Teaching and learning mathematics in the presence of new technology raises many challenges, at least for the teachers and curriculum developer involving either in instruction or pedagogical designing of the media. Many teacher are disillusioned by their experience with technology integration so far: Also, the provision of formal texts, as the main media in some countries such as ours is another challenge. In this article we argue that the philosophical view of constructivism provides the theoritical basis that assure the quality of learning in de/open institutions and enhance the role of using metaphor in curriculum development as well. The constructivism yield the problem-based learning approach and that in turn lead us to redefine the curriculum, or at least to rearrange the syllabuses of each subject material, and pay a special role for the metaphors to develop new ideas and skills. In this way, the learner sees the whole subject matter coherent that could be constructed basicly on her/his previous knowledge. At the end we shall demonstrate a chapter of a BSc course on algebra, while using the different levels of metaphors to induce new concepts and skills and develop the relevant course involved. Title:CONSTRUCTIVISM AND THE ROLE OF METAPHOR IN LEARNING MATHEMATICS Target Audience: university teachers Number of participants: 30 persons Goals: New methods of teaching Reasons for attending: share experience Needs: either powerPoint or projector Keywords: pedagogical design, curriculum development, constructivism, problem-based learning, metaphor, inquiry-based approach, finitely-generated subgroup, cyclic group, additive group of integers.