In this article two approaches to teaching and learning mathematics namely Realistic Methematics Education (RME) and the approach developed by the national Council of Teachers of Mathematics (the NCTM approach) are compared in order to find the similarities and the differences between the two approaches. Two of the most important similarities are that both approaches promote the active roles of students in the process of teaching and learning mathematics and that both approach emphasize the importance of knowladge construction in the student s mind. Two of the most important differences are that the characteristics of the RME approach are more rigid and more specified than those of the NCTM approach and that the process of knowladge construction in the RME approach tends to be more personal than that in the NCTM approach.