Perspectives on the Teaching of Geometry for the 21st Century

I. Geometry and geometry-teaching through the ages.- II. About the present ICMI study.- III. Acknowledgements.- 1. Geometry: Past and Future.- I. Everlasting geometry.- II. Finding room in the curriculum for recent geometry.- III. Space and plane.- 2. Reasoning in Geometry.- I. About reasoning in geometry.- II. Geometry from a cognitive point of view.- III. Teaching and learning geometry in contexts.- IV. Springboards to geometry.- V. The role of pupils’ spatial knowledge in the elementary teaching of geometry.- VI. Deductive and intuitive approaches to solving geometrical problems.- 3. Geometry in our World.- I. Geometry and reality.- II. Recent applications of geometry.- III. Science and technology in geometry textbooks.- 4. Computer Technology and the Teaching of Geometry.- I. Visual phenomena in the teaching/learning of geometry in a computer-based environment.- II. Proof in dynamic geometry contexts.- III. CAD tools and the teaching of geometry.- IV. The computer as a context for new possible geometrical activities.- 5. Geometry in the Classroom.- 6. The Evolution of Geometry Education since 1900.- I. The British experience.- II. The evolution of curricula as indicated by different kinds of change in geometry textbooks.- III. General tendencies in the development of geometry teaching in the past two decades.- Appendix: Influences of history and the general social development on the teaching of geometry.- 7. Changes and Trends in Geometry Curricula.- I. General considerations on curricula designs in geometry.- II. Examples of curricula designs in geometry:.- III. Looking towards the 21st century: possible trends in geometry curricula.- 8. Assessment in Geometry.- I. Dimensions of geometry and assessment.- II. Assessing reasoning abilities in geometry.- 9. TeacherQualifications and the Education of Teachers.- 10. The Way Ahead V. Villani on behalf of the International Program Committee.- Appendix Perspectives on the Teaching of Geometry for the 21st Century (Discussion Document for an ICMI Study).- List of Participants to the Catania Conference.- Addresses of the Contributors.