Resumen

Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the “official” algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses.