What proficiencies are brought tobear when students work on mathematicsproblems? And to what extent may these becaptured by knowledge categories? These arequestions that I consider in this article,as I explore notions of competency, that gobeyond knowledge to include themathematical `dispositions' that studentsbring to problems and the `practices' withwhich they engage. This exploration willdraw from two frameworks that have recentlybeen introduced in the US. In addition, Iconsider the ways in which researchknowledge is conceived and developed,reflecting upon the important role oftheory and the potential of `workinghypotheses' for connecting with practice innew ways.