P ac ice Pape
Recommended ci a ion: Dias Ras ei o, D. M. L., & Pin o, C. M. A. (2025).
Fos e ing Ma hema ical P o iciency in Highe Educa ion Th ough Digi al Escape
Rooms: The ECO-Wa e Ene gy2Be Expe ience. 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.17631539.
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.
FOSTERING MATHEMATICAL PROFICIENCY IN HIGHER
EDUCATION THROUGH DIGITAL ESCAPE ROOMS: THE ECO-
WATERENERGY2BE EXPERIENCE
D. M. L. Dias Ras ei oa,
1
, C. M. A. Pin ob
a Poly echnic Uni e si y o Coimb a (IPC/ISEC), Coimb a, Po ugal, 0000-0002-
1228-6072
b ISEP-School o Enginee ing, Poly echnic o Po o, Po o, Po ugal, 0000-0002-
0729-1133
Con e ence Key A eas: Teaching ma hema ics in enginee ing educa ion; Building
he capaci y and s eng hening he educa ional compe ences o enginee ing educa o s
Keywo ds: Digi al Escape Rooms, Calculus, Ma hema ics Highe Educa ion,
GeoGeb a
ABSTRACT
Digi al escape ooms ha e eme ged as an inno a i e pedagogical app oach,
e ec i ely combining gami ica ion, na a i e elemen s, and ma hema ical p oblem-
sol ing o enhance s uden engagemen and unde s anding in highe educa ion (O iz,
2016). This pape p esen s ECO-Wa e Ene gy2Be, an ad anced digi al escape oom
de eloped wi hin he E asmus+ p ojec MATH-DIGGER. Ta ge ed a i s -yea
uni e si y s uden s en olled in ma hema ics cou ses, he ini ia i e aims o os e
awa eness o sus ainabili y, p omo e g een cons uc ion p inciples, and suppo he
de elopmen o calculus-based p oblem-sol ing skills.
A dis inc i e ea u e o ECO-Wa e Ene gy2Be is he in eg a ion o GeoGeb a so wa e,
which acili a es he design o in e ac i e ma hema ical ac i i ies ha p omo e ac i e
lea ning and deepe concep ual unde s anding. The s udy ou lines he heo e ical
amewo k in o ming he escape oom’s design, de ails i s ins uc ional con en , and
discusses i s p ac ical implemen a ion in uni e si y se ings.
Fu he mo e, he pape examines educa ional ou comes based on p elimina y pilo
s udies conduc ed wi hin he es ablished digi al escape oom amewo k. Ini ial
indings indica e no able imp o emen s in s uden mo i a ion, comp ehension, and
app ecia ion o bo h en i onmen al and ma hema ical dimensions o he asks
1
Co esponding Au ho
D. M. L. Dias Ras ei o
[email p o ec ed]
(Ras ei o, D. M. L. D. e al., 2025). These esul s unde sco e he po en ial o digi al
escape ooms o se e as engaging and e ec i e pedagogical ools in ad anced
ma hema ics educa ion.
1 INTRODUCTION
The inco po a ion o in e ac i e and inno a i e educa ional ools in highe ma hema ics
ins uc ion is a key elemen o mode n pedagogical de elopmen (He nandez-
Ma inez, 2024). Among hese ools, digi al escape ooms ha e eme ged as highly
e ec i e pla o ms, me ging gami ica ion wi h ma hema ical igo o signi ican ly
enhance s uden mo i a ion and deepen concep ual unde s anding (Wal e s e al.,
2018). Wi hin his amewo k, he ECO-Wa e Ene gy2Be – Sus ainable Design o
Uni e si y S uden s' Residences escape oom was de eloped as pa o he MATH-
DIGGER E asmus+ p ojec (MATH-DIGGER, 2022). This escape oom imme ses
s uden s in eal-wo ld sus ainabili y challenges, ocusing on g een cons uc ion
p inciples aligned wi h he Eu opean G een Deal Policies and he Uni ed Na ions’
Sus ainabili y Goals (2015).
A cen al ea u e o he escape oom is he ac i e applica ion o calculus and geome ic
p inciples, ein o ced h ough dynamic isualiza ions and in e ac i e asks designed
using GeoGeb a. While engaging wi h he escape oom, s uden s apply and
consolida e hei p io knowledge in in e pola ion, in eg a ion, olume calcula ion, and
cu e leng h de e mina ion. Depending on he ins uc o ’s p e e ence, asks can be
comple ed ei he using GeoGeb a o h ough adi ional pen-and-pape me hods.
