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Continuous Issues in Numerical Cognition
How Many or How Much
1st Edition - May 18, 2016
Editor: Avishai Henik
Hardback ISBN:9780128016374
9 7 8 - 0 - 1 2 - 8 0 1 6 3 7 - 4
eBook ISBN:9780128017937
9 7 8 - 0 - 1 2 - 8 0 1 7 9 3 - 7
Continuous Issues in Numerical Cognition: How Many or How Much re-examines the widely accepted view that there exists a core numerical system within human beings and an innate… Read more
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Continuous Issues in Numerical Cognition: How Many or How Much re-examines the widely accepted view that there exists a core numerical system within human beings and an innate ability to perceive and count discrete quantities. This core knowledge involves the brain’s intraparietal sulcus, and a deficiency in this region has traditionally been thought to be the basis for arithmetic disability. However, new research findings suggest this wide agreement needs to be examined carefully and that perception of sizes and other non-countable amounts may be the true precursors of numerical ability. This cutting-edge book examines the possibility that perception and evaluation of non-countable dimensions may be involved in the development of numerical cognition. Discussions of the above and related issues are important for the achievement of a comprehensive understanding of numerical cognition, its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills.
Serves as an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse topic
Features chapters from leading researchers in the field
Includes an overview of the multiple disciplines that comprise numerical cognition and discusses the measures that can be used in analysis
Introduces novel ideas that connect non-countable continuous variables to numerical cognition
Neuroscientists, cognitive neuroscientists, neurophysiologists, neurologists, cognitive and developmental psychologists, graduate students, and post-doctoral fellows
Dedication
List of Contributors
Acknowledgments
Introduction
Section I: Development
Chapter 1: Development of Quantitative Thinking Across Correlated Dimensions
Abstract
1.1. The use of looking time to measure infant quantification
1.2. Generalized over what?
1.3. Mechanisms of differentiation
1.4. Mechanisms of reintegration
1.5. Conclusions
Chapter 2: Link Between Numbers and Spatial Extent From Birth to Adulthood
Abstract
2.1. Introduction
2.2. Numbers and space
2.3. Nondirectional number–space mapping
2.4. Directional number–space mapping
2.5. Conclusions
Chapter 3: Catching Math Problems Early: Findings From the Number Sense Intervention Project
Abstract
3.1. Conceptual framework
3.2. Number sense interventions
3.3. Summary and conclusions
Acknowledgment
Chapter 4: Contextual Sensitivity and the Large Number Word Bias: When Is Bigger Really More?
Abstract
4.1. Why are number words confusing?
4.2. Number words and number sense
4.3. Number word meanings
4.4. Sources of ambiguity in number word meanings
4.5. Measuring children’s responses to numerical ambiguity: the large number word bias
4.6. Implications of the large number word bias
4.7. Conclusions and future directions
Chapter 5: Learning, Aging, and the Number Brain
Abstract
5.1. Number system across the lifespan
5.2. Learning and the quantity system
Acknowledgments
Chapter 6: Development of Counting Ability: An Evolutionary Computation Point of View
Abstract
6.1. Introduction
6.2. Evolutionary computation
6.3. Current study (or how can evolutionary algorithms help in understanding the development of the counting system)?
6.4. NeuroEvolution of augmenting topologies (NEAT)
6.5. Methods
6.6. Simulations
6.7. Summary of main results
6.8. Discussion
Section II: Animal studies
Chapter 7: Number Versus Continuous Quantities in Lower Vertebrates
Abstract
7.1. Introduction
7.2. Methodologies for the study of quantity discrimination
7.3. Relative salience of continuous versus numerical information
7.4. Conclusions and future directions
Acknowledgments
Chapter 8: Going for More: Discrete and Continuous Quantity Judgments by Nonhuman Animals
Abstract
8.1. Relative quantity versus relative numerousness judgments
8.2. Relative food quantity judgments by animals and choice biases
8.3. Relative numerousness judgments by animals
8.4. Mechanism(s) for representing quantity
8.5. Conclusions
Section III: Processes and mechanisms
Chapter 9: “Number Sense”: What’s in a Name and Why Should We Bother?
