Is mathematics a barrier for engineering?

Figures & data

Figure 1. Proportion of mathematics enrolment in year 12. Based on data from Wienk (2022).

Table 1. List of variables in the data.

Variable	Description
Gender	Gender of student (Male or Female)
Citizenship	Citizenship status (Domestic or International)
Age	Age of students, categorised into 16–17, 18, 19, 20, 21, 22–25, 25+
Status	The status of the students progression (Inactive, Discontinued, Enrolled or Completed)
Standing	University assessment of eligibility to continue studying (Exclusion, Expulsion, Probation, Goodstand)
WAM	Weighted Average Mark as a percentage, average mark achieved across all units completed in the course
MATH1001	Mark (%) obtained in the MATH1001 core mathematics unit
MATH1002	Mark (%) obtained in the MATH1002 core mathematics unit
UniHighM	Mark (%) obtained in their highest level of university mathematics unit
UniLevel	Highest level of university mathematics unit the student had taken (1, 2 or 3 year level)
Repeat	An indicator for whether the student has repeated a university maths unit
NoU	Number of units of mathematics completed during university (2,3,4,5,6+)
MPE	An indicator for whether the student has completed Masters of Professional Engineering (0 or 1)
UG	An indicator for whether the student has completed any undergraduate bachelor course (0 or 1)
EngUG	An indicator for whether the student has completed engineering undergraduate bachelor course (0 or 1)
TER	Tertiary Entrance Rank, a numeric rank which reports the student's academic position relative to all students in the final year of schooling in Western Australia
HSLevel	Highest level of high school mathematics units the student had taken (MAS3CD, MAT3CD or MAT3AB)
HSHighM	Mark obtained in their top level of high school mathematics

Table 2. Summary of successful completion by highest level of mathematics taken in university and high school.

		Completion rate
	Variable	EngUG (%)	MPE (%)
	MAS3CD	74.8	57.9
HSLevel	MAT3CD	69.3	58.3
	MAT3AB	43.5	37.0
	3	93.7	62.5
UniLevel	2	85.3	67.6
	1	66.3	51.1

Table 3. Summary of completion by highest mathematics marks in university and high school.

		UniHighM		HSHighM
	Variable	Mean	SD	Mean	SD
MPE	Yes	70.9	12.8	73.1	9.1
	No	62.7	18.5	69.4	9.5
EngUG	Yes	70.8	13.2	73.8	8.7
	No	58.6	19.3	66.0	8.8

Table 4. Significant variables for model for WAM.

Variable	Coef	p-value
Age:22–25	−3.03	6.38e−4
Standing:Good	4.63	1.75e−2
Status:Discon	−6.33	1.18e−8
Status:Enrol	−2.35	1.13e−2
Status:Inactive	−8.36	6.08e−5
Repeat:Yes	−4.67	4.21e−16
NoU:5	−2.65	3.89e−2
NoU:6+	−4.72	6.94e−4
MATH1001	0.168	4.90e−9
MATH1002	0.264	<2e−16
TER	0.248	2.03e−12
UniHighM	0.0818	4.56e−4

Table 5. Significant variables for model with EngUG completion as response.

Variable	Coef	Exp(Coef)	P-value
WAM	0.204	1.22	<2e−16
UniLevel: 2	0.906	2.47	2.59e−2
TER	−0.06	0.94	2.75e−3
Age: 25+	−2.34	0.096	1.46e−2

Table 6. Significant variables for model with MPE as response.

Variable	Coef	Exp(Coef)	P-value
WAM	0.0939	1.1	3.15e−5
Age:19	−0.975	0.38	3.26e−3
Age:20	−0.804	0.45	3.26e−2
Age:21	−1.30	0.27	1.63e−2
Age:22-25	−3.11	0.045	2.34e−4
Citizenship: International	1.29	3.6	2.91e−2
MATH1001	−0.0420	0.96	1.53e−2
MATH1002	0.0374	1.04	1.38e−2
HSHighM	−0.0711	0.93	4.47e−5

Table 7. Loadings for first three principal components.

