FIRST STEPS IN NUMBER.

_A PRIMARY ARITHMETIC._

FROM PREFACE TO THE TEACHER'S EDITION.

The object of this book is to provide teachers with a record of the work done in number in the primary schools of to-day.

There has been no attempt at novelty in the subject-matter, in the arrangement of work, or in the manner of presentation. The whole is on a constructive basis. Numbers are chief; processes subordinate. What has been found to be more easily understood 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 a.s.sertion.

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 a.s.sociation. Success lies in requiring the child to _show_ what he is talking about, and in following the "step by step" rule. The book ill.u.s.trates 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 ill.u.s.trates 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 a.n.a.lysis 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 ill.u.s.trated and enforced by numerous practical examples.