Teaching of a new lesson calls the use of signs that are new to the students: they do not know their meaning and the teacher knows they do not know them. Since a sign “cannot furnish acquaintance with or recognition of [its] object” (Peirce, 2.231), the teacher has to speak of what the students do not know with words they know and understand (Condorcet, 1791-1792/1989). Consequently, signs with known meaning and signs with unknown meaning coexist in teachers' speech, and the firsts should allow the latter to be understood. Our first hypothesis is: when the teacher presupposes that the meaning of a term (a noun, a noun phrase or a verb) is unknown for the students, he uses it in association with other terms that are presupposed to be known for the students. The production of a sign is a process; a semiosis (Peirce, 1978; Morris, 1938). Regarding the unknown term, the teacher expects from the students the construction of a concept – acted knowledge (Piaget 1970; Vergnaud, 1990) – which is necessarily implicitly signified by the term. Therefore, we speak of the process of implicitation. We draw up a second hypothesis. For an effective communication, the teacher does not use a term in association with other terms when he presupposes that its meaning is known for the students. In this case, all part of the meaning of the term is kept silent; so we speak of the process of tacitation. Defending both these hypothesis means assuming that we can identify teachers' presuppositions about students' knowledge from the study of mere association of terms in teachers' speech. The part of linguistic phenomena on which we focus is therefore limited. We leave aside the syntactic and the pragmatic dimensions of language. We suggest that such an approach may be heuristic for understanding the production of teachers' speech. With contributions from philosophy (when we study signs and semiosis), epistemology and didactics (when we root our work in a theory of knowledge and learning) and linguistic (when we justify our use of the words implicit and tacit), we start our dissertation by theoretically defending our approach (part I, chap. I & II). From case studies of mathematics lessons, we build a methodology based on both teachers' observation – to access the terms they use – and interviews – to access (indirectly) their presuppositions. In our group of subjects (mathematics, chemistry and biology teachers), we succeed in predicting 80% of teachers' presuppositions related to 259 occurrences of terms (part I, chap. III). This result strongly supports the existence of implicitation and tacitation. Therefore, we pursue our work by locating their instances in 10 whole lessons of chemistry. We show that the study of their distribution in time allows detecting teaching phases that are different by 1. the way the teacher deals with the heterogeneity of the class and 2. the way students' comprehension of teachers' speech is dependent on their preexisting knowledge (part II, chap. IV & V). Thus, implicitation and tacitation processes bring new light to discussions about verbal interactions in class.
