Wo kshop
Recommended ci a ion: Chen, M., Ramesh Kuma , S., Phillips, G., Schneide , K.,
& Boussé, M. (2025). Calculus Legacy: A Ludo Didac ical Lea ning Expe ience o
Ma hema ics in Enginee ing Educa ion. 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.17631264.
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.
CALCULUS LEGACY: A LUDO-DIDACTICAL LEARNING
EXPERIENCE FOR MATHEMATICS IN ENGINEERING EDUCATION
M. Chen a, S. Ramesh Kuma a, G. Phillips b,
K. Schneide c, M. Boussé d, 1
a FSE, Maas ich Uni e si y, Maas ich , he Ne he lands
b FSE, Maas ich Uni e si y, Maas ich , he Ne he lands, 0000-0003-4443-0822
c Depa men o Ad anced Compu ing Sciences, FSE, Maas ich Uni e si y,
Maas ich , he Ne he lands, 0000-0001-6250-9011
d Depa men o Ad anced Compu ing Sciences, FSE, Maas ich Uni e si y,
Maas ich , he Ne he lands, 0000-0003-2090-0682
Con e ence Key A eas: 3. Teaching ma hema ics and physics in enginee ing
educa ion, 12. Cu iculum de elopmen and eme ging cu iculum models in
enginee ing
Keywo ds: Ludo Didac ics, Game-Based Lea ning, S uden Engagemen ,
Ma hema ics Educa ion, P oblem-Based Lea ning
ABSTRACT
Calculus is a key subjec in enginee ing educa ion bu is o en expe ienced as
abs ac and demo i a ing by s uden s. Calculus Legacy, a na a i e-d i en,
legacy-s yle boa d game, was designed using Ludo Didac ics p inciples o c ea e an
ac i e, lea ne -cen e ed en i onmen . By aligning he game wi h P oblem-Based
Lea ning, he game ans o ms calculus in o an engaging, con ex ualized, and
lea ne -d i en expe ience. In his wo kshop, pa icipan s will engage wi h a cu a ed
e sion o he game, assume unique oles, and sol e eal-wo ld-inspi ed calculus
p oblems, simula ing how s uden s collabo a e in small eams. Calculus Legacy
p o ides a conc e e example o how Ludo Didac ics can enhance ma hema ics
educa ion wi hin enginee ing p og ams. Pa icipan s will gain insigh s in o
implemen ing simila game-based s a egies in hei own cou ses o p omo e
s uden -cen e ed, ac i e lea ning and inc ease mo i a ion in STEM educa ion.
1 Co esponding au ho
M. Boussé
m.bousse@maas ich uni e si y.nl
1 BACKGROUND AND RATIONALE
1.1 Calculus in Enginee ing
Calculus is a co ne s one o enginee ing educa ion, essen ial o modelling,
analyzing, and sol ing complex p oblems in domains anging om mechanics and
he modynamics o sys ems con ol and da a science. Despi e i s undamen al ole,
calculus emains one o he mos challenging and o en demo i a ing subjec s o
i s -yea enginee ing s uden s (Tall, 1993; Lim-Teo e al., 2007). Many lea ne s
expe ience i as abs ac , echnical, and de ached om p ac ical applica ions, o en
leading o su ace-le el lea ning and disengagemen .
One key issue is he dominance o eache -cen e ed, lec u e-d i en o ma s ha
emphasize p ocedu al p o iciency o e concep ual unde s anding (Thompson &
Ha el, 2021). These adi ional me hods o en neglec he po en ial bene i s o ac i e
lea ning pa adigms such as P oblem-Based Lea ning (PBL), which p omo e
engagemen and c i ical hinking h ough eal-wo ld p oblems. In esponse, he e is a
g owing call wi hin he enginee ing educa ion communi y o eimagine how we each
calculus, mo ing owa ds s uden -cen e ed app oaches ha a e collabo a i e,
con ex ual, and engaging (Mokh a e al, 2013; Maas ich Uni e si y, 2024).
Embedding calculus ins uc ion in such amewo ks is c ucial no only o imp o e
unde s anding o ma hema ical p inciples, bu also o enhance s uden s’ con idence
and mo i a ion.
In his con ex , game-based lea ning eme ges as a powe ul pedagogical ool.
