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Relation of some of the modern concepts of mathematics to teaching in the secondary schools

Savage, Richard Preston
Scope and Method of Study: This study was written in an attempt to convey to the high school mathematics teacher some of the connotations of "modern mathematics". It discusses some extremely simple, but basic, concepts which the high school student should have even before he reaches high school, but which are not usually taught below the college level today. The preparation of the study necessitated a review of literature dealing with the teaching of mathematics from about 1945 to the present time. This literature was chiefly mathematics periodicals since up-to date mathematics textbooks are just now beginning to emerge.
Findings and Conclusions: Mathematics, as taught in the nation's high schools today, is from 200 to 2000 years old. Modern mathematics, however, is definitely on its way to the secondary schools; the movement in this direction is from the college downward. It is chiefly an attempt to make mathematics more meaningful to the student by fostering an understanding of the basic fundamentals of mathematics and of the unified structure which rests upon these fundamentals. Mathematics can no longer be divided into the separate little compartments of arithmetic, algebra, geometry, etc.; these compartments are now mixed.
There are many concepts which are so simple that they are taken for granted and, hence, never mentioned to the high school student. This study is primarily concerned with these basic concepts since the consensus of opinion among authorities in the field of mathematics education seems to be that they should be taught explicitly.