A Didactical Analysis of Teaching Practices Around Differentials Equations in Tunisian School Context

Abstract

The teaching of differential equations is often viewed from an interdisciplinary perspective that justifies the rationale for this notion in the secondary cycle. The history of the teaching of this notion in the Tunisian educational system shows a diversity of approaches which seem to evolve in the direction of modeling extra-mathematical situations and dialectic between semiotics registers. This research is part of the anthropological theory of didactics and analyzes the didactic transposition process developed by the Tunisian institution around differential equations over successive reforms. Three dimensions of analysis were taken into account in this study: a historical-epistemological dimension which makes it possible to identify the dynamic nature of the notion of differential equation through the stages of its constitution and to determine its meaning through the problems addressed in teaching and their development, an institutional dimension addressed by ecology and praxeology analyses based on the programs and official textbooks. Current institutional practices allow us to glimpse a dynamic at scale relating to the teaching of this notion. This aspect is nourished by sets of frameworks, flexibility between registers and interdisciplinary praxeology mobilized upstream and downstream of the work of algebraic resolution. Professional entry allows us to question the constraints for their effective implementation in classes. This dimension is analyzed from ten student notebooks considered as a first revealer of teaching practices in terms of resistance or change. This analysis of the notebooks make it possible to discover the main characteristics of the institutional relationship. The result of the analysis shows that the personal relationship of teachers perceived through the analysis of their didactic preparation with the object of knowledge differential equations, is not suitable to institutional relationship with this same object of knowledge.