Applying combinatorics in the design of multiversion exams

Abstract

In Spring 2020, the need for redesigning online assessments to preserve integrity became a priority to many educators. Many of us found methods to proctor examinations using Zoom and proctoring software. Such examinations pose their own issues. To reduce the technical difficulties and cost, many Zoom proctored examination sessions were shortened; to create summative assessments we supplemented the short proctored sessions with short unproctored sessions. In the aftermath of the pandemic, the method of creating a large volume of examination variants is helping us design mastery-based examinations. We review the mathematics behind choosing the size of question pools to improve integrity of the exam. Finally we provide $\text{LaTeX}$ files for generating examination variants from the pools.

Keywords:

• Question pools
• size of an assessment
• integrity of examinations
• creating mastery-based assessments
• examination generators
• Galois fields
• vector spaces
• finite projective planes
• $\text{LaTeX}$
• Python

Acknowledgments

The implementation of our paper mastery-based assessments was supported by the University of Kansas Course Transformation Grant in Spring 2022.

Disclosure statement

No potential conflict of interest was reported by the authors.