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Change and invariance : a textbook on algebraic insight into numbers and shapes /
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...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Rotterdam :
Sense Publishers,
[2016]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- Invariance and Change as an Educational ConceptInvariance and Change as Concepts for Mathematics Teachers; THE BASIC INTERPLAY BETWEEN INVARIANCE AND CHANGE; Different Types Invariance; The Taxonomy of Invariance and Change; SOME INTRODUCTORY ACTIVITIES IN INVARIANCE AND CHANGE; What Is Invariant? What Changes? An Investigative Activity about Freefall Durations; "Can This Change?" Three Experiments with Paper; "Different or the Same?" Optical Illusions; NOTES; REFERENCES; CHAPTER 2: INVARIANT QUANTITIES
- WHAT IS INVARIANT AND WHAT CHANGES?
- INTRODUCTION: UNDERSTANDING THE INVARIANCE OF QUANTITY AS A BASIS FOR QUANTITATIVE THINKINGInvariance of a Quantity: Assembling a Finite Set from Subsets; Generalization of the Principle of Invariance of Quantity: "Large Numbers"; Invariance of Quantity in Terms of Arithmetic Operations; Aspects of Equality, Invariance, and Change When Partitioning Quantities; Generalization of Partitioning: Non-Integers and the Number of Components; Summary of the Activities in Chapter 2; ACTIVITY 2.1: DIVIDING DOLLS BETWEEN TWO CHILDREN.
- MATHEMATIC AND DIDACTIC ANALYSIS OF ACTIVITY 2.1: PARTITIONING A SET INTO TWO SUBSETS: POSING PROBLEMS AND PARTITION METHODSSummary of the Roles of the Concepts of Change and Invariance inActivity 2.1: Description of Ways to Split a Set into Two Subsets; ACTIVITY 2.2: HOW TO SPLIT A FRACTION. ALMOST LIKE ANCIENT EGYPT; MATHEMATIC AND DIDACTIC ANALYSIS OF ACTIVITY 2.2: INVARIANCE OF QUANTITY AND SPLITTING OF UNIT FRACTIONS; ACTIVITY 2.3: THEY ARE ALL EQUAL, BUT & MATHEMATIC AND DIDACTIC ANALYSIS OF ACTIVITY 2.3: FROM EQUAL ADDENDS TO CONSECUTIVE ADDENDS; Summary and Comments for Question 4.