By le e aging he mo i a ional a o dances o games, such as na a i e, compe i ion,
eedback loops, and ole-playing, educa o s can acili a e deepe lea ning and make
abs ac ma hema ical concep s mo e angible and engaging (Bayeck, 2020; Oli ei a
e al., 2023). Calculus Legacy, he boa d game showcased in his wo kshop,
embodies his ision by blending Ludo Didac ics wi h PBL p inciples o c ea e an
ac i e, imme si e, and lea ne -d i en expe ience o enginee ing s uden s.
1.2 Ludo Didac ics as a cons uc i e, collabo a i e, con ex ual, and
sel -di ec ed (CCCS) eaching and lea ning app oach
Maas ich Uni e si y’s educa ional ision e ol es a ound PBL, p omo ing ac i e
lea ning h ough ou co e p inciples (EDLAB, 2017):
● Cons uc i e lea ning encou ages s uden s o build upon hei exis ing
knowledge by ac i ely in eg a ing new concep s.
● Collabo a i e lea ning p omo es co-c ea ion o knowledge h ough eamwo k,
os e ing communica ion and collec i e esponsibili y.
● Con ex ual lea ning si ua es academic concep s in au hen ic, eal-wo ld
scena ios, inc easing ele ance and ans e abili y o knowledge.
● Sel -di ec ed lea ning empowe s s uden s o plan, moni o , and e alua e hei
own lea ning ajec o ies, p omo ing au onomy and owne ship.
The CCCS p inciples ha e been linked o g ea e s uden sa is ac ion and
deepe lea ning (Dolmans e al., 2005; Be gman e al., 2012). They ha e also been
linked o imp o emen s in c i ical and c ea i e hinking, p epa ing s uden s o
eal-wo ld p oblem sol ing (Uni e si y o Illinois, 2019).
One way o ope a ionalize CCCS p inciples in inno a i e lea ning en i onmen s
is h ough Ludo Didac ics. De eloped by he U ech School o A s (HKU), Ludo
Didac ics is a pedagogical amewo k ha designs lea ning beha io and educa ion
a ound game p inciples (Renge & Hoogendoo n, 2019). I shi s ocus om
adi ional, con en -d i en eaching o lea ne -cen e ed app oaches, in a simila spi i
as PBL. A i s co e, Ludo Didac ics in eg a es me hodologies om game design o
c ea e lea ning expe iences ha a e inhe en ly engaging and meaning ul. This is
achie ed, e.g, by using he Mechanics, Dynamics, Aes he ics (MDA) amewo k,
which guides he design o he lea ning expe ience (mechanics and dynamics) and
i s emo ional impac on he lea ne (aes he ics). Also, he Epic Epis emic Can as
ensu es alignmen be ween game design and in ended lea ning ou comes (Renge &
Hoogendoo n, 2019). Ludo Didac ics na u ally aligns wi h he CCCS p inciples:
● Cons uc i e: Lea ne s ac i ely build knowledge as hey engage wi h e ol ing
challenges embedded in game scena ios.
● Collabo a i e: Many Ludo Didac ical designs emphasize eam oles,
coope a ion, and sha ed decision-making.
● Con ex ual: The na a i e-d i en na u e o Ludo Didac ics o en si ua ed
lea ning wi hin au hen ic con ex s and eal-wo ld scena ios.
● Sel -Di ec ed: Games inhe en ly gi e playe s agency, enabling s uden s o
explo e, s a egize, and e lec on hei ac ions and lea ning p og ess.
Building on p e ious e o s o align assessmen on eaching and lea ning
ac i i ies in ou p og ams wi h CCCS p inciples (Boussé e al., 2023), Calculus
Legacy ep esen s a angible ealiza ion, applying Ludo Didac ics o p omo e ac i e,
s uden -cen e ed lea ning expe iences. I enhances he lea ning p ocess and
add esses he pedagogical challenges associa ed wi h eaching calculus, such as
pe cei ed abs ac ion and lack o engagemen , by ans o ming hem in o mo i a ing,
collabo a i e, and au hen ic lea ning expe iences.
1.3 Calculus Legacy boa d game
Calculus Legacy is a na a i e-d i en, legacy-s yle boa d game de eloped o
enhance s uden mo i a ion and engagemen in calculus h ough a Ludo Didac ical
lea ning expe ience. I p omo es a lean- o wa d lea ning a i ude by imme sing
s uden s in an ac i e and collabo a i e en i onmen whe e hey ackle eal-wo ld
inspi ed challenges. The game, inanced by Comenius Teaching Fellow 2024. is
designed o ans o m he lea ning o calculus om a adi ionally passi e, abs ac
exe cise in o a meaning ul and in e ac i e jou ney ha spa ks cu iosi y and deepens
unde s anding.
