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

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ALEKS

7

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

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

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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

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

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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.