FOR SCHOOLS AND COLLEGES. BY THOMAS W. PIPER, NORMAL MASTER AND LECTURER ON MENTAL ARITHMETIC IN THE NATIONAL Author of "Mental Arithmetic for Training Colleges," and "A Chart and Handbook of the Metric System of Weights and Measures.” BIBL LONDON: GEORGE PHILIP & SON, 32 FLEET STREET. 1874. 181. f. 34. PREFACE. ARITHMETIC may be studied with two different objects, and may be taught by two different methods. The first object in studying Arithmetic is to acquire accuracy and facility in computation; the second is to cultivate the reasoning powers, by exercising them upon the various problems presented by Arithmetic. It does not necessarily follow that the two different methoas adopted for teaching Arithmetic should correspond to the two objects mentioned above; indeed, it is hoped. that the present treatise will be in itself a proof that Arithmetic may be so taught as to secure both these objects. at once. It is much to be feared that in many cases Arithmetic is taught in such a way as to exercise the memory alone; its higher object, to exercise and strengthen the reasoning faculties, being more or less completely overlooked. Rules are given, illustrated and examined upon, sometimes without any explanation at all, sometimes, however, with an explanation of the Reason of the Process following instead |