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precedes the more difficult, without respect to its scientific relation. Fractions present no greater difficulty than wholes, so they accompany the teaching of integral numbers from the beginning. The law of dependence has been carefully observed, although at first glance the arrangement may not seem to warrant this assertion.

The object of every teacher is so to present numbers that the mind of the child may grasp firmly the facts concerning them, and hold these facts tenaciously by the law of association. Success lies in requiring the child to show what he is talking about, and in following the "step by step" rule. The book illustrates these two principles. It abounds in examples which have not before appeared in print, and which are calculated to interest the child from their close connection with his varied experiences. It gives suggestions for versatility of drill, and illustrates in detail the teaching of a hundred topics.

It is expected that the work to the number ten will be taken in one year, the work to twenty in another year, and the remainder of the course outlined in the book will be covered in two years more.

A child's book accompanies this edition, which the child may use with great advantage after he becomes acquainted with figures.

It is hoped that this book will find a welcome among all persons interested in leading children by easy and sure paths to a knowledge of numbers.

GINN & COMPANY, PUBLISHERS,
BOSTON, NEW YORK, AND CHICAGO.

WENTWORTH'S

GRAMMAR SCHOOL ARITHMETIC,

350 Pages,

Is designed to give pupils of the grammar-school age an intelligent knowledge of the subject and a moderate power of independent thought.

Whether Arithmetic is studied for mental discipline or for practical mastery over the every-day problems of common life, mechanical processes and routine methods are of no value.

Pupils can be trained to logical habits of mind and stimulated to a high degree of intellectual energy by solving problems adapted to their capacities. They become practical arithmeticians, not by learning special business forms, but by founding their knowledge on reasoning which they fully comprehend, and by being so thoroughly exercised in logical analysis that they are independent of arbitrary rules.

This Arithmetic contains a great number of well-graded and progressive problems, made up for youths from ten to fourteen years of age. Definitions and explanations are made as brief and simple as possible. It is not intended that definitions should be committed to memory, but that they should be simply discussed by teacher and pupils. Every teacher, of course, will be at liberty to give better definitions, and to make a better presentation of methods, than those exhibited in the book.

In short, the chief object in view will be gained if pupils are trained to solve the problems by neat and intelligent methods, and are kept free from set rules and formulas.

A great many number-problems are given in the first pages of the book, so that the necessary facility and accuracy in computing under the four fundamental rules may be acquired; as want of accuracy and rapidity in mere calculations distracts the attention which should be given to the investigation and correct statement of numerical exercises.

The Appendix contains a short chapter on the Metric System, a chapter on Mensuration, and Miscellaneous Problems. The Metric System is treated here because the great majority of grammar-school pupils have no time for the subject, while those who have can as well learn the system at this stage of their progress as earlier. The chapter on Mensuration is suited to the ability of beginners. The intention is not to give a system of Geometry, but to render familiar those notions of Geometry that are indispensable for practical purposes. The whole subject has been illustrated and enforced by numerous practical examples.

GINN & COMPANY, PUBLISHERS,
BOSTON, NEW YORK, AND CHICAGO.

ELEMENTARY LESSONS

IN ENGLISH.

These admirable books harmonize and utilize to a surprising degree most, if not all, of the practical advantages of conflicting theories.

—Dr. G. STANLEY HALL, Johns Hopkins University.

Their universal use would raise many schoolmasters to the rank of teachers.

State Supt. M. A. NEWELL, Md

Need only their presence to recommend them.

—F. W. PARKER, Prin. Cook Co. Normal School, Ill.

The brightest and most practical book on the subject yet published.

Supt. J. O. WILSON, Washington, D.C.

None more suggestive and helpful to the young teacher.

Supt. GEO. HOWLAND, Chicago, Ill.

Better than any other.

Supt. JOHN B. PEASLEE, Cincinnati.

The only books that meet the wants of our elementary schools.

—E. V. DE GRAFF, Institute Conductor

GINN & COMPANY, PUBLISHERS,
BOSTON, NEW YORK, AND CHICAGO.

Musical Instruction is the most practical instruction given in schools; for music, unlike other branches, becomes immediately useful.

The Primary or First Music Reader. Introduction Price, 18 cts.; Allowance for old book in exchange, 5 cts.

The Second Music Reader. Introduction Price, 20 cts.; Allowance for old book, 5 cts.

The Third Music Reader. Introduction Price, 20 cts.; Allowance for old book in exchange, 5 cts.

Intermediate Music Reader. Introduction Price, 40 cts.; Allowance for old book, 10 cts. Consists of the Second and Third Music Readers in one volume.

Teacher's Manuals Are published in two volumes to accompany respectively the First Reader and Series of Charts, and the Second and Third. Introduction Price, 40 cts. each.

The Independent Music Reader. Introd. Price, 70 cts.; Allowance for old book, 20 cts.

The Abridged Independent Music Reader. Introduction Price, 60 cts.; Allowance for old book in exchange, 20 cts.

Fourth Music Reader. Introduction Price, 94 cts.; Allowance for old book in exchange, 30 cts.

Abridged Fourth Music Reader. Introd. Price, 75 cts.; Allowance for old book, 30 cts.

The National Music Charts. Introduction Price, $5.50; Easel, $1.00. Sample-leaf sent free to any address.

High School Music Reader for Mixed Voices.Introduction Price, 94 cts.; Allowance for old book in exchange, 30 cts.

Girls' High School Music Reader. Introd. Price, $1.25; Allowance for old book, 30 cts.

Hymn and Tune Book for Female Voices. Introduction Price, 60 cts.

Hymn and Tune Book for Mixed Voices. Introduction Price, 60 cts.

Independent Music Reader and Hymn and Tune Book for Mixed Voices, combined. Introduction Price, 94 cts.; Allowance for old book, 30 cts.

A valuable pamphlet on Musical Instruction in Schools mailed free on application to the publishers,

GINN & COMPANY, BOSTON, NEW YORK, AND CHICAGO.






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