	PC1	PC2	PC3
Age	0.137	0.975	0.134
WAM	−0.486		−0.240
Min	−0.443	0.100	−0.476
Max	−0.443	0.184	−0.275
TER	−0.422		0.543
HSHighM	−0.418		0.573

Figure 2. Plot of PC3 against PC1. Colour indicates high school mathematics unit and plotting symbol completions status (C = completed, D = not completed).

Table 8. Completion status by high school mathematics unit.

	MAS3CD	MAT3CD	MAT3AB
Completed	207	124	28
Discontinued	35	23	14
Enrolled	18	13	4
Inactive/Intermittent	3	1	0

Figure 3. Plot of WAM against high school mathematics marks by clusters: (a) completion status by cluster and (b) high school mathematics unit by cluster.

Table 9. Summary of clusters by key variables.

	Cluster
	1	2	3
WAM
<50	0	18	46
50–60	1	63	46
60–70	20	128	2
70–80	59	123	20
>80	45	0	0
MPE
No	42	99	58
Yes	106	151	2
EngUG
No	12	71	51
Yes	136	179	9
HSLevel
MAT3AB	4	28	12
MAT3CD	32	109	13
MAS3CD	112	113	35
HSAverage
50–60	0	12	8
60–70	5	95	28
70–80	59	123	20
>80	84	20	4

Table 10. List of variables from the survey.

Variable	Description
Gender	Gender of student (Male or Female)
YrLevel	The year level of university the student is in (1st, 2nd, 3rd MPE)
IntendMPE	An indicator for whether the student intends to complete Masters of Professional Engineering (0 or 1)
IntendEngUG	An indicator for whether the student intends to complete undergraduate engineering bachelor course (0 or 1)
HSLevel	The highest level of high school mathematics units the student had taken (MAS3CD, MAT3CD or MAT3AB)
Importance	An indicator for whether the student thinks mathematics is important to engineering
CoreRelevant	An indicator for whether the student thinks the core mathematics (MATH1001, MATH1002) is relevant to engineering
Enjoyment	An indicator for whether the student enjoys mathematics
Difficult	An indicator for whether the student finds mathematics difficult
EnhanceUnderstand	An indicator for whether the student thinks mathematics helps enhance understanding of engineering concepts
CoreSufficient	An indicator for whether the student thinks the core mathematics is sufficient to their studies of engineering
AdditionalMath	An indicator for whether the student has taken or intends to take mathematics outside of their core units

Table 11. Summary of undergraduate student characteristics and completion intention.

	Number	% IntenEngUG	% IntendMPE
Gender
Males	128	96.1	78.1
Females	44	97.7	81.8
HSLevel
MAS3CD	104	98.1	79.8
MAT3CD	58	94.8	77.6
MAT3AB	10	90.0	80.0
YrLevel
1st Year	72	93.1	80.1
2nd Year	47	97.9	70.2
3rd Year	53	100.0	84.9

Figure 4. Bar graph of main mathematics attitudes questions.

Table 12. Significant variables from fitting logistic model with Importance as response.

Variable	Coef	Exp(Coef)	P-value
Relevant: Yes	3.31	27.4	7.48e−5
Enjoy: Yes	2.40	11.01	4.53e−3
Difficult: Yes	2.59	13.3	1.70e−2
EnhanceUnder: Yes	4.44	84.8	9.17e−3

Table 13. Significant variables from fitting logistic model with IntendEngUG as response.

Variable	Coef	Exp(Coef)	P-value
Enjoy: Yes	3.00	20.1	6.94e−2

Table 14. Significant variables from fitting logistic model with IntendMPE as response.

Variable	Coef	Exp(Coef)	P-value
Enjoy:Yes	1.255	3.51	2.10e−3

Wienk, M. (2022). Year 12 mathematics participation report card (Tech. Rep.). AMSI. https://amsi.org.au/wp-content/uploads/2022/04/year-12-participation-2022.pdf.

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