Course of Study in Secondary Mathematics in the University High School, the University of Chicago

Abstract

INTRODUCTIONIn the following course of study it is aimed so to reorganize the body of secondary-school mathematics as to fit the subject effectively to the needs of the students and to make it more productive for mental life and growth. Since 1903 the departments of mathematics of the University High School and the School of Education have been developing a solution of the problem of mathematical reorganization along the lines of correlation. By the bringing together of subjects that are closely related, each is reinforced by the aid of the others, and the entire work in these subjects is unified and vitalized. For example, algebra and geometry supplement each other. Both are used to express facts about quantity. The formula and the graph are only different ways of expressing the law of a group of numerical facts. Each states the facts in generalized form and thus makes the deduction of any number of particular cases possible. Moreover, when the two forms of thought are correlated in a single course of instruction the student's comprehension of quantity is at the same time deepened and simplified-deepened because of the more enduring impression made upon the mind; simplified because the double method of attack makes it easier to overcome difficulties by supplying always a strategic alternative.The student will see the advantages of having various modes of treating the facts of quantity. Thus, he is made to realize the value of algebra by seeing the superiority of algebraic methods in 648 This content downloaded from 034.213.178.048 on May 10, 2018 12:40:06 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). SECONDARY MATHEMATICS IN UNIVERSITY HIGH SCHOOL 649important respects as compared with arithmetic and geometric methods.When the various mathematical subjects are treated separately, each tends to take on the rigid form of the final science. This leads inevitably to a certain formalism in the mode of presentation. Such formalism is not the best method for the high-school pupil. Correlation helps to avoid excessive formalism. Rigor is not carried beyond the understanding of the pupil.Leading mathematicians and professors of the teaching of mathematics have long recognized the relationship between the various subjects of secondary mathematics, especially algebra and geometry, and have advocated the desirability of teaching them together. The details of a plan for this correlation are being worked out in the University High School and the content of the first-year course is now well organized and is given in First-Year Mathematics, a textbook published by the University of Chicago Press. The second-year course is contained in Second-Year Mathematics, also published by the University of Chicago Press. Work on the thirdand fourth-year courses is progressing and it is hoped to publish them in the near future. AIMS AND VALUESAmong the purposes of secondary mathematics the following are emphasized:I. A knowledge of the fundamental facts and principles ...

Extending use of instructional exchanges to research on teacher education

“…Problems in Teaching Secondary-School Mathematics (Breslich, 1931) is an artifact from a time when compulsory schooling at the elementary school level was already widely established in the United States, there were increasing enrollments at the secondary school level, and the need to educate high school mathematics teachers was also understood as a corollary of a broader education for members of the society. The book is the second volume of two focusing on the teaching of mathematics in Grades 7-12 in the United States.…”