Complementary dimensions of the Theory of Didactic Situations in Mathematics and the Theory of Social Interactionism: Synthesizing the Topaze effect and the funnel pattern

This study examines the theory of didactic situations in mathematics (TDS) and the theory of social interactionism (TSI), employing strategies from the networking of theories schema to uncover potential complementarities between them. These theories provide different a priori perspectives on mathematics classroom interaction: TDS focuses on the functioning of mathematical knowledge in adidactic situations, while TSI centers on the emergence of mathematical meanings through the interactive accomplishment of intersubjectivity. The study gives rise to a hypothesis concerning complementary dimensions of the theoretical frameworks, particularly regarding social interaction and related classroom regulations. This hypothesis is empirically substantiated through theoretical triangulation of a dataset from a mathematics classroom. The TDS analysis, considering the mathematical knowledge in question, identifies a Topaze effect within the dataset, whereas the TSI analysis construes the empirical facts as exhibiting a funnel pattern of interaction. It is argued that the interpretations mutually enhance each other’s explanatory power. • TDS is an epistemological framework focusing on how mathematical knowledge functions in adidactic situations. • TSI is a sociocognitive framework centering on how mathematical meanings emerge and stabilize during classroom interaction. • A justificatory framework for combining TDS and TSI is developed through the examination and comparison of the theories. • The justificatory framework is used to rationalize the integration of interpretations from the TDS and TSI analyses of classroom data. • The synthesis demonstrates that TSI facilitates the recognition of the Topaze effect, while TDS reveals the causes of the funnel pattern.