Evolutionary origins and early development of number processing:
The first volume in this ground-breaking series focuses on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative conc...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2015
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Mathematical cognition and learning
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | The first volume in this ground-breaking series focuses on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative concepts and skills along with evolutionary precursors and early developmental trajectories |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xxiii, 376 S. Ill., graph. Darst. 23 cm |
| ISBN: | 9780124201330 |
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Datensatz im Suchindex
| _version_ | 1804153255706492929 |
|---|---|
| adam_text | Contents
Contributors
xi
Foreword
xiii
Preface
xxi
Part I
Number and Magnitude in Non-Human Animals
1.
At the Root of Math: Numerical Abilities in Fish
3
Christian
Agrillo,
Maria Elena Miletto Petrazzini,
and
Ange
f
о В і
sazza
Introduction
3
Overview
4
Problems and Methods of Study
4
Methodologies Adopted
6
Number vs. Continuous Quantities: Is Number More Cognitivery
Demanding?
! 3
One or Multiple Systems of Numerical Representation?
16
Ontogeny of Numerical Abilities
19
Similarities in Numerical Abilities among Fish and
between Fish and Other Vertebrates
21
Conclusions and Future Directions
25
Acknowledgments
27
References
27
2.
Foundations of Number and Space
Representations in Non-Human Species
35
Giorgio
Val/ortigara
Introduction
35
Core Knowledge of Objects
37
Core Knowledge of Number
39
Core Knowledge of Geometry
51
Conclusions
59
Acknowledgments
59
References
60
. Contents
3.
Numerical Concepts: Grey Parrot Capacities
67
Irene M. Pepperberg
Introduction 67
Alex s
Non
-numerical Capacities
70
Alex s Early Numerical Abilities
70
Training and Testing Methods 71
Labeling of Basic Quantities and Simple Heterogeneous Sets
71
Complex Heterogeneous Sets
72
Alex s More Advanced Numerical Abilities
74
Number Comprehension
74
Use of None
76
Addition of Small Quantities
77
Ord i nality
and Equivalence
80
An Exact Integer System
83
The Final Study
83
Conclusions
85
Acknowledgments
85
References
85
4.
Numerical Cognition and Quantitative Abilities
in Nonhuman Primates
91
Michael
І
.
Beran,
Audrey
E.
Panish,
and Theodore A f vans
Introduction
91
The Question of Animal Counting
92
Relative Quantity Judgments
97
Ordinalłty
Judgments
102
Quantity Illusions
104
Mechanisms for Representing Quantity and Number
105
Conclusions
щ
Acknowledgments
112
112
Part II
Number and Magnitude in Infants
and Young Children
5.
Evolutionary and Developmental Continuities
in Numerical Cognition ^
23
Ariel Starr and Elizabeth M. Brannon
124
Contents
vit
Numerical Representations in Infancy
128
Malleability
132
Causal Relation Between
ANS
Acuity and Mathematics
133
Applications
137
Conclusion
139
References
139
6.
On the Relation between Numerical and
Non-Numerical Magnitudes: Evidence
for a General Magnitude System
145
Stella F. Lourenco
Introduction
145
Analog Format for Number and Other Magnitudes
148
A General Magnitude System: Three Types of
Supporting Evidence
150
Cross-Magnitude Interactions
151
Correlations in Precision of Numerical and
Non-Numerical Representations
156
Training and Transfer
157
Potential Neural Mechanisms
160
Do Mathematical Concepts Have a Basis in
Nonsymbolic Magnitudes?
162
Conclusions
165
Acknowledgments
168
References
168
7.
Foundations of the Formal Number Concept:
How Preverbal Mechanisms Contribute
to the Development of Cardinal Knowledge
175
Kristy vanMarle
Introduction
175
Two Core Mechanisms for Representing Number
177
System
1 :
Analog Magnitude System
(ANS)
177
System
2:
Object Tracking System (OTS)
181
Number Concept Defined
185
Does the
ANS
and/or OTS Measure Up?
186
Abstract Representations
1в6
Cardinality !87
Ordinality
lô8
Arithmetic
! 89
Foundations of the
Formai
Number Concept
190
Conclusions 192
References
193
Contents
viii
8. Intuitive
Nonsymboïic
Arithmetic 201
Koieen McCrink
201
Introduction
Ordering Magnitudes
Adding and Subtracting Nonsymbolic Magnitudes
Multiplication and Division of Nonsymbolic Quantity
208
Ratio and Proportion Tasks 208
Serial Multiplication and Division in Infants and Children
212
Conclusions 216
References 2
7
9.
Analog Origins of Numerical Concepts
225
Jessica F. Cantlon
Introduction 225
The Analog Number System
226
Representation
227
Comparison
228
Arithmetic
230
Neural Basis of Analog Number
231
Analog Origins of Number Symbols
234
Neural Substrate of Human Number Symbols
237
The Analog System and Formal Mathematics Achievement
241
Conclusions
245
Acknowledgments
246
References
246
10.
