Resea ch Pape
Recommended ci a ion: P ince, R. N., & Simpson, Z. (2025). In es iga ing The
Rela ionship Be ween Ma hema ics and Re en ion and Success in Enginee ing
S udy: A Sou h A ican Case S udy. 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.17631228.
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.
INVESTIGATING HOW MATHEMATICS SKILLS UPON ENTERING
ENGINEERING STUDIES AFFECT GRADUATION AND DROPOUT
RATES: A SOUTH AFRICAN CASE STUDY
RN P ince a,1, ZS Simpson b
a Uni e si y o Johannesbu g, Johannesbu g, Sou h A ica, 0000-0002-8640-799X
b Uni e si y o Johannesbu g, Johannesbu g, Sou h A ica, 0000-0002-1263-3812
Con e ence Key A eas: Teaching ma hema ics and physics in enginee ing
educa ion
Keywo ds: s uden success; ma hema ics; e en ion and h oughpu ;
ABSTRACT
While many s uden s a e unde p epa ed o highe educa ion, especially in
ma hema ics-hea y disciplines such as enginee ing, uni e si ies a e also
unde p epa ed o he s uden s hey admi . This has esul ed in low g adua ion and
high d opou a es in enginee ing p og ams globally. In he USA, only a ound 30% o
s uden s who en e an enginee ing quali ica ion g adua e in he expec ed ime and
ewe han 60% g adua e wi hin egula ion ime plus wo yea s. To his end, we seek
o answe he ques ion: “How does s uden s’ ma hema ics abili y upon en y in o
uni e si y a ec g adua ion and d opou a es in enginee ing s udy?” We de e mine
ma hema ics abili y using wo assessmen s employed in he Sou h A ican con ex –
one a s a u o y school-lea ing assessmen and he o he an op ional highe
educa ion admission assessmen . Academic pe o mance (g adua ion and d opou )
in enginee ing s udy is assessed a he end o i s yea and again a he end o ou
and six yea s, o he same coho o s uden s. A sample o 525 s uden s is selec ed,
amongs which 23.2% d opped ou a he end o i s yea and 30.9% d opped ou a
he end o ou yea s. While only 26.5% g adua ed in egula ion ime (4 yea s),
60.4% g adua ed in egula ion ime plus wo yea s (6 yea s). Wi h ega d o whe he
ma hema ics abili y o e s insigh in o his poo pe o mance, we ind a s ong
co ela ion be ween bo h ma hema ics assessmen s and pe o mance in enginee ing
s udy. This in o ma ion can be used o in o m he ways in which cu iculum
1 Co esponding Au ho
RN P ince
p [email protected]
de elopmen and eaching and lea ning should be esponsi e o s uden s admi ed
in o enginee ing p og ams o s udy, bo h wi hin Sou h A ica and in e na ionally.
1 INTRODUCTION AND CURRENT KNOWLEDGE
Ma hema ics se es as he ounda ional language o STEM (Science, Technology,
Enginee ing, and Ma hema ics) educa ion, enabling s uden s o engage in scien i ic
inqui y, echnological de elopmen , and enginee ing design. P o iciency in
ma hema ics equips lea ne s wi h p oblem-sol ing, modelling, and analy ical skills
essen ial o ackling eal-wo ld challenges. Despi e i s cen al ole, esea ch
indica es ha ma hema ics is o en unde emphasized in STEM cu icula, poin ing o
he need o s onge in eg a ion and con ex ualiza ion o lea ning expe iences
(Simpson & P ince, 2018). Se e al s udies epo on he ela ionships be ween
nume ous p edic i e ac o s and he pe o mance and e en ion o enginee ing
s uden s (Tsui & Khan, 2023; de Win e & Dodou, 2011). Howe e , hey do no
in es iga e how na ional school-lea ing and uni e si y admission ma hema ics
assessmen s, a ec s enginee ing g adua ion and d opou a es.
