The purpose of this study is to investigate if and how information and communications technology (ICT) helps to improve first grade students´ basic geometry achievement regarding circles and triangles. Our research compares the level of geometrical competence of the students taught using our ICT oriented learning method specifically targeting 'Realistic Mathematics Education” (RME) and the van Hiele model for geometry concepts, as opposed to 'traditional” teaching methodology. The designed software consisted of a story and several activities with and without the use of computers for circles and triangles. The study involved first grade students in Crete and Athens, who were divided into two groups (experimental and control). The experimental group consisted of 113 students who were taught about circles and triangles with the support of computers. There were 121 students in the control group who were not exposed to the computer-oriented curriculum. Students in both groups were pretested and posttested for their geometry performance. The results of the study indicate that teaching and learning through ICT is an interactive process for students at the first grade level and has a positive effect for geometry learning using the background of RME and the van Hiele model.