Understanding rigid geometric transformations: Jeff's learning path for translation

YANIK H. B., Flores A.

JOURNAL OF MATHEMATICAL BEHAVIOR, vol.28, no.1, pp.41-57, 2009 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.jmathb.2009.04.003
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.41-57
  • Keywords: Rigid geometric transformations, Translations, Learning trajectory
  • Anadolu University Affiliated: Yes


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.