Analytic Geometry as a Precursor to Calculus

The teaching of calculus in the high school has been an issue quite heavily debated for the last few years. Educators, mathematicians, and textbook writers have written much concerning how and when to teach calculus. However, few people have written concerning the prerequisites necessary for calculus. The basic assumption underlying this study was that there would be advantages present if a student could have a thorough understanding of analytic geometry before he encounters a calculus course. This claim is made because; first, the student would probably be able to concentrate on the calculus itself and not be slowed by a lack of knowledge about analytic geometry. Second, since most calculus courses include some analytic geometry, some analytic geometry topics would be presented to the student for a second time. The primary objectives of this study were 1) to determine those specific topics of analytic geometry which are recommended as essential prerequisites to calculus; 2) to identify topics taught in analytic geometry which are contained in ten selected high school mathematics text books and 3) to determine if a need exists for teaching analytic geometry as a prerequisite to calculus. In reviewing the literature, the investigator located some published material which indicated a need for teaching analytic geometry as a prerequisite to calculus. A criterion list was developed by reviewing the recommendations of the School Mathematics Study Group (SMSG), University of Illinois Committee on School Mathematics (UICSM), and the Committee on the Undergraduate Program in Mathematics (CUPM), and three college calculus textbooks. The topics on the criterion list should exemplify 1) the recommendations of the mathematics study groups and 2) content of the college level analytic geometry textbook. The criterion list of analytic geometry topics was then compared with ten state-approved twelfth grade textbooks. The evaluation of the textbooks consists of finding the prescribed topics and then determining how many pages were allotted to the topic in each book. It would seem that the topic on the criterion list were important for most of the ten textbooks had some pages allotted to the discussion of each topic. No attempt was made by the investigator to determine which textbooks were better or which ones contained more material concerning analytic geometry. All the investigation attempted to do was to identify those topics in analytic geometry which were important as prerequisites to calculus and then compare this list with certain twelfth grade textbooks