JOURNAL OF MATHEMATICAL BEHAVIOR, vol.28, no.1, pp.41-57, 2009 (ESCI)
This article describes the development of knowledge and understanding of translations of Jeff, aprospective elementary teacher, during a teaching experiment that also included other rigid transformations. His initial conceptions of translations and other rigid transformations were characterized as undefinedmotions of a single object. He conceived of transformations as movement and showed no indication about what defines a transformation. The results of the study indicate that the development of his thinking about translations and other rigid transformations followed an order of (1) transformations as undefined motions of a single object, (2) transformations as defined motions of a single object, and (3) transformations as defined motions of all points on the plane. The case of Jeff is part of a bigger study that included four prospective teachers and analyzed their development in understanding of rigid transformations. The other participants also showed a similar evolution. (C) 2009 Elsevier Inc. All rights reserved.