Running head: MATH LEVELS AND COMPUTER SCIENCE
Math Levels of Computer Science Students
Rick Fillman
Institutional Research Analyst
Planning and Research Office
June 2012
MATH LEVELS OF COMPUTER SCIENCE
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Introduction
The Computer Science (CS) faculty is considering a change to the
course prerequisites for CS-11 (Introduction to Programming Concepts
and Methodology, C++) and CS-12J (Introduction to Programming
Concepts and Methodology, Java). At present the recommended
preparation for both courses lists “Eligibility for ENGL 100 and READ
100” and “Recommended Preparation: CS-1 and MATH-154”
(Elementary Algebra). The faculty are considering changing the
current recommended prep to a prerequisite of Math-152
(Intermediate Algebra).
Note that a prerequisite of MATH-152 would require that students
complete, or demonstrate mastery of, both Elementary and
Intermediate Algebra prior to enrolling in these CS courses. If such a
prerequisite were instituted, how many students might be impacted?
Would course success rates increase?
Methodology
Student records for eight years of enrollments in these Computer
Science courses were gathered. Students’ math levels at the time of
the student’s first enrollment1 in either CS-11 or CS-12J were
determined. These students become the focus of this research.
Math levels are determined by assessment/placement score,
satisfactory completion of an equivalent course elsewhere, or by
satisfactory completion of a course in the Cabrillo mathematics
sequence. Data from assessment/placement scores and equivalencies
from other institutions were gathered from the Datatel student
information system. Data for Cabrillo math enrollments where the
student successfully completed a Math course (grade of “A”, ”B”, “C”
or P”) are assembled from the Cabrillo research data warehouse.
These data are chronologically aligned with the CS course enrollments,
and the student’s math level at the time of the CS enrollment is
determined by the most recently completed Math course prior to the
term of the CS enrollment. In cases where there is no satisfactory
math completion record (the student didn’t take math at Cabrillo, or
did and received a grade of D, F, or W), then the students’
assessment/placement and/or equivalency level, if available, is used to
1
Repeat enrollments in CS courses are excluded from the analysis. The repeat rate for the time
period studied is about 8.9% for CS -11, and about 5.4% for CS-12J.
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determine the math level. For this study, the math level of some
students could not be determined. This occurs in cases where a
student never attempts to enroll in a math course at the college, or for
some reason never undergoes assessment/placement in math. Under
the proposed prerequisite, these students would be required to
undergo assessment, so their status could be determined.
How would enrollment in CS courses be affected?
If Math-152 Intermediate Algebra was established as a prerequisite for
these CS courses, about 80% of first-time enrollees both CS-11 and
CS-12J would clearly have met the hypothetical prerequisite by the
time of their enrollment in CS. This leaves possibly one in five
students whose course enrollment might be precluded or delayed, if
such a prerequisite were established.
The chart below shows the number of students who would have met or
not met this hypothetical prerequisite at the time of their first
enrollment in CS-11 or CS-12J, respectively. These data are compiled
from eight years of enrollment records from academic years 2003-04
through 2010-11.
Historical percentage of students meeting or not meeting
a hypothetical Intermediate Algebra prerequisite for CS
Headcount Percent
CS-11
Prereq. met
749
80.2%
Prereq. not met
78
8.4%
Prereq. status unknown
107
11.5%
Headcount Percent
CS12J
Prereq. met
744
79.6%
Prereq. not met
76
8.1%
Prereq. status unknown
115
12.3%
Disproportionate Impact
When considering ethnicity and gender balance in these courses, it is
helpful to review the extent to which the profile of CS students
diverges from the profile of the overall college population. Although
Latinos constitute in excess of 30% of the Cabrillo College student
body and females constitute more than 52% of students, participation
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rates for these groups in CS courses is much lower. The chart below
shows participation of these groups in the two CS courses studied.
Actual partipation rates in CS Courses
CS-11
18%
18%
Latino
Female
CS12-J
13%
21%
The introduction of the hypothetical prerequisite would likely not alter
these proportions. In other words, when the ethnic and gender
breakout of students who meet or do not meet the hypothetical are
examined, though differences among the groups is observed, the
differences are not statistically significant. The potential for
disproportionate impact appears small. Percentages of students by
under-represented status and by gender who would have met/not met
the hypothetical Math-152 prerequisite are included in Appendix A.
Does transfer-math readiness affect success in CS?
Intermediate Algebra is the so-called ‘gate-keeper’ course for transfer
level math. If students were required to successfully complete this
course before enrolling in these CS courses, would course success
increase?
Overall, for the eight years studied, the course success rate2 for
students in CS-11 is 50.9% and the course success rate for CS-12J is
51.2%. When calculated separately for the group that met the
hypothetical prerequisite as opposed to those who did not, students
who have completed Intermediate Algebra are more successful.
However, an analysis of the variance reveals that the observed
increase is statistically significant only for the CS-11 students. The
higher levels of course success in CS-12J are possibly due to chance. 3
2
Ratio of students receiving a grade of A, B, C, or Pass to the number enrolled on
the census roster.
3
For CS11 p value = .000; for CS-12J p value =.168.
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Course success rate by Intermediate Algebra completion
Hypothetical Algebra
prerequisite met?
