The origins of mathematical knowledge in childhood:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Erlbaum / Taylor & Francis
2007
|
| Schriftenreihe: | Studies in mathematical thinking and learning
|
| Schlagworte: | |
| Online-Zugang: | Table of contents only Publisher description Contributor biographical information Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 171-184) and indexes |
| Beschreibung: | XV, 196 S. graph. Darst. 24 cm |
| ISBN: | 0805857583 9780805857580 1410616487 9781410616487 |
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Datensatz im Suchindex
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| adam_text | Titel: The origins of mathematical knowledge in childhood
Autor: Sophian, Catherine
Jahr: 2007
Contents
Preface
xv
Cognitive Development and Mathematics Learning 1
Two Perspectives on the Development of Mathematical 3
Knowledge in Childhood
The Position That Counting is Foundational 4
The Comparison-of-Quantities Position 6
Nature, Nurture, and Domains of Development 8
Sense Making and the Distinction Between a Mathematics 10
of Quantities and a Mathematics of Symbols
Coming Attractions 12
Children s Counting 15
Numerical Knowledge in Infancy 16
Are Infant Discriminations Based on Continuous 17
Properties Rather Than Number?
Object Files and Numerical Collections 20
Forms of Numerical Representation 23
Large-Number Discrimination in Infancy 27
Interpretive Issues Surrounding Infancy Research 29
CONTENTS
Counting and Cardinality 32
Understanding That Counting Yields a Cardinal Value 33
Counting and Comparisons Between Sets 35
Which Comes First: Principles or Performance? 37
Where Do We Go From Here? 39
3 Quantitative Comparison Without Numbers 42
Comparing Numerical Quantities Without Numbers 43
Differentiating Number From Other Quantitative 44
Dimensions
Using Correspondence Relations to Make Numerical 50
Comparisons
Comparing Lengths 52
Distinguishing Length From Other Quantitative 53
Properties
Measuring Length 54
Comparing Areas 56
Comparing Spatial Proportions 59
Quantity Comparison in Developmental Perspective 61
4 Understanding Units 64
Counting With Units Other Than Discrete Objects 66
Developmental Implications 69
Using Units in Measuring Continuous Quantities 70
Relationships Between Unit Size, Number of Units, and 73
Aggregate Quantity
Understanding Hierarchies of Units 75
Composing and Decomposing Large Numbers 78
Place Value 80
The Importance of Incorporating the Concept of Unit 82
in Early Mathematics Instruction
5 Relations Among Quantities in Arithmetic: Additive 84
and Multiplicative Reasoning
Additive Reasoning 86
CONTENTS ix
Problem Solving 86
Additive Part-Whole Relations 89
Principles of Commutativity, Associativity, and Inversion 95
Multiplicative Reasoning 97
Ratios and Units 97
Reasoning About Many-to-One Relations 98
Multiplicative Situations and Conceptualizations of 99
Multiplicative Relations
Principles of Commutativity, Associativity, and 101
Inversion
The Conceptual Relation Between Additive and 103
Multiplicative Reasoning
6 Understanding Fractions 106
From Counting Numbers to Fractions 108
Early Forms of Fraction Knowledge 111
When Less is More 112
Fraction Subconstructs 114
The Information-Processing Demands of Fractions 115
Parts and Wholes in Understanding Fractions 118
Fractional Measurement Units 120
Successful Fraction Instruction 123
The Rational Number Project 124
A Curriculum Building on Percentages 125
What the Programs Share 126
Mathematical Development Through the Elementary Years 128
7 Implications for Developmental Psychology 131
Origins of the Concept of Unit and its Ramifications 132
for Domain Specificity
Co-optation and the Distinction Between Biologically 135
Primary and Biologically Secondary Cognitive
Abilities
Domain Specificity 137
Domain-General Processes in the Development of 141
Mathematical Knowledge
CONTENTS
Language as a Sociocultural Tool in Mathematical 142
Development
Capacity Limitations and Developmental Malleability 144
The Developmental Origins of Mathematical 147
Knowledge: A Reprise
Starting Points for Mathematical Development 147
Conceptual Transitions in Mathematical 148
Development
What Have We Learned ? 150
8 Implications for Mathematics Education 151
Conceptual Goals for Mathematics Instruction 153
Coherence in Numerical Concepts Across Grade 154
Levels
Abstraction as an Instructional Goal Across Grade 155
Levels
Integrating Concepts and Computational Skills 156
Instruction With Manipulatives 157
Alternative Solution Methods 158
Justifications 160
The Primacy of Concepts in Instruction 161
Beyond Arithmetic 162
Measurement 162
Algebra 163
Geometry 164
Instructional Recommendations 165
The Need for a Long-Term Perspective 165
A Focus on Units 166
Teaching for Generality 166
Implementing the Recommendations: The 167
El konin-Davydov Curriculum and Beyond
A Fresh Look at Mathematics Instruction 168
CONTENTS xi
References 171
Author Index 185
Subject Index 191
|
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| discipline | Pädagogik Psychologie |
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| spelling | Sophian, Catherine Verfasser aut The origins of mathematical knowledge in childhood Catherine Sophian New York [u.a.] Erlbaum / Taylor & Francis 2007 XV, 196 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Studies in mathematical thinking and learning Includes bibliographical references (p. 171-184) and indexes Mathematik Mathematics Study and teaching (Elementary) Arithmetic Study and teaching (Early childhood) Cognitive learning theory Concept learning Kind (DE-588)4030550-8 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematische Begabung (DE-588)4169099-0 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf Mathematische Begabung (DE-588)4169099-0 s Psychologie (DE-588)4047704-6 s Kind (DE-588)4030550-8 s DE-604 Mathematikunterricht (DE-588)4037949-8 s http://www.loc.gov/catdir/toc/ecip0618/2006023683.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0668/2006023683-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0701/2006023683-b.html Contributor biographical information HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017387467&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sophian, Catherine The origins of mathematical knowledge in childhood Mathematik Mathematics Study and teaching (Elementary) Arithmetic Study and teaching (Early childhood) Cognitive learning theory Concept learning Kind (DE-588)4030550-8 gnd Mathematikunterricht (DE-588)4037949-8 gnd Mathematische Begabung (DE-588)4169099-0 gnd Psychologie (DE-588)4047704-6 gnd |
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| title | The origins of mathematical knowledge in childhood |
| title_auth | The origins of mathematical knowledge in childhood |
| title_exact_search | The origins of mathematical knowledge in childhood |
| title_full | The origins of mathematical knowledge in childhood Catherine Sophian |
| title_fullStr | The origins of mathematical knowledge in childhood Catherine Sophian |
| title_full_unstemmed | The origins of mathematical knowledge in childhood Catherine Sophian |
| title_short | The origins of mathematical knowledge in childhood |
| title_sort | the origins of mathematical knowledge in childhood |
| topic | Mathematik Mathematics Study and teaching (Elementary) Arithmetic Study and teaching (Early childhood) Cognitive learning theory Concept learning Kind (DE-588)4030550-8 gnd Mathematikunterricht (DE-588)4037949-8 gnd Mathematische Begabung (DE-588)4169099-0 gnd Psychologie (DE-588)4047704-6 gnd |
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