- The Oxford Handbook of Numerical Cognition
- Dedication
- Preface
- List of Figures
- List of Tables
- List of Contributors
- Promoting Maths to the General Public
- Philosophy of Number
- Cognitive Foundations of Human Number Representations and Mental Arithmetic
- Primitives and Non-primitives of Numerical Representations
- Finger-based representation of mental arithmetic
- Linking Numbers to Space: from the mental number line towards a hybrid account
- Multi-digit Number Processing: overview, conceptual clarifications, and language influences
- How Abstract is Arithmetic?
- Arithmetic Word Problem Solving and Mental Representations
- Intuition in Mathematical and Probabilistic Reasoning
- Phylogeny and Ontogeny of Mathematical and Numerical Understanding
- Numerical and Arithmetic Abilities in Non-primate Species
- Monkey Mathematical Abilities
- Numerical Abilities and Arithmetic in Infancy
- Spontaneous Focusing On Numerosity and its Relation to Counting and Arithmetic
- How Counting Leads to Children’s First Representations of Exact, Large Numbers
- Approximate Arithmetic Abilities in Childhood
- Number Representations and their Relation with Mathematical Ability
- Numerical Cognition during Cognitive Aging
- Culture, Language, and Number
- Cognitive Linguistics and the Concept(s) of Number
- Figuring Out Children’s Number Representations: lessons from cross-cultural work
- Mathematics Learning in the USA and JAPAN: influences of language
- What is There to Learn from International Surveys of Mathematical Achievement?
- From Single-Cell Neuropathology to Mathematics Education: navigator chapter
- Neuronal Correlates of Non-verbal Numerical Competence in Primates
- Development of the numerical brain
- Arithmetic in the Child and Adult Brain
- Numerical Symbols: an overview of their cognitive and neural underpinnings
- A Theory of Magnitude: the parts that sum to number
- Basic Number Representation and Beyond: neuroimaging and computational modeling
- Mapping the Brain for Math: reversible inactivation by direct cortical electrostimulation and transcranial magnetic stimulation
- Applications of Neuroscience to Mathematics Education
- When Number Processing and Calculation is Not Your Cup of Tea
- Dyscalculia: from brain to education
- Developmental Dyscalculia as a Heterogeneous Disability
- The Contributions of Syndrome Research to the Study of MLD
- Number Processing and Arithmetic in Children and Adults with Reading Difficulties
- Genetic Developmental Disorders and Numerical Competence across the Lifespan
- Brain Correlates of Numerical Disabilities
- Computer-assisted Interventions on Basic Number Skills
- The Classification and Cognitive Characteristics of Mathematical Disabilities in Children
- Numbers in the Dark: numerical cognition and blindness
- The Neuropsychology of Acquired Number and Calculation Disorders
- Arithmetic Learning in Adults: evidence from brain imaging
- Individual Differences: Navigator Chapter
- Individual Differences in Arithmetical Abilities: The Componential Nature of Arithmetic
- Individual Differences in Basic Arithmetical Processes in Children and Adults
- Cognitive Predictors of Mathematical Abilities and Disabilities
- Affect, Motivation, Working Memory, and Mathematics
- Individual Differences in Word Problem Solving
- Individual Differences in Children’s Paths to Arithmetical Development
- Behavioural Genomics of Mathematics
- Education
- Using Learning Path Research to Balance Mathematics Education: teaching/learning for understanding and fluency
- New Possibilities for Early Mathematics Education: cognitive guidelines for designing high-quality software to promote young children’s meaningful mathematics learning
- Early Number Competencies and Mathematical Learning: individual variation, screening, and intervention
- Numbers Count: a large-scale intervention for young children who struggle with mathematics
- Developing Conceptual and Procedural Knowledge of Mathematics
- How Informal Learning Activities Can Promote Children’s Numerical Knowledge
- Index
Abstract and Keywords
Young children initially learn to ‘count’ without understanding either what counting means, or what numerical quantities the individual number words pick out. Over a period of many months, children assign progressively more sophisticated meanings to the number words, linking them to discrete objects, to quantification, to numerosity, and so on. Eventually, children come to understand the logic of counting. Along with this knowledge comes an implicit understanding of the successor function, as well as of the principle of equinumerosity, or exact equality between sets. Thus, when children arrive at a mature understanding of counting, they have (for the first time in their lives) a way of mentally representing exact, large numbers.
