Resea ch Pape
Recommended ci a ion: Naukka inen, J., Kangaslampi, R., Kaa akka, T., &
Ra a a, J. (2025). Ma hema ics Sel -E icacy and App oaches o Lea ning in
Fi s -Yea Enginee ing Ma hema ics. In Kangaslampi, R., Langie, G., Jä inen,
H.-M., & Nagy, B. (Eds.), SEFI 53 d Annual Con e ence. Eu opean Socie y o
Enginee ing Educa ion (SEFI), Tampe e, Finland. DOI:
10.5281/zenodo.17631255.
This Con e ence Pape is b ough o you o open access by he 53 d Annual Con e ence
o he Eu opean Socie y o Enginee ing Educa ion (SEFI) a Tampe e Uni e si y in
Tampe e, Finland. This wo k is licensed unde a C ea i e Commons
A ibu ion-NonComme cial-Sha e Alike 4.0 In e na ional License.
MATHEMATICS SELF-EFFICACY AND APPROACHES TO
LEARNING IN FIRST-YEAR ENGINEERING MATHEMATICS
J. Naukka inen a,
1
, R. Kangaslampi b, T. Kaa akka c,
J. Ra a a d,
a LUT Uni e si y, Lappeen an a, Finland, 0000-0001-6029-5515
b Tampe e Uni e si y, Tampe e, Finland, 0000-0002-9059-8047
c Tampe e Uni e si y, Tampe e, Finland, 0000-0002-3824-8939
d LUT Uni e si y, Lappeen an a, Finland, 0000-0002-8816-6165
Con e ence Key A eas: Teaching ma hema ics and physics in enginee ing
educa ion; Di e si y, equi y and inclusion in ou uni e si ies and in ou eaching
Keywo ds: Sel -e icacy, app oaches o lea ning, enginee ing ma hema ics, i s -
yea s uden s
ABSTRACT
This s udy explo es he ela ionship be ween sel -e icacy and lea ning app oaches
among i s -yea enginee ing s uden s in wo Finnish esea ch-in ensi e uni e si ies.
I in es iga es how ma hema ics sel -e icacy and app oaches o lea ning (deep,
su ace, and o ganised) di e be ween s uden s in in e na ional p og ams and
Finnish p og ams, as well as be ween women and men. I also examines how
app oaches o lea ning a ec s uden s' sel -e icacy, conside ing gende and
p og am di e ences. The esea ch was conduc ed in he con ex o a i s -yea
enginee ing ma hema ics cou ses, wi h a o al o 901 pa icipan s. The indings
sugges ha demog aphic di e ences in sel -e icacy exis , bu hese di e ences a e
media ed by he app oaches o lea ning. The s udy highligh s he impo ance o
1
Co esponding Au ho
J. Naukka inen
johanna.nauk[email p o ec ed]
eaching p ac ices ha suppo deep and o ganised app oaches o lea ning o
enhance s uden s' sel -e icacy and achie emen in ma hema ics.
1 INTRODUCTION
The ways in which s uden s s udy and lea n ha e been o in e es o esea che s and
educa o s since he 1960's, and he opic has been iewed om many di e en
angles. Among he ea ly indings was he dis inc ion be ween o e and meaning ul
lea ning by Ausubel and deep and su ace app oaches o lea ning by Ma on and
Säljö. Since hen, a leas six di e en s udy s a egy in en o ies encompassing
sligh ly di e en dimensions ha e been de eloped. No common iew o he co ec
numbe o dimensions has eme ged. S ill, based on he concep ual analysis o he
ins umen s, i has been sugges ed ha a leas h ee dimensions a e needed o
co e he a iance ound in s udying. (En wis le & McCune, 2004.)
In con empo a y esea ch, deep and su ace app oaches o lea ning a e o en
accompanied by a hi d app oach called a s a egic app oach o o ganised e o o
s udying (e.g. He mann e al., 2017; Rämö e al., 2023). I e e s o how sys ema ic
he s uden s a e in hei s udies and how hey manage hei ime and e o . The
esea ch on he ela ionship be ween app oaches o lea ning and academic
achie emen is subs an ial, ye he esul s a e no unanimous. Howe e , much o he
esea ch has no ed a posi i e co ela ion be ween deep app oach and academic
achie emen , a posi i e co ela ion be ween o ganised app oach and academic
achie emen , and a nega i e co ela ion be ween su ace app oach and academic
achie emen (Richa dson e al., 2012).
