The Mathematical Association of America presents this series of in-depth articles on "undergraduate mathematics education." Only eight articles have been contributed since the column's beginning in 1996, but there have already been two excellent ones for 2003. The first is titled Learning and Teaching Ordinary Differential Equations, which explores a change in the way the subject is taught, both conceptually and in the technology used to apply the material. The second article, and perhaps most intriguing, is about the difficulty students experience when learning proofs and how to construct their own based upon a given assumption. Instructional methods that could potentially enhance student's understanding are introduced.