Resea ch Pape
Recommended ci a ion: Kun, L. Á., Be ez ai, S., Lógó, E., & Szilágyi, B. (2025).
No el Adap i e En y-Le el Ma hs Assessmen Tes o So ing S uden s o
Di e en Le el Cou ses. 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.17631398.
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.
NOVEL ADAPTIVE ENTRY-LEVEL MATHS ASSESSMENT TEST FOR
SORTING STUDENTS TO DIFFERENT LEVEL COURSES
László Ákos Kuna, Szabolcs Be ez ai b,
1
, Emma Lógó c, B igi a Szilágyi d
a Budapes Uni e si y o Technology and Economics, Budapes , Hunga y
b Budapes Uni e si y o Technology and Economics, Budapes , Hunga y
0000-0002-6399-583X
c Budapes Uni e si y o Technology and Economics, Budapes , Hunga y
d Budapes Uni e si y o Technology and Economics, Budapes , Hunga y; Co inus
Uni e si y o Budapes , Hunga y; MTA–ELTE Theo y o Lea ning Ma hema ics
Resea ch G oup, 0000-0002-2566-0465
Con e ence Key A eas: Teaching ma hema ics and physics in enginee ing
educa ion,
Keywo ds: Ma hema ics in enginee ing, Assessmen es , Compe ence in
ma hema ics, Adap i e Tes ing, D opou
ABSTRACT
In enginee ing p og ams signi ican di e ences can be obse ed in he ma hema ical
p o iciency o s uden s a he beginning o hei uni e si y s udies due o he
conside able dispa i y be ween he con en o he in e media e and ad anced le el
ma h classes in he Hunga ian high school sys em. To place incoming s uden s in
cou ses ha ma ch hei knowledge in la ge-scale cou ses whe e he numbe o
s uden s exceeds 100, an e ec i e assessmen es is needed ha no only e alua es
he p ocedu al knowledge bu also he compe ences in ma hema ics. In he all o
2024, a comp ehensi e en y-le el assessmen was conduc ed among incoming
eshmen, in ol ing a o al o 2,196 s uden s a ending o six di e en acul ies.
This con ibu ion aims o p esen a no el adap i e en y-le el ma h assessmen es
o eshmen, which was pe o med be o e he s a o he i s -yea Calculus cou ses.
The es consis ed o h ee pa s, whe e he esul s o each pa we e used o selec
he se o ques ions o be asked in he nex sec ion. By analyzing he esul s o he
h ee-pa adap i e es , we aim o explo e how incoming s uden s can be g ouped
based on hei knowledge le els. This ca ego iza ion enables us o ecommend ei he
he A o B le el ma hema ics cou ses, bes sui ed o hei p o iciency.
1 INTRODUCTION
Yea s o expe ience ha e shown ha incoming eshmen a i e a uni e si ies wi h
e y di e en le els o ma hs knowledge. One eason o his is ha he Hunga ian
admission equi emen s allow en y h ough a ious ypes o p io s udies, so e en in
high school, s uden s’ educa ional pa hs could di e signi ican ly, wi h each s uden
1
Co esponding Au ho
Szabolcs Be ez ai
[email p o ec ed]
ha ing aken ad anced cou ses in di e en subjec s. As a esul , he ma h’s
knowledge le el spans a e y wide spec um, wi h an eno mous gap be ween he
weakes and he s onges . This equi es di e en cou se ma e ials and eaching
me hods in enginee ing highe educa ion. Since hese di e ences a e o en no
e lec ed in he admission sco es, i becomes necessa y o assess he incoming
s uden s’ knowledge le els o implemen di e en ia ed educa ion.
Ano he eason o he weake en ance pe o mance among i s -yea s uden s can
be a ibu ed o he long- e m e ec s o he pandemic. The COVID-19 pandemic posed
an unp eceden ed challenge e en o uni e si y ins uc o s in mode n educa ion.
Resea ch om p e ious yea s showed ha he di icul ies did no disappea wi h he
e u n o in-pe son eaching (Sipos e al., 2019, Be ez ai e al., 2024). I was expec ed
ha e en in 2024, he aces o he pandemic would s ill be e iden in he pe o mance
o incoming uni e si y s uden s.
To add ess his issue, he BME Depa men o Ma hema ics decided o implemen
di e en ia ed ma h educa ion. In Sep embe 2024, eaching Calculus began on wo
le els. The “A” le el is ecommended o s uden s who al eady possess he
ma hema ical knowledge equi ed o enginee ing s udies, while he “B” le el is o
hose who ha e signi ican de iciencies. The la e g oup may lack he necessa y
knowledge ei he because hey did no a end he ad anced cou ses o because hey
did no ully acqui e he necessa y concep s he e. A he “B” le el, in addi ion o he
i s -semes e calculus ma e ial, e o s a e made o ill in he gaps in knowledge.
