Excerpt from An Inquiry Into the Teaching of Addition and Subtraction: Thesis; Presented to the Faculty of Philosophy of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy<br><br>While the results obtained from the testing of so small a number of pupils are by no means conclusive, they are none the less significant. No generalizations not purely tentative can be based upon them alone; scientifically, they are merely suggestive, or at most but a step in the induc tion of positive knowledge; but pedagogically they are final, in that definitely showing the numerical knowledge of certain individual children who are to be taught together, they certainly indicate the numerical known to which the unknown facts of number are to be joined and through which they are to be apperceived.<br><br>About the Publisher<br><br>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com<br><br>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.