Ebook: Change and invariance: a textbook on algebraic insight into numbers and shapes

TABLE OF CONTENTS; PREFACE; ACKNOWLEDGEMENTS; CHAPTER 1: THE CONCEPT OF INVARIANCE AND CHANGE: THEORETICAL BACKGROUND; UNDERSTANDING PHENOMENA FROM THE ASPECT OF INVARIANCE AND CHANGE; The Concept of Invariance and Change; Change and Invariance from the Epistemological Perspective; Invariance and Change in the Development of Science; Invariance and Change in the Development of Mathematical Knowledge; THE CONCEPT OF INVARIANCE AND CHANGE IN THE MATHEMATICAL KNOWLEDGE OF STUDENTS; The Cognitive-Developmental Aspect of Invariance and Change; On Mathematics Instruction and Learning in School.;What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book. The world is an interplay of variation and constancy -- a medley of differences and similarities -- and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes.