Resea ch Pape
Recommended ci a ion: Immonen, P., Hi onen, J., Äijälä, M., Ra a a, J., Kuosa,
M., & Kaa akka, T. (2025). Oppo uni y Makes a Chea ? - The E ec o In igila ion
on he Resul s o a Ma hema ics Basic Skills Tes . 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.17631262.
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.
OPPORTUNITY MAKES A CHEAT? -
THE EFFECT OF INVIGILATION ON THE RESULTS OF A
MATHEMATICS BASIC SKILLS TEST
P. Immonen a,
1
, J. Hi onen b, M. Äijälä c,
J. Ra a a d, M. Kuosa e, T. Kaa akka
a LUT Uni e si y, Lappeen an a, Finland, 0000-0002-3286-6840
b Tampe e Uni e si y, Tampe e, Finland, 0000-0003-1667-2760
c LUT Uni e si y, Lappeen an a, Finland, 0000-0002-6626-4207
d LUT Uni e si y, Lappeen an a, Finland, 0000-0002-8816-6165
e LUT Uni e si y, Lappeen an a, Finland, 0000-0002-8055-1691
Tampe e Uni e si y, Tampe e, Finland, 0000-0002-3824-8939
Con e ence Key A eas: Teaching ma hema ics and physics in enginee ing
educa ion, Digi al ools and AI in enginee ing educa ion
Keywo ds: Ma hema ics basic skills, In igila ion, P oc o ing, Chea ing
ABSTRACT
The main objec i e o his a icle is o examine how non-in igila ed and in igila ed
es ing condi ions a ec he esul s o a basic ma hema ics skills es o i s -yea
enginee ing s uden s in he Finnish educa ion sys em. We also examine which subjec
a eas o in igila ed es ing pa icula ly a ec he esul s. The da a used in he s udy
consis s o es s o ganised a wo Finnish uni e si ies in 2023 and 2024.
The mean es esul is signi ican ly highe in he non-in igila ed es han in he
in igila ed es , bo h done elec onically. The di e ence in poin s be ween he es s
was s a is ically signi ican in all o he ques ions excep o he asks ela ed o
di e en ia ion, and he concep ual unde s anding o in e se and ecip ocal. The mos
signi ican dec ease in in igila ed es poin s was in he mos di icul bu easily
chea able asks ela ed o sol ing equa ions, especially igonome ic and exponen ial
equa ions, and in a ask ha equi ed calcula ing a de ini e in eg al.
1
P. Immonen
paula.immonen@lu . i
1 INTRODUCTION
1.1 Reliabili y o assessmen in online exams
Academic dishones y is likely a phenomenon olde han uni e si ies. One o i s
p e alen o ms is chea ing in academic s udies. The e o e, i should come as no
su p ise ha he ecen decades o ansi ioning s udies in o he elec onic o ma and
online en i onmen ha e b ough he age o "e-chea ing". The e a e many d i e s and
bene i s o o ganising educa ion online, bu can elec onic assessmen , speci ically he
non-in igila ed a ie y o online assessmen s, be seen as alid, o should we conside
i inhe en ly comp omised? Whe he o us such assessmen s seems o be he
ques ion o many highe educa ion eache s and s a in ecen yea s. This sho pape
will con ibu e o he a ailable da a and discussion by compa ing in igila ed and non-
in igila ed elec onic skill es s in enginee ing ma hema ics educa ion a wo Finnish
uni e si ies.
P e ious s udies (Chan & Ahn, 2023) ha e ound ha adi ional, in igila ed exams
p o ide he bes assessmen o s uden lea ning. S ill, he esul s can be in luenced by
es anxie y and s uden s' belie s abou hei abili ies. An ea lie li e a u e e iew on
ake-home exams by Beng sson (2019) addi ionally sugges s ha whe e ake-home
exams can excel in es ing highe -o de cogni i e skills, p epa ing o in-class exams
can lead o supe icial lea ning. In-class exams do no ma ch well wi h he pedagogical
heo y o cons uc i e alignmen (Beng sson 2019). Howe e , simila ly o Chan and
Ahn (2023), he mos o en ci ed d awback o ake-home exams was ha hey a e
easily comp omised by une hical s uden beha iou .
