Excerpt from Essentials of Arithmetic: Primary Book

This book is the first of a series of three intended to cover the essentials of arithmetic in the eight school years of the elementary course. It consists of five chapters, the first of which reviews the work usually done in the first and second grades, the others covering the work of the successive half grades through the fourth school year. If it is introduced in Grade II, the pupils should complete Chapter I in that year; but if it is first placed in the hands of the class in Grade III, it will suffice to take a rapid review of Chapter I, omitting such 'portions as may already be perfectly familiar to the children.

A textbook for these grades can be constructed on any one of several definite plans, or, indeed, with little attention to any system atic arrangement whatever. It may consist of a series of devices for teachers, such as games and dramatizations, all valuable in them selves but not offering the material needed in a usable textbook. To be usable a book should suggest devices of this kind, which with many others the teachers may bring into their work, but it fails of its purpose if it uses most of its limited space in this manner. The primary purpose of a textbook in arithmetic is to furnish a large amount of material which the teachers would otherwise have to die tate, and to arrange this material in a systematic order. Teachers need hundreds of examples in addition, hundreds of examples in subtraction, and so on, and they should not be required to make up, arrange, and dictate this material. Teachers always welcome sugges tions of games, of dramatizations of number relations, and of means to apply number facts to the daily experiences of the child, but such devices of teaching must necessarily come in large part from the teachers themselves.

This book stands, in the first place, for good, well-arranged mathe maties, and not for the scrappy presentation which always fails to give to the pupil that feeling of mastery of the subject-to which he is entitled; and in the second place it appeals to the pupil's human interests by relating the subject to his personal needs and to the life in which he finds himself. It seeks to balance reasonably these two features, refraining on the one hand from devoting all its space to abstract drill, and on the other hand from failing, through the sacrifice of its space to methods of teaching, to give the amount of drill that is necessary. It recognizes that the children who study its pages have already been in school from one to two years, that they not only possess a fair knowledge of number but that motives for study have already begun to be formed, and that the kindergarten stage is already passing out of their lives. Devices that are needed in Grade I are not necessary in Grade III; and the teachers, to a large extent, must be the judges as to how long they shall keep to the concrete introduction to the work, and as to the use they shall make of the numerous devices suggested in the book.

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