Resumen

Different theories assume that the learning of mathematics and sciences should be based on constructivist methods, where the students inquire about problem – situations and assign a facilitator role to the teacher. From a contrasting view, other theories advocate for giving a more central role to the teacher, which involves the explicit transmission of knowledge and the students’ active reception. In this paper, we reason that the optimization of learning requires adopting an intermediate position between these two extreme models, because of the complex dialectic between the students’ inquiry and the teacher’s transmission of knowledge. We base our position on a model with anthropological and semiotic assumptions about the nature of mathematical and scientific objects, as well as on the structure of human cognition.