Les séries de problèmes, un genre au carrefour des cultures : une première synthèse

Abstract

Résumé. Cet article propose une présentation du volume « les séries de problèmes, un genre au carrefour des cultures » et une vue d'ensemble des principales questions qui y sont abordées. La première partie décrit le contexte du projet qui y a donné naissance au sein du labex HASTEC, ainsi que l'objectif du volume et les conditions dans lesquelles il a été préparé. La seconde partie décrit le coeur du projet scientifique. On présente d'abord (2.1) une définition de son thème directeur, les problèmes qu'elle pose et les différentes manières dont il a été compris par les contributeurs ou contributrices. On résume ensuite (2.2) quatre grandes directions d'interprétation possibles des « séries de problèmes » en termes d'histoire culturelle : en lien à des visées encyclopédiques ; en lien à des fins pédagogiques ; comme objet de transformation et de réappropriation permanente ; comme support de légitimité savante.Abstract. Series of problems, a genre at the crossroads of cultures: a first synthesis. This paper presents the volume entitled "series of problems, a genre at the crossroad of cultures" and offers a general view of the main questions that are addressed in it. The first part describes the institutional context of the project that gave rise to it within labex HASTEC, as well as the objective of this volume and the conditions in which it was prepared. The second part describes the core of the scientific project. It first presents (2.1) a definition of its leading subject, the problems this definition raises and the various ways in which it has been understood by the contributors. It then summarizes (2.2) four main directions of possible interpretation of "series of problems" in terms of cultural history: in relation to encyclopedic intentions; in relation to didactic ends; as an object of permanent transformation and re-appropriation; as support of scientific legitimacy. Préambule

How history of mathematics can help to face a crisis situation: the case of the polemic between Bernoulli and d’Alembert about the smallpox epidemic

“…We introduced the term pre-transitional object to characterize texts where a potential to become transitional object in an interaction with teachers was identified. The first texts we used in this sense were studied in the frame of the interdisciplinary research project entitled "Series of problems at the crossroad of cultures" (Bernard, 2015): we have shown in Bernard and Gosztonyi (2018) how the reading sessions originally planned to provoke discussions related to problem-based teaching could generate various encounters with the texts, depending on the participants' preliminary experiences and problems.…”

Teachers’ practices and resources in the Hungarian “Guided Discovery” approach to teaching mathematics: presenting and representing “series of problems”

“…One of the specificities of the GD approach identified in preliminary research of the first author (Gosztonyi, 2020) is that long and complex teaching trajectories 3 based on "series of problems" are used and developed by teachers. The term "series of problems" (SoP) itself was originally introduced in the frame of an interdisciplinary history of science project as a more or less undetermined methodological tool to analyse the structure of historical texts in different periods and cultures (Bernard, 2015). In the specific Hungarian context, Gosztonyi used the term SoP as a list of problems with a consciously chosen ordering which is relevant for one or several educational purposes.…”

Series of problems in Clairaut’s Elements of Geometry: interaction between historical analysis and mathematics education research

“…2 This ongoing study is deeply inspired by a preliminary historical analysis of the GD. Important elements for the study of GD, concerning its historical roots and some key principles, were developed (Gosztonyi, 2015) in the framework of the interdisciplinary history of science research project called "Series of problems at the crossroad of cultures" (Bernard, 2015a) (henceforth HistSoP). The term 'series of problems' itself was originally introduced in this framework.…”