Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves students' problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them unders

• Why do some students achieve more than others? • Do we have to wait until pupils are "ready"? • Can children discover math for themselves? • Does language interfere with the learning of math? This classic text, written from the viewpoint of the math teacher, provides answers to these and many more questions. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New chapters have been included on cognition, pattern, and ICT.

Excerpt from An Algebraic Arithmetic: An Exposition of the Theory, and Practice of Advanced Arithmetic The introduction of elementary algebra into the schools is of more doubtful value for two principal reasons. The conceptions of geometry can be represented by fig ures and objects, and are therefore readily grasped by the child, but those of algebra can be so represented only to a very limited degree; and, for the most part, are abstractions the nature of which the child comprehends with difficulty. Moreover, the time that can be allotted to the subject in the grammar school is barely sufficient to carry the pupil over the essentially uninteresting details of algebraic manipulation that necessarily precede any but the Simplest applications of the science. But while the wisdom of introducing elementary algebra into the schools may, for these and minor reasons, be seriously questioned, the experience of several years as a teacher has led the author to the conclusion that the application of certain algebraic conceptions to arithmetic would contribute largely toward the rational presentation of the subject, thus increasing its disciplinary value, and at the same time preparing the way for a natural transi tion to the algebra of the high school. These conceptions are the use of letters as the general representatives of (positive) numbers and of the equation to express their relations. 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.

Reprint of the original, first published in 1860.