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44(1)
Les trois articles qui constituent le premier numéro du volume 44 témoignent d’une grande diversité dans les thématiques abordées et les systèmes éducatifs considérés : l’interdisciplinarité en mathématiques et sciences physiques en Grèce, l’enseignement de la multiplication en France ou encore une étude comparative de l’enseignement des fonctions quadratiques dans cinq pays (Brésil, France, Japon, Espagne et Vietnam). Les approches théoriques utilisées dans ces travaux sont la Théorie de l’Action Conjointe en Didactique, la Théorie Anthropologique du Didactique ou la Théorie des Situations Didactiques. Les trois langues de publication de la revue sont représentées, en l’occurrence le français, l’espagnol et l’anglais.
1. Interdidactique des mathématiques et de la physique
Focusing on the Greek educational system, this article deals with the didactic discontinuities manifested at the mathematics-physics interface, concerning the mathematical concept of the parabola. This type of conic is exploited in physics for modelling the ballistic motion of projectiles. As a Greek high school physics teacher, our interest is drawn to a curricular effect associated with the transfer of mathematical concepts into the science classroom. Indeed, high school science students (16-17 years old) discover the graphical representation and the equation of the parabola for the first time, in physics, long before the subject of conic sections was taught in mathematics. As a result, it is the teacher in charge of physics who transmits the first basic knowledge to the students, according to his or her own conceptions, while the introduction of the concept by the teacher of mathematics is delayed during the school year. We are interested in understanding the deep motives of the curricula designers regarding the two disciplines, about which no official moments of synergy are created, until now. The fragmentation of this knowledge (but also of many others) is likely to lead to learning obstacles. We apply a method of didactic analysis of school textbooks, developed from the notions of tool-object dialectic, semiotic register, rationality framework and praxeologies. The results show remarkable didactic discontinuities, which can be overcome by implementing a teaching based […]
2. Ressources pour revitaliser la recherche sur l’enseignement et l’apprentissage de la multiplication à l’école élémentaire
Based on documentary sources available in the Guy Brousseau collection, we study a set of teaching decisions designed and tested over several years within the framework of the Theory of Didactical Situations in a French primary school. The analysis and the interpretation of the productions found allows us to make visible new knowledge that enriches the activity of the researcher in didactics of mathematics as well as that of the teacher educator. Initially, the research focused on division, and in the course of this trajectory, we approached the process of inventing a technique for constructing a multiplication algorithm.
3. Une étude comparative de l'enseignement des équations quadratiques dans cinq curricula scolaires : le Brésil, la France, le Japon, l'Espagne et le Vietnam
Comparative studies often aim to identify and explain differences and similarities of didactic phenomena in different school contexts. In mathematics education, comparative studies have been undertaken with a variety of aims, about a diversity of mathematics topics and their results depend on the theoretical approach, methods, and levels at which the comparison is done. We start by presenting the theoretical and methodological bases, according to the anthropological theory of the didactic (ATD), based on which we have carried out a comparative study about a specific mathematical theme in the context of 5 different educational systems. More concretely, this paper focuses on comparing the institutionally offered curricula by 5 countries (Brazil, France, Spain, Japan and Vietnam) concerning the algebraic resolution of quadratic equations, through the analysis of curricula and a selection of representative textbooks. We aim to identify common and alternative didactic choices and the possible reasons for these choices, as well as the set of conditions and constraints set up in the different school contexts when this piece of knowledge is planned to be taught.