BY
DAVID EUGENE SMITH
GINN AND COMPANY
BOSTON · NEW YORK · CHICAGO · LONDON
COPYRIGHT, 1911, BY DAVID EUGENE SMITH
ALL RIGHTS RESERVED
911.6
The Athenæum Press
PREFACE
A book upon the teaching of geometry may be plannedin divers ways. It may be written to exploit a newtheory of geometry, or a new method of presenting thescience as we already have it. On the other hand, itmay be ultraconservative, making a plea for the ancientteaching and the ancient geometry. It may be preparedfor the purpose of setting forth the work as it now is,or with the tempting but dangerous idea of prophecy.It may appeal to the iconoclast by its spirit of destruction,or to the disciples of laissez faire by its spirit ofconserving what the past has bequeathed. It may bewritten for the few who always lead, or think they lead,or for the many who are ranked by the few as followers.And in view of these varied pathways into the jointdomain of geometry and education, a writer may wellafford to pause before he sets his pen to paper, andto decide with care the route that he will take.
At present in America we have a fairly well-definedbody of matter in geometry, and this occupies a fairlywell-defined place in the curriculum. There are notwanting many earnest teachers who would change boththe matter and the place in a very radical fashion.There are not wanting others, also many in number, whoare content with things as they find them. But by farthe largest part of the teaching body is of a mind towelcome the natural and gradual evolution of geometrytoward better things, contributing to this evolution as[Pg iv]much as it can, glad to know the best that others haveto offer, receptive of ideas that make for better teaching,but out of sympathy with either the extreme of revolutionor the extreme of stagnation.
It is for this larger class, the great body of progressiveteachers, that this book is written. It stands for vitalizinggeometry in every legitimate way; for improving thesubject matter in such manner as not to destroy thepupil's interest; for so teaching geometry as to make itappeal to pupils as strongly as any other subject in thecurriculum; but for the recognition of geometry forgeometry's sake and not for the sake of a fancied utilitythat hardly exists. Expressing full appreciation of thedesirability of establishing a motive for all studies, so asto have the work proceed with interest and vigor, it doesnot hesitate to express doubt as to certain motives thathave been exploited, nor to stand for such a genuine,thought-compelling development of the science as is inharmony with the mental powers of the pupils in theAmerican high school.
For this class of teachers the author hopes that thebook will prove of service, and that through its perusalthey will come to admire the subject more and more,and to teach it with greater interest. It offers no panacea,it champions no single method, but it seeks to setforth plainly the reasons for teaching a geometry of thekind that we have inherited, and for hoping for a gradualbut definite improvement in the science and in themethods of its presentation.
DAVID EUGENE SMITH
[Pg v]