Ma hema ics p o iciency plays a c i ical ole in enginee ing educa ion, speci ically,
in luencing s uden s' academic success, con idence, and o e all pe o mance in
enginee ing p og ammes. A s ong ounda ion in ma hema ics enhances s uden s'
abili y o g asp complex enginee ing concep s, while inadequa e ma hema ical
p epa edness o en leads o challenges in cou sewo k. Fo example, insu icien
ma hema ical skills may esul in acul y dedica ing addi ional ime o e isi ing
undamen al opics, such as igonome y and geome y, a he han ocusing on
co e enginee ing p inciples (G ayson e al., 2018). Longi udinal s udies u he
highligh a posi i e co ela ion be ween ma hema ics achie emen and pe o mance
in enginee ing subjec s like mechanics, unde sco ing he necessi y o s ong
ma hema ical compe encies o success in applied enginee ing disciplines (Bischo
e al., 2015). Ma hema ics is a signi ican ac o in enginee ing s uden success, wi h
s uden s who ha e s onge ma hema ical backg ounds and be e pe o mance in
ma hema ics mo e likely o succeed and comple e hei enginee ing deg ees (Tsui &
Khan, 2023).
Beyond cogni i e abili y, a ec i e ac o s—such as a i udes, belie s, and sel -
e icacy in ma hema ics—also in luence s uden pe o mance. Resea ch on i s -yea
enginee ing s uden s sugges s ha a posi i e ma hema ical mindse is linked o
imp o ed academic ou comes, emphasizing he impo ance o os e ing con idence
and mo i a ion in ma hema ics educa ion (Panaou a e al., 2024). In esponse o
hese challenges, schola s ad oca e o inno a i e eaching s a egies ha p omo e
ac i e lea ning and eal-wo ld applica ions o ma hema ical concep s, helping
s uden s b idge he gap be ween heo e ical knowledge and p ac ical p oblem-
sol ing (Pepin e al., 2021).
In he Sou h A ican con ex , conce ns abou s uden p epa edness in enginee ing
s udy pe sis , necessi a ing a deepe unde s anding o s uden s’ ma hema ical
capabili ies upon en y (Sco e al., 2007; CHE, 2013). The Sou h A ican Na ional
Cu iculum and Assessmen Policy S a emen (CAPS) de ines ma hema ics as a
symbolic and no a ional language used o desc ibe nume ical, geome ic, and
g aphical ela ionships, emphasizing i s ole in c i ical hinking, p oblem-sol ing, and
access o ad anced ma hema ical s udy (DBE, 2011). Simila ly, he Na ional
Benchma k Tes s’ (NBT) Ma hema ics assessmen e alua es s uden s’ abili y o
apply ma hema ical concep s om he school cu iculum in highe educa ion
con ex s, pa icula ly in disciplines such as Ma hema ics, Chemis y, Physics, and
Enginee ing (Bohlmann & B aun, 2006; Bohlmann e al., 2017).
Gi en he c i ical ole o ma hema ics in enginee ing educa ion, his pape examines
he p edic i e alidi y o wo ma hema ics assessmen s o enginee ing p og ammes
in Sou h A ica, explo ing hei e ec i eness in de e mining s uden s’ likelihood o
academic success and p og ession.
2 METHODOLOGY
In Sou h A ica, wo assessmen s o school-lea e s' ma hema ical p o iciency a e
a ailable. The i s is he Na ional Senio Ce i ica e (NSC) assessmen s; hese a e
no m- e e enced, meaning sco es a e ‘s anda dised’ o ‘no med’ o a i e-yea olling
a e age. Thus, while candida es may pe o m well compa ed o he no m, hey may
s ill ail o mee a ce ain s anda d in he subjec being es ed. In he NSC, s uden s
a e a ed on he achie emen scale gi en in Table 1. S uden s wishing o s udy
enginee ing a uni e si y mus w i e he NSC Ma hema ics assessmen and ob ain a
a ing o 5 o abo e.
