A Study of Pupils Reading Geometry

Abstract

The study presented here is based on an approach to the teaching of mathematics which takes linguistic problems into account. In this approach, these linguistic problems are considered in relation to the acquisition of mathematical knowledge within the classroom situation. What is required, we suggest, is not merely an analysis of learner utterances, teacher utterances or the wording of the text book. These utterances can only be fully grasped if they are related to their conditions of production, to the knowledge structure of the speaker or listener and to his relationship with others during the exchange. In other words, the discourse situation, as defined by A. Culioli (1976) cannot be ignored. One of the functions of the discourse situation is the transmission of meaning, meaning which derives from the cognitive constructs of the subject and which cannot be totally defined without reference to the context of the utterance. The meaning is constructed by the locutor/speaker and reconstructed by the interlocutor/listener through the referential values in the context of the utterance... . In the previous symposium, “Language and Language Acquisition”, the importance of allowing for the situational constraints of language exchange, and the essential role of speaker and listener in the creation of meanings within this situation were stressed by M. Brossard (1981), and, at the end of the meeting, an appeal was made by F. Lowenthal (1982) for a development of contextual linguistics. The approach to the problems raised here is related to that analysed by J.B. Grize at the present congress, namely the representation of a microworld (which Grize calls schematization) elaborated by the speaker and reconstructed by the listener in function of his prior knowledge. The readjustement and adaptation resulting from this reconstruction are driving forces in the growth of knowledge.