selence blindfold; he would tear the bandage from his eyes, that he might kno❤ the way to them again." In confirmation of the preceding remarks, and as fully expressive of the anthor's views on this subject, the following quotation is taken from the prefaco to Pestalozzi's system. "The PESTALOZZIAN 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 favoured sister, GEOMETRY, either in precision of ideas, in clearness and certainty of demonstration, in practical utility, or in the sublime deductions of the most interesting truths. "In the regular order of instruction, arithmetic ought to take precedence of geometry, as it has a more immediate connexion 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 diminution; and, when rationally taught, affords to the youthful mind the most advantageous exercise of its reasoning powers, and that for which the human intellect becomes early ripe, while the more advanced parts of it may try the energies of the most vigorous and matured understanding." January, 1829 THE AUTHOR. To change an Improper Fraction to a Whole or Mixed Number, น 105 107 To find the Greatest Common D.visor of two or more Numbers, (referenee,) 115 To reduce Fractions of Different Denominators to a Common Denominator, 117 tion 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 lower, To change Vulgar or Common Fractions to Decimals, To reduce Compound Numbers to Decimals of the highest Denomination, 142 To reduce Decimals of higher Denominations to Whole Numbers of lower 141 Addition of Decimals, Concise Rule for oalculating Interest in New York State, Commission, Insurance, Stock, Loss and Gain, Time, Rate per cent., and Amount, given, to find the Principal, Time, Rate per cent., and Interest, being given, to find the Principal, The Principal, Interest, and Time, being given, to find the Rate per cent., 166 The Principal, Rate per cent., and Interest, being given, to find the Time, 168 Application of Ratio by Rule, 181 Ratio, or the Relation of Numbers, To compute the Interest on Notes with Endorsements-three modes. Practice in Compound Numbers,. Fellowship-by Analysis-by Ratio, Duodecimals-Multiplication of Duodecimals, Questions on the foregoing, To calculate Difference in Time, Method of assessing taxes, ex. 12,13, 204 164 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 Solid Contents of a Globe, 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 "Questions on the foregoing." This course embraces the whole of the first 20 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 school, 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. Lest some may mistake the object of the figures in the parentheses, it may here 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. |