Author Description

This book is written without the least regard to any demand but those of children and of life and mental activity generally. In places where the author is mistaken he cannot plead that he has been hampered by artificial considerations. His object in writing it has been solely the earnest hope that the teaching of this subject may improve and may become lively and interesting. Dulness and bad teaching are synonymous terms. A few children are bom mentally deficient, but a number are graduaUy made so by the efforts made to train their growing faculties. A subject may easily be over-taught, or taught too exclusively and too laboriously. Teaching which is not fresh and lively is harmful, and in this book it is intended that the instruction shall be interesting. Nevertheless a great deal is purposely left to the enterprise of the student and the living voice of the teacher, and the examples given for practice are insufficient. The author has usually found that examples and illustrations are likely to be most serviceable, and least dull, when invented from time to time in illustration of the principles which are then being expounded; but a supple- mentary collection of exercises for practice is necessary also, in order to consolidate the knowledge and establish the principles as an ingrained habit. Wearisome over-practice and iteration and needlessly long sums should be avoided; because long sums, other than mechanical money addition, seldom occur in practice, and especially because many kinds of future study, especially the great group of sciences called Natural Philosophy, will be found to afford plenty of real arithmetical practice; and even ordinary life affords some, if an open mind is kept. The cumbrous system of weights and measures still surviving in this country should not bo made use of to furnish cheap arithmetical exercises of preposterous intricacy and uselessness. There is too much of real interest in the world for any such waste of time and energy. The mathe