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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 |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Rotterdam :
Sense Publishers,
[2016]
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 037 | |n Title purchased via APUC SHEDL / ScopNet ebook agreement |n Education (Springer-41171) | ||
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| 100 | 1 | |a Sinitsky, Ilya, |e author. | |
| 245 | 1 | 0 | |a Change and invariance : |b a textbook on algebraic insight into numbers and shapes / |c Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and Bat-Sheva Ilany (Hemdat Hadarom Academic College of Education, Israel). |
| 264 | 1 | |a Rotterdam : |b Sense Publishers, |c [2016] | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (xiii, 378 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references. | ||
| 520 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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? | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Symmetry (Mathematics) | |
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| 650 | 0 | |a Mathematical models. | |
| 650 | 0 | |a Algebra. | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 0 | |a Mathematics |x Philosophy. | |
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| 700 | 1 | |a Ilany, Bat-Sheva, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Sinitsky, Ilya. |t Change and invariance. |d Rotterdam : Sense Publishers, [2016] |z 9789463006972 |w (OCoLC)962095479 |
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