Reconstructions are critical in giving body to the history of dance. For student dancers, participating in reconstructions is a participation in both the legacy of dance and in dance as a form of cultural discourse. When choreographers generate movement vocabulary and improvisational parameters together with performers, the resulting collaborative open structures expand the choreographic arena. Although the initial idea of the dance is that of the choreographer, the dance would not exist if it were not for the dancers' involvement in the choreographic process. Reconstructing dances as collaborative open structures raises challenging questions for educators. How can such dances be reconstructed? How can student dancers be prepared for participation in this expanded arena? The works of several choreographers engaged in collaboration are explored. The author concludes with an examination of pedagogical possibilities of reconstructions by using as an example one of her choreographic reconstructions with university students.