Continuous Issues in Numerical Cognition

How Many or How Much

1st Edition - May 18, 2016
Editor: Avishai Henik
Language: English
Hardback ISBN:
9 7 8 - 0 - 1 2 - 8 0 1 6 3 7 - 4
eBook ISBN:
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 ab… 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.

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

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Avishai Henik