Classroom discourse constitutes a fundamental activity in which learners can acquire knowledge. A multifaceted phenomenon, any enacted classroom discussion entails the enmeshment of social, cultural, curricular, and modality factors. Focusing specifically on discourse in the context of mathematical discussion activities in the asynchronous online modality, we propose use of Weinberger and Fischer’s (2006) Argumentative Knowledge Construction framework for design research. We contend that this framework, suitably amended to meet the particular needs of mathematics courses, may enable in-depth analysis of major dimensions of students’ knowledge construction as they engage in activities in an asynchronous modality. Research using this framework in the context of face-to-face mathematical learning (Keene, Williams, & McNeil, 2016) and in online settings in other disciplines (Schrire, 2006; Clark & Sampson, 2008; Dubovi & Tabak. 2020) has been reported.