In this article, we examine how it is possible, in the teaching and learning of geometry, to bridge the gap between problems involving drawings and figures, which is essential to the learning of mathematical proof. More precisely, the way students' drawing perception has to evolve, from Iconic Visualization to Non-Iconic Visualization (Duval, "Annales de Didactique et de Sciences Cognitives", 10, 5-53, 2005). We show that the Instrumental Deconstruction process is multifaceted and central in this evolution. We present a theoretical framework, in relation with an experiment based on a 3D dynamic geometry environment. Based on a case study, we show that construction tasks with specific representations make the instrumental work play a key role in the learning of geometry.