Keywords: bootstrapping, cardinality, children, counting, development, early childhood, equinumerosity, integers, language, natural numbers, numbers, preschool, successor function
Barbara W. Sarnecka, University of California, Irvine
Meghan C. Goldman, University of California, Irvine
Emily B. Slusser, San Jose State University
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- The Oxford Handbook of Numerical Cognition
- Dedication
- Preface
- List of Figures
- List of Tables
- List of Contributors
- Promoting Maths to the General Public
- Philosophy of Number
- Cognitive Foundations of Human Number Representations and Mental Arithmetic
- Primitives and Non-primitives of Numerical Representations
- Finger-based representation of mental arithmetic
- Linking Numbers to Space: from the mental number line towards a hybrid account
- Multi-digit Number Processing: overview, conceptual clarifications, and language influences
- How Abstract is Arithmetic?
- Arithmetic Word Problem Solving and Mental Representations
- Intuition in Mathematical and Probabilistic Reasoning
- Phylogeny and Ontogeny of Mathematical and Numerical Understanding
- Numerical and Arithmetic Abilities in Non-primate Species
- Monkey Mathematical Abilities
- Numerical Abilities and Arithmetic in Infancy
- Spontaneous Focusing On Numerosity and its Relation to Counting and Arithmetic
- How Counting Leads to Children’s First Representations of Exact, Large Numbers
- Approximate Arithmetic Abilities in Childhood
- Number Representations and their Relation with Mathematical Ability
- Numerical Cognition during Cognitive Aging
- Culture, Language, and Number
- Cognitive Linguistics and the Concept(s) of Number
- Figuring Out Children’s Number Representations: lessons from cross-cultural work
- Mathematics Learning in the USA and JAPAN: influences of language
- What is There to Learn from International Surveys of Mathematical Achievement?
- From Single-Cell Neuropathology to Mathematics Education: navigator chapter
- Neuronal Correlates of Non-verbal Numerical Competence in Primates
- Development of the numerical brain
- Arithmetic in the Child and Adult Brain
- Numerical Symbols: an overview of their cognitive and neural underpinnings
- A Theory of Magnitude: the parts that sum to number
- Basic Number Representation and Beyond: neuroimaging and computational modeling
- Mapping the Brain for Math: reversible inactivation by direct cortical electrostimulation and transcranial magnetic stimulation
- Applications of Neuroscience to Mathematics Education
- When Number Processing and Calculation is Not Your Cup of Tea
- Dyscalculia: from brain to education
- Developmental Dyscalculia as a Heterogeneous Disability
- The Contributions of Syndrome Research to the Study of MLD
- Number Processing and Arithmetic in Children and Adults with Reading Difficulties
- Genetic Developmental Disorders and Numerical Competence across the Lifespan
- Brain Correlates of Numerical Disabilities
- Computer-assisted Interventions on Basic Number Skills
- The Classification and Cognitive Characteristics of Mathematical Disabilities in Children
- Numbers in the Dark: numerical cognition and blindness
- The Neuropsychology of Acquired Number and Calculation Disorders
- Arithmetic Learning in Adults: evidence from brain imaging
- Individual Differences: Navigator Chapter
- Individual Differences in Arithmetical Abilities: The Componential Nature of Arithmetic
- Individual Differences in Basic Arithmetical Processes in Children and Adults
- Cognitive Predictors of Mathematical Abilities and Disabilities
- Affect, Motivation, Working Memory, and Mathematics
- Individual Differences in Word Problem Solving
- Individual Differences in Children’s Paths to Arithmetical Development
- Behavioural Genomics of Mathematics
- Education
- Using Learning Path Research to Balance Mathematics Education: teaching/learning for understanding and fluency
- New Possibilities for Early Mathematics Education: cognitive guidelines for designing high-quality software to promote young children’s meaningful mathematics learning
- Early Number Competencies and Mathematical Learning: individual variation, screening, and intervention
- Numbers Count: a large-scale intervention for young children who struggle with mathematics
- Developing Conceptual and Procedural Knowledge of Mathematics
- How Informal Learning Activities Can Promote Children’s Numerical Knowledge
- Index