Albe Bandu a’s sel -e icacy heo y sugges s ha “expec a ions o pe sonal mas e y
a ec bo h ini ia ion and pe sis ence o coping beha io ” (Bandu a, 1977, p. 193).
The s onge he indi idual’s pe cei ed sel -e icacy is, he mo e ac i e he e o s o
achie e a pa icula ou come become. Acco ding o he heo y, he majo sou ces o
e iciency expec a ions a e pe o mance accomplishmen s (pe sonal successes),
ica ious expe ience (obse ing o he s), e bal pe suasion ( eedback), and
emo ional a ousal (posi i e/nega i e expe iences). (Ibid.) Sel -e icacy is a commonly
used concep also in esea ch on ma hema ics educa ion, whe e a lo o a en ion
has been di ec ed o i s magni ude (S ee e al., 2024). I has been s udied as an
ou come, a p edic o , and a media ing a iable (ibid.), which illus a es well he
complica ed ela ionship be ween sel -e icacy and o he ac o s ela ed o lea ning
ma hema ics. S udies on sel -e icacy as a p edic o o ma hema ics achie emen
sugges ha sel -e icacy co ela es posi i ely wi h achie emen among 15-yea -old
s uden s (Hille e al., 2022) as well as uni e si y unde g adua e s uden s (Zaka iya,
2021).
E en hough bo h app oaches o lea ning and sel -e icacy in lea ning ma hema ics
ha e been s udied ex ensi ely, s udies o hei ecip ocal ela ionship a e a e.
Lahdenpe ä e al. (2019) compa ed s uden s’ app oaches o lea ning and sel -
e icacy in wo pedagogically di e en unde g adua e ma hema ics cou ses. They
disco e ed ha s uden s wi h a deep app oach o lea ning had signi ican ly highe
ma hema ics sel -e icacy han s uden s wi h a su ace app oach o lea ning in bo h
o he s udied con ex s. They did no , howe e , make any assump ions abou he
ela ional mechanisms o he wo concep s, as hei in e es lay in he e ec s o he
di e en pedagogical a angemen s. Kulcsá (2020) ocused on he ela ionship
be ween ma hema ics sel -e icacy, lea ning app oaches and ma hema ics
achie emen in bachelo -le el enginee ing s uden s and ound s a is ically signi ican
co ela ions bu also did no elabo a e on he na u e o he ela ionship be ween sel -
e icacy and lea ning app oaches.
In con as o he a o emen ioned esea ch, Zaka iya e al. (2022) explici ly aimed o
explain he causal ela ionship be ween sel -e icacy and app oaches o lea ning in
enginee ing ma hema ics cou ses. They a gued ha he causali y a ises om sel -
e icacy egula ing decisional p ocesses, and hus a ec ing lea ning app oaches.
They ound suppo o hei hypo hesis h ough s uc u al equa ion modelling. An
a gumen o he opposi e di ec ion o he causali y could be p esen ed based on he
media ion o academic achie emen , whe eby app oaches o lea ning a ec
ma hema ics lea ning, which s eng hens he ma hema ics sel -e icacy ia
accomplishmen s, eedback and emo ions. I is also plausible ha he ela ionship
be ween sel -e icacy and app oaches o lea ning is bidi ec ional wi h he po en ial o
a posi i e cycle in which a deep app oach o lea ning s eng hens sel -e icacy, which
in u n di ec s he lea ne owa ds u he sea ch o meaning, o o a nega i e cycle
in which a su ace app oach o lea ning weakens sel -e icacy, which hen di ec s
lea ning e en mo e owa ds o e lea ning and memo isa ion. How he o ganised
app oach o lea ning i s his pic u e and ela es o sel -e icacy emains o be
unde s ood.
Undoub edly, bo h sel -e icacy and app oaches o lea ning a e in luenced by many
addi ional ac o s. A me a-analysis o gende di e ences in academic sel -e icacy
sugges s ha males ha e highe ma hema ics sel -e icacy, wi h he gende
di e ence inc easing wi h age (Huang, 2013). A la ge s udy o middle school
s uden s ound ha Asian coun ies demons a e low and Wes e n coun ies ha e
high ma h sel -e icacy ega dless o hei le el o p o iciency (Lee, 2009). Simila
indings can also be ound among uni e si y s uden s (Han e al., 2015). Resea ch
on cul u al o gende di e ences in app oaches o lea ning ma hema ics is less
common. Rämö e al. (2023) disco e ed ha among i s -yea enginee ing
ma hema ics s uden s, gende was no associa ed wi h deep app oaches o lea ning.