The Small-Large
Divìde: A
Case of Incompatible
Numerical Representations in Infancy
253
Tãsha
Postd and Sara
Cordes
Introduction
253
Distinct Systems of Representation: Evidence of Continuity
across
Development
and Phytogeny
254
Evidence for Two Systems in Infancy
257
Small versus Small Discriminations
258
The Small-Large Divide
258
Tracking Small Sets with the AIMS: Exceptions to the Rule
259
Signal Clarity of the
ANS 261
Taxed Working Memory
262
Overcoming the Small-Large Divide
264
Children s Acquisition of Numerical Language
264
Increasing Precision in the
ANS
across Development
266
Contents ix
Open Questions and Future Directions
267
What Parameters Help Infants Succeed at
Small-Large Comparisons?
268
Is the Small-Large Incompatibility Receptive to
Feedback or Training?
268
Conclusions
269
References
269
11.
The Influence of Multisensory Cues on
Representation of Quantity in Children
277
Joseph M. Baker and Kerry E.
fordan
Introduction
277
Representation of Number without Language
278
Development of Intersensory Integration
281
Beneficial Effects of Multisensory Stimulation on Cognition and
Learning
284
Does Multisensory Information Improve Numerical Abilities?
286
How Does Multisensory Information Improve
Numerical Competence?
289
Unanswered Questions and Future Directions
292
Conclusions
294
References
295
Part
Number judgments: Theoretical Perspectives
and Evolutionary Foundations
12.
The Precision and Internal Confidence of
Our Approximate Number Thoughts
305
Justin Hafberda and Darko
Odie
Introduction
305
Behavioral and Neural Signatures of the
ANS 306
A Psychophysical Model for
ANS
Representations
311
How to Think of a Weber Fraction (w) in the
Approximate Number System
(ANS) 315
Weber Fraction Conceptualized as a Scaling Factor
320
How a Weber Fraction (w) Indexes Individual
Differences in
ANS
Precision
324
The Relation between the Weber Fraction and
Internal Confidence
327
Conclusion
329
References
330
x
Contents
13.
The Evolution of Number Systems
335
David
С
Geary, Daniel
ß. Berch,
and
Kathleen Mann Koepke
Introduction
335
The Evolutionary Functions of Number Sense
in Nonhuman Species
336
Foraging
336
Mating
340
Quantitative Processing in the Evolution of
Human Decision Making
342
The Evolutionary Emergence of Symbolic Representation
342
The Evolution of Numerical Heuristics and Decision Making
344
From Continuous Magnitude Perception to Discrete Numerical
Representation
345
From Approximation to Numerical Thinking
346
Conclusions
348
References
349
Index
355
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| isbn | 9780124201330 |
| language | English |
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| spelling | Evolutionary origins and early development of number processing ed. by David C. Geary ... 1. ed. Amsterdam [u.a.] Elsevier 2015 xxiii, 376 S. Ill., graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier Mathematical cognition and learning 1 Includes bibliographical references and index The first volume in this ground-breaking series focuses on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative concepts and skills along with evolutionary precursors and early developmental trajectories Number concept Number concept in animals Number concept in children Numeration Cognition Cognition fast Number concept fast Number concept in animals fast Number concept in children fast Numeration fast Rechenfähigkeit (DE-588)4671320-7 gnd rswk-swf Erlernbarkeit (DE-588)4523167-9 gnd rswk-swf Kind (DE-588)4030550-8 gnd rswk-swf Tiere (DE-588)4060087-7 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Tiere (DE-588)4060087-7 s Rechenfähigkeit (DE-588)4671320-7 s Erlernbarkeit (DE-588)4523167-9 s DE-604 Kind (DE-588)4030550-8 s Geary, David C. 19XX- Sonstige (DE-588)140175970 oth Mathematical cognition and learning 1 (DE-604)BV042510540 1 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027945071&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evolutionary origins and early development of number processing Mathematical cognition and learning Number concept Number concept in animals Number concept in children Numeration Cognition Cognition fast Number concept fast Number concept in animals fast Number concept in children fast Numeration fast Rechenfähigkeit (DE-588)4671320-7 gnd Erlernbarkeit (DE-588)4523167-9 gnd Kind (DE-588)4030550-8 gnd Tiere (DE-588)4060087-7 gnd |
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| title | Evolutionary origins and early development of number processing |
| title_auth | Evolutionary origins and early development of number processing |
| title_exact_search | Evolutionary origins and early development of number processing |
| title_full | Evolutionary origins and early development of number processing ed. by David C. Geary ... |
| title_fullStr | Evolutionary origins and early development of number processing ed. by David C. Geary ... |
| title_full_unstemmed | Evolutionary origins and early development of number processing ed. by David C. Geary ... |
| title_short | Evolutionary origins and early development of number processing |
| title_sort | evolutionary origins and early development of number processing |
| topic | Number concept Number concept in animals Number concept in children Numeration Cognition Cognition fast Number concept fast Number concept in animals fast Number concept in children fast Numeration fast Rechenfähigkeit (DE-588)4671320-7 gnd Erlernbarkeit (DE-588)4523167-9 gnd Kind (DE-588)4030550-8 gnd Tiere (DE-588)4060087-7 gnd |
| topic_facet | Number concept Number concept in animals Number concept in children Numeration Cognition Rechenfähigkeit Erlernbarkeit Kind Tiere Aufsatzsammlung |
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