Improving Decision Making on Mathematics Course Placement
Explore the use of ALEKS assessment scores to predict success in mathematics or statistics courses through logistic regression modeling. Understand the impact of the ALEKS score on course placement decisions and student outcomes based on data analysis and statistical methods.
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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 ? 1 ? ??? = + ?? 10
Logistic Regression Use maximum likelihood estimation to obtain estimates: ?and ?. ? ?+ ?? 1 + ? ?+ ?? ? = 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 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 sub- score of 20 or greater. 30