Acco ding o he s udy by Chan and Ahn (2023), conduc ed du ing COVID-19
es ic ions, non-in igila ed online exams can p o ide meaning ul in o ma ion abou
s uden lea ning and do no lead o signi ican chea ing based on he sco es being
consis en wi h hose o in igila ed exams. Ano he e iew on academic in eg i y in
online assessmen by Holden e al. (2021) pain s a mo e inconsis en pic u e. In 4 ou
o 8 s udies, highe ac ions o chea ing we e epo ed in online s udies; in wo s udies,
he chea ing was simila online and on-si e; and in wo s udies he (sel -) epo ed
chea ing was lowe in online ac i i ies. The e iew pu s he numbe o s uden s who
engage in online "e-chea ing" a 29 - 41% o he pa icipan s, whe eas o " adi ional"
classes, he epo ed igu es we e sligh ly lowe , a 21 - 32%.
The a ailabili y o ma h sol e applica ions exace ba es he endency o chea on
homewo k and es s aken a home. Sloan-Lynch e al. (2022) ha e no ed ha hese
ools acili a e chea ing in ma hema ics by allowing s uden s o bypass he need o
concep ual unde s anding. S uden s who do no unde s and he cou se con en migh
be mo e likely o chea in he cou se's online exams. Noo behbahani e al. (2022)
sugges ha one way o educing mo i a ion o chea is by aking he s uden s' lea ning
s yles be e in o accoun .
Many s uden s encoun e signi ican di icul ies wi h basic concep s, such as a ional
unc ions. In a sys ema ic e iew, Lima e al. (2019) iden i ied ac ions, unc ions, and
linea equa ions as he mos equen ly men ioned p oblema ic a eas in highe
educa ion ma hema ics s udies. They also no ed issues wi h a ional exp essions,
loga i hms, igonome y, geome y, p oposi ions, decimal numbe s, and ma hema ical
no a ions (Lima e al., 2019). Acco ding o Me sämuu onen and Tuohilampi (2017), a
he end o Finnish uppe seconda y school, he s uden s' p o iciency is s onges in
algeb a and unc ions, and weake in geome y and s a is ics. In addi ion, Laa ikainen
(2022) ound ha p o iciency in in eg al asks is gene ally weake han in o he asks
in he Finnish ma icula ion exam. Lukin (2023) no ed ha , o example, calcula ing
de ini e in eg als wi hou elec onic de ices is conside ed challenging o Finnish uppe
seconda y school s uden s. Ma hema ics Basic Skills Tes esul s om 2006-2017
we e analysed by Myllykoski e al. (2018). The weakes compe encies we e ound in
igonome y, di e en ia ion, and loga i hms es ques ions. Challenges in hese opics,
which a e c ucial in uni e si y-le el ma hema ics, may con ibu e o he p opensi y o
chea in ake-home es s.
The e a e many aspec s o conside when in e p e ing indi idual esul s o bo h non-
in igila ed and in igila ed es s, including ma h anxie y. Nume ous s udies ha e
indica ed ha ma h anxie y migh cause exam unde pe o mance (e.g., Ashc a &
Moo e, 2009). Acco ding o he old esea ch heo y o he aud iangle, h ee
componen s a e needed o aud o chea ing in an educa ional se ing. These
componen s include he oppo uni y, he incen i e, he p essu e o need o chea , and
he a ionalisa ion o a i ude ha jus i ies chea ing o onesel (e.g., Holden e al.,
2021). While he oppo uni y is ypically a ailable in online es s, he p essu e o
pe o m may con e sely be lowe han in on-si e exams (Holden e al., 2021). As online
exams a e o en pe cei ed as easy o chea in, a s uden can unde s andably
a ionalise ha chea ing is p e alen among pee s, ega dless o whe he i is ue.
1.2 Ma hema ics Basic Skills Tes
Tampe e Uni e si y o Technology began analysing he ma hema ical skills o
incoming enginee ing s uden s wi h he Ma hema ics Basic Skills Tes (BST) as ea ly
as 2002 (Jou senlah i e al., 2016). The o iginal BST has been mode nised and is s ill
used a Tampe e Uni e si y. Since 2023, he BST has also been used a LUT
Uni e si y. The es consis s o 16 basic ma hema ics asks and is implemen ed using
STACK (Sys em o Teaching and Assessmen using a Compu e Algeb a Ke nel)
(Sangwin, 2013), au oma ically e alua ing s uden s' esponses. Kangaslampi e al.
