The Teaching of Geometry at the Pre-College Level : Proceedings of the Second CSMP International Conference Co-Sponsored by Southern Illinois University and Central Midwestern Regional Educational Laboratory

## Boolean algebra of cyclic classes). Any n-gon has a unique decomposition as a sum of n-gons of the atomic cyclic classes. (vi) Any cyclic class consists of all n-gons with the property that certain atomic components are the zero n-gon. Front Matter....Pages I-VIII Background....Pages 1-4 The CSMP Development of Geometry....Pages 5-9 Geometry Conference Recommendations....Pages 10-11 n -Gons....Pages 12-33 Inversive Geometry....Pages 34-45 The Problem of Relating Mathematics to the Possibilities and Needs of Schools and Children....Pages 46-60 An Example of the Passage from the Concrete to the Manipulation of Formal Systems....Pages 61-76 Geometrical Activities for the Upper Elementary School....Pages 77-118 The Teaching of Geometry Present Problems and Future Aims....Pages 119-136 Geometry Between the Devil and the Deep Sea....Pages 137-159 Topology in the High School....Pages 160-177 Some Experiments on Structured Learning....Pages 178-200 Topology and Transformations in High School Geometry....Pages 201-205 The Use of Research Problems in High School Geometry....Pages 206-213 Geometric Algebra for the High School Program....Pages 214-224 The Geometry Relevant to Modern Education....Pages 225-241 A First Introduction to the Notion of Topological Space....Pages 242-254 The Introduction of Metric by the Use of Conics....Pages 255-271 The Position of Geometry in Mathematical Education....Pages 272-276 The Geometry and Algebra of Reflections (and of 2 × 2 Matrices)....Pages 277-299 On the Teaching of Geometry a Potpourri....Pages 300-310 A Foundation of Euclidean Geometry by Means of Congruence Mappings....Pages 311-314 Learning and Teaching Axiomatic Geometry....Pages 315-327 The Development of Euclidean Geometry in Terms of Translations....Pages 328-334 A Logical Approach to the Teaching of Geometry at the Secondary Level....Pages 335-358 Problems and Possibilities in the Assessment and Investigation of Mathematics Learning....Pages 359-373 Genetic Development of the Congruence Axioms....Pages 374-376 Back Matter....Pages 377-387