The purpose of this study is to investigate if information and communications technology (ICT) helps improve kindergarten students' basic mathematical achievement regarding addition. Our research compares the level of mathematical competence of the students taught using our ICT oriented learning method which specifically takes advantage of "Realistic Mathematics Education" (RME) for the concept of addition, as opposed to traditional teaching methodology. The designed software consisted of a story and several activities with and without the use of computers for addition. It was designed following the background of the RME theory. The study dealt with kindergarten students in Crete, who were divided into two groups (experimental and control). The experimental group consisted of 165 students who were taught addition with the support of computers. There were 170 students in the control group which were not exposed to the computer oriented curriculum. Students in both groups were pre-tested and post-tested for their mathematical achievement. The results of the study indicated that teaching and learning through ICT is an interactive process for students at the kindergarten level and has a positive effect for the learning of addition using the background of the RME theory. Also, the most important result of this study was that this teaching intervention appeared to be more effective for the kindergarten students with medium-level mathematical abilities.