Hellmich, Eugene W. (Eugene William), 1902-||Beach, James W.
M.S. (Master of Science)
Department of Mathematics
The major objective of a unit prepared combining the two topics of locus and coordinate geometry was to make more efficient use of time by teaching the two topics simultaneously rather than by teaching them separately!, Other objectives were: to cover the topic of locus, to demonstrate the interrelationships between algebra and geometry, to review the algebra, to review some previously covered theorems from a different point of view, to strengthen the student's concept of graphing, and to father develop the concepts of deductive proof. A thorough study and review of recent geometry textbooks disclosed that no such teaching aids presented locus and coordinate geometry simultaneously. These textbooks did suggest, however, that the methods of coordinate geometry might be used to prove theorems of plane geometry. Therefore, the unit began with a development of the fundamental concepts and vocabulary of coordinate geometry. These concepts were then utilized as the basis for proving the traditional locus theorems. The writer taught the unit early in the second semester of the school year 1961-1962, to three tenth grade geometry classes at West Rockford Senior High School, in Rockford, Illinois. Ninety students were enrolled in these three classes. At first some of the students had considerable difficulty understanding the concepts of coordinate geometry, but in time most students did well and enjoyed the algebraic approach to locus. Although a few students learned little, many of the better students preferred algebraic proof to geometric proof. The general student interest generated by observing that familiar geometric theorems could be proven by algebra and techniques of graphing motivated most students to work at a level correspondent with their respective capabilities. Unfortunately, it was necessary to spend four more days on this unit than is necessary in the regular chapter on locus. More coordinate geometry was covered, however, than is usually taught in the eleventh year at West High School, leaving a savings of approximately two weeks time. In the writers opinion, the students preformed at least as well on this unit as they would have on the standard chapter on locus, indicating that locus and coordinate geometry may be combined without any significant loss of academic achievement. The unit was extremely successful as an opportunity to review algebra, which is normally neglected in the tenth year program. Almost all students profited by this exposure to algebraic ideas. Most students were able to see clearly some interrelationships between algebra and geometry and to realize that proof is not limited to geometry, but is the very essence of all mathematics.
Gustafson, Roy David, "Coordinate geometry and locus" (1962). Graduate Research Theses & Dissertations. 1967.
Northern Illinois University
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