Howe e , su ace and o ganised lea ning was highe o emale s uden s, al hough
he gende di e ence was only s a is ically signi ican a one o he i e poin s a
which i was measu ed. In con as , Tossa ainen e al. (2021) sugges ha No dic
male enginee ing s uden s ha e mo e ins umen al in e es s in ma hema ics
(in e es ed in esul s and use ulness) and emale s uden s ha e mo e in insic
ma hema ical in e es s (enjoy lea ning and ma hema ical hinking), he la e o which
is commonly associa ed wi h deep lea ning and he p io wi h o ganised o su ace
lea ning. Un o una ely, we could no loca e any p e ious esea ch on cul u al
di e ences in app oaches o lea ning ma hema ics.
This s udy aims o shed some ligh on ma hema ics sel -e icacy and how i s -yea
enginee ing s uden s app oach lea ning (deep, su ace and o ganised app oach) in a
Finnish esea ch-in ensi e uni e si y and examine he possible cul u al and gende
di e ences in he espec i e concep s.
Ou esea ch ques ions a e:
1. How do he ma hema ics sel -e icacy and he app oaches o lea ning di e
be ween
a. S uden s in in e na ional p og ams and Finnish p og ams?
b. Women and men s uden s?
2. How is he s uden s' ma hema ics sel -e icacy a ec ed by hei app oaches o
lea ning (deep, su ace, and o ganised app oach), whe he hey a e men o
women, and whe he hey a e in a Finnish o in e na ional p og am?
2 METHODOLOGY
The s udy was conduc ed in he con ex o a i s -yea enginee ing ma hema ics
cou se a wo esea ch-in ensi e uni e si ies in Finland in he au umn o 2023. The
o al numbe o pa icipan s was 901, including 616 males and 270 emales (wi h 15
unspeci ied). O hese, 793 s uden s we e en olled in Finnish enginee ing p og ams
a ei he o he wo pa icipa ing uni e si ies, while 108 we e in in e na ional
enginee ing p og ams whe e he language o ins uc ion was English. A LUT
Uni e si y, da a was collec ed om s uden s in he depa men s o Ene gy
Technology, Mechanical Enginee ing, Elec ical Enginee ing, and Sus ainabili y
Science wi hin he LUT School o Ene gy Sys ems. A Tampe e Uni e si y,
pa icipan s came om all Bachelo o Science p og ams in enginee ing. The da a on
in e na ional s udy p og ams used in his a icle was collec ed om ou Bachelo o
Science p og ams a LUT Uni e si y: Ene gy Enginee ing, Elec ical Enginee ing,
and Mechanical Enginee ing (implemen ed in coope a ion wi h Hebei Uni e si y o
Technology in China), and Technology and Enginee ing Science p og am
(implemen ed by LUT).
S uden s’ sel -assessmen s o hei sel -e icacy and app oaches o lea ning we e
conduc ed h ough online es s on he Moodle pla o m. S uden s ga e a w i en
consen o pa icipa e, and we e in o med abou hei igh o wi hd aw om he s udy
a any ime wi hou he need o gi e a eason. Resea ch pe mission was ob ained
om bo h uni e si ies in ol ed in he s udy. The s udy adhe ed o he e hical
p inciples o he Finnish Na ional Boa d on Resea ch In eg i y. As he pa icipan s
we e adul s who ga e in o med consen and we e no in any physical o men al
dange , no e hical e iew was equi ed (TENK 2019). Pa icipan s comple ed he
su ey a he beginning o hei i s enginee ing ma hema ics cou se in Augus and
Sep embe 2023.
The ques ionnai e consis ed o Like -scale s a emen s on app oaches o lea ning
and sel -e icacy (Pa pala & and Lindblom-Ylänne, 2012; Zimme man & Ki san as,
2007). Responses we e collec ed, anonymised, and combined o analysis. The
esponses we e con e ed in o nume ical alues anging om 1 o 5, wi h 1
co esponding o " o ally disag ee" and 5 o " o ally ag ee." Subsequen ly, a e age
sco es we e calcula ed o deep app oach, su ace app oach, o ganised app oach
(each based on ou s a emen s), and sel -e icacy (based on eigh s a emen s). The
s a is ical signi icance o di e ences be ween g oups was es ed wi h Welch wo-
sample - es and he e ec sizes we e es ed using Cohen’s d. The ela ionship
be ween sel -e icacy, gende , p og am, and he h ee app oaches o lea ning was
examined using mul iple linea eg ession analyses. All s a is ical analyses we e
pe o med using R S udio.
