Can Free-Response Questions Be Approximated by Multiple-Choice Equivalents?

TL;DR

This study investigates whether well-designed multiple-choice questions can effectively approximate free-response questions in physics exams, offering a balance between assessment accuracy and grading efficiency.

Contribution

It demonstrates that carefully crafted multiple-choice questions can reflect student performance on free-response questions, preserving assessment quality while simplifying grading.

Findings

Multiple-choice questions can approximate free-response performance.

Weighted choices reflect different levels of student understanding.

Careful design maintains assessment validity.

Abstract

We discuss a study to evaluate the extent to which free-response questions can be approximated by multiple-choice equivalents. Two carefully designed research-based multiple-choice questions were transformed into a free-response format and administered on the final exam in a calculus-based introductory physics course. The original multiple-choice questions were administered in another, similar introductory physics course on the final exam. Our findings suggest that carefully designed multiple-choice questions can reflect the relative performance on the free-response questions while maintaining the benefits of ease of grading and quantitative analysis, especially if the different choices in the multiple-choice questions are weighted to reflect the different levels of understanding that students display.