telligence and good sense. It is easy to make a boy, who does not reason, repeat, by rote, any technicr.! rules, which a common writing master, with magisteria! solemnity, may lay down for him; but a child who reasons will not be thus easily managed; he stops, frowns, hesitates, questions his master, is wretched and refractory, until he can discover why he is to proceed in such an, such a manner; he is not content with seeing his preceptor make figures and lines on the slate, and perform wondrous operations with the self-complacent dexterity of a conjurer; he is not content to be led to the treasures of science blindfold; he would tear the bandage from his eyes, that he might know the way to them again." In confirmation of the preceding remarks, and as fully expressive of the author's views on this subject, the following quotation is taken from the preface to Pestalozzi's system. "The PE: TALOZZIAN plan of teaching ARITHMETIC, as one of the great branches of the mathematics, when communicated to children upon the principles detailed in the following pages, needs not fear a comparison with her more favored sister, GEOMETRY, either in precision of ideas, in clearness an 1 certainty of demonstration, in practical utility, or in the sublime deductions of the most interesting truths. "In the regular order of instruction, arithme.icsought to take precedence of geometry, as it has a more immediate connection with it than some are willing to admit. It is the science which the mind makes use of in measuring all things that are capable of augmentation or dimination; and, when rationally taught, affords to the youthful mind the most advantage us exercise of its reasoning powers, and that for which the human intal ect becomes early ripe, while the more advanced parts of it may try the nergies of the most vigorous and matured understanding." January, 1829 THE AUTHOR Multiplication of Federal Money,.. Division of Federal Money,. ... ... ... ... ... .... To multiply by 4, 3, 54, &c.,............................ Questions on the foregoing-Bills of goods sold,.. Reduction-Tables of Money, Weight, Measure, &c.,..................... Questions on the foregoing, To multiply a Fraction by a Whole Number,...... To multiply a Whole Number by a Fraction,..................... .115 To find the Least Common Multiple of two or more Numbers,...... ..119 To find the Greatest Common Divisor of two or more Numbers, (reference,) 120 To reduce Fractions of Different Denominators to a Common Denominator, 122 To reduce Whole Numbers to the Fraction of a greater Denomination,. To reduce a Fraction to Whole Numbers of less Denominations,.. To reduce Fractions of a higher Denomination to a lower,... To reduce Fractions of a tower Denomination into a higher,. 126 To reduce Compound Numbers to Decimals of the highest Denomination,..149 To reduce Decimals of higher Denominations to Whole Numbers of lower Concise Rule for calculating Interest in New York State,. ..... Time, Rate per cent., and Amount, given, to find the Principal,.......... 173 Time, Rate per cent., and Interest, being given, to find the Principal,......176 The Principal, Interest, and Time, being given, to find the Rate per cent.,..176 The Principal, Rate per cent,, and Interest, being given, to find the Time,..178 Compound Interest-Compound Interest by Table,. To find the Area of a Triangle,. The Diameter of a Circle being given, to find the Circumference, The Circumference of a Circle being given, to find the Diameter,. To find the Area of a Circle,.... To find the Area of a Globe,.. To find the Solid Contents of a Globe,. To find the Solid Contents of a Cylinder,.. To find the Solid Contents of a Pyramid,. SUGGESTIONS TO TEACHERS ON THE METHOD OF USING THIS WORK. For a course of Mental Arithmetic, adapted to the capacities of very young pupils, they may take the Mental Exercises in each rule, as far as the first Example for the Slate. This course is not meant to include any of the exercises styled "Questums on the foregoing." This course embraces the whole of the first 27 pages, together with the Arithmetical Tables, extending to the Appendix. The necessity of impressing these Tables on the minds of pupils at an early age is sufficiently obvious. When the pupil is perfect master of this course, as will, most probably, be the case after one or two reviews, the teacher will find no difficulty in making him understand the Operations by Slate. He may then take the whole in course, In every sc' ool, it would be well to institute classes; and as there are seldom 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 occasional corrections. By this, the reader will perceive, that the work may be used to advantage in monitorial schools, as the former editions have been. In large schools, these corrections may be made by an advanced scholar, instead of the teacher. Whenever an advanced scholar takes up the book with a view of profiting from it, he should omit nothing as he progresses, but make it his practice to qualify himself to answer any question, in the mental exercises, rules, or respecting the reason of the operations. Teachers will find it to be a useful occupation for their scholars, to assign them a morning lesson, to be recited as soon as they come into school. With little exertion on the part of teachers, pupils in this way may be made assiduous and ambitious, very much to their advantage, and to the credit of their teachers. The mental questions, under the head of" Questions on the foregoing," will, intelligently answered, furnish to committees an admirable test of the pupil's knowledge of this subject. The Appendix is designed for those who have time and opportunity to devote to the study of the more abstruse parts of Mathematics. Note.-Leat some may mistake the object of the figures annexed to the questions, it may nere be remarked, that these figures are separate answers, left without assigning any value to them, reserving this particular for the discretion of the pupil, which he must necessarily exercise, in order to obtain the answer which follows, that being the aggregate of the whole. The above directions are those which seem the best to the author; but as every intelligent teacher has a way of his own, which, though not intrinsically the best, is, perhaps, the best for him, the subject is respectfully submitted to his own choice. |