Semiotics is the study of symbols and the creation of their meaning through social interactions. In this paper, we explore more deeply the socially situated nature of semiotics by extending current semiotics theories and frameworks from the perspective of emergent modeling. The first expansion is to replace the interpretant (meaning associated with symbols) with a construct that comes from social constructivism, namely taken-as-shared mathematical ideas. The second involves integrating purpose into semiotic frameworks. Finally, we broaden the time span that is typical for semiotic analyses to account for 5 weeks of collective activity and describe an argumentation analytic technique for doing so. We do all of this from the point of view of instructional designers who use realistic mathematics education and consider emergent modeling as a lynchpin of instruction.