An analysis of a course of study in ninth grade algebra designed to teach postulational thinking
Koca, Harlan James
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Although tenth grade Geometry is taught within a framework of postulates, utilizing the deductive method of thinking, the typical ninth grade Algebra text uses, primarily, an inductive approach and pays nothing but lip service to the axiomatic foundation which, in fact, undergirds the whole of Algebra. The author wondered why this difference in approach to the two subjects existed. In his reading, he found that several authors felt that Algebra should be taught in a rigorour, deductive fashion, while others contended that ninth graders would not be mature enough, intellectually, to cope with the abstraction that a postulational approach to Algebra would require. Clearly, there was a need to attempt to teach Algebra, at least in part, as a postulational system in order to determine whether or not pupils could effectively learn Algebra treated in this manner. With the approval and encouragement of Frank Allen, Chairman of the Department of Mathematics, Lyons Township High School and Junior College, La Grange, Illinois, and with the consent of George S. Olsen, Superintendent-Principal, classes were chosen in which such an approach to Algebra could be attempted by the author. It was determined that new materials should be written in order to supplement the text book used and this was accomplished with the invaluable guidance of Dr. Eugene Hellmich, Chairman, Department of Mathematics, Northern Illinois University, and Dr. Rodney Anderson, who was, at the time, also on the staff of the Mathematics Department at Northern Illinois University. Without the assistance of these men, this study could not have been made. In addition, the author wishes to thank Miss Elizabeth Pry, of Lyons Township High School, who conducted the class for the control group, the various teachers at Lyons who taught Plane Geometry to the experimental and control groups and the author's wife who spent many hours in preparing and editing the manuscript.