(2024) ha e used he BST o compa e esul s be ween men and women and be ween
Finnish and in e na ional s uden s.
The da a used in his a icle consis s o he esponses o he BST aken by Finnish
s uden s pa icipa ing in he i s i s -yea ma hema ics cou se a he beginning o he
academic yea in 2023 and 2024. The BST consis ed o 16 asks, each wo h one
poin . The numbe s used in he ques ions we e andomised. The ques ions o he BST
wi h example numbe s a e p esen ed in Table 1. The poin s ha s uden s ecei ed on
he BST did no a ec hei cou se g ade. Howe e , as an incen i e, s uden s who ook
he es we e awa ded a small numbe o poin s on he associa ed cou se, i espec i e
o hei esul s on his es .
S uden s had 50 minu es o comple e he es . They we e ins uc ed o ake he es
independen ly, wi hou calcula o s, ma hema ical so wa e, o o he ma e ials. In 2023,
LUT Uni e si y and Tampe e Uni e si y s uden s ook he BST in a non-in igila ed
en i onmen ; he e o e, hey canno be ensu ed ha hey ollowed he gi en
ins uc ions. In 2024, s uden s in LUT ook he elec onic es in an in igila ed
class oom, whe e an in igila o ensu ed ha he s uden s ollowed he ins uc ions. In
Tampe e, he es was also in igila ed; s uden s ook he es in a ideo-in igila ed
exam class.
Table 1. The ques ions o he BST.
1. Compu e he alue o he s a emen 𝑥4+ 𝑥3 when 𝑥 = 4.
2. Wha is he in e se ecip ocal o −5.
3. Simpli y he ollowing s a emen |6 − √5| + |1 − √5|.
4. Compu e he alue o unc ion 𝑓(𝑥)=√7 + 5
𝑥− 4 when he a iable 𝑥 ge s assigned a
alue 𝑥 = 25.
5. Simpli y he s a emen 𝑎2−4
𝑎−2 (Assuming he denomina o is no ze o.).
6. Le 𝑓(𝑥) = 3𝑥 + 1. Calcula e he alue o he composi e unc ion (𝑓 ∘ 𝑓)(𝑥) a poin 𝑥 =
2.
7. Sol e he i s -deg ee equa ion 5𝑥 − 8 = 0.
8. Sol e he hi d-deg ee equa ion 4𝑥3−80𝑥 = 0.
9. Sol e he ac ional equa ion 𝑥2
𝑥−6 + 3 = 0.
10. Sol e he i s -deg ee inequali y 2𝑥 + 6 < 0 Inpu you solu ion as "𝑥 < 𝑎" o "𝑥 > 𝑎",
whe e 𝑎 is he accu a e alue o he oo .
11. Compu e he alues o he ollowing s a emen s, when 𝑎 = 5 and 𝑏 = 5, (−𝑎)𝑏, −𝑎𝑏,
𝑎−𝑏, −𝑎−𝑏.
12. Find a solu ion o he equa ion sin𝑥 = √3
2 loca ed in he i s quad an 0 ≤ 𝑥 ≤ π
2.
13. Find he smalles solu ion o cos(5𝑥) = 0 wi hin he i s o second quad an s 0 ≤ 𝑥 ≤
π.
14. Di e en ia e 𝑓(𝑥) = 7𝑥4+ 5
15. Calcula e he de ini e in eg al ∫(4𝑥4− 3𝑥2+ 1) d𝑥
3
−1 .
16. Sol e he exponen ial equa ion
3𝑥=10.
1.3 Resea ch ques ions
This a icle in es iga es how non-in igila ed and in igila ed es ing si ua ions a ec he
esul s o he basic skills es o i s -yea enginee ing s uden s in he Finnish
educa ion sys em. I also analyses which subjec a eas in igila ed es ing pa icula ly
impac s uden s' esul s.
The objec i es o he s udy a e summa ised in he ollowing esea ch ques ions:
1. How do non-in igila ed and in igila ed es ing si ua ions a ec s uden s' sco es
on he basic skills es ?
2. In which subjec a eas does non-in igila ed es ing pa icula ly a ec s uden s'
compe ence?