Table 1. Na ional Senio Ce i ica e (NSC) scale o achie emen (G ades 10-12) (DBE 2009,
p. 5)
Ra ing code
Desc ip ion
Sco e (%)
7
Ou s anding achie emen
80-100
6
Me i o ious achie emen
70-79
5
Subs an ial achie emen
60-69
4
Adequa e achie emen
50-59
3
Mode a e achie emen
40-49
2
Elemen a y achie emen
30-39
1
No achie ed
0-29
The Sou h A ican Na ional Benchma k Tes (NBT) in Ma hema ics (MAT)
de e mines whe he school-lea e s a e able o ans e hei school-lea ing
Ma hema ics knowledge o con ex s ha a e ound in Sou h A ican highe educa ion.
The NBT MAT es aims o assess candida es’ abili y wi h espec o a ious
ma hema ical opics: p oblem sol ing and modelling, use o algeb aic p ocesses and
unc ions; basic igonome y; spa ial
pe cep ion; analy ic and ci cle geome y; da a
handling and p obabili y; and logical skills (CEA, 2024). The NBT Ma hema ics (MAT)
assessmen employs selec - esponse i ems as mapped on o he espec i e MAT
assessmen speci ica ion ables. Responses a e sco ed ei he as igh o w ong, and
he unidimensional h ee-pa ame e (a, b, c) I em Response Theo y (IRT) model,
whe e a = i em disc imina ion, b = i em di icul y, and c = i em guessing/pseudo-
chance a e used o sco e he pe o mance o he examinee (Yen & Fi zpa ick 2006,
p. 114).
Pe o mance on he NBTs is cap u ed as a sco e ou o 100, which is u he
classi ied acco ding o h ee benchma k le els: p o icien , in e media e, and basic.
These benchma ks a e se h ough a Modi ied Ango S anda d Se ing p ocess
(Hamble on and Pi oniak 2006). Because a la ge numbe o es - ake s all in o he
in e media e band, i has been ound use ul o use he a i hme ic mean o spli his
band in o wo: uppe in e media e and lowe in e media e. Table 2 shows how hese
benchma ks a e gene ally in e p e ed.
Table 2. NBT MATHEMATICS Benchma k Le els (ex ac ed om P ince 2016, p. 26)
P o icien
Pe o mance sugges s ha academic pe o mance will no
be ad e sely a ec ed, and s uden should be able o cope
wi h he demands o egula p og ammes o s udy.
In e media e Uppe
Challenges exis such ha academic p og ess will be
a ec ed. S uden s a e likely o need complemen a y suppo
(addi ional u o ials, wo kshops, augmen ed cou ses,
language in ensi e wo k).
In e media e Lowe
Challenges exis such ha academic p og ess will be
a ec ed. S uden s need o be placed in an ex ended deg ee
p og amme.
Basic
Se ious challenges exis , and s uden s a e unlikely o cope
wi h uni e si y s udy.
In his pape , we in es iga e he ela ionship be ween s uden s’ achie emen on he
NSC and NBT MAT assessmen s, on he one hand, and hei academic s anding
and pe o mance in enginee ing s udy, on he o he . Academic s anding is measu ed
a he end o i s yea , whe e a s uden has ei he d opped ou (DROP) o is s ill
busy s udying (BUSY), and he end o ou and six yea s, whe e a s uden may also
ha e g adua ed (GRAD).
One-way analysis o a iance (ANOVA) was used o de e mine he ela ionship
be ween academic s anding (a e one, ou and six yea s) and pe o mance on he
NSC and NBT Ma hema ics assessmen s. S ack ba cha s and Chi-squa ed es s o
independence we e used o de e mine he ela ionship be ween academic s anding
(a e one, ou , i e and six yea s) and NSC and NBT Ma hema ics le els.
