FIRST LESSONS IN ARITHMETIC, · COMBINING THE ORAL METHOD, WITH THE METHOD OF TEACHING THE COMBINATIONS DESIGNED FOR BEGINNERS. BY CHARLES DAVIES, LL.D. AUTHOR OF ELEMENTARY ALGEBRA, ELEMENTS OF SURVEYING, NEW-YORK: PUBLISHED BY A. S. BARNES,& CO. CINCINNATI:-H. W. DERBY & CO. 1851. Edico T. 118.49.25. Entered according to Act of Congress, in the year 1849, BY CHARLES DAVIES, In the Clerk's Office of the District Court of the United States for the PREFACE. THIS book, entitled FIRST LESSONS IN ARITHMETIC, is designed for beginners. It explains the first steps in a course of Arithmetical instruction. It begins with counting, and using the common language, the pupil is advanced step by step through all the simple combinations of numbers. In order that the pupil may be impressed with the fact that numbers express a collection of units, or things of the same kind, the unit, in the beginning, is represented by a star, and the child should be made to count the stars in all cases where they are used. Having once fixed in the mind a correct impression of numbers, it was deemed no longer necessary to represent the unit by a symbol; and hence, the use of the star is then discontinued. Having presented the combinations of numbers by the common language, we next teach them by means of figures: that is, we so train the mind that it shall, by the aid of the eye alone, catch instantly the idea which any combination of figures is designed to express. We thus present the combinations of figures purely through the arithmetical symbols, so that the pupil is not obliged to pause a: every step and translate his conceptions into common language, and then re-translate them into the language of arithmetic For example, when he sees two numbers, as 4 and 8, to be added, he shall not pause and say, 4 and 8 are 12, but shall be so trained as to repeat 12 at once, as is always done by an experienced accountant. So, if the difference of these numbers is to be found, he shall at once say 4, and not 4 from 8 leaves 4. If he desires their product, he will say 32; if their quotient, 2: and the same in all similar cases. This is all to be done by the simple process of reading; and the method consists, 1st. In teaching the arithmetical alphabet, and 2dly. In teaching the combinations of the alphabét, which become the exponents, or signs, of ideas. After this is done, the pupils of a class should be taught to read together, all the combinations, in the same manner as they practise reading lessons in our common language. Having gone through with all the combinations of the unit, forming the arithmetic of whole numbers, we next consider its divisions, forming the arithmetic of fractions. On this part of the work great care has been bestowed. Each fraction, from one-half to one-twelfth, inclusive, is treated separately, and the general method is commended to the careful examination of teachers. NEW YORK, AUGUST, 1849. |