This paper addresses the evidence that secondary school students use to imply that they understand something in mathematics. As part of a larger study, an open-ended questionnaire probing several aspects of metacognitive self-knowledge, was administered to students (N=72) in four schools. Two previously identified types of understanding were identified in the students' responses: (1) instrumental (knowing how to do a piece of mathematics) and (2) relational (knowing why it works). Analysis of the data revealed that students who associated understanding with explaining also reported engaging in frequent mathematical discussions with other students. This result suggests a connection between metacognitive functioning and social interaction consistent with Vygotsky's views on learning. Observations of students in one of the classrooms participating in the study are used to add depth to the questionnaire data and suggest implications for teaching. Contains 17 references. (DDR)