The aim of this article is to discuss proposal related to the teaching of Geometry defended by the Modern Mathematics Movement (MMM) on the basis of an analysis of the theses and dissertations with these movement as a central theme. These analyses indicate that Geometry, in the elementary school, was neglected in these curriculum innovations, despite the fact that proposals for change had not been conceived in this way. The text raised questions related to the teaching of Geometry, which merit further investigation in order that the role of Geometry in the MMM be better understood. We believe that research based in the notion of school culture will bring answers to many of these questions, contributing significantly to a better understanding of the MMM.