IN planning the present book, the author has kept in mind three aspects of the teacher's preparation: the need of the perspective gained through a comprehen sion of the larger teaching problems concerned in the teaching of arithmetic, the need of a clear insight into the content of arithmetic, and the need of an understand ing of arithmetic method. The book exploits no new doctrine. It lays no claim to completeness. It has been prepared with the primary aim of supplying the practical needs of prospective teachers, or teachers new in the ser vice. On account Of the efiort made to refresh the mind of the reader in the subject matter of arithmetic, the read ing frequently goes beyond the requirements of the grades, this being especially noticeable in the treatment of percen tage and in the solution of problems. If any dogmatism appears in the context, it is the result of efiorts to be clear and convincing.