The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.

C. G. Jung's work in his later years suggested that the seemingly divergent sciences of psychology and modern physics might, in fact, be approaching a unified world model in which the dualism of matter and psyche would be resolved. Jung believed that the natural integers are the archetypal patterns that regulate the unitary realm of psyche and matter, and that number serves as a special instrument for man's becoming conscious of this unity. Writen in a clear style and replete with illustrations which help make the mathematical ideas visible, Number and Time is a piece of original scholarship which introduces a view of how "mind" connects with "matter" at the most fundamental level.

Excerpt from The Psychology of Number and Its Applications to Methods of Teaching Arithmetic In presenting this book on the Psychology of dumber it is believed that a special want is supplied. There is no subject taught in the elementary schools that taxes the teacher's resources as to methods and devices to a greater extent than arithmetic. There is no subject taught that is more dangerous to the pupil in the way of deadening his mind and arresting its development, if bad methods are used. The mechanical side of training must be joined to the intellectual in such a form as to prevent the fixing of the mind in thoughtless habits. While the mere processes become mechanical, the mind should by ever-deepening insight continually increase its power to grasp details in more extensive combinations. Methods must be chosen and justified, if they can be justified at all, on psychological grounds. The concept of number will at first be grasped by the pupil imperfectly. He will see some phases of it and neglect others. Later on he will arrive at operations which demand a view of all that number implies. Each and every number is an implied ratio, but it does not express the ratio as simple number. The German language is fortunate in having terms that express the two aspects of numerical quantity. 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.

The Psychology of Number and Its Applications to Methods of Teaching Arithmetic is a groundbreaking work in the field of mathematics education. Written by J. A. (James Alexander) McLellan and John Dewey, two leading figures in the field of education psychology, this book offers a new approach to the teaching of arithmetic, based on the principles of child psychology and the latest research in the field. The book provides a clear and practical guide to teaching arithmetic in a way that is engaging, effective, and enjoyable for students. A must-read for anyone interested in the psychology of learning or the history of education. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

"Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind"--Provided by publisher.