Linking inquiry and transmission in teaching and learning mathematics

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