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Making Better Decisions on Placement in
Mathematics Courses
W. Robert StephensonIowa State University
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Outline ALEKS Logistic Regression Calculus I (MATH 165) Introductory Statistics
(STAT 101/104)
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ALEKS Assessment and Learning in
Knowledge Spaces Online, adaptive assessment Assesses mastery in eight
areas of mathematics
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ALEKSEquations and InequalitiesExponentials and
LogarithmsExponents and PolynomialsGeometry and Trigonometry
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ALEKSLinear and Quadratic
EquationsRadical ExpressionsRational ExpressionsReal Numbers
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ALEKS
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ALEKS The ALEKS score is the
weighted combination of the 8 sub-scores.
Scores range from 0 to 100.
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PredictionWe wish to use the ALEKS
score to predict the probability of “success” in a mathematics or statistics course.
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“Success” A– or better B– or better C– or better PASS (D– or better)
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Logistic RegressionProb(Success) = pProb(Failure) = 1 – pSimple Logistic Model
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Logistic RegressionUse maximum likelihood
estimation to obtain estimates: .
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Calculus I1,099 students who took
MATH 165 fall 2011.72% Frosh, 28% SophALEKS
mean: 72.95, std dev: 14.92
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Calculus I
50
100
150
Cou
nt
20 30 40 50 60 70 80 90 100
ALEKS Score
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Calculus I
25%
29%
22%
7%9% 8%
50
100
150
200
250
300
350
Co
unt
A B C D F X
Letter Grade
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Calculus ILe
tter
Gra
de
0.00
0.25
0.50
0.75
1.00
< 5
0
50 t
o 6
0
60 t
o 7
0
70 t
o 8
0
80 t
o 9
0
90 t
o 1
00
ALEKS Category
A
B
C
D
F
X
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Calculus I
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pred
icte
d P
rob
abili
ty
0 10 20 30 40 50 60 70 80 90 100ALEKS
Y A– or better B– or better C– or better PASS
0.7955
0.7163
0.4484
0.1696
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Calculus IThere is fairly good agreement
between the predicted probabilities of “success” and the observed probabilities, with the possible exception of A– or better.
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Calculus IUsing ALEKS for placement
recommendations seems reasonable.
Current recommendation: ALEKS of 65 or greater.
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Intro Statistics156 students who took STAT
101/104.CLAS: 59%, CALS: 25%ALEKS
mean: 50.1, std dev: 23.28
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Intro Statistics
5
10
15
Co
un
t
0 10 20 30 40 50 60 70 80 90 100 110
ALEKS Score
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Intro Statistics
29%
40%
19%
5%2%
4% 10
20
30
40
50
60
70
Cou
nt
A B C D F XLetter Grade
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Intro StatisticsLe
tter
Gra
de
0.00
0.25
0.50
0.75
1.00
< 30 30 to 40 40 to 50 50 to 60 60 to 80 80 to 100
ALEKS Category
A
B
C
D
FX
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Intro Statistics
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pre
dic
ted P
robab
ility
0 10 20 30 40 50 60 70 80 90 100ALEKS TOTAL
Y A- or better B- or better C- or better PASS
0.7955
0.7163
0.4484
0.1696
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Intro StatisticsThere is not as good
agreement between the predicted probabilities of “success” and the observed probabilities as there is when using ALEKS with Calculus I.
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Intro StatisticsUsing ALEKS for placement
recommendations is not as accurate for Introductory Statistics.
Current recommendation: ALEKS of 35 or greater.
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Sub-scoresThe ALEKS score is a weighted
average of the 8 area sub-scores.Some of the areas may have
little to do with prerequisite knowledge for success in introductory statistics.
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Predicting PASSThe use of the sub-score for
rational expressions does a better job of predicting the probability a student passes an introductory statistics course.
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Intro Statistics
10
20
30
40
Count
0 10 20 30 40 50 60 70 80 90 100 110Rational Expressions sub-score
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Rational Expressions
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Pre
dic
ted P
robab
ility
0 10 20 30 40 50 60 70 80 90 100Ratl
Y PASS Ratl PASS Ratl 2
0.9592
0.9338
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Intro StatisticsUse the Rational Expressions
sub-score for placement in an introductory statistics course
Suggested recommendation: Rational Expressions sub-score of 20 or greater.