Educt 118.98.295 Harvard College Library Dec. 20, 1918. Transferred from Copyright, 1893, University Press: INTRODUCTION. IT T has been said that the "new education" proceeds to give the child an experience, instead of presupposing one for him. Pupils become practical, not by learning forms of reasoning, but by exercising the reason upon their own plane of comprehension. In such a spirit this ELEMENTARY ARITHMETIC has been prepared. It presents three years' work, based upon carefully graded exercises which may be used as a means of training pupils to think, and of teaching at the same time the practical application of numbers to ordinary business transactions. In order to enter satisfactorily upon the work provided for in the following pages, the pupils should be familiar with all the combinations of numbers through twenty. The training necessary to attain this familiarity is best secured by leading pupils to discover the relations of numbers by means of objects, and through this teaching to gradually free thought from dependence upon sense representation. PART I. (Third Year in School.) The first and hardest step in solving an arithmetical question is to determine the processes required; the second, to state the different steps of the solution in proper arithmetical form. It is very important that children should master the fundamental processes so thoroughly that they come to serve thought without loss of time or energy. The patient following of these graded exercises and drills should secure this result. The tables of "Endings," in addition (see pages 58, 61, etc.), have the same practical use as the multiplication table, and should be as thoroughly applied. Each chapter presents, in general, division and multiplication as converse processes, followed by subtraction and addition on the same general plan. In the beginning each number is viewed as a whole, divisible into equal parts, and the parts are viewed in relation to the whole and to each other. A number is separated by division, united by multiplication; separated by subtraction, united by addition. |