Coverart for item
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 Bat-Sheva 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 Bat-Sheva Ilany (Hemdat Hadarom Academic College of Education, Israel)

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 Bat-Sheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
Creator
Contributor
Author
Subject
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 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
Member of
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, Bat-Sheva
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 Bat-Sheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
Instantiates
Publication
Copyright
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 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
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 Bat-Sheva Ilany (Hemdat Hadarom Academic College of Education, Israel)
Publication
Copyright
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 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
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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