  We outline an unified introduction to the evolution equations of classical
and quantum systems intended for a high school students audience. The attempt
consists in circumventing the lack of mathematical knowledge with the use of
simplified forms of numerical analysis. The aim is to allow students to
approach theoretical features as well as computational aspects of the evolution
equations. In particular, the possibility to compute and analyze approximate
solutions of the dynamical laws of classical, stochastic and quantum mechanics
enables to highlight the distinctive role played by probability in different
contexts. As computer support for numerical analysis we selected the
spreadsheet. It is a work environment usually presented in high school and it
is an ideal tool for an intuitive approach to numerical computation through
recursive algorithms. The proposal was presented to an audience composed by
students of the course of Didactics of Physics and of high school Science
teachers.