Analysis is unde aken on one coho o enginee ing s uden s o e a pe iod o six
yea s. This coho consis s o 525 i s - ime en e ing s uden s in an enginee ing
acul y a a highe educa ion ins i u ion in Sou h A ica.
3 RESULTS
O he 525 s uden s, 437 (83.2%) achie ed he NSC Ma hema ics wi h sco es ha
we e a ed a Le el 7 (80 – 100%). In con as , on he NBT MAT, only 18.1% o he
incoming s uden s achie ed ‘p o icien ’ NBT MAT sco es. The majo i y, 81.9%, had
sco es in he In e media e and Basic bands. O mo e conce n, 37.7% had sco es in
he Lowe In e media e and Basic p o iciency bands.
Table 3. Pe o mance on he NSC MATHEMATICS Tes
NSC Ma hema ics Le el
N = 525
5
11 (2.1)
6
77 (14.7)
7
437 (83.2)
Table 4. Pe o mance on he NBT MATHEMATICS Tes
Ma hema ics P o iciency
N = 525
Basic
13 (2.5)
In e media e Lowe
185 (35.2)
In e media e Uppe
232 (44.2)
P o icien
95 (18.1)
As can be seen in Table 5, nea ly a qua e (23.2%) o he coho d opped ou a he
end o i s yea and jus mo e han a qua e (26.5%) o he coho g adua ed in he
egula ion ime o ou yea s, by which ime d op ou had inc eased o 30.9%. A he
end o egula ion ime plus one yea , 48.8% o he coho had g adua ed while a he
end o egula ion ime plus wo yea s, 60.4% o he coho had g adua ed. A he end
o egula ion ime plus wo yea s ou s uden s who had p e iously d opped ou had
e u ned and we e ei he s ill busy o had g adua ed.
Table 5. Academic s anding a he end o i s yea (AS1), egula ion ime (ASn – ou yea s),
egula ion ime plus one yea (ASn1 – i e yea s) and egula ion ime plus wo yea s (ASn2 –
six yea s)
Cha ac e is ic
AS1 N = 525
ASn N = 525
ASn1 N = 525
ASn2 N = 525
GRAD
0 (0.0)
139 (26.5)
256 (48.8)
317 (60.4)
BUSY
403 (76.8)
224 (42.7)
109 (20.8)
50 (9.5)
DROP
122 (23.2)
162 (30.9)
160 (30.5)
158 (30.1)
One-way ANOVA was done o he NSC Ma hema ics sco es (Fig. 1a) as well as o
he NBT Ma hema ics sco es (Fig. 1b). This analysis e eals ha he e is a
signi ican di e ence in mean alues [F(2, 522) = 55.13, p = 0.000] o he NSC
Ma hema ics assessmen sco es ac oss he h ee academic s anding g oups a e
ou yea s. Fig. 1b shows he esul s o a Tukey HSD es o di e ence be ween he
means. The e was a s a is ically signi ican di e ence be ween all pai s o g oups.
This can be seen in he ac ha all 95% con idence in e als do no con ain he
alue ze o, indica ing ha he di e ences a e signi ican . Simila esul s we e
ob ained o he NBT Ma hema ics assessmen sco es [F(2, 522) = 52.3, p = 0.000]
ac oss he h ee academic s anding g oups a e ou yea s.
A he end o six yea s, one-way ANOVA was done o he NSC Ma hema ics sco es
(Figu e 2a) and o he NBT Ma hema ics sco es (Figu e 2b). This analysis e eals
ha he e is a signi ican di e ence in mean alues [F(2, 522) = 35.28, p = 0.000] o
he NSC Ma hema ics assessmen sco es ac oss he h ee academic s anding
g oups a e six yea s. Figu e 2a shows he esul s o a Tukey HSD es o
di e ence be ween he means. The e was a s a is ically signi ican di e ence
be ween wo o he h ee pai s o g oups. This can be seen in he ac ha all bu he
di e ence be ween BUSY and GRAD had 95% con idence in e als ha do no
con ain he alue ze o, indica ing ha he di e ences a e signi ican . Simila esul s
we e ob ained o he NBT Ma hema ics assessmen sco es [F(2, 522) = 30.32, p =
0.000] o he NBT Ma hema ics assessmen sco es ac oss he h ee academic
s anding g oups a e six yea s. Howe e , in his ins ance, he di e ence be ween
DROP and BUSY was no s a is ically signi ican . This can be seen in he ac ha
he 95% con idence in e al con ains he alue ze o, indica ing ha he di e ences
a e no signi ican .
