  We discuss a study to evaluate the extent to which free-response questions
could 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 final exam. Findings suggest
that carefully designed multiple-choice questions can reflect the relative
performance of 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.
