This study applies a framework for mathematical cognition and learning (Bossé, et al., 2018a; Bossé et al., 2019; Bossé et al., 2018b) to examples of students' comprehension of geometric concepts related to angles. This framework utilizes key concepts from second language acquisition (SLA) to elucidate processes involved in mathematical learning. The present study analyzes concrete examples of student-teacher and student-student discourse to illustrate how students at different stages of development build their understanding of mathematical principles and concepts regarding angles. The findings indicate that students at different framework levels learn, process, and communicate about angles in observably different ways that share similarities with mathematical learning and SLA.