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telligence and good senne. It is easy to make a boy, who does not reason, topruh, by rute, any technical rules, which a colomon writing nuaster, with mannerlal mlonunity, may lay dowu for him; but a child who reasons will mot be tbus easily inanaged; he stops, fruwas, hesitates, questions his mas wr, to wretched and refractory, until he can discover why he is to proceod in such and such a manner; he is not content with seeing his preceptor make figures and lines on the slalo, and perfurn, wondrous Operations with The self-complacent dexterity of a conjurer; he is not conteni w be led to The treasures of science blindfold; he would coas the bandage froin huis eyes, that he might know the way to inein again."
iu confirmation of the preceding remarks, and as fully expressive of the ontlaur's views on this subject, the following quotation is taken from the prufucr tu l'estalozzi's system.
“ 11e PESTALOZZIan plan of teaching ARITHMETIC, as one of the great branches of the mathematics, when coinniunicated to children upon the principles detailed in the following pages, necds not fear a comparison with her inore favured sistor, GEOMETRY, eillier in precision of ideas, in clearness and certainty of demonstration, in practical utility, or in the suba Lue deductions of the most interesting truths..
" Ju the regular order of instruction, arithinetic ought to take precedence of geometry, as it has a inore immediate connection with it than some aro willing lo ailmit. It is the science which the inind makes use of in teas uring all things that are capable or augmentation or diminution; and, wben ratioually taught, affords to the youthful mind the most advantage eus exercise of its reasoning powers, and that for which the human iniel. lect becomes early ripe, while the more advanced parts of wax lry ubo energies of the laust vigorous and matured understanding"
TABLE OF CONTENTS.
Adelit.on of t'ederal Money,....................
Division of Fractions--To divide a Fraction by a Whole Number,.........128
To reduce a Fraction to Whole Nunibers of less Denominations,........ 139
Bubtraction of Deciinals,...................................
..231 | Diacoust,... que
Extraction of the squarr Root-its Application .......................... 248
To find the Solid Contents of a Globe,.........
SUGGESTIONS TO TEACHERS
ON THE ULTHOD OF USING THIS WORK.
Por u conre of Mental Arithmetic, adapted to the capacities of very yormy pupils, they may take the Mental Éxereisen in each rile, as far as the tirst Example for the State. This course is nul ineant i wclude any of the exercises styled “ Questions on the foregoing."
This course embraces the whole of the first 27 pages, together with the Arith. netical Tables, extending to the Appendix. The neressity of impressing wese Tables on the minds of pupils at an early age is sufficiently obvious. When the pupil is perfect master of this course, as will, not probably, be the case after one or two reviews, the teacher will find no ditfirewlty in making him "undur stand the Operations by Slute. He may then take the whole in course.
In every school, it would be well to institute classes; and as there are seldur any answers given to the mental questions, the pupils may be allowed to read in their turns the questions from the book; thus giving the teacher no further trouble than occasionul corrections. By this, the reader will perceive, that the work may be used to advantage in monitorial schools, as the former editionis have been. In large schools, these corrections may be made by an advarced scholar, instead ut'the teacher. Whenever an advanced scholar takes up the book with a view of profiting from it, he should omit nothing us he progrosses, but make it his practice to quality himself to answer any question, in the mental exerciser, rules, or respecting the reason of the operations.
Teachers will find it to be a useful occupation for their scholars, to arrign them a morning lesson, to be recited as soon as they come into school. With little exertion on the part of touchers, pupils in this way may be male assidvono and ambitious, very much to their advantage, and tu the credit of theis teachers,
The mental questions, under the head of “ Questions on the foregoing,” will, Intelligently answered, furnish to cunimitlees un admirable test of the pupil's krwledge of this subject.
lbe Appendix is designed for those who hare tine and opportunity to devote to the study of the cure abstruse parts of Mathemutics.
Nole.-lest some may mistake the object of the figures annexed to the ques dio is, it may here he remarked, that there bgures are separute answers, les without ansigiring any value to them, reserving this particticar for the discretion of the pupil, which he must necessarily rxercise, in order to ublain the answer which follows, that being the aggregate of the whole.
T'he above directions are those which seen the best to the author ; hut us overy intelligent leucher has a way of his own, which, thuugh not intrinsicully the best, is, perhaps, the best for him, the subject is inseclfully submitted to he own clanica