The paper discusses the perspectives of teaching geometry based on the study The International Commission on Mathematical Instruction ICMI. Bearing in mind the current needs in geometry teaching, we considered that the topics of space and spatial reasoning should be part of it as key issues, as well as teaching approaches, RME, learning through (re)discovering mathematical ideas, the role of textbooks in the initial mathematics education, and so on. Therefore, this research paper offers a general insight into our need to deal with these topics, and invites researchers from the broader mathematical community, who we herewith familiarize with the results of our research in the sphere of initial geometry teaching in Serbia.