Though a good deal of research has been written already concerning the acquisition or teaching of written positional notation, difficulties do persist for pupils in early school years. Written multidigit number cannot be reduced to a simple transcription of spoken expression: actually it implies and conveys a new body of mathematical knowledge, which has to be mastered. In French school, that question arises in primary first year - cours préparatoire or CP, 6-7 years old. When entering CP, pupils initially regard numbers, in essence, according to the spoken designation they're now familiar with - a designation they generally associate with one-by-one numbering activities. Class dynamics demand that the teacher build mediations which cannot ignore the pupil's preexisting knowledge. Yet the teaching should eventually present numbers without naming them: so how can we deal with the spoken number when teaching numeration ? Can we consider it as a useful tool, and not as an apparent obstacle to abstraction? Throughout this work, we investigate the underlying mathematical foundations to cover the various strategies available to the teacher. We review the current state of research, and describe the recurring difficulties still encountered by pupils in primary years. We comment on different approaches in use within the French School system, through the analysis of school texts and reporting of actual class experimentations. Then we offer revisions in the teaching of numeration - from which we derive new perspectives in practice.
