Agreement has become widespread that students' peer-to-peer argumentation should play a central role in science classrooms. Coordinating evidence with claims lies at the heart of a skilled argument. Yet evidence takes numerous forms that pose different interpretational challenges. Might cognitive limitations on the part of the individual student in this regard constrain the potential effectiveness of classroom discourse? This possibility has received limited recent attention relative to the contemporary sociocultural focus on examining and optimising patterns of classroom discourse. We examine seven forms of evidence in the context of two scenarios and document the challenges eighth-grade students exhibit in relating them to a claim. Our analysis led us to propose an overarching challenge across the different forms: establishing the "relation" that two assertions (claim and evidence) bear to one another, rather than address only one of the two and from the perspective of one's own beliefs. In Study 1, we present this analysis and report on the limited levels of mastery students exhibit across the different evidence types and in Study 2 on an effort to foster such mastery in early adolescent students.