ON GENERAL METHOD.-The author is permitted to quote a bulletin on "The Teaching of Primary Numbers," by Prof Frank F. Bunker, of the San Francisco State Normal School "The study of every topic generally included in a cour arithmetic can be begun either from the objective side or the side of the purely formal. For instance, in beginning study of fractions the teacher can give a more or less exte course wholly within the field of the concrete, or she may cl to begin with the formal and mechanical side, -the side whi concerned alone with the various manipulations of fraction bols. Just so with square root, with division, with multip tion, or in fact with almost any phase of arithmetic. On th hand, there is the field of the objective, -the concrete; or other, the field of the formal. Careful observation of pra work will show, as we have just said, that facility in one will by no means give facility in the other. A child, by ca teaching in the field of the concrete, will soon acquire great in adding simple fractions, and yet he may never have those same fractions expressed by figure symbols. He does by reason of the fact that to him a fraction is as much a con thing as is his dog or his horse. To him, adding fractio nothing more than calling up and counting mental imag familiar things. On the other hand, the mind is never devoid of mental images than when engaged in formal cal tion. To have images of things floating around at such a means that attention is diverted, with ineffectiveness as a c quence. Obviously, the child needs training in both these f He needs to be accurate and tolerably rapid in the mecha From a standard work on arithmetic, published about forty years ago, is taken the following extract, which accords with the more recent authorities on number-teaching: “All reasoning is comparison. A comparison requires a stan dard, and this standard is the fixed, the axiomatic, the known The law of correct reasoning, therefore, is to compare the comples to the simple, the theoretic to the axiomatic, the unknown to the known. The law is kept prominently before the mind in the development of this work, and upon it are based its solutions and explanations." AS TO SUBJECT-MATTER. — The book is graded to suit the men tal capacity of the pupil as he moves upward, through the grammar grades of the public schools. Not all subjects to be found in other arithmetics are treated, but the matter of relation is presented so effectively, that it is believed the pupil will be able to apply the principles to the many details which may arise in his experience. Though the book begins, nominally, with the third year of school, it is evident to any sensible teacher, that, in some schools, the book should not be in the hands of pupils below the fourth year. It is also true, that in schools that give emphasis to primary-number teaching, the first few pages of this book can be mastered readily in the latter part of the second year. The teacher should always remember to provide inductive exercises, to make clear any principle not fully mastered by the pupil. There is no better test of a pupil's insight than original problems, which should be required at every step of progress. AS TO TYPOGRAPHY. - Much care has been exercised to make this book superior to others in artistic finish. Its attractive style adds to its value as a text. With the hope that this book will inspire deeper interest in the subject, and will be of service to all who may use it, the consideration of schools and teachers everywhere is invited. FRANK J. BROWNE. |