The Resource Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
Resource Information
The item Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a twodigit 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
 Language
 eng
 Extent
 1 online resource (xiii, 378 pages)
 Contents

 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 CognitiveDevelopmental 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: NonIntegers 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
 Isbn
 9789463006972
 Label
 Change and invariance : : a textbook on algebraic insight into numbers and shapes
 Title
 Change and invariance
 Title remainder
 : a textbook on algebraic insight into numbers and shapes
 Statement of responsibility
 Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
 Language
 eng
 Summary
 What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a twodigit 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
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 Sinitsky, Ilya
 Dewey number
 516.1
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QA174.7.S96
 LC item number
 S58 2016eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Ilany, BatSheva
 http://library.link/vocab/subjectName

 Symmetry (Mathematics)
 Mathematics
 Mathematical models
 Algebra
 Geometry, Algebraic
 Mathematics
 Label
 Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 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 CognitiveDevelopmental 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: NonIntegers 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
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 378 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9789463006972
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 SPR964657030
 ocn964657030
 Label
 Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 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 CognitiveDevelopmental 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: NonIntegers 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
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 378 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9789463006972
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 SPR964657030
 ocn964657030
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Changeandinvarianceatextbookonalgebraic/jk6nacMYak/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Changeandinvarianceatextbookonalgebraic/jk6nacMYak/">Change and invariance : : a textbook on algebraic insight into numbers and shapes, Ilya Sinitsky (Gordon Academic College of Education, Shaanan Religious College of Education, Israel) and BatSheva Ilany (Hemdat Hadarom Academic College of Education, Israel)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>