The present research presents a unique strategy for the teaching of the fundamentals of geometry and mathematics for design students. It was possible to plan a series of activities in which puzzles, problem- solving strategies and geometrical concepts were to be related in a structurally integrated fashion. This structure, which was planned to allow the reconstruction of knowledge on geometry by design students, went through two stages of exploration and analysis. Initially, the challenges were interpreted according to the instructor´s viewpoint, hereby represented by the author. In this first stage, the author tried to answer the following questions: What thinking strategies are at play? In what way can the contents be explored? What are the solutions to the challenges and how can they be obtained ? Secondly, the challenges were presented to the students, who interacted with the instructor in an individual manner. From then on, the students were able to discover new relationships. Their expectations, reactions and thinking strategies were observed by the author along five two-hour meetings and then analyzed. Three PUC-Rio design students took part in the research, which involved taping of their dialogues with the instructor while attempting to solve the problems presented to them. In terms of theoretical framework, one can say that the investigation was, at first, strongly influenced by van Hiele`s model for the development of geometrical thinking. In this case, the first three of the five thinking levels proposed by van Hiele (visualization, analysis and informal deduction) were noticeable. As to the grouping and reorganization attempts, not only of the parts in the proposed exercise structures but also of the exercises themselves (considering these as parts of a bigger structure), they were mostly based on the gestalt structuralist viewpoint, having Max Wertheimer as the main theoretician. Another essential reference was George Polya, for having shown the importance of figure sketching, of the use of auxiliary problems as well as of the heuristic thinking involved in the process of problem resolution.