Date of Award
Master's Essay - Restricted
Master of Science (MS)
Mathematical and Statistical Sciences
Miriam E. Connellan
Until recent years the content of most high school geometry courses was essentially the same from school to school. Proof, congruences, constructions, and similarity were core concepts, taught on the basis of the Euclidean approach. Now, even at the secondary level, students are investigating some aspects of non-Euclidean geometry and learning methods of solving geometric problems different from the traditional methods based on Euclid.
Currently we are being told that teaching is no longer a matter of imparting facts and developing certain skills. Our essential task as teachers is to teach each individual how to teach himself in order that he might continue his education long after he has finished formal schooling. Our rapidly changing culture and technology make this imperative. The young person of today may have to prepare himself for several different kinds of occupations in the course of a lifetime as ones become obsolete, unfulfilling, or yield too little financially.
Releasing our students from the narrow confines of the traditional geometry course is a matter of keeping with the times mathematically. Happily, students are now spared the illusion that the Euclidean approach is "all there is" to geometry. At the end of year of study, they should have less of a sense of having "completed" a course in geometry. The inclusion of even a few new topics should reveal to them that many doors are yet to be opened.
George, Mary Francis, "An Introduction to Transformation Geometry" (1971). Master's Essays (1922 - ). 604.