The Number Systems and Operations of Arithmetic. An Explanation of the Fundamental Principles of Mathematics which Underlie the Understanding and Use of Arithmetic, Designed for In-Service Training of Elementary School Teachers Candidates Service Training

Content: Front Matter, Page iii Copyright, Page iv PREFACE, Pages ix-xi CHAPTER 1.1 - THE ORIGIN OF NUMERICAL THINKING, Pages 3-31 CHAPTER 1.2 - THE NATURAL OPERATIONS WITH THE NATURAL NUMBERS, Pages 32-44 CHAPTER 1.3 - THE NATURAL LAWS FOR THE NATURAL OPERATIONS, Pages 45-62 CHAPTER 1.4 - THE INVERSE OPERATIONS AND CONVERGENCE; THE NUMBER SYSTEMS GENERATED BY THESE OPERATIONS, Pages 63-138 CHAPTER 1.5 - CLASSIFICATION OF THE NUMBER SYSTEMS AS ABSTRACT SYSTEMS, Pages 139-155 CHAPTER 1.6 - SUMMARY, Pages 156-166 CHAPTER 2.1 - COMPUTATION WITH THE NATURAL NUMBERS, Pages 169-216 CHAPTER 2.2 - COMPUTATION WITH RATIONAL NUMBERS, Pages 217-221 CHAPTER 2.3 - COMPUTATION WITH REAL NUMBERS; DECIMAL REPRESENTATION, Pages 222-248 CHAPTER 2.4 - COMPUTATION WITH THE COMPLEX NUMBERS, Pages 249-259 INDEX, Pages 261-265 ELEMENTARY VECTORS, Page ibc1 MODERN MATHEMATICS IN SECONDARY SCHOOLS, Page ibc2 The Number Systems and Operations of Arithmetic was written for the single purpose of explaining to elementary school teachers (both in-service and in-training) the nature of those basic principles of mathematics which form the foundations and structural framework of arithmetic, and how the familiar formal algorithms of arithmetic stem from these structural principles