Continuous Issues in Numerical Cognition

How Many or How Much
 
 
Academic Press
  • 1. Auflage
  • |
  • erschienen am 18. Mai 2016
  • |
  • 456 Seiten
 
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978-0-12-801793-7 (ISBN)
 

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
  • Englisch
  • San Diego
  • |
  • USA
Elsevier Science
  • 13,94 MB
978-0-12-801793-7 (9780128017937)
0128017937 (0128017937)
weitere Ausgaben werden ermittelt
  • Cover
  • Title Page
  • Copyright Page
  • Dedication
  • Contents
  • List of Contributors
  • Acknowledgments
  • Introduction
  • References
  • I - Development
  • Chapter 1 - Development of Quantitative Thinking Across Correlated Dimensions
  • 1.1 - The Use of Looking Time to Measure Infant Quantification
  • 1.1.1 - Early Work on Infant Perception: The Advent of Looking Time Measures
  • 1.1.2 - Studies of Infant Number
  • 1.2 - Generalized over what?
  • 1.3 - Mechanisms of differentiation
  • 1.3.1 - Redundant Cues
  • 1.3.2 - Unitization
  • 1.3.3 - Selective Attention
  • 1.3.3.1 - Object Segregation
  • 1.3.3.2 - Language
  • 1.4 - Mechanisms of reintegration
  • 1.4.1 - Proportional Scaling and Spatial Division
  • 1.4.2 - Symbolic Representation
  • 1.4.2.1 - Measurement
  • 1.4.2.2 - Proportional Reasoning and Probabilities
  • 1.4.2.3 - Fractions
  • 1.4.2.4 - Number Line Estimation
  • 1.5 - Conclusions
  • References
  • Chapter 2 - Link Between Numbers and Spatial Extent From Birth to Adulthood
  • 2.1 - Introduction
  • 2.2 - Numbers and space
  • 2.3 - Nondirectional number-space mapping
  • 2.3.1 - Specificity of the Nondirectional Number-Space Mapping
  • 2.4 - Directional number-space mapping
  • 2.4.1 - Origins of a Directional Number-Space Mapping
  • 2.4.2 - Use of Space to Represent Other Dimensions
  • 2.5 - Conclusions
  • References
  • Chapter 3 - Catching Math Problems Early: Findings From the Number Sense Intervention Project
  • 3.1 - Conceptual framework
  • 3.1.1 - Number Sense in the 3- to 6-Year-Old Age Period Refers to Core Knowledge of Number, Number Relations, and Number Op...
  • 3.1.1.1 - Number
  • 3.1.1.2 - Number Relations
  • 3.1.1.3 - Number Operations
  • 3.1.2 - Number Sense Follows a Developmental Progression
  • 3.1.3 - Number Sense in Kindergarten Predicts Success in Mathematics
  • 3.1.4 - Deficiencies in Number Sense can be Identified Early
  • 3.1.5 - Number Sense is Malleable and Targeted Help in Number Sense Leads to Improved Math Achievement in School
  • 3.2 - Number sense interventions
  • 3.2.1 - Participants
  • 3.2.2 - Experimental Design
  • 3.2.3 - Overview of the Number Sense Curriculum
  • 3.2.3.1 - Number
  • 3.2.3.2 - Number Relations
  • 3.2.3.3 - Number Operations
  • 3.2.3.4 - Number-List Practice
  • 3.2.4 - Findings in the First 3 Years
  • 3.2.5 - Revisions in the Fourth Year Along With Findings
  • 3.3 - Summary and conclusions
  • Acknowledgment
  • References
  • Chapter 4 - Contextual Sensitivity and the Large Number Word Bias: When Is Bigger Really More?
  • 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
  • 4.4.1 - Sets Versus Individuation
  • 4.4.2 - Syntax and Morphology
  • 4.4.3 - Lexical Ambiguity
  • 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
  • References
  • Chapter 5 - Learning, Aging, and the Number Brain
  • 5.1 - Number system across the lifespan
  • 5.1.1 - Number System in Development and Young Adulthood
  • 5.1.2 - Number System in Aging
  • 5.2 - Learning and the quantity system
