Excerpt from Measurements of Some Achievements in Arithmetic The purpose of this monograph is to set forth the results of an attempt to derive a series of scales in the fundamental Opera tions of arithmetic. Thus the problem is closely related to the general movement for the measurement of educational products by means of objective scales. The method followed in the development of these scales is most clearly related to the methods used by Dr. Buckingham1 in the development of his Spelling Scale and by Dr. Trabue in the completion-test Language Scales.2 In the development of these scales the fundamental' idea was to derive a series of scales which would indicate the type of problems and the difficulty of the problems that a class can solve correctly. Accordingly, each of the scales is composed of as great a variety of problems as the fundamental operations can well permit. These problems, beginning with the easiest that can be found, gradually increase in difficulty until the last ones in each series are so difficult that only a relatively small percentage of the pupils in the eighth grade are able to solve them correctly. In the determination of the relative difficulty of these problems, the relative per cents of correct answers Obtained by submitting them to large numbers of school children were taken as a basis. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.