Excerpt from Complete Graded Arithmetic: Third GradeThe alliance of oral, often called mental, Arithmetic with the written lessons illustrates the author's confidence in the principle of grading the topics and developing them through examples. No severer test of a theory can be applied than by putting it into exclusive practice. Written lessons may be given in which for weeks and months, even for terms and years, the pupils may conceal their failure to understand their work, but oral Arithmetic is the complete revelation of the progress and position of class and pupil in the science. It is impossible for a teacher to conduct an oral recitation which is beyond the pupils' comprehension. Interest at once ceases, and there are no answers to the questions. The successful union of oral and written lessons, as seen in all 'these pages, is an artistic achievement in pedagogy.In itself oral work unquestionably deserves the prominence it receives in these pages. Mental Arithmetic promotes atten tion, concentration, accuracy, ingenuity, skill, familiarity, and confidence. It tests all written work as to the essential point, whether or not the process is understood. It secures the edu cation of the class by the efforts of individuals, who are fol lowed and criticised by their fellows. It is a language training of the highest value.This series emphasizes to an unusual degree the necessity of employing the imagination in the study of Arithmetic. Most teaching of Arithmetic has appealed to the memory almost to the exclusion of the other faculties. Though the development of the reason is earnestly desired, little or no intelligent effort has been put forth with the certainty of accomplishing this object. The author has made it very clear that thinking or reasoning in mathematics involves the exercise of the imagi nation. Since faculties grow strong by exercise, work must be provided which will compel the exercise of the imagination.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.