Identifying and assessing relational understanding in ordinary differential equations

Is it possible to assess conceptual understanding of ordinary differential equations and their solutions? There is significant tension between students learning mathematics for understanding and students learning to drill a set of algorithms to solve standard ODE exercises. This paper presents the Framework for Relational Understanding of Procedures, a categorization of assessable conceptual knowledge. Example conceptual knowledge we examine in this project include relating a graphical representation of an ODE to a symbolic one, checking a result, and knowing why a particular solution method might be applicable. We applied this framework to three techniques taught in Ordinary Differential Equations: separation of variables, solving a first order linear ordinary differential equation, and Euler´s method and developed a set of assessment items. These assessment questions were then transformed into knowledge pieces and moved into an online platform and elaborated. Thus, the assessment can be administered either in traditional pencil-and-paper form or through a learn-as-you-assess online web site.