Pe o mance in Ma hema ical Fac s and Calcula ions
in ela ion o social, educa ional, and cul u al di e ences.
Fu he mo e, i would be in e es ing o expand he numbe
o cou ses e alua ed o obse e he pa e n be ween gende s
and o include mo e complex asks; his should allow speci ic
ma hema ical a eas o be iden i ied in which gende di e ences
can easily be de ec ed (Chacón-Moscoso e al., 2019). These new
de elopmen s would po en ially e eal di e ences ela ed o he
coun y, ac o ial in a iance, di e en ial i em unc ioning (DIF),
and he in luence o open-ended (as opposed o mul iple choice)
ques ions (Chacón-Moscoso e al., 2016).
P ac ical Value, Implica ions o
Educa ional In e en ion
I should be no ed ha he es s applied in his s udy could be
used o an ea ly diagnosis o gende di e ence, and wi h espec
o child en wi h low ma hema ical pe o mance.
CONCLUSIONS
In conclusion, esul s emphasizing ha males ou pe o m
emales in ma h do no hold ue in he key ma hema ical
a eas analyzed wi h he excep ion o ma hema ical luency in he
Chilean sample, whe e he e ec size was small. The e o e, he
acquisi ion o complex abili ies should be he same o males and
emales. A a scien i ic le el and in he news media, ca e should
be exe cised when epo ing on gende di e ences because i
can in luence own opinion o he gi ls o hei ma hema ical
abili y. To he bes knowledge o he au ho s, his s udy is
he i s o examine gende di e ences in basic ma h skills in
Spanish-speaking popula ions ha e eals conside able gaps in
in e na ional s udies on he opic.
DATA AVAILABILITY STATEMENT
The aw da a suppo ing he conclusions o his a icle will be
made a ailable by he au ho s, wi hou undue ese a ion.
ETHICS STATEMENT
The s udies in ol ing human pa icipan s we e e iewed
and app o ed by Chilean Commission o Scien i ic and
Technological In es iga ion (CONICYT, in i s Spanish
ac onym). The p o ocol was app o ed by he E hics Commi ee
o Uni e sidad de la F on e a (Ac 066-2017, on Shee 036-17).
The s udy was in acco dance wi h he s anda ds o he e hical
commi ee o Uni e sidad Au ónoma de Chile and wi h
he ag eemen be ween he Region o Mu cia’s Comunidad
Au ónoma h ough he Depa men o Educa ion and
Uni e si ies, and Uni e sidad de Mu cia. W i en in o med
consen o pa icipa e in his s udy was p o ided by he
pa icipan s’ legal gua dian/nex o kin.
AUTHOR CONTRIBUTIONS
VP, JF-C, and DM concep ualized and designed he s udy. MS
acqui ed he da a. VP, JF-C, and SC-M analyzed and in e p e ed
he da a. VP, JF-C, and DM w o e he manusc ip . JF-C p epa ed
he igu es and ables. SC-M discussed esul s and e iewed
w i ing. All he au ho s ead and app o ed he inal e sion o
he manusc ip .
FUNDING
This s udy has been suppo ed by he Chilean na ional
p ojec s Fondecy Regula 2018 ID1181472, Anid/Fondecy
Regula ID1210172 and Fondecy Regula 2019 ( e . numbe
1190945) and by a ellowship o esidencies ab oad o young
esea che s om Ma e Nos um (2017). Also, his esea ch
has been suppo ed by he ERDF Andalusia Ope a ional
P og am 2014–2020, go e nmen o Andalusia, Spain
( e . US-1263096); he VI Own Resea ch and T ans e
Plan (VIPPITUS), Uni e sidad de Se illa, Spain ( e . VIPP
PRECOMPETI 2020/1333).
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