The "Jacob Method": an example of application of cognitive theories in the period of the introduction of Calculus in Austrian secondary mathematics instruction

Our study focuses on a practical mathematics teaching method applied in Austrian secondary schools at the beginning of the twentieth century. The method, proposed by Josef Jacob, the Director of a “Gymnasium” in Vienna, was inspired by the cognitive theories of Ernst Mach, who recognized this by writing the preface to the volume in which the method is described. We present its theoretical framework and give some examples of application, in particular to infinitesimal calculus.