1 making better decisions on placement in mathematics courses w. robert stephenson iowa state...
Post on 18-Jan-2016
220 Views
Preview:
TRANSCRIPT
1
Making Better Decisions on Placement in
Mathematics Courses
W. Robert StephensonIowa State University
2
Outline ALEKS Logistic Regression Calculus I (MATH 165) Introductory Statistics
(STAT 101/104)
3
ALEKS Assessment and Learning in
Knowledge Spaces Online, adaptive assessment Assesses mastery in eight
areas of mathematics
4
ALEKSEquations and InequalitiesExponentials and
LogarithmsExponents and PolynomialsGeometry and Trigonometry
5
ALEKSLinear and Quadratic
EquationsRadical ExpressionsRational ExpressionsReal Numbers
6
ALEKS
7
ALEKS The ALEKS score is the
weighted combination of the 8 sub-scores.
Scores range from 0 to 100.
8
PredictionWe wish to use the ALEKS
score to predict the probability of “success” in a mathematics or statistics course.
9
“Success” A– or better B– or better C– or better PASS (D– or better)
10
Logistic RegressionProb(Success) = pProb(Failure) = 1 – pSimple Logistic Model
11
Logistic RegressionUse maximum likelihood
estimation to obtain estimates: .
12
Calculus I1,099 students who took
MATH 165 fall 2011.72% Frosh, 28% SophALEKS
mean: 72.95, std dev: 14.92
13
Calculus I
50
100
150
Cou
nt
20 30 40 50 60 70 80 90 100
ALEKS Score
14
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
15
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
16
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
17
Calculus IThere is fairly good agreement
between the predicted probabilities of “success” and the observed probabilities, with the possible exception of A– or better.
18
Calculus IUsing ALEKS for placement
recommendations seems reasonable.
Current recommendation: ALEKS of 65 or greater.
19
Intro Statistics156 students who took STAT
101/104.CLAS: 59%, CALS: 25%ALEKS
mean: 50.1, std dev: 23.28
20
Intro Statistics
5
10
15
Co
un
t
0 10 20 30 40 50 60 70 80 90 100 110
ALEKS Score
21
Intro Statistics
29%
40%
19%
5%2%
4% 10
20
30
40
50
60
70
Cou
nt
A B C D F XLetter Grade
22
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
23
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
24
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.
25
Intro StatisticsUsing ALEKS for placement
recommendations is not as accurate for Introductory Statistics.
Current recommendation: ALEKS of 35 or greater.
26
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.
27
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.
28
Intro Statistics
10
20
30
40
Count
0 10 20 30 40 50 60 70 80 90 100 110Rational Expressions sub-score
29
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
30
Intro StatisticsUse the Rational Expressions
sub-score for placement in an introductory statistics course
Suggested recommendation: Rational Expressions sub-score of 20 or greater.
top related