2 METHODOLOGY
The s udy in ol ed i s -yea enginee ing s uden s om wo Finnish uni e si ies,
Tampe e Uni e si y and LUT Uni e si y. In 2023, 121 s uden s om LUT Uni e si y
pa icipa ed in he s udy, and in 2024, 96 s uden s pa icipa ed. The es included
s uden s om Finnish-language enginee ing p og ams. Consen o pa icipa e in he
s udy was ob ained om he pa icipan s. A LUT Uni e si y, he da a was collec ed
om s uden s o he LUT School o Ene gy Sys ems (LES) depa men s o Ene gy
Technology, Mechanical Enginee ing, Elec ical Enginee ing and Sus ainabili y
Science. In 2023, 674 s uden s om Tampe e Uni e si y pa icipa ed in he s udy, and
in 2024, 633 s uden s pa icipa ed. A Tampe e Uni e si y, he da a was collec ed om
i s yea s uden s o all Bachelo o Science p og ammes in enginee ing.
The pa icipan s comple ed he elec onic BST a he beginning o hei i s
ma hema ics cou se. S uden s' answe s we e collec ed, and he di e ences be ween
he means and s anda d de ia ions o he inal sco e and he means o ques ion-
speci ic sco es we e compa ed. All s a is ical analyses we e pe o med using Ma lab.
3 RESULTS
In he BST, a co ec answe in each o he 16 ques ions ga e he s uden one poin ,
excep ques ion 11, which ga e 0.25 poin s o each o i s ou sepa a e pa s. Due o
echnical di icul ies wi h ques ion 10 in 2023, i was le ou o he analysis, making he
maximum sco e 15. In he non-in igila ed es aken in 2023 by s uden s o bo h
uni e si ies (n=795), he mean sco e was 11.05 poin s wi h a s anda d de ia ion (SD)
o 2.70 poin s. When BST was an in igila ed es in 2024 (n=729), he mean sco e was
8.51 poin s wi h an SD o 2.60 poin s. The di e ence o means is s a is ically highly
signi ican , as indica ed by a wo-sample - es , (1522)=18.69, p< .001. The
pa icipa ing uni e si ies' indi idual means a e ound in Table 2.
Table 2. Basic Skills Tes mean poin s and s anda d de ia ions by uni e si y.
Non-in igila ed (2023)
In igila ed (2024)
Uni e si y
N
Mean
SD
N
Mean
SD
LUT (LES)
121
10.81
2.91
96
7.84
2.82
Tampe e
674
11.10
2.66
633
8.61
2.55
Bo h
795
11.05
2.70
729
8.51
2.60
The his og ams o he es esul s a e p esen ed in Figu e 1. They show an e iden
change in he dis ibu ion o poin s. Rega ding op sco es, 7.92 % o s uden s sco ed
mo e han 14 poin s in he non-in igila ed es , whe eas only 0.69 % eached his le el
in he in igila ed es . On he o he hand, he pe cen age o s uden s sco ing 8 poin s
o less was 14.84 % in he non-in igila ed es and 46.64 % in he in igila ed es .
Fig. 1. Basic Skills Tes sco e dis ibu ions.
The majo di e ence in he ac ion o s uden s sco ing less han 8, along wi h he
absence o o he explana ions – such as di e ences in s uden skill dis ibu ions
ac oss di e en yea s – p o ides a ough es ima e o he pe cen age o s uden s e-
chea ing: 31.80%.
This igu e should be conside ed a high o maximum es ima e as al e na i e
explana ions a e no explo ed. The pe cen age, howe e , ag ees wi h Holden e al.
(2023) igu es o 29 - 41% chea ing o online exams.
The mean sco es o indi idual es ques ions (Figu e 2) show a poin d op o each
ques ion when compa ing he esul s o he non-in igila ed BST o he in igila ed BST.
Pe o ming a wo-sample Welch's - es o each ques ion indi idually indica es ha
he sco e di e ence be ween he non-in igila ed and in igila ed es s is s a is ically
signi ican o all ques ions excep Ques ions 2 and 14. Table 3 lis s he means, hei
di e ences and p- alues o Welch's - es o each ques ion.
Fig. 2. (a) Mean poin s pe ques ion in he Basic Skills Tes . (b) Same da a, o de ed by
mean sco e in he non-in igila ed es .
Table 3. Basic skills es mean poin s by ques ion, s anda ds de ia ions, di e ences o
means, and Welch's - es s a is ic alues and p- alues.
