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

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