Title: Optimal Weighting for Exam Composition,
Abstract: A problem faced by many instructors is that of designing exams that
accurately assess the abilities of the students. Typically these exams are
prepared several days in advance, and generic question scores are used based on
rough approximation of the question difficulty and length. For example, for a
recent class taught by the author, there were 30 multiple choice questions
worth 3 points, 15 true/false with explanation questions worth 4 points, and 5
analytical exercises worth 10 points. We describe a novel framework where
algorithms from machine learning are used to modify the exam question weights
in order to optimize the exam scores, using the overall class grade as a proxy
for a student's true ability. We show that significant error reduction can be
obtained by our approach over standard weighting schemes, and we make several
new observations regarding the properties of the "good" and "bad" exam
questions that can have impact on the design of improved future evaluation
methods.