Making Better Decisions
on Placement in
Mathematics Courses
W. Robert Stephenson
Iowa State University
1
Outline
 ALEKS
 Logistic Regression
 Calculus I (MATH 165)
 Introductory Statistics
(STAT 101/104)
2
ALEKS
 Assessment and Learning in
Knowledge Spaces
 Online, adaptive assessment
 Assesses mastery in eight
areas of mathematics
3
ALEKS
Equations and Inequalities
Exponentials and Logarithms
Exponents and Polynomials
Geometry and Trigonometry
4
ALEKS
Linear and Quadratic
Equations
Radical Expressions
Rational Expressions
Real Numbers
5
ALEKS
6
ALEKS
 The ALEKS score is the
weighted combination of the
8 sub-scores.
 Scores range from 0 to 100.
7
Prediction
We wish to use the ALEKS
score to predict the
probability of “success” in a
mathematics or statistics
course.
8
“Success”
 A– or better
 B– or better
 C– or better
 PASS (D– or better)
9
Logistic Regression
Prob(Success) = p
Prob(Failure) = 1 – p
Simple Logistic Model
𝑝
𝑙𝑜𝑔
= α + 𝛽𝑥
1−𝑝
10
Logistic Regression
Use maximum likelihood
estimation to obtain
estimates: 𝛼 and 𝛽.
𝛼+
𝛽𝑥
𝑒
𝑝=
1 + 𝑒 𝛼+ 𝛽𝑥
11
Calculus I
1,099 students who took
MATH 165 fall 2011.
72% Frosh, 28% Soph
ALEKS
mean: 72.95, std dev: 14.92
12
Calculus I
ALEKS Score
13
Calculus I
Letter Grade
14
Calculus I
15
Calculus I
0.7955
0.7163
0.4484
0.1696
16
Calculus I
There is fairly good agreement
between the predicted
probabilities of “success” and
the observed probabilities, with
the possible exception of A– or
better.
17
Calculus I
Using ALEKS for placement
recommendations seems
reasonable.
Current recommendation:
ALEKS of 65 or greater.
18
Intro Statistics
156 students who took
STAT 101/104.
CLAS: 59%, CALS: 25%
ALEKS
mean: 50.1, std dev: 23.28
19
Intro Statistics
ALEKS Score
20
Intro Statistics
Letter Grade
21
Intro Statistics
22
Intro Statistics
0.7955
0.7163
0.4484
0.1696
23
Intro Statistics
There is not as good agreement
between the predicted
probabilities of “success” and
the observed probabilities as
there is when using ALEKS
with Calculus I.
24
Intro Statistics
Using ALEKS for placement
recommendations is not as
accurate for Introductory
Statistics.
Current recommendation:
ALEKS of 35 or greater.
25
Sub-scores
The 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.
26
Predicting PASS
The use of the sub-score for
rational expressions does a
better job of predicting the
probability a student passes
an introductory statistics
course.
27
Intro Statistics
Rational Expressions sub-score
28
Rational Expressions
0.9592
0.9338
29
Intro Statistics
Use the Rational Expressions
sub-score for placement in an
introductory statistics course
Suggested recommendation:
Rational Expressions subscore of 20 or greater.
30