The game consis s o six, 90-minu e sessions aligned wi h six weeks o
cou se con en , whe e s uden s wo k in small eams, each assuming unique oles,
see Figu e 1. Using an e en -ca d deck sys em, s uden s a e con on ed wi h
decision-making scena ios, applied calculus asks, and na a i e wis s ha os e
collabo a ion and c i ical hinking. The legacy mechanics ensu e ha choices made
in one session impac subsequen sessions, sca olding ma hema ical concep s
p og essi ely ac oss he cou se. The game e ol es and changes o e ime
depending on how playe s in e ac wi h i , o e ing a one-o -a-kind gameplay
expe ience o e e y g oup. The e ol ing na a i e, pai ed wi h ole-playing and
p oblem-sol ing, encou ages con inuous engagemen , collabo a ion, and au hen ic
lea ning expe iences in line wi h CCCS and Ludo Didac ical p inciples. To assess i s
impac , we conduc ed a play es wi h BSc Ci cula Enginee ing s uden s, see Figu e
2. The game session c ea ed a lean- o wa d and collabo a i e en i onmen o he
s uden s o explo e solu ions o a eal-wo ld, calculus-based p oblem.
Each o he Calculus Legacy sessions a e designed based on speci ic
calculus- ela ed concep s ha a e adi ionally included in i s -yea enginee ing
cu icula. These include opics such as unc ions, limi s, de i a i es and hei
applica ions, in eg als and hei applica ions and di e en ial equa ions. To in eg a e
hese concep s in o he game, we ha e in oduced a laye o engaging, ela able and
unique na a i es o each. Fo example, applica ion o de i a i es a e explo ed
h ough a ege able ga den op imiza ion ask whe e s uden s aim o calcula e he
op imal empe a u e, cos and e ilize usage. S uden s explo e in eg als by
decoding a ecipe, whe e he quan i ies o he ing edien s ha e been encoded in
a ious in eg al ypes. As o in eg al’s applica ions, s uden eams ha e o design
hei own chalice-shaped bee glass by compu ing i s olume and a eas whils
adhe ing o cons ain s in oduced by he e en ca ds.
Fig. 1. Concep ual illus a ion o he Calculus Legacy boa d game, showing he key
componen s such as e en ca ds, playe ole and goal ca ds, and a collabo a i e eam
wo kspace, designed o enhance mo i a ion, collabo a ion, and communica ion in an
educa ional se ing. No e ha a u o is always p esen as a guide on he side.
1.4 Rele ance o enginee ing educa ion
The in eg a ion o PBL and he CCCS p inciples can be highly bene icial o e ec i e
enginee ing educa ion, especially in ma hema ics ins uc ion (Dolmans e al., 2005;
Mokh a e al., 2013). Ludo Didac ics o e s a p ac ical, c ea i e, and play ul
design me hodology o ansla e hese p inciples in o engaging, meaning ul, and
au hen ic eaching and lea ning expe iences ha esona e wi h enginee ing s uden s.
In his wo kshop, we showcase Calculus Legacy as a angible example o how PBL,
CCCS, and Ludo Didac ics can be in eg a ed o imp o e ma hema ics educa ion by
os e ing deepe concep ual unde s anding and s uden mo i a ion. These me hods
align wi h he pedagogical app oaches in Educa ion o Sus ainable De elopmen
(UNESCO, 2017; Gue a & Holgaa d, 2013), he ision desc ibed in he SEFI annual
epo 2023-2024, p ecisely wi h he Leona do da Vinci medal winne , P o esso in
Enginee ing Educa ion and PBL, Ane e Kolmos (Fe do á, 2024), and he ision o
he Eu opean Highe Educa ion A ea (Eu opean Commission, 2024, Chap e 5.3).
By o e ing pa icipan s a cu a ed expe ience o his boa d game, we p o ide a
p ac ical bluep in o in eg a ing s uden -cen e ed, game-based lea ning in o
enginee ing cu icula. This con ibu es o b oade cu iculum de elopmen e o s
ha call o ac i e and meaning ul lea ning expe iences (Bayeck, 2020; Oli ei a e
al., 2023). Ul ima ely, his wo kshop aims o inspi e educa o s ac oss disciplines o
apply hese design p inciples in hei own cou ses and con ex s.
