Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, neuropsychological, behavioral, and interactional levels. Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical Cognition examines research in mathematical education methods and their neurodevelopmental basis, focusing on the underlying neurodevelopmental features that must be taken into account when teaching and learning mathematics. Cognitive domains and functions such as executive functions, memory, attention, and language contribute to numerical cognition and are essential for its proper development. These lines of research and thinking in neuroscience are discussed in this book to further the understanding of the neurodevelopmental and cognitive basis of more complex forms of mathematics – and how to best teach them. By unravelling the basic building blocks of numerical thinking and the developmental basis of human capacity for arithmetic, this book and the discussions within 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.
1. Introduction - p. xiii 2. Chapter 1. From quantical to numerical cognition: A crucial passage for understanding the nature of mathematics and its origins - p. 1 3. Section I: Advanced mathematics, reasoning and problem solving - p. 23 4. Chapter 2. Toward an inhibitory control theory of the reasoning brain in development - p. 27 5. Chapter 3. Maths and logic: Relationships across development - p. 45 6. Chapter 4. Cerebral underpinning of advanced mathematical activity - p. 71 7. Section II: Math education - p. 92 8. Chapter 5. Looking at the development of mathematical knowledge from the perspective of the framework theory approach to conceptual change: Lessons for mathematics education - p. 95 9. Chapter 6. Subtraction by addition: A remarkably natural and clever way to subtract? - p. 117 10. Chapter 7. Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations - p. 143 11. Chapter 8. Learning and education in numerical cognition: We do need education - p. 181 12. Section III: Intervention studies - p. 203 13. Chapter 9. Supporting early numeracy: The role of spontaneous mathematical focusing tendencies in learning and instruction - p. 207 14. Chapter 10. Developmental course of numerical learning problems in children and how to prevent dyscalculia: A summary of the longitudinal examination of children from kindergarten to secondary school - p. 229 15. Chapter 11. Neurocognitive mechanisms of numerical intervention studies: The case of brain stimulation - p. 263 16. Chapter 12. Intervention studies in math: A metareview - p. 301 17. Section IV: Math deficiencies and difficulties - p. 308 18. Chapter 13. The complex pathways toward the development of math anxiety and links with achievements - p. 311 19. Chapter 14. What predicts the development of fact retrieval speed and calculation accuracy in children with (and without) arithmetic disabilities (AD). What can we learn from longitudinal studies? - p. 327 20. Chapter 15. Early neurocognitive development of dyscalculia - p. 359 21. Chapter 16. Early difficulties in numerical cognition - p. 383 22. Index - p. 399
Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, neuropsychological, behavioral, and interactional levels. Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical Cognition examines research in mathematical education methods and their neurodevelopmental basis, focusing on the underlying neurodevelopmental features that must be taken into account when teaching and learning mathematics. Cognitive domains and functions such as executive functions, memory, attention, and language contribute to numerical cognition and are essential for its proper development. These lines of research and thinking in neuroscience are discussed in this book to further the understanding of the neurodevelopmental and cognitive basis of more complex forms of mathematics – and how to best teach them. By unravelling the basic building blocks of numerical thinking and the developmental basis of human capacity for arithmetic, this book and the discussions within 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.
1. Introduction - p. xiii 2. Chapter 1. From quantical to numerical cognition: A crucial passage for understanding the nature of mathematics and its origins - p. 1 3. Section I: Advanced mathematics, reasoning and problem solving - p. 23 4. Chapter 2. Toward an inhibitory control theory of the reasoning brain in development - p. 27 5. Chapter 3. Maths and logic: Relationships across development - p. 45 6. Chapter 4. Cerebral underpinning of advanced mathematical activity - p. 71 7. Section II: Math education - p. 92 8. Chapter 5. Looking at the development of mathematical knowledge from the perspective of the framework theory approach to conceptual change: Lessons for mathematics education - p. 95 9. Chapter 6. Subtraction by addition: A remarkably natural and clever way to subtract? - p. 117 10. Chapter 7. Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations - p. 143 11. Chapter 8. Learning and education in numerical cognition: We do need education - p. 181 12. Section III: Intervention studies - p. 203 13. Chapter 9. Supporting early numeracy: The role of spontaneous mathematical focusing tendencies in learning and instruction - p. 207 14. Chapter 10. Developmental course of numerical learning problems in children and how to prevent dyscalculia: A summary of the longitudinal examination of children from kindergarten to secondary school - p. 229 15. Chapter 11. Neurocognitive mechanisms of numerical intervention studies: The case of brain stimulation - p. 263 16. Chapter 12. Intervention studies in math: A metareview - p. 301 17. Section IV: Math deficiencies and difficulties - p. 308 18. Chapter 13. The complex pathways toward the development of math anxiety and links with achievements - p. 311 19. Chapter 14. What predicts the development of fact retrieval speed and calculation accuracy in children with (and without) arithmetic disabilities (AD). What can we learn from longitudinal studies? - p. 327 20. Chapter 15. Early neurocognitive development of dyscalculia - p. 359 21. Chapter 16. Early difficulties in numerical cognition - p. 383 22. Index - p. 399