This pape p esen s a comp ehensi e analysis o he p ac ical implemen a ion o he
digi al escape oom, ou lining wo key asks and he s uden in e ac ions necessa y o
hei comple ion. Sec ion 2 p o ides he con ex ual backg ound and desc ibes he
p ac ical ac i i ies in ol ed. This is ollowed by Sec ion 3, which de ails he educa ional
implica ions and ini ial indings om he game's applica ion. Finally, he pape
concludes wi h a discussion on key insigh s and di ec ions o u u e esea ch.
2 CONTEXT AND PRACTICAL WORK
2.1 Digi al Escape Rooms and Ma hema ical Educa ion
Digi al escape ooms a e gami ied, na a i e-d i en lea ning en i onmen s ha
engage pa icipan s in sol ing ma hema ical puzzles, ei he collabo a i ely o
indi idually. This app oach os e s expe ien ial lea ning, acili a ing bo h knowledge
acquisi ion and consolida ion (López-Pe nas e al., 2019). Con empo a y pedagogical
esea ch highligh s hei e ec i eness in enhancing p oblem-sol ing skills, os e ing
collabo a ion, and inc easing in insic mo i a ion in highe educa ion ma hema ics
(Bhu ah e al., 2024, Mag eñán e al, 2023).
2.2 ECO-Wa e Ene gy2Be: Concep and S o yline
The na a i e implemen ed wi hin he escape oom is designed o inspi e hope,
si ua ing s uden s in a pos -ca as ophe eco e y scena io ha unde sco es he u gen
need o sus ainable econs uc ion. S uden s collabo a i ely engage in ma hema ical
modeling and compu a ional asks o dimension and cons uc sus ainable esidences,
wa e ese oi s, and was ewa e sys ems. This con ex no only os e s cogni i e
engagemen h ough ma hema ics bu also aises awa eness o en i onmen al
sus ainabili y and he p inciples o he ci cula economy.
The na a i e is as ollows. In he wake o a de as a ing bombing ha des oyed hei
ci y, a g oup o de e mined s uden s aces he o midable challenge o ebuilding om
he uins. Wi h hei homes des oyed and hei u u e unce ain, hey ealize hey mus
ake ma e s in o hei own hands. Despi e he sca ci y o esou ces, hey come
oge he , d i en by a sha ed sense o pu pose and a desi e o c ea e some hing
meaning ul om he chaos. Thei ision is o a new beginning - one ha no only
es o es hei ci y bu also emb aces sus ainabili y and esilience. Thei i s ask is o
es ablish a place o call home. Using he MaxWhe e labo a o y as hei empo a y
shel e , he s uden s sea ch he w eckage o ma e ials o cons uc du able
esidences. Guided by hei ingenui y and esol e, hey ans o m deb is in o
dwellings, each a es amen o hei esilience and esou ce ulness. Howe e , he
s uden s' ambi ion ex ends beyond me e su i al. Awa e o he impo ance o
sus ainable li ing in a wo ld a aged by des uc ion, hey aim o inco po a e eco-
iendly elemen s in o hei new communi y. They ins all wa e collec ion sys ems o
ha es ainwa e , ensu ing a s eady supply o d inking and sani a ion, and ecycle
was ewa e , minimizing was e and conse ing aluable esou ces. Sola panels a e
placed on oo ops, ha nessing he powe o he sun o p o ide ene gy o hei g owing
se lemen . Wi h each panel, hope is ekindled, cas ing ligh on he da kness ha once
en eloped hei ci y. I becomes a symbol o esilience, a beacon o p og ess shining
b igh ly agains he backd op o de as a ion. As hei communi y akes shape, so does
hei uni y and sense o pu pose. Despi e hei ha dships, he s uden s wo k i elessly,
hei hands blis e ed, and spi i s es ed, bu ne e once wa e ing in hei
de e mina ion. Toge he , hey a e no me ely building homes bu a place o hope. As
he sun se s o e hei makeshi ci y, cas ing golden shadows ac oss hei humble
abodes, he s uden s celeb a e oge he —p oud, esilien , and eady o con on
wha e e challenges lie ahead. Fo in he ace o des uc ion, hey disco e ed no only
despai bu also he s eng h o ebuild, b ick by b ick, o ging a u u e imbued wi h
hope.
The MATH-DIGGER p ojec (MATH-DIGGER, 2022), unded by he E asmus+
ini ia i e, seeks o p omo e inno a i e digi al solu ions o ma hema ics educa ion a
he uni e si y le el. Speci ically, he MaxWhe e en i onmen con ibu es by p o iding
imme si e 3D i ual spaces ideal o complex, in e ac i e educa ional asks. The 3D
en i onmen plays a pi o al ole in he in eg a ion o s o y elling, ma hema ical igo ,
and in e ac i e p oblem-sol ing wi hin he ECO-Wa e Ene gy2Be expe ience.
