The hermetic teaching of mathematics: a critical view based on semiotic representation registers

This paper proposes a discussion, under the conception of the semiotic representation registers by Raymond Duval, about the meaning of hermetic teaching of mathematics, closed in itself, in relation to the way the semiotic registers are used. This teaching method, criticized by mathematical education researchers, is seen as based on registers that usually come from a single semiotic system, and even when more than one system are employed, these do not consider the possibilities of semiotic articulation which assumes the simultaneous recognition of semiotic elements that might be related in each system under analysis. Another discussion proposed is how this situation can be overcome with a teaching practice which really prioritizes the articulation between registers based on Duval’s idea of mathematics learning.