This report concerns an inquiry into the nature and character of conceptual transformation through a process of argumentation in a community of mathematical inquiry. Its theoretical approach is based on Vygotsky’s theory of social cognition, which in turn is grounded in the broader framework of Hegelian and Marxist dialectical theories, and systems. The study explores mechanisms of conceptual transformation in dialogical group setting with 21 fifth grade students in a community of mathematical inquiry format. It concludes that the process follows a dialectical model, which the author illustrates through an analysis of group discussion of the concept of infinity.