The information and communication technologies of Web 2.0 are arriving in our schools, allowing the design and implementation of new learning environments with great educational potential. This article proposes a pedagogical model based on a new geometry technology-integrated learning environment, called "Geometry 2.0," which was tested with 39 sixth grade students from a public school in Madrid (Spain). The main goals of the study presented here were to describe an optimal role for the mathematics teacher within "Geometry 2.0," and to analyse how dynamic mathematics and communication might affect young students' learning of basic figural concepts in a real setting. The analyses offered in this article illustrate how our "Geometry 2.0" model facilitates deeply mathematical tasks which encourage students' exploration, cooperation and communication, improving their learning while fostering geometrical meanings.