Relations entre les grandeurs et les nombres dans les mathématiques de l'école primaire. Évolution de l'enseignement au cours du 20e siècle. Connaissances des élèves actuels.

摘要

During the last 150 years, relationships between quantities and numbers have deeply changed in academic mathematics, taught mathematics, and in everyday life. We want to understand these relationships at french primary school in mathematics education nowadays and foresee other possibilities for the future. Our framework is the antropological theory of the didactic (Chevallard).We have particularly developed the study of the teaching of metrical system, system of place value for whole numbers and links between both; and started the study of relationships between calculation (meaning, rules of calculation, types of numbers) and quantities (notably length and diagrams with dimensions).Our study is developing into three directions which echo one to another:- links between quantities, numbers, calculation and everyday life pratice before the reform of modern mathematics; breaks the reform caused in these links. Our analysis is based on a corpus of texts made up of national curriculum and textbooks mainly from 2nd and 3rd grades, over the 20th century;- academic mathematical knowledge. On the one hand, we want to identify transposed knowledge at several periods, on the other hand, we want to identify conditions for mathematical theories (possibly to be written) which could be used as reference for the teaching of quantities, numbers and calculation. For that, we take into account mathematical and didactical needs: notably tasks, rationales of rules for students, consistency of knowledge, continuity of learning;- knowledge of present students (277 on 5th grade). We want to better define some potential breaks and gaps highlighted with studies of links and academic knowledge.