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OF

INTELLECTUAL ARITHMETIC:

AN INDEPENDENT TREATISE UPON THE

BASIS OF MENTAL ARITHMETIC,

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BY ORESTES M. BRANDS, A. M.

Physiology, Hygiene, and the Effects of Stimulants and Narcotics

upon the Human System.

Copyright, 1877,
BY HENRY B. MAGLATHLIN.

RIVERSIDE, CAMBRIDGE:

ELEOTROTYPED AND PRINTED BY

H. 0. HOUGHTON AND COMPANY.

LALAND STANFORD JUNIOR UNIVERSITY

INTRODUCTION.

OH
RAL exercises in numbers of an inductive nature,

in the estimation of sound educators, have a peculiar power in strengthening and maturing the mind.

The appreciation of mental arithmetic as a means of education has given rise to urgent demands for improved methods of teaching the science.

To meet in a degree new educational wants, this manual, based upon the works of Benjamin Greenleaf, has been prepared. Its lessons recognize the normal growth of the reasoning powers. The aim throughout has been to make the subject treated attractive and interesting ; and by easy steps to advance the learner by sure progress.

Some pages of slate or blackboard work have been appended. These may be used in supplementing the oral exercises of the text, and the same form of solution be shown to apply alike to mental and written problems.

In the preparation of the present edition of this book, credit is due to J. V. Jackman for testing the copy in the schoolroom and for many valuable suggestions.

TO TEACHERS.

THE extent to which the book can be dispensed with by the class, in recitation, should be determined by the nature of the lesson and the attainment of the pupil.

When the book is not used, each question should be repeated by the pupil after the teacher, and the required solution should always be given promptly, and in every case should form a complete sentence.

A brief form of analysis only is given in the book, so as to allow the fullest scope for the exercise of ingenuity, judgment, and discrimination on the part of the pupil in the invention of others.

No form of solution, however, should be permitted to pass, unless it is neatly expressed, and is entirely accurate.

Each example can be taken as a model for many original examples to be dictated by the teacher. In no other way than by giving a multiplicity of examples, can a teacher fix firmly in the minds of his pupils the principles which he is imparting.

Mental and written arithmetic should always be combined. Hence the wise teacher will always follow up what the pupil has learned, with suitable examples, illustrating the same principles, which will require the use of pencil or crayon.

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1. 1. Count ten. How many ones in ten ?

2. Count twenty, or two tens. How many ones in two tens? In twenty?

3. Count thirty. How many tens have you counted ? How many ones in three tens? In thirty ?

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