A study of the correlation between maths grades in Danish secondary schools and the grades in four mathematically oriented subjects in the computer science undergraduate programme at Aalborg University.

1. An Analysis of Grades in the Computer Science and
Software Degree Programmes
20 August 2014
Hans Hüttel1 and Mikkel Meyer Andersen2
1Department of Computer Science
2Department of Mathematical Sciences
Aalborg University
Denmark

2. Part I
Background

3. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
A cause for concern
In 2012 there was concern about increasing failure rates in
certain courses in the degree programmes in computer science
and software. These were
I Discrete Mathematics (2nd semester) (DM)
I Algorithms and Data Structures (3rd semester) (AD)
I Syntax and Semantics (4th semester) (SS)
I Computability and Complexity (5th semester) (BK)
Is there a pattern to these observations? Is it
connected to the backgrounds of students?

4. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
The four upper secondary education pro-grammes
in Denmark
I The STX and HF programmes consist of a broad range of
subjects in the fields of the humanities, natural science
and social science.
I The HHX programme focuses on business and
socio-economic disciplines in combination with foreign
languages and other general subjects.
I The HTX programme has its focus on technological and
scientific subjects in combination with general subjects.
There are 146 schools with STX and/or HF, 60 offering HHX
and 38 with HTX.

5. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Admission requirements
I Prospective students must have passed certain subjects,
including the level A course in maths, in order to be
admitted to our degree programmes in computer science
and software.
I In each of the secondary programmes, prospective
students will have received four grades in each subject
I To pass, the mean of these four grades must be at least 2.
Thus, you can pass if you receive e.g. the grades 4, 02, 02
and 00 in maths.

6. The AAU system
for registering
student data
24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
The data material
We have obtained our data material from STADS.
I 287 students have information about maths grades from
high school
I 138 students have complete CS/SW grade information
(DM, AD, SS, BK)
I 52 students overlap (high school grades and complete
CS/SW grades)
All students are enrolled in the current version of our degree
programmes (post-2010).
Until 2012 no information was available concerning high school
grades.

7. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
What are we analyzing?
We consider the following derived information.
MATHS denotes the mean of all 4 high school maths
grades
GotU is set to Yes if, at any time, the grade ’U’
(no-show at exam) was given in CS/SW courses
(DM, AD, SS, BK), else No
Failed is set to Yes if, at any time, a grade -3 or 00 was
given in CS/SW courses (DM, AD, SS, BK), else
No

8. Part II
Do students’ secondary school grades matter?

9. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Where do students come from?
n Percent
HF 6 2.1
HHX 8 2.8
HTX 179 62.4
STX 94 32.8
HF
HHX
HTX
STX
2 4 6 8 10 12
MATH
No significant difference between mean of MATHS for STX and HTX.

10. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
A connection with failure/no-show?
All 287 students (some had not passed all 4 courses that we
consider):
●
No Yes
2 4 6 8 10 12
GotU
MATH
No Yes
2 4 6 8 10 12
Failed
MATH
GotU Mean Median SD Q025 Q975
No 7.25 7.62 2.90 2 12.00
Yes 5.07 5.00 2.15 2 10.55
Failed Mean Median SD Q025 Q975
No 7.35 7.75 2.73 2.40 12
Yes 5.93 6.00 2.97 1.68 12
Two-sided t tests for H0 of equal means in both tables are statistically significant.

11. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
School grades vs. failure at AAU
Only 52 students with complete data (none of which had a U):
●
●
No Yes
2 4 6 8 10 12
Failed
MATH
Failed Mean Median SD Q025 Q975
No 8.60 8.50 2.16 3.53 12
Yes 6.02 5.75 2.81 2.50 12
Two-sided t test for H0 of equal means is statistically significant.

12. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
School grades vs. average grade
HF
HHX
HTX
STX
−2 0 2 4 6 8 10 12
CS/SE grade mean
n = 52

13. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Correlations
Variable 1 Variable 2 n Correlation p value
MATHS DM 239 0.515 < 1010
MATHS AD 125 0.408 2.3 · 106
MATHS SS 117 0.414 3.4 · 106
MATHS BK 53 0.597 2.4 · 106

14. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Conditional independence
This model is based on students with complete information, i.e.
n = 52.
GradeDM
GradeBK
MATH
GradeSS
GradeAD
MATHS and (SS, AD) are conditionally independent given DM and BK.

15. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
What if we had restricted admission?
A cut-off at grade 4:
MATHS 4 (20%) MATHS 4 (80%)
Failed No 26 159
Yes 31 71
54% of those with MATHS 4 failed and 31% of those with MATHS 4 failed.
A cut-off at grade 7:
MATHS 7 (48%) MATHS 7 (52%)
Failed No 75 110
Yes 62 40
45% of those with MATHS 7 failed and 27% of those with MATHS 7 failed.
Both contingency tables are statistically significant according to Fisher’s exact test.

16. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
What if we had restricted admission?
Comparison of average grades in the four courses (n = 52)
FALSE
TRUE
−2 0 2 4 6 8 10 12
MATH = 4
CS/SE grade mean
●●
FALSE
TRUE
−2 0 2 4 6 8 10 12
MATH = 7
CS/SE grade mean)
CS/SW grade mean Mean Median SD Q025 Q975
MATHS 4 1.56 1.50 2.29 -1.37 4.83
MATHS = 4 5.91 5.88 3.55 -0.19 11.46
MATHS 7 2.37 2.00 2.05 -1.16 5.8
MATHS = 7 6.89 7.75 3.47 -0.30 11.5

17. Part III
Computer Science vs. Software

18. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Course grades
DM Mean Median SD Q025 Q975
CS 5.84 5.5 3.58 0 12
SW 4.56 4.0 3.86 0 12
AD Mean Median SD Q025 Q975
CS 3.36 2 3.66 0 12
SW 2.99 2 3.53 0 10
SS Mean Median SD Q025 Q975
CS 7.13 7 3.82 0 12
SW 6.29 7 4.49 -3 12
BK Mean Median SD Q025 Q975
CS 6.45 7 4.30 0 12
SW 5.13 7 4.82 -3 12
No statistically significant mean difference.

19. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
An overall picture
Overall Mean Median SD Q025 Q975
CS 5.70 4 4.08 0 12
SW 4.74 4 4.35 -3 12
The difference of the means of 0.954 now becomes statistically
significant (p = 0.009). Mean difference 95% confidence
interval is [0.24; 1.67].

20. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Conditional independence
GradeDM
GradeSS
GradeAD
GradeBK
Note the same structure as before, where MATHS was
included. This is a different sample of students (with complete
grades for DM, AD, SS and BK).

21. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Pairwise correlations
Variable 1 Variable 2 n Correlation
DM AD 138 0.638
DM SS 138 0.667
DM BK 138 0.608
AD SS 138 0.620
AD BK 138 0.544
SS BK 138 0.817
All correlations statistical significant different from 0 with p value 1010.

22. Part IV
Some tentative conclusions

23. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
Some observations
I Data analyses based on data from STADS can be quite
revelatory!
I Maths grades from secondary school do matter both with
respect to failure and average grades.
I The independence model points towards there being a
separate problem for the Algorithms and Data Structures
course.

24. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
What we cannot (and should not) do
I We cannot do anything about whatever happens in the
Danish secondary school system.
I We cannot blame the course Discrete Mathematics for
whatever problems we may see.

25. 24
An Analysis of Grades
Hans Hüttel and Mikkel
Meyer Andersen
Aalborg University
Denmark
What we might want to do
I Ensure a notion of progression through a collaborative,
long-term joint effort by the lecturers involved in the
courses.
I Actively discourage students with low maths grades from
applying.
Do we want a notion of restricted admission?
I Conduct qualitative interviews to find out more about the
underlying rationales.
I Use data from STADS to perform other data analyses.
Should we include an analysis of drop-out rates? !
(Probably.)

26. A quote from the report
Undersøgelse af frafaldet på datalogiuddannelserne
(SFI, 2009)
All groups [focus groups comprised of drop-outs and MSc
students] compare computer science with medical
school. Medicine has a reputation as being a demanding
degree programme, and it is difficult to be admitted to the
programme is difficult. Because of this you know that you
have to work hard in order to finish your degree.
Entrance to the computer science programmes is easy,
no-one is aware of what the studies really imply and
therefore one has no expectations wrt. what is really
required of you. The participants therefore suggest a
change of the image that the degree programmes in
computer science have. If one knows that getting a
computer science degree is just as demanding as getting
a degree in medicine, more people will realize right from
the start that they do not have what it takes.
(My translation)