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E-raamat: Evolutionary Origins and Early Development of Number Processing

Edited by (University of Missouri, Columbia, MO, USA), Edited by (University of Virginia, Charlottesville, VA, USA), Edited by (National Institute of Child Health and Human Development, NIH, Rockville, MD, USA)
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Inaugurating a series intended to provide a broad survey of cutting edge research in mathematical cognition and learning, researchers in psychology and education explore number and magnitude in non-human animals, number and magnitude in infants and young children, and number judgments: theoretical perspectives and evolutionary foundations. Among their topics are grey parrot capacities for numerical concepts, numerical cognition and quantitative abilities in non-human primates, intuitive non-symbolic arithmetic, analog origins of numerical concepts, the precision and internal confidence of people's approximate number thoughts, and the evolution of number systems. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

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.

  • Brings together and focuses the efforts and research of multiple disciplines working in math cognition.
  • The contributors bring vast knowledge and experience to bear on resolving extant substantive and methodological challenges to help advance the field of basic number processing.
  • Introductory sections and summaries will be included to provide background for non-specialist readers.

Arvustused

"...this and forthcoming companion volumes in the series should prove to be of particular interest to a diverse audience of students, researchers, and educators across domains both within and beyond the boundaries of psychological thought." --PsycCRITIQUES

