The issue of how to assess learning is addressed in the context of an investigation of student understanding of the work-energy and impulse-momentum theorems. Evidence is presented that conceptual and reasoning difficulties with this material extend from the introductory to the graduate level and beyond. A description is given of the development of an instructional sequence designed to help students improve their ability to apply the theorems to real motions. Two types of assessment are compared. The results demonstrate that responses to multiple-choice questions often do not give an accurate indication of the level of understanding and that questions that require students to explain their reasoning are necessary. Implications for the preparation of teaching assistants are discussed.