Ques ion
2023
2024
Di e ence o
means
Welch's - es
Mean
SD
Mean
SD
p
1
0.95
0.23
0.90
0.30
0.05
3.53
< 0.001
2
0.92
0.28
0.91
0.29
0.01
0.70
0.481
3
0.75
0.44
0.53
0.50
0.22
9.04
< 0.001
4
0.84
0.37
0.78
0.41
0.06
2.90
0.004
5
0.82
0.38
0.71
0.45
0.11
5.13
< 0.001
6
0.65
0.48
0.42
0.49
0.23
9.24
< 0.001
7
0.96
0.18
0.93
0.26
0.03
3.02
0.003
8
0.81
0.39
0.67
0.47
0.14
6.36
< 0.001
9
0.74
0.43
0.50
0.50
0.25
10.22
< 0.001
10
-
-
-
-
-
-
-
11
0.76
0.34
0.63
0.37
0.13
7.37
< 0.001
12
0.62
0.49
0.23
0.41
0.39
16.88
< 0.001
13
0.41
0.49
0.14
0.35
0.26
12.08
< 0.001
14
0.88
0.32
0.87
0.33
0.01
0.55
0.580
15
0.42
0.49
0.09
0.29
0.32
15.76
< 0.001
16
0.53
0.50
0.21
0.41
0.32
13.81
< 0.001
Ques ions 1, 2, 7, and 14 had he highes mean sco es in bo h yea s. The di e ence
in poin s be ween he wo yea s was he smalles o hese ques ions, a mos 0.05
poin s in each case. Ques ion 1 in ol ed inding he alue o a unc ion gi en a speci ic
a iable alue, Ques ion 2 es ed concep ual unde s anding o he e ms in e se and
ecip ocal, Ques ion 7 equi ed sol ing a i s -deg ee equa ion, and Ques ion 14 was
a di e en ia ion p oblem.
Ques ions 12, 13, 15, and 16 we e he lowes -sco ing ques ions in bo h yea s. They
also had he g ea es poin s di e ence be ween he wo yea s, d opping mo e han
0.25 poin s each. Ques ions 12, 13, and 16 in ol ed sol ing equa ions – speci ically,
he i s wo we e igonome ic equa ions, while he hi d was an exponen ial equa ion.
In Ques ion 15, s uden s had o calcula e a de ini e in eg al.
4 DISCUSSION AND CONCLUSIONS
In ou e alua ion, all ques ions in he BST a e a Bloom's axonomy le els 1-2 and
a e no aimed a es ing highe -o de cogni i e skills. In bo h he non-in igila ed es
and in he in igila ed es , he esul s o BST ques ions 1, 2, 7, and 14 did no di e
e y much. These ques ions in ol ed unc ions, unde s anding he concep s o an
in e se and a ecip ocal, linea equa ions, and di e en ia ion. This aligns wi h he
indings o Me sämuu onen and Tuohilampi (2017).
Ques ions 12, 13, 15, and 16 p o ed o be he mos di icul ones in bo h es
se ings. Addi ionally, he di e ences o he esul s in he in igila ed and non-
in igila ed es s we e he la ges o hese ques ions. The bigges d ops in BST
esul s mi o some o he indings o Lima e al. (2019) and Myllykoski e al. (2018),
in which common di icul ma hema ical a eas such as igonome y and loga i hms
(o exponen ial unc ions) we e iden i ied. The ques ion in ol ing a de ini e in eg al
also p o ed o be di icul . E alua ion a de ini e in eg al in ol es i s inding he
inde ini e in eg al and sub ac ing he in eg al's alue a he lowe limi om i s alue
a he uppe limi . Sub ac ion by hand may be di icul o a s uden ha is used o
using a symbolic calcula o . Acco ding o Laa ikainen (2022), Lukin (2023), and
Pe älä (2023), he s uden s’ compe ence in in eg als has been lowe han in o he
ields o ma hema ics in he ma hema ics es o he Finnish ma icula ion exam. This
is also in line wi h ou obse a ions.
The di icul ques ions o he BST a e easily sol ed wi h symbolic calcula o s, AI
ools, o o he ma h sol e applica ions. While al e na i e explana ions o he
di e ence could no be accoun ed o , e-chea ing is a possible explana ion o
di e ences o he magni ude ha was obse ed in he esul s. Based on ou
obse a ions, we sugges ha s uden s a e mo e likely o chea , when chea ing is
easy and he ask a hand equi es a li le mo e complexi y o a longe sol ing
echnique han o he s. This co esponds o wha is sugges ed by Sloan-Lynch e al.
