Introducing an old calculating instrument in a new technologies environment: a praxeological analysis of students' tasks using different registers

TL;DR

This paper analyzes how students solve tasks involving the Chinese abacus across different registers such as physical, virtual, and paper-based, highlighting implications for understanding and teaching number sense and place-value systems.

Contribution

It introduces a praxeological framework to analyze students' tasks with the Chinese abacus in various technological environments, emphasizing the importance of register diversity.

Findings

Students can solve tasks using multiple registers including material, virtual, and paper.

Different registers influence students' understanding of number concepts.

The analysis informs teaching strategies and resource design for number sense development.

Abstract

The Chinese abacus is the resource presented in this paper, to teach and learn number sense and place-value system at primary level. The Chinese abacus can be material, virtual (software) or drawn on a worksheet. We present three tasks and analyse them in term of techniques and relative knowledge. We show how these tasks can be solved by students in different registers (material, software, paper-and-pencil, fingers, oral) which is important for both students' understanding and teachers' activity. KEYWORDS Material and virtual resources, praxeology, task, technique, technology, register, number sense, place-value system, Chinese abacus. R{\'E}SUM{\'E} Le boulier chinois est la ressource pr{\'e}sent{\'e}e dans cet article, pour enseigner et apprendre la construction du nombre et le syst{\`e}me de num{\'e}ration d{\'e}cimal {\`a} l'{\'e}cole. Le boulier chinois peut {\^e}tre mat{\'e}riel, virtuel (logiciel) ou dessin{\'e} sur une feuille. Nous pr{\'e}sentons trois t{\^a}ches et les analysons en terme de techniques et connaissances sous-jacentes. Nous montrons comment ces t{\^a}ches peuvent {\^e}tre r{\'e}solues par des {\'e}l{\`e}ves dans diff{\'e}rents registres (mat{\'e}riel, logiciel, papier-crayon, mains, oral) ce qui est important pour la compr{\'e}hension des {\'e}l{\`e}ves et {\'e}galement pour l'activit{\'e} des professeurs.