This wo kshop also suppo s he g owing emphasis in enginee ing educa ion on
de eloping ans e sal skills, such as eamwo k, p oblem-sol ing, and e lec i e
hinking. By os e ing collabo a ion and con ex ual lea ning, Calculus Legacy equips
u u e enginee s wi h bo h echnical expe ise and he abili y o apply knowledge
c ea i ely in eal-wo ld, p ojec -based se ings.
Fig. 2. Real-li e play es o he Calculus Legacy boa d game, ea u ing s uden s ac i ely
collabo a ing o design a chalice-shaped bee glass. In his session, s uden s b ains o m
how o compu e he olume and su ace a ea o he glass. Each s uden has a dis inc ole
and hidden pe sonal goal, adding an ex a laye o s a egy and engagemen .
2 WORKSHOP OBJECTIVES
2.1 Ta ge audience
The a ge audience o his wo kshop a e educa o s om all ields wi hin
enginee ing. This wo kshop does no equi e any specialised knowledge in calculus
o pa icipa e because i is a cu a ed expe ience om he o iginal boa d game.
2.2 Expec ed lea ning ou comes
The goals o his wo kshop a e wo- old: 1) o amilia ise pa icipan s wi h he co e
concep s and educa ional a ionale o Ludo Didac ics by engaging hem in a cu a ed
play expe ience o Calculus Legacy, and 2) o inspi e and empowe educa o s om
di e se enginee ing disciplines o c i ically e lec on and explo e how Ludo Didac ics
could be adap ed and implemen ed wi hin hei own eaching con ex s. The in ended
lea ning ou comes (ILOs) o he wo kshop a e:
1. Desc ibe he ludo-didac ical p inciples wi hin he con ex o cons uc i e,
con ex ual, collabo a i e, and sel -di ec ed (CCCS) lea ning p inciples.
2. Explo e he ludo-didac ical app oach in hei own eaching p ac ices.
We aim o achie e his h ough an in e ac i e game session - which will
comp ise mos o he wo kshop, ollowed by a sho pos -discussion o sha e
expe iences and insigh s. This will p o ide he pa icipan s a i s -hand expe ience o
Ludo Didac ics.
2.3 T ans e abili y
Al hough Calculus Legacy was c ea ed o calculus, i s unde lying s uc u e is highly
ans e able ac oss STEM disciplines. Ludo Didac ics p o ides an adap able design
me hodology o o he con ex s and lea ning objec i es. The game’s ole sys em,
e en -ca d mechanics, and legacy o ma a e con en -neu al, making hem sui able
o o he ields such as physics, compu e science, o in e disciplina y cou ses such
as sus ainabili y and p oduc design. By modi ying he na a i e and ask s uc u e,
educa o s can c a engaging, game-based lea ning en i onmen s ailo ed o hei
speci ic domains. Such adap abili y suppo s b oade adop ion o s uden -cen e ed,
ac i e lea ning app oaches wi hin enginee ing educa ion.
3 WORKSHOP DESIGN
3.1 Time plan
This wo kshop is di ided in o h ee pa s consis ing o an in oduc ion, a play
expe ience, and a pos -discussion, along wi h p e- and pos -wo kshop ma e ials, see
Table 1. Ma e ials o all ac i i ies can be downloaded ia he link in he oo no e2.
Table 1. Wo kshop ime plan
Run ime
Ac i i y
Desc ip ion
5 min
Sho
in oduc ion
B ie in oduc ion o he wo kshop.
30-35 min
Play expe ience
Pa icipan s play a cu a ed e sion o Calculus Legacy
in small g oups.
15-20 min
Pos -discussion
Pa icipan s engage in a guided discussion o explo e
oppo uni ies, challenges, and con ex ual adap a ions
o hei ields.
In he p e-wo kshop ma e ial, we p o ide explana ions abou he main p inciples
o Calculus Legacy and he ules o he game. Reading he p e-wo kshop con en
p io o he onsi e wo kshop is ecommended and bene icial o he p og ession o he
game session bu comple ion is no manda o y and does no limi pa icipa ion.
Du ing he wo kshop, he sho in oduc ion ensu es all pa icipan s unde s and
he basic ules o Calculus Legacy. In he in e ac i e play es , he p o ided game
session is inspi ed om he inal boa d game bu sho ened and ailo ed o a wide
audience wi hou p io knowledge. The pos -discussion will be guided by a se o
s uc u ed e lec ion ques ions, encou aging pa icipan s o link hei gameplay
expe ience explici ly o CCCS p inciples and e lec on how Ludo Didac ics could be
applied in hei own eaching. Pa icipan s will also be p omp ed o sha e po en ial
ba ie s and enable s o implemen ing game-based lea ning in hei con ex s.
Examples include: implemen a ion o la ge coho s, adap a ion o o he subjec s,
and in eg a ion wi h exis ing cu icula o assessmen s a egies. The discussion aims
o gene a e ac ionable insigh s and inspi e pa icipan s o expe imen wi h Ludo
Didac ics and game-based lea ning in hei cou ses and cu icula.
A e he onsi e wo kshop, pos -wo kshop ma e ial will be p o ided ia a
download link consis ing o : a concise Ludo Didac ics p ime wi h some examples
2 Wo kshop ma e ial link
h ps://su d i e.su .nl/ iles/index.php/s/NxU65Yeky ZaDhS
and a guide o un he cu a ed game session a hei home uni e si y. This will
u he dissemina e ou ideas and enable pa icipan s o adop simila s a egies.
3.2 In e ac i i y
The wo kshop design ensu es a high le el o in e ac i i y: 1) pa icipan s engage
di ec ly in he game-based lea ning ac i i y (“lea ning by doing”), 2) he game is
designed o p omo e small-g oup discussion and eamwo k, 3) he design also
c ea es an imme si e, sha ed lea ning expe ience, 4) because o he ole sys em,
e e y pa icipan /playe b ings unique game abili ies o he able, and 5) in he
pos -discussion o he wo kshop pa icipan s sha e hei pe sonal game expe ience.
4 WORKSHOP RESULTS
The wo kshop a ac ed 8 pa icipan s in ol ed in enginee ing educa ion and coming
om di e en backg ounds, mainly ma hema ics and physics educa o s. Immedia ely
ollowing he wo kshop, pa icipan s comple ed a b ie e alua ion, using he
in e ac i e ool Wooclap, o e alua e he e ec i eness o he wo kshop and assess
he ex en o which he in ended lea ning ou comes (ILOs) a e achie ed.
To assess ILO1, which ocuses on pa icipan s’ unde s anding o Ludo
Didac ical p inciples in he con ex o CCCS lea ning, we included Like -scale based
and open-ended ques ions. The esul s o he Like -scale we e gene ally posi i e,
see Table 2.
Table 2: Resul s o he pos -wo kshop su ey wi h Like -scale a ing om 1 o 5
(1= I s ongly disag ee and 5 = I s ongly ag ee).
S a emen
A e age a ing
The wo kshop was use ul o me
4.0
I lea ned some hing abou Ludodidac ics and CCCS
3.9
I am in e es ed in implemen ing Ludo Didac ics in my eaching
3.6
In he open-ended ques ions, he audience exp essed he challenges and
oppo uni ies wi h he implemen a ion o Ludo Didac ics in enginee ing educa ion. In
e ms o oppo uni ies, he pa icipan s men ioned he modula i y o he app oach
gi en he adap abili y o he na a i e alongside he inc ease in lea ne engagemen
h ough enjoyable and in e ac i e sessions. As o he challenges, hey highligh ed
he ime cons ain s in de eloping e ec i e ye non-demo alising exe cises i ing he
Ludo Didac ical app oach, ha dships wi h engaging passi e s uden s and ime aken
o unde s and he p oblem. Addi ionally, he audience indica ed ha hey especially
app ecia ed he in e ac i eness, collabo a i e and un hands-on expe ience.
To e alua e ILO2, conce ning pa icipan s’ abili y o explo e he applicabili y o
Ludo Didac ics wi hin hei own educa ional p ac ice, pa icipan s we e in i ed o
p o ide w i en e lec ions on po en ial applica ions wi hin hei ield. The e lec ions
included he in e es o implemen a ion o PBL, de ining an asso men o exe cises
sui ed o Ludo Didac ics and e en inclusion o eal-li e da a. Scopes o
imp o emen mainly included w i en and clea e ins uc ions ega ding he e en s
om he s a .
To conclude, he wo kshop was success ul in aising awa eness abou
Ludodidac ics and i s po en ial applicabili y in STEM educa ion o make eaching
lea ne -cen ed, aligning wi h he p inciples o PBL.
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