How to teach mathematics: Some suggestions from Herbartian tradition

The German Johann Friedrich Herbart (1776-1841), recognized in mathematical psychology as a forerunner in the measurement of mental phenomena – in a study of psychic events which was not only qualitative but also quantitative, based upon mathematics (specifically, calculus) –, stood out also for his activity in the psycho-pedagogical field and for his theory of education, in which mathematics played a fundamental role. His contribution was, in particular, considerable for mathematics education between 1800 and 1900 in the world of German culture, where important reformist tendencies in the study of teaching problems matured. After a brief sketch of Herbart’s life and work, the paper will focus on these aspects, giving methodological suggestions which can be relevant and useful for mathematics education of today.