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CHILDREN'S ARITHMETICS BY GRADES
WILLIAM E. CHANCELLOR, M.A.
GLOBE SCHOOL BOOK COMPANY
NEW YORK AND CHICAGO
HARVARD COLLEGE L.BRAY
JANUARY 25, 1924
Copyright, 1901, by
M. P. I
" At about eight or nine there begins a new period,
President G. STANLEY HALL, LL.D.,
Council, National Educational Association, 1901.
474 WEST BROADWAY
This book is for boys and girls who know thoroughly addition, subtraction, multiplication, and division, who understand clearly what common fractions and decimals are, who are familiar with counting and comparison, and who can use in simple problems the facts of weights and measures. For these the new work here includes the multiplication and division of fractions by fractions and of decimals by decimals, and further extension and application of the principles of ratio, proportion, percentage, cancellation, and equation. The rest of the book consists of drills and tests in the use of the fundamental and intermediate principles involved in the theory of practical arithmetic.
The plan of this book is to treat a topic and then to review it in connection with problems in preceding topics. One topic after another is taken up with such thoroughness as seems appropriate to the stage of the pupil's advancement; and some of the topics are repeated once or twice in the course of these pages. This plan secures an essentially spiral treatment. Subjects are introduced, but by no means exhausted before we pass to new subjects or to old subjects displayed in new matter.
It is sound child psychology to believe that boys and girls in fourth, fifth, and sixth grades have singular power and even pleasure in undergoing the exercises of drill in any and every subject. It is fortunate that there is such a period in t? mental and physical life as that passed by children usually in their fourth, fifth, and sixth grades at school. It is unfoitunate that sufficient advantage has not yet been taken of this age by the text-book writers. In particular in arithmetic we have many excellent books and monographs discussing methods, devices, and exercises in teaching the elementary facts of number from one to twenty, and very many books discussing and exemplifying arithmetic as a science. Most of these latter books are logical, but not psychological. They are treatises upon arithmetic, manuals for adult teachers rather than for young students. But in a bibliography of many hundred titles one finds not ten books and essays which even try to present or to demonstrate proper methods of presenting to boys and girls nine to twelve years of age such fundamental and intermediate operations as are indicated in this book. Our pedagogical philosophers have clear and correct ideas of the minds of six year old children; and our text-book writers have at least scientifically arranged the topics of arithmetic for fifteen year old boys and girls. But I fail to find any considerable number of authors who have deliberately set before themselves the state of mind of the boys and girls who are likely to need such a book as this.
On the other hand, we find year by year our business men saying that the boys and girls who leave school at the ages of twelve to fourteen know nothing accurately in arithmetic, not even the fundamental operations. This is a curious fact in view of the other fact that the very power of the ten to twelve year old child is to undergo drill. This book is an effort to present interesting forms of such drill as will develop quickness and accuracy.
It is not meant that we are to question the principle that “the problem is the unit of arithmetic.” It is meant that siccess in the problem is conditioned by mere mechanical facility and correctness in number-manipulation. There ought to be many problems in considerable variety in every arithmetic text-book. Every characteristic problem ought to be thoroughly studied and completely understood, and this as early in the child's life as possible.
Author and publishers desire to acknowledge the valuable suggestions of Superintendent Frank E. Spaulding, Ph.D., of Passaic, N. J., in reviewing the proofs of these pages.
SUGGESTIONS TO TEACHERS
1. The preface explains the general purpose of the book.
2. Read the book itself. The purposes of certain special features appear only when considered in relation to other features.
3. Read also Book III of this Series, which shows what pupils of this grade may be expected to know, or at least to have studied. Whenever the pupils of a class seem weak in matters necessarily preliminary to the grade in which they are, it is essential to review these matters both in instruction and in the pupils' own work. But never expect a class as a whole to know accurately and thoroughly every topic in any subject. Aim for perfect knowledge and proficiency, and one secures surprisingly good results from some pupils. Time may be wasted in undue drill of the whole class or in undue attention to individuals. It is very easy in arithmetic to spend an unnecessary amount upon single topics. A book upon the spiral plan, but which does not neglect thorough study of each topic as it is introduced or renewed, affords at frequent intervals an opportunity to find out the facts as to the conditions of the class and of its individual pupils.
4. It is unwise to ask children always to solve examples by the method of the book or by that of the teacher. Often children see through problems in ways distinctly individual. If their solutions are logical, correct, clear, and brief, we ought not only to accept but even to welcome them.
5. One kind of exercises is more valuable than any other in arithmetic: setting by pupils of their own problems and finding the solutions. Exactly as we encourage in our language-courses writing by the pupils themselves of various kinds of compositions, so also ought we to encourage the