Existing systems of education have some elements promoting learning as an objective, but are mainly coherent as systems only around enrollment targets. This paper builds an accountability framework of actors and the four design elements of accountability (delegation, financing, information and motivation) to emphasize that effectiveness in promoting learning requires systems of education that are coherent, in two ways. First, each accountability relationship has to be coherent across its elements, that is, the delegation of what agents are asked to do has to be coherent with the financing, information, and motivation, rather than "pay for one thing and expect another." Second, the relationships have to be coherent across relationships of accountability. That is, if teachers are accountable both to their employer and indirectly to parents/students/communities, then if these two have very different objectives the accountability of teachers will be made incoherent. Such incoherence can explain why small changes in the "right" direction (towards that of high performing systems or demonstrated in other contexts) might consistently fail even where a directed and coherent reform could have major impact.