  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.
