Geometric Visualization: How to Acquire It Using Dynamic Geometry Systems?

Teaching/learning geometry is arduous for people with visualization deficiencies. We present here our recent research concerning dynamic geometry systems and their influence in learners´ mental representations of geometric objects: how the comprehension of concepts in geometry can be improved. Our psychological supports are PIAGET and VYGOTSKY researches, and our mathematical support is the VAN HIELE ´s model, which deals with geometric reasoning. We also used some theories from problem resolution and knowledge representation, mainly the ones commonly used by computer and cognitive scientists. In order to evaluate our research we developed two experimental procedures: 1. with naif learners, exploring the content of triangles: classifications, sides, etc; 2. with advanced learners, investigating contents, volume calculations, and formula deductions using the CAVALIERI´s principle. The results show that introducing dynamic geometry systems in these processes has improved learners´ performances on visualization of geometric objects and comprehension of geometric concepts.