The construct "mathematical knowledge for teaching" (MKT) has received considerable attention in the mathematics education community in recent years. The development and refinement of the MKT construct, including the components of common content knowledge (CCK) and specialized content knowledge (SCK), came from research into elementary teachers' practices. In this article, we argue that various issues arise as these constructs are used in research on secondary and post-secondary teachers. For example, elementary teachers typically differ from teachers of higher grades in their content preparation. What then is the relationship of CCK to SCK for those holding a bachelors degree or higher in mathematics? The MKT construct is based on CCK being knowledge held or used by an average mathematically literate citizen and that SCK is different. However, among those teaching in secondary and post-secondary contexts, what should be considered CCK? Is conceptual understanding of the CCK among those with bachelor's degrees or higher level mathematics the same as SCK? We examine these questions as well as others that arose from our examination of definitions of CCK and SCK as we attempted to utilize those definitions to characterize the nature of MKT at secondary and undergraduate levels. We illustrate these issues with data from two instructional settings.