Tradition in whole number arithmetic

The main topics discussed by the panel and the resulting questions to be answered are introduced along with some bibliographic references. The main topics of discussion concern the relationships between tradition and the verbal and non-verbal representations of numbers, numbers and artefacts of arithmetic, and the role of technological devices in emulating traditional abaci and allowing direct interaction with the screens of multi touch devices in counting activities. Another crucial issue concerns the different languages that can be present in a classroom for historical and cultural reasons. This represents a challenge for teachers, who must cope with the ways in which words can shape the specific connotations of the meanings of numbers. Although all of these facets of numbers need to be coordinated with the standard mathematical concepts, they also appear in the multimodal representations that are used to teach them, such as words, textbooks, notes and teachers’ and students’ gestures. All of these factors intertwine and sometimes conflict with the richness of the representations and practices that children encounter outside school in their everyday lives.