Improvements in teaching and learning using CAS

In this work we wish to present an innovative proposal for a differential equations course supported by software tools. The aims we have placed in such experience are principally three: - we are interested in showing the students of the concrete applications of the daily life that can be described and interpreted through the use of the differential equations, discovering in such a way, the real adhesion between experience and mathematical environment, giving motivation to the students for the study of the subject; - we want to add the interactive use of mathematical software to the traditional used didactic methodologies: in fact studies recently performed have put in evidence than the interactive use of such tools allows to arrive at a superior abstraction level in the solution of mathematical problems, avoiding more easily the happen of misconception due to the creation of wrong mental models; - we want to stimulate the student to have a more critical attitude towards the solution of the problem described by a differential equation. It is well known in fact that the differential equations represent a base tool in the mathematical modelling in varied applicative fields as physic, astronomy, economic sciences and others. According to the problem which has determined the equation and to the kind of differential equation which is wanted to solve, we wish that the student to establish in critical way if it is necessary to find a solution qualitative or quantitative.