Emthusiasm about the introduction of computers into mathematics education is widespred. But, the perspectives about the relationship between mathematics education and computer are diverse. The purpose of this study is to examine theoretical background for using computers in mathematics education. In spite of the pedagogical possibilities of computers. only a small minority of mathematics teachers are using computers in mathematics classroom. It is natural to seek this obstacles within theoretical background of the teachers who manage computers, In this study, We discuss the problems in the two sides. First, due to increased computer activity, relationship of mathematics in school with mathematics in society is changing. It is tension between academic mathematics and practical mathematics. School mathematics have to be changed toward stressing practical mathematics. Second problem is the dialectical relationship between the individual and the collective. While maintaining a respect for the individuality of student contributions. We take into account the social dimension of mathematical meaning-making. We discussed theoretical clarification of work collaborative learning. We propose the case study for the roles of computer in collaborative mathematics learning.