Fig. 1a. Di e ences be ween mean NSC
Ma hema ics sco es o Academic S anding
ca ego ies a e ou yea s (wi h 95%
con idence in e als)
Fig. 1b. Di e ences be ween mean NBT
Ma hema ics sco es o Academic S anding
ca ego ies a e ou yea s (wi h 95%
con idence in e als)
Fig. 2a. Di e ences be ween mean NSC
Ma hema ics sco es o Academic S anding
ca ego ies a e six yea s (wi h 95%
con idence in e als)
Fig. 2b. Di e ences be ween mean NBT
Ma hema ics sco es o Academic S anding
ca ego ies a e six yea s (wi h 95%
con idence in e als)
Figs. 3a and 3b a e s ack ba cha s o NSC Ma hema ics le els and NBT
Ma hema ics p o iciency le els e sus Academic S anding a he end o egula ion
ime ( ou yea s). In Fig. 3a, i can be seen ha G adua ion inc eased om le el 5 o
le el 7 while D opou dec eased o e hese le els. In Fig. 3b, i can be seen ha
g adua ion inc eased om lowe in e media e le el o p o icien (basic is an
excep ion, due o he low numbe s in his ca ego y), while d opou dec eased as
NBT Ma hema ics pe o mance inc eased om lowe in e media e o p o icien .
Figs. 4a and 4b a e s ack ba cha s o NSC Ma hema ics le els and NBT
Ma hema ics p o iciency le els e sus Academic S anding a he end o egula ion
ime plus wo yea s (six yea s). In Fig. 4a, i can be seen ha g adua ion inc eased
om le el 5 o le el 7 while d opou dec eased ac oss hese le els. In Fig. 4b, i can
be seen ha g adua ion inc eased om basic le el o p o icien while d opou
dec eased as pe o mance on he NBT MAT inc eased om basic o p o icien
le els.
Fig. 3a. Academic S anding ca ego ies by
NSC Ma hema ics p o iciency a he end o
ou yea s (X-squa ed = 40.202, d = 4, p-
alue = 3.932e-08)
Fig. 3b. Academic S anding ca ego ies by
NBT Ma hema ics p o iciency bands a he
end o ou yea s (X-squa ed = 80.688, d =
6, p- alue < 2.576e-15)
Fig. 4a. Academic S anding ca ego ies by
NSC Ma hema ics p o iciency bands a he
end o six yea s (X-squa ed = 38.646, d =
4, p- alue = 8.243e-08)
Fig. 4b. Academic S anding ca ego ies by
NBT Ma hema ics p o iciency bands a he
end o six yea s (X-squa ed = 47.615, d =
6, p- alue = 1.411e-08)
4 DISCUSSION AND CONCLUSIONS
The indings indica e a s ong co ela ion be ween s uden s' ma hema ics p o iciency
and hei likelihood o pe sis ence and g adua ion in enginee ing p og ammes.