(2022). Beng sson (2019) ecommends agains using ake-home exams o es ing
he lowes axonomic le el skills due o he ample oppo uni y, eadily a ailable ools,
and he ease o e-chea ing in he es s. Based on ou esul s, we echo his
ecommenda ion.
Rega ding he aud iangle heo y (e.g., Holden, 2021), we conclude ha he
absence o p essu e o incen i e o chea (i.e., no cou se poin s awa ded based on
es pe o mance) did no elimina e he chea ing phenomenon in case o he BST.
This obse a ion may call in o ques ion he alidi y o he heo y in ou con ex –
namely, ha p essu e, incen i e, o need a e p e- equisi e ac o s o chea ing. On
he o he hand, i is also possible ha s uden s expe ienced a di e en ype o
p essu e, such as a social need o a oid e ealing hei lack o basic skills o he
eache , o ea o losing ace. Al e na i ely, s uden s may ha e been unce ain
abou whe he poo es pe o mance could ha e undisclosed epe cussions.
Pe haps he mos signi ican piece o ad ice we can o e based on hese esul s is
ha i you genuinely wan o assess he s uden s' le el o comp ehension a he
beginning o hei uni e si y s udies using cogni i ely less challenging asks, he es
should be in igila ed ega dless o whe he i a ec s he cou se g ade.
In u u e esea ch, mo e e o should be de o ed o p oducing mo e obus da a on
how many and wha kind o s uden s eso o e-chea ing, unde wha ci cums ances
hey do i , and wha exac ly d i es hem. This da a would help imp o e ou
e alua ion me hods and mo e conclusi ely e alua e he alidi y o non-in igila ed
online exams.
5 ACKNOWLEDGEMENTS
An a i icial in elligence applica ion, SCOPUS AI, was used o ind he e e ence
li e a u e. The AI applica ion was used also o English language e inemen o he
inal e sion o he manusc ip .
REFERENCES
Ashc a , M. H., & Moo e, A. M. (2009). Ma hema ics anxie y and he a ec i e d op
in pe o mance. Jou nal o Psychoeduca ional Assessmen , 27(3), 197-205.
h ps://doi.o g/10.1177/0734282908330580
Beng sson, L. (2019). Take-Home Exams in Highe Educa ion: A Sys ema ic
Re iew. Educa ion Sciences, 9(4), 267. h ps://doi.o g/10.3390/educsci9040267
Chan J.C.K., & Ahn D. (2023). Unp oc o ed online exams p o ide meaning ul
assessmen o s uden lea ning. In P oceedings o he Na ional Academy o
Sciences. h ps://doi.o g/10.1073/pnas.2302020120
Holden, O. L., No is, M. E., & Kuhlmeie , V. A. (2021). Academic in eg i y in online
assessmen : A esea ch e iew. F on ie s in Educa ion, 6, 639-814.
h ps://doi.o g/10.3389/ educ.2021.639814
Jou senlah i, J., Ali-Löy y, S., & Pohjolainen, S. (2016). De eloping Lea ning and
Teaching in Enginee ing Ma hema ics wi h and wi hou Technology. In SEFI 2016
Annual Con e ence P oceedings Eu opean Socie y o Enginee ing Educa ion SEFI.
Kangaslampi, R., Hi onen, J., Kaa akka, T., Immonen, P., Äijälä, M., Bhayo, B.,
Naukka inen, J., & Kuosa, M. (2024). Fi s -Yea Enginee ing S uden s’ Ma hema ical
Skills And Pe cep ions O S udying Ma hema ics. In P oceedings o he 52nd Annual
Con e ence o he Eu opean Socie y o Enginee ing Educa ion (pp. 578-587).
h ps://doi.o g/10.5281/zenodo.14254744
Laa ikainen, V. (2022). In eg aalilasken a ja sen osaaminen pi kän ma ema iikan
ylioppilaski joi uksissa. Mas e ’s hesis. Uni e si y o Helsinki.
h p://hdl.handle.ne /10138/351956
Lima, P. D. S. M., Sil a, L. D. A., Felix, I. M. & B andao, L. D. O. (2019) Di icul ies in
Basic Concep s o Ma hema ics in Highe Educa ion: A Sys ema ic Re iew. In 49 h
