Between arithmetic and algebra: a space for the spreadsheet? Contribution to an instrumental approach

In this research work, we have a didactical look on the integration of a computer tool into mathematics teaching: the spreadsheet. We have related research about spreadsheet to an instrumental approach perceived as essential to analyze the questions of technological integration. This approach allowed us to extend to this technology the theoretical framework of instrumentation. These theoretical elements are being used in the analysis of the professional resources and the teaching practices, in order to understand the difficulties in the integration of the spreadsheet. In this paper, we mainly describe this theoretical work, then some of its didactical consequences. Nowadays, there is a firm institutional will to integrate the technologies of information and communication to the practices and curricula in France. In mathematics, teachers are encouraged to use Internet and various software: dynamic geometry and symbolic calculation software, spreadsheets, etc. Our research deals with the spreadsheet, which officially first appeared in middle school, then in high school; it was motivated by the following observations