Assessment issues in elementary numerical analysis [education]

Summary form only as given. Many ideas presented in elementary numerical analysis do not lend themselves well to traditional "by the clock" examination questions. Students are often given theoretical and/or applied projects to investigate advanced ideas. Examples include case studies of numerical methods applied to specific problems and mathematical derivations or proofs. By thinking about complicated problems over time, it is hoped that students gain some "sense" of how numerical analysis works. Problems can arise in the assessment of these projects. Students have a natural tendency to talk to one another about homework assignments, and it is often not clear when healthy discussion crosses the line to unauthorized collaboration. Instructors can change assignments from term to term, but an increasing number of solved problems have appeared on the Web and in solution manuals, further complicating the task of assessment. The author outlines a strategy in which collaboration on homework assignments is encouraged, and insight gained (from whatever source) is welcomed. In-class examinations are structured to pinpoint individual thinking and initiative. This approach to assessment in numerical analysis has been used for several years at a large state university in the USA with positive results. Several examples of examination questions, and guidelines on how to grade them, are given. Comparisons with other popular approaches are also made.