The power of mathematical inscriptions, such as graphs, is often attributed to the fact that they summarize a lot of information independent of their contextual particulars. There is evidence, however, that even quintessential experts and scientists have difficulties interpreting graphs when they are unfamiliar with the entities represented and with the procedures that translated material entities into graphs. In this case study, which derives from an ongoing ethnographic research project, the author shows that the understanding of graphs in one hatchery is deeply integrated in the understanding of the local particulars; the "meaning" of graphs and other mathematical inscriptions exists in their close integration into the work process, which has both unconscious embodied and conscious social significations. At the same time, existing understanding is further articulated and elaborated through the analysis of graphs and the work processes from which they derive; that is, understanding is reflexively elaborated. A dialectical model of understanding and meaning is provided: Understanding is the prerequisite of analysis and explanation, which in turn is a prerequisite for the evolution of understanding.