Several years ago we presented an experimental, discovery-learning approach to the active learning of greedy algorithms. This paper presents GreedEx, a visualization tool developed to support this didactic method. The paper states the design goals of GreedEx, makes explicit the major design decisions adopted, and describes its main characteristics in detail. It also describes the experience of use, the usability evaluations conducted, and the evolution of GreedEx in these years in response to the findings of the usability evaluations. Finally, the positive results obtained in an evaluation of educational effectiveness are shown. The paper has three main contributions. First, the GreedEx system itself is an innovative system for experimentation and discovery learning of greedy algorithms. Second, GreedEx is different from other visualization systems in its support to higher levels of learning, in particular evaluation tasks. Finally, GreedEx is an example of a medium-term research project, where an educational system was designed from explicit learning goals and was later refined in a user-centered design process involving instructors and students, before carrying out a successful evaluation of educational effectiveness.