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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In the mid-1990s, a team of math education researchers at the Université du Québec à Montréal (UQAM) developed a role-playing approach for use in the initial training of primary teachers. Since its introduction, this approach has been the topic of several articles, thus allowing its potential to be analyzed from various angles. We Bexported^this role-playing technique to the initial math training of school teachers in France, believing that the approach could benefit the practices of these future teachers. The approach provides an opportunity for the trainers first to observe the emerging practices being used by the trainees and then to intervene in the trainees' zone of proximal development with regard to these practices. For our study, we created a role-play-based training scenario in which future teachers must help a student having difficulties with a task related to decimal numbers. In this article, we document the knowledge and practices demonstrated by the future teachers under these circumstances as well as the possibilities for trainers to use these results to help advance the trainees' development. Résumé Au milieu des années quatre-vingt-dix, une approche par jeu de rôles (JdR) a été développée à l'UQAM (Université du Québec à Montréal) par une équipe de didacticiens des mathématiques en