Summary of the Third Discussion Session

Abstract

During this discussion, LACOMBE firstly specifies the role of language, and of the teacher’s speech, in problems concerning the acquisition of mathematical concepts. WEINZWEIG, next, proposes the use of many different contexts to enable the child to develop the concept of addition. COHORS-FRESENBORG then explains how dynamical mazes can be used to enable deaf children to solve mathematical problems. He also describes the different approaches adopted by deaf and by hearing children, when solving these problems. LOWENTHAL insists on the use of non-verbal formalisms introduced by means of finite automata, as representation systems: this should broaden the field of application of WEINZWEIG’s and COHORS-FRESENBORG’s techniques. This leads to further questions: do we have to attach such importance to finite state automata? do the devices suggested by LOWENTHAL deserve the name of “formalisms”? This provokes a long discussion about the interactions between “notation for” and “realisation of” a concept: MARKOVITS and WEINZWEIG claim that a notation should only be introduced after the child has realised the concept, while COHORS-FRESENBORG and LOWENTHAL explain that their systems can play several roles and help the child to allow a concept to emerge;