André Revuz Didactics Laboratory

Cet article présente une revue de littérature systématique sur les MLD (mathematical learning disabilities, difficulties ou disorder) dans le domaine Mathematics education au cours des quinze dernières années. Les principaux résultats sont exposés à partir de différents critères : la terminologie et les définitions couramment utilisées, les régions géographiques qui s’intéressent à cette question, l’âge des participants aux recherches, le contenu mathématique traité et l’objet d’étude principal des recherches (identification, intervention ou caractéristiques de l’élève).

This article purports to analyze the role conferred to the requesting State in domestic extradition procedures. Despite the existence of a judicial control over extradition, the majority of States included in this study continue to view extradition as a political prerogative of the executive and leave the requesting State with little or no means to defend its request. This article argues in favor of the consolidation of the role of judicial authorities in the determination of extradition requests, along with a reinforcement of the requesting State’s ability to participate in this process.

Cake filtration represents one of the several different mechanical methods to separate particles from liquids. Cake filtration offers, in comparison to other mechanical particle-liquid separation techniques, the advantageous possibility of direct solids post-treatment. This enables particle washing by cake permeation and the comparatively lowest mechanically achievable solid moisture contents. If the boundary conditions for cake filtration are not fulfilled, alternative separation techniques such as density separation, depth, cross-flow, or blocking filtration must be used. Surface filtration can be subdivided principally into blocking, cross-flow, and cake filtration. To characterize the whole cake filtration process, several experimental methods and model equations from different authors are available, which are all based on a similar physical fundament. The procedures and apparatuses for the mechanical solid-liquid separation in general and in particular for cake filtration are under permanent research and development in view of new challenges and requirements to the separation results.

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform –which was eventually itself replaced in the longer term – provides some keys to understanding the influence of mathematical theories on teaching and learning. The paper studies changes related to place value, a notion that was deeply impacted by the introduction of numeration bases other than ten in 1970, and their subsequent removal in the 1980s. What the author terms ‘numeration units’ (ones, tens, hundreds, thousands, etc.) and ‘powers-of-ten written in figures’ (1, 10, 100, 1000, etc.) are key tools for describing and understanding changes. The author identifies two theories that have formed the basis for place value teaching in the 20th century, and examines some aspects of their influence. The paper also addresses epistemological issues in the relation between academic mathematics and school mathematics, and highlights the role of units in the teaching of basic arithmetic.

El texto propone un primer enfoque sucinto e incompleto de una de las teorías claves de la didáctica de las matemáticas, es decir la teoría antropológica de lo didáctico. Se presentan tres rasgos característicos de la teoría: su focalización en las determinaciones sociales de los fenómenos indagados, su pauta de análisis de las culturas humanas basada en el modelo praxeológico, su enfoque institucional e epistemológico en la enseñanza-aprendizaje.

Dans cet article, nous menons des analyses didactiques d’études de cas de séances de géologie en école primaire. Nous conduisons nos analyses dans les cadres théoriques de l’apprentissage par problématisation et de l’action conjointe en didactique. Nos conclusions portent sur les conditions didactiques qui permettent à l’élève d’étudier en classe. Elles interrogent également le travail mené par les professeurs pour aménager ces conditions. Enfin, la comparaison des résultats produits permet de discuter les convergences et les divergences des deux cadres théoriques mobilisés dans cet article, et d’établir des possibilités de travaux communs.

We introduce the notion of circular words with a combi- natorial constraint derived from the Zeckendorf (Fibonacci) numera- tion system, and get explicit group structures for these words. As a first application, we give a new result on factors of the Fibonacci word abaababaabaab.... Second, we present an expression of the sequence A004146 of (S) in terms of a product of expressions involving roots of unity. Third, we consider the equivalent of p-adic numbers that arise by the use of the numeration system defined by the Fibonacci sequence instead of the usual numeration system in base p. Among such F-adic numbers, we give a characterization of the subset of those which are ra- tional (that is: a root of an equation of the form qX = p, for integral values of p and q) by a periodicity property. Eventually, with the help of circular words, we give a complete description of the set of roots of qX = p, showing in particuler that it contains exactly q F-adic elements. Classically, a (finite) word is a finite sequence of elements (or letters) of a given set, the alphabet. Here, we mean by circular word a finite word w0 ...wn in which the last letter, wn, is assumed to be followed by the first one, w0. This definition gives rise to interesting properties when circular words are assumed to be admissible, that is, made of letters in the alphabet {0,1} without any two successive letters equal to 1. These properties derive from an underlying algebraic structure: the set of admissible circular words of fixed even length is an abelian group, which can be explicitely written as a product of finite monogenetic groups.