Abstract
Most authorities recognize the fact that mechanical drill unaccompanied by insight and understanding yields disappointing results in the mastery of any subject. To offset the danger of becoming only a drill sergeant, or merely a digit pulled about by the strings of habit, I have undertaken to acquaint myself with background material for the teaching of mathematics. I have undertaken it also for another motive. I realize that the development and maintenance of interest in mathematics depend largely on the presentation of the subject by the teacher. I know, too, that even brighter students progress faster when they are interested--when they see a purpose. There is definitely a high correlation between achievement in mathematics and the pupil's attitude toward it.|I hope to achieve from this study a richer background; to augment my ideas of the beauty, value, meaning, and importance of mathematics; to gain an appreciation of its present day needs; to make an acquaintance with its progress in America; and to acquire a proper esteem for some leading American mathematicians. With a good background the teacher who desires proper attitudes in the pupil may more successfully motivate interest and progress. That teacher may be able to realize the truth of Kasner’s and Newman’s statement:|". . . .with the aid of mathematics and the imagination the very small, the very large-- all things may be brought within man’s domain."|The preceding thoughts imply that I recognize, as I do, the validity of the pedagogical viewpoint that, for an individual to use effectively any particular body of technique, his knowledge should extend a reasonable distance beyond the level at which he will apply the technique.|Felix Morley says, "Education .... should be exciting and not boring; a cooperative quest and not a regimented route march.I agree with Mr. Morley. Unfortunately, however, education is not always a cooperative quest. Immediate ends tend to obscure a teacher’s vision and impel him to teach pages in a course of study--a subject--rather than children who have infinite possibilities. This study should serve to set up new guide posts along the road to improved teaching and learning.|It becomes the purpose of this thesis to find in the writings of authorities on mathematics and its applications ideas and counsels which will be valuable and useful additions to the teacher’s background and inspirational aids to teaching. The following chapters will be concerned with what critics say of the general need for mathematical training, the conditions that make motivation necessary, some applications of high school mathematics, its cultural values, a brief account of the advance of mathematics in America, and some thumbnail sketches of American mathematicians.|Just as we wish the surgeon to be more than a skillful technician so we may expect the teacher to be more than a drill sergeant. Assuming he has a technical knowledge of high school mathematics he should be a better teacher who likewise recognizes some of its values.|I dedicate the labours involved in assembling the following pages to my belief that teachers|".... need not only a thorough acquaintance with general knowledge (as well as with their specialized subjects), but also a passion for translating that knowledge to others sufficiently intense to weather the rigors of classroom life."