2.3 P ac ical Wo k
The digi al escape oom is s uc u ed in o an in oduc o y phase ollowed by a se ies
o ma hema ical challenges dis ibu ed ac oss di e en ooms.
Du ing he in oduc o y phase, s uden s a e imme sed in he na a i e, amilia ising
hemsel es wi h he hemes o des uc ion and esilience. They na iga e he
MaxWhe e imme si e en i onmen , whe e hey gain a deepe unde s anding o he
con ex o sus ainable econs uc ion. The p ima y objec i e o he game is o s uden s
o p og ess h ough he a ious ooms and loo s, ul ima ely eaching he oo op,
whe e a celeb a o y ga he ing awai s hem. To achie e his, s uden s mus design a
esiden ial complex ha includes wa e ese oi s and was ewa e managemen
sys ems, applying key sus ainabili y concep s wi h a pa icula ocus on wa e ecycling
and ene gy e iciency.
The game is ca e ully designed o acili a e s uden s' unde s anding o co e calculus
concep s, including in e pola ion, in eg a ion, and de i a i es. Calcula ions may be
ca ied ou using adi ional me hods, such as pen and pape , a calcula o , o any
a ailable so wa e ools, ei he independen ly o in combina ion. Fo he pu poses o
his pape , all calcula ions will be p esen ed using GeoGeb a, as i is one o he
de elope pa ne s o he MATH-DIGGER p ojec .
Fig. 1. All spaces o he Escape Room
Du ing he escape oom expe ience, s uden s a e g an ed h ee a emp s o p og ess
om one oom o he nex un il hey each he inal oom, whe e he a o emen ioned
celeb a o y e en akes place. Hin s a e p o ided in each oom o assis s uden s;
howe e , he use o hin s and unsuccess ul a emp s will nega i ely a ec hei inal
sco es. The GeoGeb a so wa e is s a egically u ilised o c ea e in e ac i e
isualisa ions and enable dynamic p esen a ions o ma hema ical asks. Below a e wo
examples o he asks p esen ed o he s uden s.
Example (De e mining he Volume o a Sus ainable Residence):
Fig. 2. Room 1 S uden s' Tasks
In he example depic ed in Fig. 2, s uden s a e asked wi h calcula ing he olume o
a esidence, isualising he p oblem wi hin GeoGeb a. Using ou poin s (ei he
selec ed by he s uden o p ede e mined), he playe mus comple e he ollowing
asks:
• De e mine he coe icien s o a quad a ic unc ion ha in e pola es he ex e nal
shape o he building using poin s B, C, and D. Once he coe icien s a e
calcula ed, he playe can e i y hei accu acy by en e ing he alues ( ounded
o wo decimal places) and clicking he "Check Coe icien s" bu on. I he
coe icien s u n g een, he playe has en e ed he co ec alues and may
p oceed.
• Calcula e he building's olume. I is impo an o no e ha he building consis s
o a cylinde and a 3D objec o med by he o a ion o he p e iously de e mined
in e pola ed cu e. A e ob aining he olume in dm³, he playe mus ound he
alue o he nea es whole numbe and en e i in he olume alue box. Upon
clicking he "Ve i y Volume" bu on, i he inse ed olume u ns g een, he
playe will know ha he alue is co ec .
Example 2 (B idge Leng h Calcula ion):
Fig. 3. B idge Leng h Tasks
In he example p esen ed in Fig. 3, s uden s a e asked wi h de e mining he leng h o
a b idge be ween wo buildings. To accomplish his, hey mus :
• De e mine he coe icien s o he pa abola ha app oxima es he b idge's
con ou , ounding he coe icien alues o h ee decimal places.
• Calcula e he leng h o he b idge cu e, measu ed in kilome es, om he
"Begin" o he "End" poin s.
GeoGeb a suppo s s uden s’ concep ual unde s anding o calculus by enabling
dynamic isualisa ion o how modi ica ions o ma hema ical objec s, such as poin s,
cu es, o unc ions, a ec ela ed alues. In he con ex o he escape oom, s uden s
u ilise GeoGeb a’s buil -in ools o compu e de i a i es and in eg als, and o sol e
equa ions ele an o he p oblem scena ios.
These a e p elimina y indings, hough we inco po a e s uden eedback below, which
sugges s inc eased con idence in applying calculus echniques and a heigh ened
in e es in sus ainabili y hemes. Al hough u he empi ical alida ion is necessa y,
hese ini ial quali a i e insigh s poin o he escape oom's pedagogical alue in
enhancing engagemen and concep ual unde s anding.