The goal is no o seg ega e s uden s bu o p o ide a suppo i e lea ning en i onmen
ha os e s he de elopmen o s uden s wi h a ying capabili ies. Di e en ia ed
g ouping can help ensu e ha e e y s uden begins hei uni e si y s udies a he le el
mos app op ia e o hem and can g adually ca ch up o he highe -le el equi emen s.
The e ec i eness o di e en ia ed ins uc ion is suppo ed by nume ous s udies. The
comp ehensi e analysis by Smale-Jacobse e al. (Smale-Jacobse, 2019)
demons a ed ha di e en ia ed educa ion in high school has a posi i e impac on
s uden s’ academic pe o mance, especially when eaching me hods a e adap ed o
indi idual lea ning needs. Thei esea ch sugges s ha di e en ia ed ins uc ion no
only esul s in mo e s able and deepe knowledge bu also p oduces be e long- e m
academic ou comes. Fu he mo e, he s udy o Young indica es ha a di e en ia ed
app oach can acili a e a seamless ansi ion be ween high school and highe
educa ion by allowing o he in eg a ed de elopmen o s uden s wi h di e se le els
o p epa edness (Young, 2006).
1.1 Mo i a ion and goals
The pu pose o he en ance assessmen was o e eal he le el o high school
ma hema ical knowledge among s uden s en e ing he uni e si y, since he signi ican
di e ences in he le els o knowledge acqui ed in high school educa ion, which pose
di ec challenges o uni e si ies. In esponse, he uni e si y is adap ing by o ming
di e en ia ed educa ional g oups based on s uden s’ knowledge le els, p o iding
oppo uni ies o s uden s wi h a ying backg ounds o de elop hei ma hema ical
skills a hei own pace and le el. The da a collec ed du ing he assessmen enables
a sys ema ic analysis o he knowledge s uden s acqui ed du ing hei high school
s udies.
To place incoming s uden s in cou ses ha ma ch hei knowledge in la ge-scale
cou ses an e ec i e assessmen es is needed ha no only e alua es he p ocedu al
knowledge bu also he compe ences in ma hema ics. As a solu ion a no el online
adap i e en y-le el ma h assessmen es was in oduced. The es consis ed o h ee
pa s, whe e he esul s o each pa we e used o selec he se o ques ions o be
asked in he nex sec ion. By analyzing he esul s o he h ee-pa adap i e es , we
aim o explo e how incoming s uden s can be g ouped based on hei knowledge
le els. This ca ego iza ion enables us o ecommend ei he he A o B le el
ma hema ics cou ses, bes sui ed o hei p o iciency.
2 METHODOLOGY
2.1 Tes sys em: EduBase
The en ance es ing was ca ied ou using EduBase (www.edubase.ne ), an online
pla o m ha o e s cus omizable es ing and lea ning solu ions (Szilagyi e al., 2020).
One o i s ou s anding ea u es is he eal- ime da a collec ion and eedback sys em,
which allows ins uc o s immedia e access o in o ma ion ela ed o s uden s’
pe o mance. EduBase also u ilizes ad anced an i-chea ing echnologies o ensu e
he eliabili y and c edibili y o he es s. Addi ionally, he pla o m p o ides
pa ame e izable ques ions, making i easy o cus omize and adap exam ques ions.
EduBase s ands ou o i s ull scalabili y, allowing i o be easily used by g oups
anging om small classes o la ge co po a ions. The sys em in eg a es seamlessly
wi h a ious educa ional sys ems, connec ing wi h exis ing pla o ms such as LMSs o
o he co po a e sys ems. This ease o in eg a ion and lexible managemen enables
EduBase o pe o m e ec i ely in di e en educa ional se ings, om school educa ion
o co po a e aining (Be ez ai e al., 2019).
2.2 Adap i e assessmen es
The adap i e es is an assessmen me hod designed o e alua e s uden s’ knowledge
and abili ies, pa icula ly in ma hema ical compe encies. The essence o he es is
ha he di icul y le el o he ques ions dynamically adjus s based on he esponses,
so ha h oughou he examina ion, he ques ions ha bes ma ch he s uden ’s ac ual
knowledge and skills a e p esen ed. The main ea u es o he assessmen es s a e
• Adap i e Ques ions: Du ing he es , he di icul y o he ques ion se a ies
acco ding o he s uden ’s esponses.