3 RESULTS
The means and s anda d de ia ions o he h ee di e en app oaches o lea ning
and sel -e icacy o all he s uden g oups s udied a e p esen ed in Table 1. They
show ha s uden s gene ally had ela i ely high deep app oaches and ela i ely low
su ace app oaches o lea ning, wi h o ganised app oach o lea ning and sel -
e icacy somewhe e in be ween hem.
Table 1. The app oaches o lea ning and sel -e icacy o di e en esponden s
N
Deep
M(SD)
Su ace
M(SD)
O ganised
M(SD)
Sel -e icacy
M(SD)
All
901
4.06 (.55)
2.65 (.71)
3.70 (.76)
3.68 (.53)
In e na ional p og ams
108
4.24 (.69)
2.69 (.93)
4.09 (.77)
3.84 (.55)
Finnish p og ams
793
4.04 (.53)
2.65 (.67)
3.65 (.74)
3.66 (.53)
Women
270
4.11 (.52)
2.75 (.71)
3.92 (.70)
3.77 (.53)
Men
616
4.04 (.57)
2.61 (.70)
3.62 (.75)
3.65 (.53)
We obse ed di e ences in he mean alues o sel -e icacy and app oaches o
lea ning be ween s uden s in he in e na ional p og am and in he Finnish p og am,
see Table 2. By he Welch wo-sample - es , he mean alue o sel -e icacy was
signi ican ly highe o he s uden s o he in e na ional p og am (M=3.84) compa ed
o he Finnish p og am (M=3.66), (134.65)=3.14, p=0.002, wi h a small- o-medium
e ec size by Cohen’s d (d=0.37). Also, he mean alues o deep app oach o
lea ning (in e na ional M=4.24, Finnish M=4.03, (124.33)=2.90, p=0.004) and
o ganised lea ning (in e na ional M=4.09, Finnish M=3.65, (134.9)=5.61, p<.001)
we e highe o he s uden s in he in e na ional p og am. The e ec size was
medium o o ganised lea ning (d=0.60) and small o sel -e icacy (d=0.33). No
di e ence was obse ed in he su ace app oach o lea ning alues be ween he
g oups (in e na ional M=2.69, Finnish M=2.65, (122.57)=0.50, p=0.617).
Table 2. Di e ences in app oaches o lea ning and sel -e icacy be ween s uden s in
in e na ional and Finnish deg ee p og ams
Va iable
Mean
(In e na ional)
Mean
(Finnish)
p- alue
Cohen's d
Deep App oach
4.24
4.04
2.91
0.004
0.37
Su ace App oach
2.69
2.65
0.50
0.617
0.07
O ganised Lea ning
4.09
3.65
5.61
<0.001
0.60
Sel -E icacy
3.84
3.66
3.14
0.002
0.33
Di e ences we e also obse ed be ween women and men, see Table 3. By he
Welch wo-sample - es , he mean alue o sel -e icacy was signi ican ly highe o
women (M=3.77) compa ed o men (M=3.65), wi h (514.97)=3.25, p=0.001, bu he
e ec size by Cohen’s d was small (d=0.32). Fo he app oaches o lea ning, he e
we e di e ences in he mean alues o su ace app oach (women M=2.75, men
M=2.61), wi h (507.23)=2.74, p=0.006, and o ganised lea ning (women M=3.92,
men M=3.62), wi h (544.77)=5.86, p<0.001. The size o he e ec on he su ace
app oach was small (d=0.20), o o ganised lea ning medium (d=0.60). No di e ence
in he mean alues o he deep app oach was obse ed be ween women and men.
Table 3. Di e ences in app oaches o lea ning and sel -e icacy be ween emale and male
s uden s
Va iable
Mean (women)
Mean (men)
p- alue
Cohen's d
Deep App oach
4.12
4.04
2.10
0.036
0.15
Su ace App oach
2.75
2.61
2.74
0.006
0.20
O ganised Lea ning
3.92
3.62
5.86
<0.001
0.60
Sel -E icacy
3.77
3.65
3.25
0.001
0.32
To examine he p edic o s o sel -e icacy we conduc ed mul iple linea eg ession
analyses. In he ini ial model (Model 1), he s udy g oup (in e na ional s. Finnish
p og ams) and gende we e included as p edic o s. In he ex ended model (Model 2),
we added he h ee app oaches o lea ning: deep app oach, su ace app oach, and
o ganised lea ning.
