Verso una storia della psicologia cognitiva applicata:Ernst Mach, il “metodo Jacob” e l’insegnamento della matematica in Austria agli inizi del Novecento

The contribution illustrates research carried out in the History of Mathematics Education based on integrated fields; that of the History of Psychology and the Mathematics Education. The research concentrated on identifying the method-ological principles used in the teaching of Mathematics in the Austrian Secondary Schools, particularly in the city of Trieste before the First World War. Regarding the methodologies adopted in the Trieste Secondary Schools during the last years of the Hapsburg period, the influence of epistemological theories was identified, which had its author in the Austrian Physicist and Philosopher Ernst Mach (1838-1916). On the basis of his ideas, the so-called ‘Jacob Method’ was developed, named after the person who proposed it, Josef Jacob (1859-1918). It was applied in the teaching of Mathematics in the Austrian Gymnasium. This ‘practical’ method, which is analysed from a historical and epistemological point of view in the contri-bution, is illustrated in a text (Jacob, 1913) whose preface is written by Mach him-self. Mach recognizes paternity of the cognitive theories, first of all of the general principle of the economic function of Science (understood as ‘Economy of Thought’) which inspired Jacob when he wrote the work.