• Mo e Accu a e Assessmen : s uden s a e measu ed based on ques ions ha
bes sui hei capabili ies ensu ing mo e accu a e e alua ion.
• Mo i a ing E ec : Adap i e es ing is gene ally mo e mo i a ing o s uden s,
as i a oids es s ha a e oo ha d o oo easy.
• Time E iciency: Due o i s adap i i y, he es can usually be comple ed in a
sho e ime compa ed o adi ional, s a ic es s.
Du ing he es , s uden s we e allowed o use only pape and pencil wi hou calcula o ,
which simpli ied he adminis a ion and e iew p ocess.
2.3 Adap i e assessmen es s uc u e
In he i s phase (Basic Ques ions), he s uden s’ gene al ma hema ical knowledge
and p ocedu al calcula ion skills was measu ed wi h ques ions based on basic
ope a ions, iden i ies, linea equa ions, inequali ies, basic igonome ic unc ions and
elemen a y analy ic geome y. Mos o he asks we e sol able wi h 10 h g ade
knowledge. In his pa , a o al o 20 ques ions had o be answe ed wi hin 10 minu es.
Subsequen ly, he s uden s we e di ided in o wo g oups based on whe he hey had
a ended op ional ma hema ics classes (i.e. Facul a ion) du ing hei high school
s udies o no (Facul a ion (F) o Non-Facul a ion (NF)). In his phase, he s uden s
had o sol e 15 o 16 ques ions, and hey we e gi en 50 minu es. The ques ions ully
co e ed he high school ma hema ics cu iculum, and some ques ions we e iden ical
o bo h g oups o ob ain a mo e accu a e pic u e o he s uden s’ knowledge le el, as
well as o de e mine he bo de line be ween he wo g oups. A e he es s we e
comple ed, he EduBase sys em p o ided immedia e eedback, which allowed us o
immedia ely assign he s uden s o he nex le el.
In he hi d phase, he s uden s we e di ided in o ou g oups, which we e named as
ollows: Facul a ion+ (F+), Facul a ion- (F-), Non Facul a ion+ (NF+), and Non
Facul a ion- (NF-). The classi ica ion was based on whe he he es ake achie ed
below o abo e 50% in he second block. I he pe o mance was abo e 50% and he
s uden had a ended ad anced classes, hey con inued he es a he F+ le el; i
below, hen a he F- le el. Fo s uden s who did no a end ad anced classes, he
NF+ and NF- le els we e simila ly es ablished. In his phase, he numbe o asks
a ied, al hough an iden ical 40-minu e ime ame was p o ided o e e y g oup.
This mul i-le el assessmen enabled a mo e p ecise measu emen o he s uden s’
high school knowledge and he o ma ion o di e en ia ed g oups ha accu a ely
e lec he s uden s’ p io ma hema ical knowledge and he di e ences a ising om
hei high school s udies. In his phase, simila ly o he p e ious le el, s uden s
ecei ed some ques ions om he es se o he adjacen highe o lowe -le el g oup.
This me hod allowed o a mo e p ecise delinea ion o he blu ed bounda ies be ween
he g oups, p o iding a mo e de ailed pic u e o he ine di e ences in s uden s’
knowledge le els.
Fig. 1. The es ing p ocess wi h he numbe o ques ions and he alloca ed ime
A sample es o all es le els is p esen ed in he Appendix ha can be downloaded
om he ollowing link: h ps://bi .ly/448wY8x
3 RESULTS
In he all o 2024, a comp ehensi e en y-le el assessmen was conduc ed among
incoming eshmen. Six acul ies wi h 12 enginee ing p og ams (ci il, anspo a ion,
ehicle, chemical, bio echnology, en i onmen al, elec ical, mechanical, ene gy,
mecha onics, indus ial design and compu e enginee ing), 2 na u al sciences
p og ams (ma hema ics, physics), in ol ing a o al o 2,196 s uden s.
Ou goal was no only o assess s uden s’ knowledge bu also o c ea e clus e s so
ha s uden s could be placed in a g oup co esponding o hei p o iciency le el om
he i s week o he academic yea . To achie e his, we had o es ablish a anking
me hod ha would no collec i ely dis o any g oup bu would clea ly de e mine he
app op ia e placemen o s uden s nea classi ica ion bounda ies. Fo example, i a
s uden who did no a end ad anced ma hema ics classes pe o med well a he
second and hi d le els, hen despi e no ha ing aken an ad anced ma hema ics
cou se, i hey answe ed co ec ly he common ques ions om he highe -le el se , we
needed o ewa d his o some ex en . To de elop his model, we i s needed o
examine he aw esul s.