Muu info

Research-based reference focused on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children.
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(32)
Christian Agrillo
Maria Elena Miletto Petrazzini
Angelo Bisazza
Introduction
3(1)
Overview
4(1)
Problems and Methods of Study
4(9)
Methodologies Adopted
6(7)
Number vs. Continuous Quantities: Is Number More Cognitively Demanding?
13(3)
One or Multiple Systems of Numerical Representation?
16(3)
Ontogeny of Numerical Abilities
19(2)
Similarities in Numerical Abilities among Fish and between Fish and Other Vertebrates
21(4)
Conclusions and Future Directions
25(2)
Acknowledgments
27(1)
References
27(8)
2 Foundations of Number and Space Representations in Non-Human Species
35(32)
Giorgio Vallortigara
Introduction
35(2)
Core Knowledge of Objects
37(2)
Core Knowledge of Number
39(12)
Core Knowledge of Geometry
51(8)
Conclusions
59(1)
Acknowledgments
59(1)
References
60(7)
3 Numerical Concepts: Grey Parrot Capacities
67(24)
Irene M. Pepperberg
Introduction
67(3)
Alex's Non-numerical Capacities
70(1)
Alex's Early Numerical Abilities
70(4)
Training and Testing Methods
71(1)
Labeling of Basic Quantities and Simple Heterogeneous Sets
71(1)
Complex Heterogeneous Sets
72(2)
Alex's More Advanced Numerical Abilities
74(11)
Number Comprehension
74(2)
Use of "None"
76(1)
Addition of Small Quantities
77(3)
Ordinality and Equivalence
80(3)
An Exact Integer System
83(1)
The Final Study
83(2)
Conclusions
85(1)
Acknowledgments
85(1)
References
85(6)
4 Numerical Cognition and Quantitative Abilities in Nonhuman Primates
91(32)
Michael J. Beran
Audrey E. Parrish
Theodore A. Evans
Introduction
91(1)
The Question of Animal Counting
92(5)
Relative Quantity Judgments
97(5)
Ordinality Judgments
102(2)
Quantity Illusions
104(1)
Mechanisms for Representing Quantity and Number
105(6)
Conclusions
111(1)
Acknowledgments
112(1)
References
112(11)
Part II Number and Magnitude in Infants and Young Children
5 Evolutionary and Developmental Continuities in Numerical Cognition
123(22)
Ariel Starr
Elizabeth M. Brannon
Introduction
123(1)
Cross-Species Comparisons
124(4)
Numerical Representations in Infancy
128(4)
Malleability
132(1)
Causal Relation Between ANS Acuity and Mathematics
133(4)
Applications
137(2)
Conclusion
139(1)
References
139(6)
6 On the Relation between Numerical and Non-Numerical Magnitudes: Evidence for a General Magnitude System
145(30)
Stella F. Lourenco
Introduction
145(3)
Analog Format for Number and Other Magnitudes
148(2)
A General Magnitude System: Three Types of Supporting Evidence
150(12)
Cross-Magnitude Interactions
151(5)
Correlations in Precision of Numerical and Non-Numerical Representations
156(1)
Training and Transfer
157(3)
Potential Neural Mechanisms
160(2)
Do Mathematical Concepts Have a Basis in Nonsymbolic Magnitudes?
162(3)
Conclusions
165(3)
Acknowledgments
168(1)
References
168(7)
7 Foundations of the Formal Number Concept: How Preverbal Mechanisms Contribute to the Development of Cardinal Knowledge
175(26)
Kristy vanMarle
Introduction
175(2)
Two Core Mechanisms for Representing Number
177(8)
System 1: Analog Magnitude System (ANS)
177(4)
System 2: Object Tracking System (OTS)
181(4)
"Number Concept" Defined
185(1)
Does the ANS and/or OTS Measure Up?
186(4)
Abstract Representations
186(1)
Cardinality
187(1)
Ordinality
188(1)
Arithmetic
189(1)
Foundations of the Formal Number Concept
190(2)
Conclusions
192(1)
References
193(8)
8 Intuitive Nonsymbolic Arithmetic
201(24)
Koleen McCrink
Introduction
201(3)
Ordering Magnitudes
204(2)
Adding and Subtracting Nonsymbolic Magnitudes
206(2)
Multiplication and Division of Nonsymbolic Quantity
208(8)
Ratio and Proportion Tasks
208(4)
Serial Multiplication and Division in Infants and Children
212(4)
Conclusions
216(1)
References
217(8)
9 Analog Origins of Numerical Concepts
225(28)
Jessica F. Cantion
Introduction
225(1)
The Analog Number System
226(5)
Representation
227(1)
Comparison
228(2)
Arithmetic
230(1)
Neural Basis of Analog Number
231(3)
Analog Origins of Number Symbols
234(3)
Neural Substrate of Human Number Symbols
237(4)
The Analog System and Formal Mathematics Achievement
241(4)
Conclusions
245(1)
Acknowledgments
246(1)
References
246(7)
10 The Small—Large Divide: A Case of Incompatible Numerical Representations in Infancy
253(24)
Tasha Posid
Sara Cordes
Introduction
253(1)
Distinct Systems of Representation: Evidence of Continuity across Development and Phylogeny
254(3)
Evidence for Two Systems in Infancy
257(2)
Small versus Small Discriminations
258(1)
The Small—Large Divide
258(1)
Tracking Small Sets with the ANS: Exceptions to the Rule
259(5)
Signal Clarity of the ANS
261(1)
Taxed Working Memory
262(2)
Overcoming the Small—Large Divide
264(3)
Children's Acquisition of Numerical Language
264(2)
Increasing Precision in the ANS across Development
266(1)
Open Questions and Future Directions
267(2)
What Parameters Help Infants Succeed at Small-Large Comparisons?
268(1)
Is the Small-Large Incompatibility Receptive to Feedback or Training?
268(1)
Conclusions
269(1)
References
269(8)
11 The Influence of Multisensory Cues on Representation of Quantity in Children
277(28)
Joseph M. Baker
Kerry E. Jordan
Introduction
277(1)
Representation of Number without Language
278(3)
Development of Intersensory Integration
281(3)
Beneficial Effects of Multisensory Stimulation on Cognition and Learning
284(2)
Does Multisensory Information Improve Numerical Abilities?
286(6)
How Does Multisensory Information Improve Numerical Competence?
289(3)
Unanswered Questions and Future Directions
292(2)
Conclusions
294(1)
References
295(10)
Part III Number Judgments: Theoretical Perspectives and Evolutionary Foundations
12 The Precision and Internal Confidence of Our Approximate Number Thoughts
305(30)
Justin Halberda
Darko Odic
Introduction
305(1)
Behavioral and Neural Signatures of the ANS
306(5)
A Psychophysical Model for ANS Representations
311(16)
How to Think of a Weber Fraction (w) in the Approximate Number System (ANS)
315(5)
Weber Fraction Conceptualized as a Scaling Factor
320(4)
How a Weber Fraction (w) Indexes Individual Differences in ANS Precision
324(3)
The Relation between the Weber Fraction and Internal Confidence
327(2)
Conclusion
329(1)
References
330(5)
13 The Evolution of Number Systems
335(20)
David C. Geary
Daniel B. Berch
Kathleen Mann Koepke
Introduction
335(1)
The Evolutionary Functions of Number Sense in Nonhuman Species
336(6)
Foraging
336(4)
Mating
340(2)
Quantitative Processing in the Evolution of Human Decision Making
342(6)
The Evolutionary Emergence of Symbolic Representation
342(2)
The Evolution of Numerical Heuristics and Decision Making
344(1)
From Continuous Magnitude Perception to Discrete Numerical Representation
345(1)
From Approximation to Numerical Thinking
346(2)
Conclusions
348(1)
References
349(6)
Index 355
David C. Geary is a cognitive developmental and evolutionary psychologist at the University of Missouri. He has wide ranging interests but his primary areas of research and scholarly work are childrens mathematical cognition and learning and Darwins sexual selection as largely but not solely related to human sex differences.

Professor Geary directed a 10-year longitudinal study of childrens mathematical development from kindergarten to ninth grade, with a focus on identifying the core deficits underlying learning disabilities and persistent low achievement in mathematics. The study was funded by the National Institutes of Health (US), including through a MERIT award to professor Geary. One result has been the identification of the school-entry number knowledge that predicts economically-relevant mathematical competencies in adolescence. As a follow-up, professor Geary is directing a second longitudinal study, funded by the National Science Foundation (US), to identify the preschool quantitative competencies that predict this school-entry number knowledge. Professor Geary has also published conceptual and theoretical articles on individual differences in childrens mathematical learning, as well as a book published by the American Psychological Association, Childrens mathematical development (1994); recently translated into Korean. Professor Geary has also contributed to applied and policy related work on this topic, serving, for instance, on the Presidents National Mathematics Advisory Panel, and chairing its learning processes task group.

