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In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.
Introduction. I. Geometry and Geometry-Teaching through the Ages; C. Mammana, V. Villani. II. About the Present ICMI Study; V. Villani. III. Acknowledgements; V. Villani. 1: Geometry: Past and Future. I. Everlasting Geometry; V. Lundsgaard Hansen. II. Finding Room in the Curriculum for Recent Geometry; J. Malkevitch. III. Space and Plane; A. Douady. 2: Reasoning in Geometry. I. About Reasoning in Geometry; R. Hershkowitz. II. Geometry from a Cognitive Point of View; R. Duval. III. Teaching and Learning Geometry in Contexts; M. Bartolini Bussi, P. Boero. IV. Springboards to Geometry; R. Lehrer, T. Romberg. V. The Role of Pupils' Spatial Knowledge in the Elementary Teaching of Geometry; R. Berthelot, M.H. Salin. VI. Deductive and Intuitive Approaches to Solving Geometrical Problems; K. Jones. 3: Geometry in our World. I. Geometry and Reality; J. Malkevitch. II. Recent Applications of Geometry; W. Meyer. III. Science and Technology in Geometry Textbooks; P. Legisa. 4: Computer Technology and the Teaching of Geometry. Introduction; I. Osta. I. Visual Phenomena in the Teaching/Learning of Geometry in a Computer-Based Environment; C. Laborde. II. Proof in Dynamic Geometry Contexts; C. Hoyles, K. Jones. III. CAD Tools and the Teaching of Geometry; I. Osta. IV. The Computer as a Context for New Possible Geometrical Activities; K.-D. Graf, B. Hodgson. 5: Geometryin the Classroom; R. Douady, B. Parzysz. 6: The Evolution of Geometry Education since 1900. I. The British Experience; H.B. Griffiths. II. The Evolution of Curricula as Indicated by Different Kinds of Change in Geometry Textbooks; M. Galuzzi, et al. III. General Tendencies in the Development of Geometry Teaching in the Past Two Decades; H.B. Griffiths, M. Neubrand. Appendix: Influences of History and the General Social Development on the Teaching of Geometry; M. Galuzzi, M. Neubrand. 7: Changes and Trends in Geometry Curricula. I. General Considerations on Curricula Designs in Geometry; V. Lundsgaard Hansen. II. Examples of Curricula Designs in Geometry; C.E. Vasco, et al. III. Looking Towards the 21st Century: Possible Trends in Geometry Curricula; V. Lundsgaard Hansen. 8: Assessment in Geometry. I. Dimensions of Geometry and Assessment; M. Niss. II. Assessing Reasoning Abilities in Geometry; J. Pegg, et al. 9: Teacher Qualifications and the Education of Teachers; M. Niss. 10: The Way Ahead; V. Villani on behalf of the International Program Committee. Bibliography. Appendix: Perspectives on the Teaching of Geometry for the 21st Century. List of Participants to the Catania Conference. Addresses of the Contributors. Index.