There is a distinction between spatial abilities and geometric knowledge, but there are also several links: The relation is dialectical in the sense that at first learning geometry bears on children's spatial abilities which can in turn improve with their learning of geometry. However, this distinction and dialectical relation is not always sufficiently taken into account in teaching. On another hand, psychology is also interested in spatial abilities outside school and has developed some interesting concepts and technological tools based on virtual reality. This led a multi-disciplinary team of the university of Geneva involving mathematics educators, psychologists and specialists of educational technology to develop a research project using a virtual city to make students of grades 2 to 4 develop some spatial abilities and improve their geometrical knowledge. This paper presents the background of this project and a first pilot study.