Professor Gearys interests in evolution are reflected in two of his other books published by the American Psychological Association, The origin of mind: Evolution of brain, cognition, and general intelligence (2005), and Male, female: The evolution of human sex differences (1998, 2010 second edition). The corresponding empirical work ranges from the study of changes in brain volume during hominid evolution to human mate choices to hormonal responses to simulated (video game) competition. Professor Gearys current interests in this area follow from several of his collaborative studies on the effects of prenatal toxin exposure on sex differences in cognition and behavior in mice. Specifically, traits related to Darwins sexual selection are often exaggerated relative to other traits. These would include, for example, the bright plumage of the males of many species of bird that in turn is a good indicator of their behavioral and genetic health. These traits are particularly sensitive to environmental disruption, even in healthy individuals. Professor Gearys in progress book, The evolution of vulnerability, is focused on these traits in humans and how they can be used to identify at-risk populations and individuals.

Daniel B. Berch is Professor of Educational Psychology and Applied Developmental Science at the University of Virginias Curry School of Education. Prior to this position, he was Associate Dean for Research and Faculty Development at the Curry School. Before coming to the University of Virginia, Professor Berch served as Associate Chief of the Child Development and Behavior Branch at the National Institute of Child Health and Human Development, NIH. His previous federal service included a year spent as a Senior Research Associate at the U. S. Department of Education, advising the Assistant Secretary for Educational Research and Improvement. Professor Berch is a cognitive developmental psychologist with interests ranging from the development of numerical cognition and mathematical learning disabilities (MLD) to evolutionary perspectives on education. He has published articles on childrens magnitude representations, the development of number sense, and the role of working memory in MLD. He is senior editor of the book, Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (co-edited by Michele Mazzocco).

Among other honors, he received the NIH Award of Merit, was elected Fellow of the American Psychological Associations Division of Experimental Psychology, served as an ex officio member of the U.S. Department of Educations National Mathematics Advisory Panel commissioned by President George W. Bush, was elected to the Evolution Institutes Scientific Advisory Board (and chairs its Education Subcommittee), was appointed to the AIM Academys Research Advisory Board, and served as a member of the Professional Advisory Board of the National Center for Learning Disabilities for six years. During the past several years, Professor Berch has been working on the implications of evolutionary theory for educational research and practice, publishing a book chapter on instructing evolved minds, serving as one of the Evolution Institutes primary organizers of a 2013 conference on evolutionary perspectives in educational research funded by the American Educational Research Association, and is co-author (with David Geary) of an article entitled Evolutionary Approaches to Understanding Childrens Academic Achievement” to be published in Wileys forthcoming online reference work, Emerging Trends in the Social and Behavioral Sciences.

Kathleen Mann Koepke, Ph.D., is Director of the Math and Science Cognition and Learning, Development & Disorders Program in the Child Devlopment and Behavior Branch (CDBB) of the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health (NIH), Rockville, MD (kmk@nih.gov).

Dr. Mann Koepke oversees a research program focused on developing and supporting research and training initiatives to increase knowledge relevant to the development of math and science cogniton, reasoning, knowledge, and abilities, both in animals and in humans from birth through all years of formal education in diverse learners with and without disabilities. This research focus recently lead to her serving as co-Guest Editor of a special journal issue regarding the co-occurrence of math and reading disabilities (Mann Koepke, K and Miller, B. (Eds.) At the Intersection of Math & Reading Disabilities. Journal of Learning Disabilities. 2013: 46(6)).

She is a lifecourse developmental cognitive neuroscientist/psychologist with a passion to serve the cognitively challenged and/or disabled via promoting new and innovative basic research and theoretically-grounded evidence-based intervention strategies to maximuze function. Dr. Mann Koepke has served in the Division of Extramural Programs across the National Institute on Aging (NIA), the National Institute of Nursing Research (NINR), and now NICHD, overseeing research on cognitive and neurological development and disorders, including neurobiological, behavioral and caregiving research foci. She has served on numerous federal and national committees aimed at advancing research and services for young learners and persons with cognitive and/or physical disability or differences, co-authoring numerous calls for new research to close significant gaps, as well as peer-reviewed publications. Prior to coming to NIH, she was faculty in Neurology (Psychology) at Washington University-St. Louis School of Medicine where she managed the universitys Alzheimers Disease Research Center (supported in part by grant P50AG05681), and served as Director of its Education Core and its Rural Outreach Satellite. While there, expanding on her enthusiasm for the use of newly developed technologies as tools for cognition, she developed and regularly contributed to the first-ever freely available web-based online educational support system for anyone interested in Alzheimers disease (AD) and for formal and informal dementia patient caregivers; the cite has garnered numerous national and international awards. This early online educational service has been used & replicated around the globe as a model for online disease/disabilty-focused educational support service.