3 EDUCATIONAL IMPLICATIONS AND INITIAL FINDINGS
Pilo s udies conduc ed wi h a p io digi al escape oom, also de eloped wi hin he
amewo k o he MATH-DIGGER p ojec , ha e yielded se e al no ewo hy
educa ional ou comes:
• Enhanced s uden engagemen , as e lec ed in inc eased pe sis ence in ask
comple ion and mo e e ec i e collabo a i e in e ac ions;
• Imp o ed concep ual unde s anding in key a eas, including calculus, geome y,
and ounda ional p inciples o sus ainabili y;
• Mo e posi i e a i udes owa d ma hema ics, accompanied by a heigh ened
awa eness o en i onmen al sus ainabili y issues.
Feedback om s uden s:
• S uden 1: “The ER#1 game e ec i ely highligh ed he ele ance o
sus ainabili y and sola ene gy, p omo ing an educa ional, in e ac i e, and
inno a i e app oach. Th oughou he asks ca ied ou wi hin he digi al escape
oom, i became e iden ha Ma hema ics and Physics play essen ial oles in
unde s anding and applying concep s ela ed o ene gy e iciency and he use
o enewable esou ces. The p ac ical ac i i ies no only ein o ced he
applica ion o heo e ical knowledge bu also encou aged c i ical e lec ion on
global issues conce ning he cons uc ion o a mo e sus ainable u u e.”
• S uden 2: “The applica ion o ools such as GeoGeb a and he g aphing
calcula o enabled he wo k o be conduc ed wi h p ecision, he eby
demons a ing how digi al esou ces can acili a e he esolu ion o complex
p oblems. By in eg a ing ma hema ical calcula ions, g aphical analyses, and
sus ainable p ac ices, he p ojec illus a ed he easibili y o employing ac i e
eaching me hodologies o aise s uden awa eness on c i ical issues such as
sus ainabili y”.
• S uden 3: “The ER#1 is an engaging me hodology ha os e s c i ical hinking,
e ec i e in eg a ion o en i onmen al and ma hema ical hemes, and
de elopmen o digi al skills and p oblem-sol ing abili ies”.
These indings p o ide ini ial e idence o he educa ional po en ial o digi al escape
ooms o suppo bo h cogni i e and a ec i e lea ning ou comes in ma hema ics
educa ion (Ras ei o, D. M. L. D. e al., 2025).
The ECO-Wa e Ene gy2Be escape oom seeks o u he alida e hese indings, wi h
a ocus on os e ing a comp ehensi e unde s anding and p ac ical applica ion o
calculus wi hin he con ex o sus ainabili y.
4 CONCLUSIONS AND FUTURE DIRECTIONS
Digi al escape ooms, exempli ied by ECO-Wa e Ene gy2Be, cons i u e inno a i e
pedagogical ins umen s wi h demons a ed po en ial o enhance ma hema ics
educa ion a he e ia y le el. By in eg a ing ma hema ical igou , sus ainabili y-
o ien ed con en , and imme si e digi al echnologies, such as hose o e ed by
MaxWhe e and GeoGeb a, hese en i onmen s signi ican ly en ich he lea ning
expe ience, os e ing heigh ened s uden engagemen and sus ained in e es .
Such in e ac i e pla o ms no only ende abs ac ma hema ical concep s mo e
accessible and conc e e bu also encou age collabo a i e p oblem-sol ing, he eby
cul i a ing c i ical hinking skills and ein o cing he applicabili y o ma hema ics o eal-
wo ld challenges, pa icula ly hose ela ed o sus ainabili y.
To u he ad ance he ield, u u e implemen a ions should ocus on la ge-scale
alida ion s udies and compa a i e esea ch o e alua e he e ec i eness o digi al
escape ooms in enhancing s uden s’ ma hema ical easoning, mo i a ion, and long-
e m knowledge e en ion. Mo eo e , ex ending his app oach o encompass a b oade
ange o ma hema ical opics o in e disciplina y con ex s could ampli y i s educa ional
impac , suppo ing mo e ans o ma i e shi s in eaching and lea ning p ac ices.
ACKNOWLEDGEMENTS
All au ho s would like o hank he MATH-DIGGER E asmus p ojec – MATHema ics
DIGi al Escape Rooms, No. 2021-1-PT01-KA220-HED-000032234. An au ho was
pa ially suppo ed by by CIDMA unde he FCT (Po uguese Founda ion o Science
and Technology) Mul i-Annual Financing P og am o R&D Uni s.
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