A Survey Course for Teachers

Abstract

Much has been said and written concerning so called courses in high schools and colleges. In mathematics such courses are usually called General and are offered to freshmen. In college, the students enrolled in these courses often have had meager high school training and in general are poorly prepared. They seem to possess neither the desire to broaden their mathematical horizon, nor the capacity for the proper appreciation. One noteworthy exception is the course on The Significance of at the University of Buffalo.* After teaching a general mathematics course for college freshmen with results that were none too encouraging we decided to experiment with a survey course for mathematics majors offered to seniors and students beginning graduate work. Consequently, in the summer session of 1941 we offered a course called Mathematics for High School Teachers, its general aim or objective being stated in its description in the college catalogue: Topics from Higher Algebra and Geometry Designed to Strengthen Academically Teachers of High School Mathematics. Recognizing that the study of mathematics begins somewhere in the middle and proceeds both toward its beginnings or foundations and toward abstract generalizations, an effort was made to take the class in both directions as far as time and abilities would warrant. The outline for the course included the following topics :t 1. Definitions of mathematics. 2. Evolution of the number system: development of the number system from basic postulates; other number systems; elementary number theory. 3. Algebra and logic; Boolean algebra and other algebras. 4. Fundamental theorem of algebra. 5. Infinite series. 6. Criterion for ruler and compass constructions; trisection of an angle, duplication of the cube, squaring the circle. 7. Statistics, probability, interpolation, extrapolation. 8. Geometries: Lobachevskian, Riemannian, projective, modern. 9. The n nth roots and logarithms of complex numbers. 10. Meaning of topology. 11. for recreation; mathematical puzzles. 12. Selected topics from the history of mathematics; famous mathematicians, historical and contemporary.