Prereq. met
Prereq. not met
Prereq. status unknown
CS-11
Percent
55.3%
29.5%
35.5%
CS12J
Total(N)
749
78
107
Percent
56.9%
44.8%
35.0%
Total(N)
260
29
80
Though the potential increase for course success among CS-11
students is statistically significant, the explanatory power is weak,
explaining only around 3% of the variance4. Other factors, perhaps,
have a stronger predictive power.
Other factors which influence success in CS
Student success can be attributed to a mix of factors. To expand the
number of factors considered, other variables such as ethnicity, in the
form of under-represented5 or not, and students’ cumulative Cabrillo
grade point average (GPA) were added to the statistical model. Both
prove to be statistically significant in relation to success in these CS
courses, and will account for a slice of the variance.6
Comparatively, a student’s GPA is the strong predictor of success in
these CS courses. It is a stronger indicator than completion of
Intermediate Algebra. In this model, cumulative GPA accounts for
perhaps 17% of the variance in success in CS-11 and around 12% of
the variance in CS-12J. This might suggest that good study habits are
a better predictor than the level of math preparation. Following this,
the next largest accounting for variance in this model is having met
the Intermediate Algebra prerequisite. Finally, while underrepresented
status has a statistically significant inverse association with success, it
is a rather weaker indicator, accounting for just slightly over 1% of the
variance in the model.7
4
The R square value is .032 for CS-11.
Underrepresented includes Native Americans, African Americans, Filipinos, Hispanic/Latino and
Pacific Islanders, with Latino by far the most numerous of the under-represented groups.
6
The p values for GPA are .000 for both CS-11 and CS-12J; the p values for underrepresented
status are .000 for CS-11 and .035 for CS-12J.
7
The R square value for GPA is .172 for CS-11 and .119 for CS-12J; the R square value for
underrepresented status is .015 for CS-11 and .012 for CS-12J.
5
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Taking a broader a look at math levels
Thus far, this report has addressed the question of establishing a
hypothetical prerequisite, which frames the question in binary terms
(yes or no) around a specific level in the math sequence. The weaker
than expected explanatory power of meeting or not meeting this
hypothetical prerequisite may be related to the fact that the question
is very specific. Students at all levels of math are enrolling in CS
courses. If the methodology were altered to consider the array of
math levels of individual students, would math preparedness emerge
as a stronger predictor of success in Computer Science?
When a scalar variable for math level8 used in place of the binary
met/not met the hypothetical Intermediate Algebra prerequisite, math
preparation now emerges as a more powerful predictor of success for
students in CS-11 (C++), explaining about 10% of the variance in
success. However, this is less so for students in CS-12J (Java), where
the explanatory power is about 3.6% of total variance.9
The chart in Appendix B shows success CS-11 and CS-12 according to
math level. It is interesting to note that the math level associated
with the tipping point – the point where the success in CS-11 and CS12J start to reliably exceed 50%, is one level above transfer-level for
CS-11, and transfer-level for CS-12J.
Throughout this report, the observed association between math
preparedness and success is stronger for C-11 (C++ programming)
than for CS-12J (Java programming.) One is tempted to develop
hypotheses as to what accounts for this difference. Is the C++
programming language more mathematical? Or are other factors are
work? These are questions for future research.
Summary
Instituting a prerequisite of Intermediate Algebra for CS-11 and CS12J
would reduce enrollment by up to 20% in the short term, but would
not likely have a disproportionate impact on participation rate of
under-represented students or of females. Even though Intermediate
Algebra completion is correlated with success in CS-11 (though not
8
Math levels consist of 3 levels below transfer level, transfer or college entry-level, and five other
levels which represent the math sequence as determined by the prerequisite hierarchy. For
reference, Math-152 (Intermediate Algebra) is one level below transfer.
9
With scalar math levels, the R square values are .100 for CS-11 and .036 for CS-12J.
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CS-12J), multivariate statistical analysis reveals that Algebra
completion has a relatively small predictive value (not significant for
CS-12J), and that general academic preparedness is a stronger
predictor of success in these courses. When the statistical model is
reconfigured to use across-the-board math levels, then a rather strong
correlation between math preparation and success emerges for CS-11,
less so for CS-12J.
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Appendix A
CS‐11 student ethnicity by math level
Hypothetical prerequisite
Under‐represented
not
Met
22.4%
70.1%
Not‐met
26.9%
65.4%
p= 0.357
CS‐12J student ethnicity by math level
Hypothetical prerequisite
Female
Male
Met
20.4%
70.8%
Not‐met
31.0%
51.7%
p= 0.098
CS‐11 student gender by math level
Hypothetical prerequisite
Under‐represented
not
Met
18.3%
81.7%
Not‐met
12.8%
87.2%
p= 0.230
CS‐12J student gender by math level
Hypothetical prerequisite
Female
Male
Met
18.5%
80.8%
Not‐met
13.8%
86.2%
p= 0.525
Appendix B
Success in CS‐11 and CS12‐J by math level
Student's math 3 l evels 2 l evel s 1 l evel s Tra ns fer 1 l evel s 2 l evel s 3 l evel s 4 l evel s 5 l evel s bel ow bel ow bel ow
Level
a bove
a bove
a bove
a bove
a bove
level Success in CS11
15.4% 31.7% 41.5% 44.6% 66.3% 75.3% 69.1% 82.2% 89.5%
Tota l hea dcount (N)
Success in CS12J
Tota l hea dcount (N)
13
63
188
251
98
77
81
45
19
16.7% 50.0% 45.9% 54.6% 64.5% 73.9% 72.7% 66.7% 100.0%
6
22
74
108
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