| EpiDEMES |
3 | 2024
Numéro Spécial associé aux travaux de l'école thématique du CNRS Didactique et Épistémologie des Mathématiques et leurs Interactions pour la Médiation et l’Enseignement Supérieur
1. L’algorithme : pourquoi et comment le définir pour l'enseigner
The question of the definition of what is an algorithm is recurrent. It is found in teaching, at different levels and particularly in secondary education because of the recent evolutions in high school, with immediate consequences in higher education. It is found in mediation, with the different meanings that the word “algorithm” is charged with in the media space. It is also found in research, with issues in different branches of computer science, from foundations in computability and complexity to applications in big data. Beyond the issue of definition, it is the raison d’être of the notion of algorithm that should be questioned: what do we want to do with it and what is at stake? It is by trying to specify this that we can identify didactic elements that are likely to help teach the algorithm, in interaction with mathematics or not, and to different audiences.
2. Quelques pistes pour l'étude des situations d'informatique débranchée
Computer science unplugged is a scientific popularization project initiated in the 1990s by a team of New Zealand researchers. It enables participants to discover the major concepts of computer science, without a computer, through physical activies or the use of physical material, and also to initiate them into the computer science research process. This device, which is currently widely considered by both mediators and teachers, requires an in-depth analysis as a tool for transmitting knowledge. This analysis is currently in its beginning. Through three examples of popularization situations in computer science unplugged, we propose lines of thought based on observations with the perspective of a more complete didactic analysis of these situations and their transposition into classrooms.
3. Théorie des Situations Didactiques et situations de preuve : étude de deux exemples
The framework of the theory of didactical situations is based on "experimental epistemology". It allows us to question mathematics and learning situations. This text will present mathematical and experimental tools derived from this theory for thinking about a typology of situations for didactic use. In particular, it will focus on didactic variables and proof situations. Two examples will illustrate these aspects. From the fields of game theory on the one hand and number theory on the other, these examples will be discussed and revisited: the Race to 20 and the Frobenius problem.
4. Mechanisms for mathematical modelling: the study and research paths at university level
This paper addresses the problem of integrating mathematical modelling into first-year mathematics courses at university level. Our research focuses on identifying mechanisms that facilitate the dissemination of mathematical modelling in university mathematics education. Within the framework of the anthropological theory of the didactic (ATD), our work over recent decades has focused on the design, implementation, and analysis of the study and research paths (SRP) as a teaching device persuading a double purpose: making students aware of the rationale of mathematical contents through the experience of modelling activities; and connecting these mathematical contents through a whole modelling process. We draw upon empirical findings from the implementation of an SRP on population dynamics withfirst-year students at university level, and its ‘migration’ to other university settings, to identify valuable mechanisms for integrating mathematical modelling into university institutions. More concretely, we analyse the mechanisms facilitating two central dialectics for the SRP and for modelling: the dialectics of questions and answers and that of media and milieu.
5. Physique en première année d’université : que nous apprend une analyse ancrée en didactique des mathématiques ?
This text reports on a workshop of the DEMIMES thematic school, the aim of which was to discuss how didactic theories can equip teachers in higher education to analyse exercises and problems texts and anticipate student difficulties. We present an analysis of a first-year university physics problem using theoretical tools from mathematics didactics: the anthropological theory of the didactic and the activity theory specific to didactics. We have chosen a Newtonian mechanics problem concerning the fall of a ball in a liquid, whose mathematical treatment involves vectors and a differential equation. We introduce the theoretical tools used and the problem chosen, then present the analyses, and discuss the contributions of the two theories. The workshop also showed that didactic analyses could shed light on the differences between the mathematics used in mathematics courses and those used in physics courses at university.