Cognitive and dialogic patterns shaping strategic flexibility in collaborative mathematical problem-solving

Little is known about strategic flexibility in collaborative mathematical problem-solving. In this study, we investigate how cognitive levels and dialogic moves, together with their collective uptake, relate to strategic flexibility. To do so, we combine the Florida taxonomy of cognitive behavior (FTCB) with the teacher scheme for educational dialogue analysis (T-SEDA) to analyze a 29-minute dialogue among four pre-service mathematics teachers solving a geometry problem. Most dialogue contributions involved lower-order thinking and surface-level dialogic moves. The combined framework distinguished actual strategy shifts, unrealized opportunities for strategic reconsideration, and local checking-and-correction moments. Opportunities to reconsider strategy arose when higher-order contributions coincided with making reasoning explicit or challenging a proposal, but were infrequent, largely steered by one participant, and rarely taken up collectively. From this, we conclude that strategic flexibility may benefit from the collective uptake of cognitively demanding contributions. Methodologically, integrating FTCB and T-SEDA traces how cognitive depth and dialogic function relate to such uptake.