First I will show how it is possible to solve a classical and difficult geometric problem using an analysis and synthesis reasoning led with a dynamic and experimental way (determine a triangle admitting 3 given rays -with the same origin- as bisectors). We will discover the richness of this wider approach which is a true mathematic research.
Second, I will present a sequence of various examples, showing how to use Cabri to illustrate all parts of Mathematics apart of geometry: analysis, statistics, simulations, space representations, analytic geometry and so on..
At last, I will show how we can completely change the classical way of introducing in our teaching the square and the inverse functions ( x ¾®x² and x ¾® 1/x): I call it an inversed way. After that, I will present some inversed problems that are problems especially created for training students in this new ways of thinking and searching.
In my conclusion, I will speak about general inversed problems that are particular problems we can use out of the paper and pencil field