In focus for this paper is a concern with a) how students and teachers in desk interaction in mathematics lessons claim to know, understand and see things, i.e. what their epistemic stance is, and b) how the construction of epistemic authority varies between different students and groups of students both within and between classrooms. Epistemic stances might be seen as peripheral phenomena, but turn out to be the primary means by which students and teachers establish, sustain, and question their understanding of the subject matter. Previous work shows that participants use a variety of resources, including verbal and non-verbal (e.g. prosody, gestures and other embodied displays) epistemic stance markers, for situating their actions within the epistemic ecology of the situation. In this paper, the analysis highlights how student participation and access to epistemic authority is established, sustained and changed. The analysis shows that subtle differences in the way teachers and students establish desk interaction on a given topic is of large importance for the way students have access to epistemic authority, and that the variation in epistemic ecology of the situations seems to be related to student performance, as measured in tests or by grades.