3.1 P ocedu al Skill Assessmen esul s – Basic Ques ions
This was he i s pa o he en ance assessmen , comple ed by 1372 s uden s. The
a e age sco e was 58.72%, wi h a s anda d de ia ion o 19.4%. Fig. 2/a illus a es he
dis ibu ion o esul s, which shows ha he esul s ollow a no mal dis ibu ion. This
sec ion was success ully comple ed by s uden s wi h s ong compu a ional skills.
Gi en ha he ime limi was 10 minu es, app oxima ely 30 seconds we e a ailable
pe ques ion. Inco ec answe s o en esul ed om common concep ual e o s, which
allowed us o analyze ypical mis akes a e e alua ing he es .
Fig. 2. Resul s Block 1: a) his og am o esul s and b) change o esul s by asks
E.g. he six h ques ion o he es was as ollows: Wha is he alue o 𝑙𝑜𝑔3(27)?
S uden s a e expec ed o be amilia wi h loga i hms a an in e media e le el. In his
case, he a gumen o he base-3 loga i hm was a commonly used powe o h ee.
The e o e, hose who unde s ood he concep could ecognize he esul immedia ely.
Fig. 2/b p esen s he pe cen age dis ibu ion o esponses o he i s 20 ques ions,
ca ego ized in o co ec answe s, inco ec answe s, unanswe ed ques ions, and
unopened ques ions. The esul s indica e a g adual decline in he p opo ion o co ec
answe s om he i s ques ion onwa d. This is na u al, as he di icul y o he ques ions
inc eased o e ime. While he i s ques ion had a co ec esponse a e o 94.04%,
by he end o he es , his a e had d opped o only 11.41%. This s eady decline
sugges s ha s uden pe o mance de e io a ed as he es p og essed. The a e o
unanswe ed ques ions also ollowed an inc easing end. As he es p og essed, mo e
s uden s le ques ions unanswe ed, especially owa d he end. This sugges s ha ime
cons ain s may ha e played a ole in s uden s’ abili y o comple e he es . The
p opo ion o unopened ques ions showed a consis en inc ease. This end implies
ha , s uden s inc easingly skipped ques ions wi hou e en opening hem. This esul
aligns wi h he declining p opo ion o co ec answe s and he ising numbe o
unanswe ed ques ions, sugges ing ha s uden s’ ocus, o mo i a ion diminished o e
ime, and ime managemen may ha e been a signi ican challenge.
O e all, he ends obse ed in he Fig. 2/b sugges ha s uden pe o mance declined
as he es p og essed, suppo ed by he dec ease in co ec esponses and he
inc ease in unanswe ed and unopened ques ions
3.2 Second block (NF and F)
The second block con ains exe cises ha s uden s may ha e encoun e ed du ing
hei seconda y school s udies. The e we e no unusual asks in his pa , hey had o
apply wha hey had lea ned.
Fig. 3. Resul s Block 2: a) NF and b) F g oups
The numbe o es ed s uden s in he NF g oup was 402. The a e age esul o his
g oup was 35.93 ± 16.84%. In con as , 969 s uden s we e es ed in he F g oup, whe e
he ollowing esul was ob ained: 51.4 ± 13.34%. I is also e iden ha nea ly one-
hi d (29.3%) o i s -yea s uden s did no a end elec i e cou ses, meaning ha a
signi ican numbe o s uden s lack essen ial knowledge (e.g., igonome ic unc ions),
which is c ucial o success ul pe o mance in highe echnical educa ion.
Looking a he his og ams (see Fig. 3.), i is also appa en ha s uden s who did no
a end Facul a ion pe o med poo ly, wi h sligh ly mo e han a hi d achie ing esul s
be ween 30-40%. The numbe o s uden s sco ing abo e 70% was minimal. Nea ly
h ee-qua e s o hem did no each 50%, meaning hey con inued he es on he NF-
b anch.
3.3 Thi d block (NF-, NF+, F-, F+)
The esul s o he ou di e en es s (i.e. NF-, NF+, F- and F+) a e shown in Fig. 4,
while he esul s a e lis ed in Table 1. I is e iden ha o he 287 s uden s p og essing
on he NF- b anch, app oxima ely 40% again sco ed be ween 30-40%, and he e we e
no pe o mances abo e 80%. Mos s uden s on he NF- b anch s uggle wi h
signi ican knowledge gaps, making he ein o cemen o high school knowledge a
c ucial elemen in hei calculus educa ion. The a e age sco e o s uden s es ed on
he NF+ b anch was no much highe han ha o hose on he NF- b anch, bu hey
ecei ed mo e di icul asks. Thei esul s we e no pa icula ly good ei he , as only a
ew achie ed sco es be ween 70-90%, and he e we e no pe o mances abo e 90%.
