The purpose of this study is to review the changes that computers have on mathematics itself and on mathematics curriculum. The study aims at investigating different applications of computers in education in general, and mathematics education in particular and their applications on mathematics curriculum and on teaching and learning of mathematics. There are three broad categories of the applications of computers in the field of mathematics education: computer assisted instruction (CAI), student (educational) programming and general purpose educational tools such as spreadsheets, databases and computer algebra systems (CAS). This study presents a historical background and attempts to describe the paradigmatic shift in the use of computers in mathematics education from behavioristicly oriented CAI movement towards constructivist based student programming movement.