S uden s wi h an NSC Ma hema ics le el 5 ace a high isk o d opping ou , wi h
p obabili ies o 82%. Simila ly, hose a he NBT Ma hema ics Basic le el ha e a
d opou p obabili y o 46.2%. In con as , s uden s wi h an NSC Ma hema ics le el 7
demons a e a 29.7% likelihood o g adua ing in egula ion ime and a 65% chance
wi hin he ex ended pe iod o six yea s, while hose wi h a P o icien NBT
Ma hema ics le el exhibi signi ican ly highe success a es—60% wi hin egula ion
ime and 87.4% wi hin he ex ended ime. These esul s unde sco e he c i ical ole
o ma hema ical compe ency in enginee ing educa ion, emphasizing bo h cogni i e
and a ec i e ac o s. To enhance s uden success, ins i u ions should be esponsi e
o he ma hema ical needs o s uden s iden i ied h ough he NSC and NBT
Ma hema ics assessmen s. Tsui and Khan (2023) highligh s he need o be e
in eg a ion o ma hema ics eaching wi hin enginee ing cu icula o suppo s uden
e en ion and unde s anding. The in o ma ion in Table 2 also sugges s ha
ins i u ions need o implemen inno a i e eaching s a egies such as u o ials and
wo kshops ha in eg a e ma hema ical p inciples wi h enginee ing applica ions,
os e ing bo h concep ual unde s anding and p ac ical p oblem-sol ing skills.
REFERENCES
Bischo , G., Zwöl e , A., & Rubeša, D. (2015). Co ela ion be ween enginee ing
s uden s’ pe o mance in ma hema ics and academic success. 122nd ASEE Annual
con e ence and exposi ion. Ame ican Socie y o Enginee ing Educa ion,
Washing on D.C.
Bohlmann, C. and B aun, M. (2006). Cogni i e Academic Ma hema ics P o iciency,
in G iesel, H. (ed) Access and En y Le el Benchma ks, he Na ional Benchma k
Tes s P ojec , 35-41. A ailable a :
h p://www.hesa.o g.za/si es/hesa.o g.za/ iles/2006_HESA_Access and En y Le el
Benchma ks.pd (Accessed 24 Feb ua y 2015).
Bohlmann, C., P ince, R. and Deacon, A. (2017). Ma hema ical E o s Made by High
Pe o ming Candida es W i ing he Na ional Benchma k Tes s. Py hago as. 38. pp. 1
– 10.
Cen e o Educa ional Assessmen s (CEA). (2024). The Na ional Benchma k Tes s
Na ional Repo : 2024 In ake Cycle Da a Repo . Cape Town: Cen e o Educa ional
Assessmen s. A ailable a : h ps://www.nb .ac.za/con en /na ional- epo -2024
(Accessed 24 Feb ua y 2025).
CHE. (2013). A p oposal o unde g adua e cu iculum e o m in Sou h A ica: The
case o a lexible cu iculum s uc u e. A ailable a :
h p://www.che.ac.za/si es/de aul / iles/publica ions/Full_Repo .pd (Accessed 21
May 2025).
de Win e , J. C. F., & Dodou, D. (2011). P edic ing academic pe o mance in
enginee ing using high school exam sco es. In e na ional Jou nal o Enginee ing
Educa ion, 27(6), 1343–1351
Depa men o Basic Educa ion. (2009). Na ional examina ions and assessmen .
Repo on he Na ional Senio Ce i ica e examina ion esul s 2009. P e o ia: DBE.
A ailable a :
h p://www.educa ion.go .za/LinkClick.aspx? ile icke =l3hlVk9sypk%3d& abid=92&po
alid=0&mid=4359& o cedownload= ue. (Accessed 28 Feb ua y 2025).
DBE. (2011). Na ional Cu iculum S a emen (NCS) Cu iculum and Assessmen
Policy S a emen : G ades 10‒12 (Gene al): Ma hema ics. P e o ia: Depa men o
Basic Educa ion.
G ayson, J. M., Wood, T. A., Robinson, R. J. M., Plumblee, J. M., & P ince-Nelson,
S. (2018). The In luence o Ma hema ical P epa edness on S uden Pe o mance in
an Enginee ing S a ics Cou se. ASEE Sou heas e n Sec ion Con e ence.