  • 5.2.1 - Training the Arithmetic Abilities in the Developing and Adult Brain
  • 5.2.2 - Training the Number System in the Young and Aging Brain Also Coupled With Brain Stimulation
  • Acknowledgments
  • References
  • Chapter 6 - Development of Counting Ability: An Evolutionary Computation Point of View
  • 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
  • 6.5.1 - Stimuli
  • 6.5.2 - Procedure
  • 6.5.3 - Genetic Algorithm Parameters
  • 6.5.4 - Calculation of Fitness Function
  • 6.6 - Simulations
  • 6.6.1 - Simulation 1: From Size Perception to Counting (Katz et al., 2013)
  • 6.6.2 - Results
  • 6.6.2.1 - Counting Score (Score of the Final Counting Test)
  • 6.6.2.2 - Generations
  • 6.6.2.3 - Inner Nodes (A Measurement for Network Complexity)
  • 6.6.3 - Simulation 2: Continuous Versus Discrete (Katz et al., 2013)
  • 6.6.4 - Results
  • 6.6.4.1 - Counting Score
  • 6.6.4.2 - Generations
  • 6.6.4.3 - Inner Nodes
  • 6.6.5 - Simulation 3a: Adding a Subitizing Task
  • 6.6.6 - Results
  • 6.6.6.1 - Counting Score
  • 6.6.6.2 - Generations
  • 6.6.6.3 - Inner Nodes
  • 6.6.7 - Simulation 3b: Continuous Versus Discrete With Subitizing
  • 6.6.8 - Results
  • 6.6.8.1 - Counting Score
  • 6.7 - Summary of main results
  • 6.8 - Discussion
  • 6.8.1 - Complexity of the Net
  • References
  • II - Animal Studies
  • Chapter 7 - Number Versus Continuous Quantities in Lower Vertebrates
  • 7.1 - Introduction
  • 7.2 - Methodologies for the study of quantity discrimination
  • 7.2.1 - Free Choice Tests
  • 7.2.1.1 - Shoal Quantity Discrimination
  • 7.2.1.2 - Control for Continuous Quantities in Shoal Quantity Discrimination
  • 7.2.1.3 - Preventing Access to Continuous Quantities
  • 7.2.1.4 - Food Quantity Discrimination
  • 7.2.1.5 - Control for Continuous Quantities in Food Quantity Discrimination
  • 7.2.2 - Training Procedures
  • 7.3 - Relative salience of continuous versus numerical information
  • 7.4 - Conclusions and future directions
  • Acknowledgments
  • References
  • Chapter 8 - Going for More: Discrete and Continuous Quantity Judgments by Nonhuman Animals
  • 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
  • References
  • III - Processes and Mechanisms
  • Chapter 9 - "Number Sense": What's in a Name and Why Should We Bother?
  • 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
  • 9.4.1 - Number Line Estimation and Anchor Points
  • 9.4.2 - Number Discrimination and Decisional Aspects
  • 9.4.3 - Nonsymbolic Number Discrimination and the Influence of Continuous Visual Cues
  • 9.4.4 - Number Discrimination and Domain-General Factors
  • 9.5 - Moving forward: building a bridge between cognitive psychologists and mathematics educators for the sake of education...
  • References
  • Chapter 10 - The Distribution Game: Evidence for Discrete Numerosity Coding in Preschool Children
  • 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
  • 10.6.1 - Count Condition
  • 10.6.2 - Estimation Condition
  • 10.7 - Summary and conclusions
  • References
  • Chapter 11 - Magnitudes in the Coding of Visual Multitudes: Evidence From Adaptation
  • 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)
  • 11.3.1 - Method
  • 11.3.1.1 - Participants
  • 11.3.1.2 - Apparatus
  • 11.3.1.3 - Displays
  • 11.3.1.4 - Design
  • 11.3.1.5 - Procedure
  • 11.3.2 - Results and Discussion
  • 11.3.3 - Conclusions
  • 11.3.4 - Interlude: Visual Unitization for Large Multitudes
  • 11.4 - Experiment 2: what is the unit in number adaptation? (Abdul-Malak & Durgin, 2009)