The 37.4% o he s uden s a ending he specializa ion cou se sco ed abo e 50% and
we e placed in he F+ g oup. I can be said ha bo h g oups pe o med be e in he
specializa ion ack han in he non-specializa ion ack. The specializa ion es s
included pa s o he ma e ial (e.g., di e en ial calculus) ha he s uden s will
encoun e in hei i s semes e a he uni e si y. Fo hem, much o he ma e ial om
single- a iable calculus will be amilia . The F- es had mo e p ocedu al asks (e.g.,
calcula ing he alue o he de i a i e a a gi en poin ), while among he F+ asks,
he e we e ques ions ha we e unusual o Hunga ian s uden s, es ing a deepe
unde s anding o he concep s.
Fig. 3. Resul s Block 3: a) NF-, b) NF+, c) F- and d) F+ g oups
4 CLUSTERING STUDENTS
Du ing he so ing o s uden s o A o B le els g oup limi s also had o be conside ed,
so i was necessa y o de ine a anking ha would make he esul s o es e s a
di e en le els compa able. Fo his he a ious es esul s needed o be weigh ed in
such a way ha indi iduals wi h good abili ies, bu modes p io knowledge would no
be placed in a lowe le el. Table 2 p o ides in o ma ion abou he applied weigh s.
Table 1. Weigh s o a ious es applied o clus e ing s uden s
Block 1
Block 2
Block3
Tes
Weigh
Tes
Weigh
Tes
Weigh
Basic
1.0
NF
0.9
NF-
0.9
NF+
1.0
F
1.1
F-
1.1
F+
1.2
Conside ing he pe o mances in di e en pa s wi h a ious weigh s, a single sco e
could be assigned o each s uden . The inal sco e o he assessmen es is shown in
Figu e 4. The his og ams show ha s uden s who ook he es designed o
specializa ion cou ses gene ally pe o med be e , esul ing in a dis ibu ion ha shi ed
o he igh . In con as , in he g oups whe e s uden s did no a end Facul a ion
classes, he dis ibu ion shi ed o he le , indica ing lowe a e age pe o mance. I is
wo h highligh ing ha in he Non-Facul a ion plus (NF+) g oup, he es esul
dis ibu ion was nea ly iden ical o he esul s o he wo specializa ion g oups. This
sugges s ha al hough hese s uden s did no ecei e ad anced high school
ma hema ics educa ion, hey achie ed simila esul s o hei specializa ion
coun e pa s on he en y es .
4.1 Applied clus e s
Fo so ing he s uden s, a clus e ing me hod in ol ing he admission poin s and he
adap i e assessmen es s esul s was applied. Fo he admission poin s ( o al o 500
poin s), we de e mined wo key h eshold alues: 350 and 400 poin s, while o he
en y es esul s, he 40% and 70% alues we e used. The esul s shows ha he F+
g oup has high admission poin s and s ong es esul s. A simila end can be
obse ed o he NF+ and F- g oups as well. An especially in e es ing obse a ion is
ha in he NF- g oup, high admission poin s a e ound despi e none o he s uden s
achie ing he 70% h eshold on he en y es , and in ac , only a ew came close o
he 50% pe o mance le el. This leads o he conclusion ha admission poin s alone
do no p o ide enough ounda ion o assess he expec ed success du ing uni e si y
s udies, and hey also o e oo li le guidance o implemen ing di e en ia ed
educa ion. The g oups we e o med so ha le el A included s uden s wi h s able
knowledge su icien o mas e he uni e si y cu iculum, while le el B included
s uden s who also needed ime o co e he high school cu iculum du ing he cou se.
Fig. 4. S uden clus e s based on hei admission poin s and assessmen es esul s
5 CONCLUSION
Gi en ha ma hema ics plays a c ucial ole in he success o enginee ing s udies, i is
essen ial ha s uden s begin hei s udies wi h a solid ounda ion. The e o e, i is
necessa y o s uden s o ecei e di e en ia ed, emedial ma hema ics educa ion
ailo ed o hei knowledge le el in he i s semes e o p o ide a solid ounda ion in
Calculus du ing he i s semes e a e illing in any missing knowledge. By he end o
he semes e , e e y s uden mus be well-p epa ed no only o he mul i a iable
calculus and linea algeb a cou ses in he sp ing semes e bu also equipped wi h
ma hema ical knowledge ha allows hem o apply wha hey ha e lea ned in
ma hema ics o hei majo subjec s. Ou adap i e measu emen indica es signi ican
