Developing problem solving competences through the resolution of contextualized problems with an Advanced Computing Environment

The paper shows how problem solving competences can be developed by solving contextualized problems using an Advanced Computing Environment (ACE). An ACE is a computer system which enables its user to perform numeric and symbolic computations, graphical representations in two and three dimensions, insert embedded components and create interactive worksheet, all in the same user-friendly environment. An ACE allows students to approach a problematic situation in the way that most suits their thinking, to use different types of representations according to the chosen strategy and to display the whole reasoning together with verbal explanation in the same page: in other words, they can fulfill all the processes that problem solving involves. This paper analyzes a problem solving activity with an ACE proposed by the Department of Mathematics of the University of Turin, and clarifies, also through examples, how the use of the ACE makes it possible to solve real and relevant problems, facilitates the comprehension of the situation and of the Mathematics laying behind and enhance critical thinking.