Abstract
9.1. Importance of number sense
9.2. Assessment of number sense
9.3. Relation between number sense and mathematics achievement
9.4. Issues with measuring number sense
9.5. Moving forward: building a bridge between cognitive psychologists and mathematics educators for the sake of educational math practice
Chapter 10: The Distribution Game: Evidence for Discrete Numerosity Coding in Preschool Children
Abstract
10.1. An interesting idea
10.2. Two issues with ANS theory
10.3. Adult’s estimation of numerosity
10.4. Children’s estimation of numerosity
10.5. Study 1: The distribution game
10.6. Study 2: A computer-controlled variant
10.7. Summary and conclusions
Chapter 11: Magnitudes in the Coding of Visual Multitudes: Evidence From Adaptation
Abstract
11.1. Units and the subitizing range
11.2. Aftereffects and the perception of texture element density
11.3. Experiment 1: magnitude estimation of visual number under conditions of adaptation (Huk & Durgin, 1996)
11.4. Experiment 2: what is the unit in number adaptation? (Abdul-Malak & Durgin, 2009)
11.5. Experiment 2b: the effects of clumping
11.6. Experiment 3: disembodied sheep legs
11.7. Experiment 4: evidence for the success of unitization
11.8. General discussion and conclusions
Chapter 12: Ordinal Instinct: A Neurocognitive Perspective and Methodological Issues
Abstract
12.1. Scientific knowledge and developments
12.2. Neural and cognitive foundations of numerical knowledge
12.3. Methodological issues in studying ordinality
12.4. Symbolic versus nonsymbolic representation
12.5. Ordinal instinct and developmental dyscalculia
12.6. Conclusions
Chapter 13: Discrete and Continuous Presentation of Quantities in Science and Mathematics Education
Abstract
13.1. Introduction
13.2. Study 1: comparison of perimeters
13.3. Study 2: comparison of ratios
13.4. Study 3: comparison of areas and numbers in continuous and discrete presentation modes
13.5. Discussion
Acknowledgment
Chapter 14: Interaction of Numerical and Nonnumerical Parameters in Magnitude Comparison Tasks With Children and Their Relation to Arithmetic Performance
Abstract
14.1. Introduction
14.2. Approximate number system and mathematics development
14.3. Nonsymbolic magnitude discrimination task and visual parameters
14.4. Developmental dyscalculia and the state of the ANS
14.5. Working memory, mathematics performance, and the ANS task context
14.6. Mathematics performance, working memory, and inhibition
14.7. Visuospatial memory, mathematics, and construction play
14.8. Conclusions
Section IV: Models
Chapter 15: Symbolic and Nonsymbolic Representation of Number in the Human Parietal Cortex: A Review of the State-of-the-Art, Outstanding Questions and Future Directions
Abstract
15.1. Number in the brain
15.2. Nonsymbolic number in the brain
15.3. Symbolic number in the brain
15.4. Abstract representation of numerical magnitudes
15.5. Nonnumerical magnitudes
15.6. Conclusions
Chapter 16: What Do We Measure When We Measure Magnitudes?
Abstract
16.1. Introduction
16.2. Rethinking the premises
16.3. From “approximate number system” to “approximate magnitude system”
16.4. Developmental model of the AMS
16.5. Summary
Chapter 17: How Do Humans Represent Numerical and Nonnumerical Magnitudes? Evidence for an Integrated System of Magnitude Representation Across Development
Abstract
17.1. Introduction
17.2. Theory of integration across magnitudes: the general magnitude system
17.3. Shared neural coding for number and other magnitudes
17.4. Developmental origins of a general magnitude system
17.5. Integration across numerical and nonnumerical magnitudes in human adults
17.6. Developmental continuity of the general magnitude system
17.7. Conclusions
Chapter 18: Sensory Integration Theory: An Alternative to the Approximate Number System
Abstract
18.1. Introduction
18.2. Concept
18.3. Sensory cues remain to influence numerosity processes even when they are seemingly controlled
18.4. Sensory integration and ANS tasks
18.5. Sensory integration and arithmetic
18.6. Conclusions
Subject Index
No. of pages: 456
Language: English
Published: May 18, 2016
Imprint: Academic Press
Hardback ISBN: 9780128016374
eBook ISBN: 9780128017937
AH
Avishai Henik
Dr. Avishai Henik is a Professor of Psychology at Ben-Gurion University of the Negev. He holds a consulting editorial position with several journals (e.g., Psychonomic Bulletin and Review, Journal of Experimental Psychology: General) and serves regularly as an ad-hoc reviewer for various journals in the field and for granting agencies. Dr. Henik has over 300 publications of which most are in peer-reviewed journals. He has edited or co-edited three books in the area of numerical cognition. A leader in the field, he was awarded a prestigious European Research Council (ERC) Advanced Researcher grant to continue his cutting-edge research on the contribution of non-countable dimensions to the development and understanding of numerical cognition.
Affiliations and expertise
Distinguished Professor Emeritus of Psychology, Department of Psychology, Ben-Gurion University of the Negev, Beer-Sheva, Israel