| Sumario: | The article presents information on the geometry course in high schools of the U.S. It is assumed that the geometry course in the question asked refers to one commonly taught in the tenth grade. While the present geometry course contributes to each of the goals mentioned, it does so in a very trivial manner. The important information about geometrical objects and their measures is now taught in elementary school. From 324 B.C. to A.D. 1827, only Euclidean geometry existed as a means of studying space, and the only controversial question was the possibility of proof of the parallel postulate. Today geometry must be conceived of as a study of spaces. Instruction in geometry must be brought more and more into relation with algebra and its structures, and developed to permit and exhibit the use of algebraic structures and techniques. Geometric instruction should be included in every year of study beginning in grade seven and continuing through grade twelve. It should grow in complexity and abstraction, and at all times be related to algebraic methods that enable it to become embedded in a vector-space structure.
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