matics knowledge, and in a position to engage with the community, albeit in a junior role. She recognizes that it has rules and believes that she has the potential to access and manipulate these rules--despite her beliefs about innate ability reported above. Sarah thus demonstrates an identity of "legitimate peripheral participant" which is lacking in the other students with the possible exception of Larry, who, as we have already seen, looks for usable connections within mathematics. Given the predominant pattern of institutional relationships and their corresponding epistemologies, it is unsurprising that the majority of the students were unclear about the central role of proof. As we shall see, Sarah outlook led her to take a different and unusual stance on this matter too