Tacitation and implicitation: the construction of semiotic tools for representing mathematics teaching

Representations are an account of reality. Their construction involves several choices: what to represent, how to represent, from which point of view. Here, we introduce tools to represent mathematics teaching through the study of sign exchanges. We first emphasize how signs are tightly related to different shares of knowledge of sign users. In the regular case, sign exchanges are considered to rest on a kind of shared obviousness. The knowledge imbalance between actors of the didactical situation renders this shared obviousness minimal, and therefore requires distinguishing different kinds of sign exchange processes. From the notion of semiosis, we define the processes of tacitation and implicitation. We present a field study from these theoretical concepts and discuss some implications for future research.