Semiotic bundle approach and Onto-Semiotic Approach: a dialogue between two theories on an arithmetic-algebraic problem

This research rests on the analysis of a mathematical task, about an arithmetic-algebraic problem and its solution, using theoretical tools from two main frames: the Semiotic Bundle Approach (SBA) and the Onto-Semiotic Approach (OSA). The activity has been examined by two original video recordings of the group composed of five pupils of primary education students. By presenting an empirical case of networking of theories, the objective is to begin to dialogue with the two approaches, reading the asymmetries present between their languages, with the aim of getting some new insights into the mathematical problem. Whereas the SBA, in a systematic approach, is particularly apt to focusing the relationships among the different multimodal semiotic resources used by the students in the short timescales of the classroom story (an embodied cognitive focus), the OSA incorporates a set of conceptual tools to address the analysis of the different facets that interact in a mathematical education process. Mainly the SBA describes the importance of the bundle of signs (like gestures, words, written signs) for mathematical thinking and communication and its multimodality, and the OSA favours the description of objects and processes that emerge from the mathematical practices. The results from this joint analysis provide a rich insight into the observed phenomenon and help to initiate a dialogue between theories in Mathematics Education, within a Semiosphere generated by the networking between SBA and OSA.