Konstantinos Nikolantonakis, Laurent Vivier: Positions numeration in any base for future Elementary school teachers in France and Greece: one discussion via Registers and Praxis


The numeration in any base for whole numbers is a mathematical topic which introduces new registers of representation. We reinterpret the question for treatments in the new registers in the language of praxeologies: new praxis is to be built. In this paper, our first objective is to examine the cognitive distinction between treatment and conversion made by Duval for the registers of numeration in base other than ten. Two inquiries was made and analyzed with the Statistical Implicative Analysis (SIA) that has permitted to show two cognitive difficulties for coding numbers into the position numeration in any base that comes from: 1) the base is different from ten and 2) the base is greater than ten. Our second objective concerns the technological potential of polynomial writing. The SIA permits us to show that this register is important for the success of the types of tasks and for the construction of techniques in any base
MENON: Journal Of Educational Research, http://www.kosmit.uowm.gr/site/journal (ISSN: 1792-8494)
Full article: ISSUE 2a, 2013 (p. 99-114)