Morphological Transition of Schooling in 19th-Century France

Abstract

The transformation over time of level sets—the sets of states for which a given function takes a given value—has no reason to be regular, especially in social science, where the structure of these level sets of a given variable may be altered by a fluctuating demography or disrupted by unexpected events, and where the actors contribute to shaping their space through investment policies. The pioneering construction of graphic derivatives of set-valued maps renews the understanding of dynamic level sets in social science. The exemplary case of schooling in 19th-century France shows the set derivatives of level sets and illustrates how the Franco-Prussian War of 1870–1871 disturbed the directions taken in 1867. A comparison of the observed changes of level sets with those observed under rational theoretical policies leads to the conclusion that the actors behaved with the ambition of optimizing the overall schooling incidence while reducing the gap between boys and girls.