Proportionality and linear function Didactic characteristics, causes and effects of curriculum changes and reforms in compulsory french school system ; Proportionnalité et fonction linéaire Caractères, causes et effets didactiques des évolutions et des réformes dans la scolarité obligatoire
In France, the concepts of ratio and proportion have disappeared from secondary education syllabuses since 1970, when the linear function was supposed to reformulate the proportionality between magnitudes. But in the new organization of teaching contents, the linear function is only an example of a numerical relation, so that nowadays people teaching at any level of education can neither use the linear function nor ratios and proportions to deal properly with elementary arithmetic problems. Looking for a logical and functional articulation of the notions of numbers, variables and functions for a long term learning process emphasizes the fact that dealing with the environment of magnitudes through the practice of ratios, measures and proportionality is absolutely necessary in the genesis of these concepts. Today, French compulsory education, mainly concerned with pupils' future schooling tends to ignore the notions that used to have a strong status in the organisation of a mathematical knowledge which is still in use in popular culture and the working world. Giving up the concepts of ratio and proportion has not been compensated by the expected supplementary steps necessary as much for school institutions as for social and professional institutions. The sense of failure felt by society following this conceptual break from the knowledge of proportionality can't be solved by any pedagogical or psychological remedy. The various institutions involved have to treat this problem by a scientific, technical and political approach with "micro" and "macro" didactical knowledge, the ignorance of which has probably been one of the causes of the difficulties generated by the successive reforms. ; En France les concepts de rapport et de proportion ont disparu des programmes du secondaire depuis 1970 où la fonction linéaire est censée reformuler la proportionnalité entre grandeurs. Mais dans la nouvelle organisation des savoirs à enseigner la " fonction linéaire " n'est qu'un exemple banal de relation numérique de telle sorte ...