The THE MACMILLAN COMPANY MACMILLAN & CO., LIMITED THE MACMILLAN CO. OF CANADA, LTD. TORONTO BY JOHN W. HOPKINS SUPERINTENDENT OF THE GALVESTON PUBLIC SCHOOLS 66 AND P. H. UNDERWOOD TEACHER OF MATHEMATICS, BALL HIGH SCHOOL, GALVESTON, TEXAS AUTHORS OF MENTAL ARITHMETIC, PRIMARY ARITHMETIC," 99 66 New York THE MACMILLAN COMPANY 1912 All rights reserved AND "As regards the method of teaching algebra, I would make it, in the earlier stages, as much a generalized arithmetic as possible. Results obtained by algebra would be verified by arithmetical instances; and the use of a formula would be indicated as including any number of instances. Elaborate (and to my mind wearisome) processes, useful for solving artificial combinations of difficulties, would be at least deferred. With a comparative beginner, progress towards new ideas or new stages of old ideas can, I think, best be made by the simplest instances, and it is on this account that I would build algebra entirely on arithmetical foundations so far as concerns the teaching of beginners." -Professor Forsyth, M.A., D.Sc., F.R.S., Cambridge. "It is assumed that pupils will be required throughout the course to solve numerous problems which involve putting questions into equations. Some of hese problems should be chosen from mensuration, from physics, and from commercial life. The use of graphical methods and illustrations, particularly in connection with the solution of equations, is also expected." - Extract from the Report of the American Mathematical Society, 1903. |