In Model 1, p edic ing sel -e icacy wi h he s uden g oup and gende , bo h g oup
and gende we e signi ican p edic o s o sel -e icacy (R^2 = 0.022, F(2,883)=10.09,
p<0.001). S uden s in he Finnish s udy p og ams sco ed lowe on sel -e icacy han
in e na ional p og ams (β=−0.167, =−3.093, p=0.002). Women sco ed highe on
sel -e icacy han men (β=0.125, =3.273, p=0.001).
In Model 2, whe e he app oaches o lea ning we e added as p edic o s, he e ec o
g oup and gende became nonsigni ican , sugges ing ha hei ini ial e ec s we e
media ed by he app oaches o lea ning (R^2 = 0.304, F(5,880)=76.97, p<0.001). In
his model:
• The deep app oach was posi i ely associa ed wi h sel -e icacy (β=0.258,
=9.294, p<0.001).
• The su ace app oach was nega i ely associa ed (β=−0.141, =−7.077,
p<0.001).
• O ganised lea ning was posi i ely associa ed (β=0.288, =13.640, p<0.001).
• Nei he g oup (β=−0.002, p=0.965) no gende (β=0.036, p=0.243) emained
signi ican .
The esul s indica e ha while he s udy g oup and gende ini ially appea o
in luence sel -e icacy, hei e ec s a e media ed h ough he app oaches o lea ning.
Speci ically, he highe sel -e icacy sco es associa ed wi h he in e na ional s uden
g oup and emale pa icipan s a e explained by hei s onge adop ion o a deep o
o ganised app oach o lea ning and lowe use o a su ace app oach. The
ela ionship be ween he measu ed sel -e icacy and he sel -e icacy p edic ed by
app oaches o lea ning is p esen ed in Figu e 1.
Figu e 1. Measu ed sel -e icacy e sus sel -e icacy p edic ed by app oaches o lea ning
4 DISCUSSION
Ou indings sugges ha , in ou con ex , he e a e demog aphic di e ences in he
ma hema ics sel -e icacy o unde g adua e enginee ing s uden s. Some o hese
di e ences, such as women’s highe sel -e icacy han men’s, seem su p ising in he
ligh o p e ious esea ch. Howe e , hey may no ha e much p ac ical signi icance
as sel -e icacy appea s o be ela ed o app oaches o lea ning in a way ha
elimina es he demog aphic e ec s. The s udy con i ms he posi i e associa ion o a
deep app oach o lea ning and he nega i e associa ion o a su ace app oach o
lea ning o sel -e icacy ha has been no ed in he li e a u e (Lahdenpe ä e al.,
2019; Kulcsá , 2020). I also d aws a en ion o he posi i e connec ion be ween sel -
e icacy and o ganised app oach o lea ning which was he connec ion wi h he
la ges e ec in ou s udy, bu has no ecei ed much a en ion in p e ious esea ch.
This s udy in es iga ed he ela ionship be ween sel -e icacy and app oaches o
lea ning unde he assump ion ha he la e in luences he o me , whe eas o he
schola s such as Zaka iya e al. (2022) ha e aken he opposi e app oach. We
main ain ha he e is a clea ela ionship be ween sel -e icacy and app oaches o
lea ning clea ly, bu ha mo e esea ch is needed o ully unde s and i s di ec ions
and mechanisms. We also sugges ha complemen ing he o en pola ised
concep ion o deep and su ace app oaches o lea ning wi h he o ganised app oach
o lea ning in hese s udies can g ea ly enhance ou unde s anding o he
phenomenon and also sugges no el p ac ical implica ions o imp o ing he
eaching o and achie emen in ma hema ics a uni e si y le el.
On he p ac ical side, his s udy sugges s ha eaching p ac ices ha suppo deep
and o ganised app oaches o lea ning ha e g ea po en ial o inc ease s uden s’ sel
e icacy and hus also ha e an impac on hei achie emen in ma hema ics. One
example o such a p ac ice is he Ex eme App en iceship me hod which was no iced
o elici highe le els o deep and o ganised app oaches o lea ning and lowe le els
o su ace app oach o lea ning han he mo e adi ional lec u e-based eaching
model (Lahdenpe ä e al., 2019). Ano he example is lipped lea ning, which
suppo ed a deep app oach o lea ning in he enginee ing ma hema ics cou se be e
han lec u e-based eaching (Rämö e al., 2023).
5 ACKNOWLEDGEMENTS
An a i icial in elligence applica ion, DeepL, was used o English language
e inemen o he inal e sion o he manusc ip .
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