  • 11.4.1 - Methods
  • 11.4.1.1 - Participants
  • 11.4.1.2 - Design and Procedure
  • 11.4.1.3 - Displays
  • 11.4.1.4 - Measurement
  • 11.4.2 - Results
  • 11.4.2.1 - Matching
  • 11.4.2.2 - Aftereffects
  • 11.4.3 - Discussion
  • 11.5 - Experiment 2b: the effects of clumping
  • 11.5.1 - Results and Discussion
  • 11.6 - Experiment 3: disembodied sheep legs
  • 11.6.1 - Methods
  • 11.6.1.1 - Participants
  • 11.6.1.2 - Procedure
  • 11.6.2 - Results and Discussion
  • 11.7 - Experiment 4: evidence for the success of unitization
  • 11.7.1 - Method
  • 11.7.1.1 - Participants
  • 11.7.1.2 - Stimuli
  • 11.7.1.3 - Design
  • 11.7.1.4 - Procedure
  • 11.7.2 - Results and Discussion
  • 11.8 - General discussion and conclusions
  • 11.8.1 - Magnitudes All the Way Down?
  • 11.8.2 - What is the Unit?
  • 11.8.3 - Relative Number System
  • 11.8.4 - Conclusions Regarding Adaptation
  • 11.8.5 - Conclusions Regarding Visual Number
  • References
  • Chapter 12 - Ordinal Instinct: A Neurocognitive Perspective and Methodological Issues
  • 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
  • References
  • Chapter 13 - Discrete and Continuous Presentation of Quantities in Science and Mathematics Education
  • 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
  • References
  • Chapter 14 - Interaction of Numerical and Nonnumerical Parameters in Magnitude Comparison Tasks With Children and Their Relatio...
  • 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
  • References
  • IV - Models
  • Chapter 15 - Symbolic and Nonsymbolic Representation of Number in the Human Parietal Cortex: A Review of the State-of-the-Art, O...
  • 15.1 - Number in the brain
  • 15.2 - Nonsymbolic number in the brain
  • 15.2.1 - Adult Studies
  • 15.2.2 - Developmental Studies
  • 15.3 - Symbolic number in the brain
  • 15.3.1 - Adult Studies
  • 15.3.2 - Developmental Studies
  • 15.4 - Abstract representation of numerical magnitudes
  • 15.4.1 - Developmental Studies
  • 15.5 - Nonnumerical magnitudes
  • 15.5.1 - Symbolic Numbers and Nonnumerical Magnitudes
  • 15.5.2 - Nonsymbolic Numbers and Nonnumerical Magnitudes
  • 15.5.3 - Continuous Visual Properties in Nonsymbolic Dot Arrays
  • 15.6 - Conclusions
  • References
  • Chapter 16 - What Do We Measure When We Measure Magnitudes?
  • 16.1 - Introduction
  • 16.1.1 - Nonsymbolic Magnitudes
  • 16.1.2 - Main Theories in Numerical Cognition
  • 16.2 - Rethinking the premises
  • 16.3 - From "approximate number system" to "approximate magnitude system"
  • 16.4 - Developmental model of the AMS
  • 16.4.1 - Major Landmarks of the AMS Development
  • 16.4.2 - Cultural Experience and Education
  • 16.4.3 - Perception of Proportions
  • 16.4.4 - Relative Versus Absolute Size Discrimination
  • 16.5 - Summary
  • References
  • Chapter 17 - How Do Humans Represent Numerical and Nonnumerical Magnitudes? Evidence for an Integrated System of Magnitude Repre...
  • 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
  • 17.5.1 - Transfer of Subliminally Primed Magnitude Information
  • 17.5.2 - Transfer of Representational Precision Across Magnitudes
  • 17.6 - Developmental continuity of the general magnitude system
  • 17.7 - Conclusions
  • References
  • Chapter 18 - Sensory Integration Theory: An Alternative to the Approximate Number System
  • 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
  • References
  • Subject Index
  • Back cover

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