Numeration units (ones, tens, hundreds, etc.) are an epistemological foundation for place value. Here, we assume that they are a didactic support in countries where spoken numbers are incongruent with written numbers. In France, teaching practices neglect the relations between units, and numeration units are typically used only to designate the positions of digits. Our research, which adopts the didactical engineering framework, aims to develop a set of reference tasks for grades 1 to 5 to support a consistent learning of place value with numeration units. This article reports the theoretical framework on which our research is based, and illustrates it with some examples of tasks designed for grade 3 students and implemented in classrooms.

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Semiotic analysis of mathematical activity, a didactic need in the context of school adaptation. The research we are conducting seeks to understand what is being played out between the actors (students, teacher) which could enlighten us on some difficulties for teaching mathematics in special education. It explores the semiotic dimension of mathematical activity. In this paper a learning situation of the decimal numeration is proposed to three students with intellectual disabilities in a Medical-Educational Institute. The analyse is based on the different signs activated (Arzarello, 2006 ;Radford, 2003) through interactions between students during a brief episode. The study points out the presence of "semiotic misunderstandings" and the role of interactions in the activity, including social interactions, between students or with the teacher.Résumé. La recherche que nous menons cherche à comprendre ce qui se joue entre les acteurs (élèves, enseignant) et qui pourrait éclairer certaines difficultés à faire apprendre des mathématiques dans le contexte de l'adaptation scolaire. Pour ce faire, nous étudions en particulier la dimension sémiotique de l'activité mathématique. Le support est une situation d'apprentissage de la numération décimale, proposée à trois élèves handicapés atteints de déficience intellectuelle dans un Institut Médico-Éducatif. Les analyses s'appuient sur les différents signes activés lors des interactions, lorsqu'ils font des mathématiques (Arzarello, 2006 ;Radford, 2003). L'étude pointe la présence de « malentendus sémiotiques » et le rôle des interactions, y compris sociales, entre élèves ou avec l'enseignante dans l'activité.

MYRG2015-00203-FED). The opinions expressed herein are those of the authors.The first two authors wrote the chapter with the collaboration of other working group members. Historical BackgroundZou (2015) summarised findings from historical investigations of arithmetic in ancient China, including how number units were derived and named and how numbers were represented with rod or bead calculation tools and with symbols. Siu (2015) studied the book of Tongwen Suanzhi (同文算指) (Rules of Arithmetic Common to Cultures, 1614) and reviewed how counting rods and the abacus were gradually replaced with written calculations in China. Sun (2015), also discussing early Chinese development, presented the use of advanced number names and