Heterogeneous Contributions to Numerical Cognition
Learning and Education in Mathematical Cognition
- 1st Edition - May 27, 2021
- Imprint: Academic Press
- Editors: Wim Fias, Avishai Henik
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 8 1 7 4 1 4 - 2
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 7 4 1 5 - 9
Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, ne… Read more
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Request a sales quoteArithmetic 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.
- A novel innovative reference on the emerging field of numerical cognition and neurodevelopment underlying mathematical education
- Includes an overview of the multiple disciplines that comprise numerical cognition written by world-leading researchers in the numerical cognition and neurodevelopment fields
- Features an innovative organization with each section providing a general overview, developmental research, neurocognitive mechanisms, and discussion about relevant studies
Neuroscientists, cognitive neuroscientists, neurophysiologists, educators, education researchers, neurologists, cognitive and developmental psychologists, graduate students, and post-doctoral fellows
- Cover image
- Title page
- Table of Contents
- Copyright
- Contributors
- Introduction
- Chapter 1: From quantical to numerical cognition: A crucial passage for understanding the nature of mathematics and its origins
- Abstract
- The problems of using blurry concepts and sloppy terminology in numerical cognition
- Characterizing “number,” and what is to be qualified as “numerical”
- Quantical vs numerical cognition: A crucial distinction
- Number: Not just language and symbols, but evolving cultural preoccupations and practices that generate them
- Concluding remarks with a challenging scientific question: How do we get from quantical to numerical cognition?
- Section I: Advanced mathematics, reasoning and problem solving
- Chapter 2: Toward an inhibitory control theory of the reasoning brain in development
- Abstract
- The paradoxes of cognitive development
- From linear to nonlinear dynamic models of cognitive development
- Inhibitory control and misleading heuristics in the lab
- Inhibitory control and misleading heuristics in the classroom
- Conclusion
- Chapter 3: Maths and logic: Relationships across development
- Abstract
- Transitive inferences and linear representations of order
- Conditional inferences and thinking about possibilities
- Transitive reasoning and mathematics skills
- Summary and conclusions
- Chapter 4: Cerebral underpinning of advanced mathematical activity
- Abstract
- Introduction
- Neural correlates of advanced math knowledge
- Does formal mathematics rely on visual experience?
- Neural correlates of deductive reasoning
- Effects of math expertise on the brain
- Discussion and perspectives
- Section II: Math education
- Chapter 5: Looking at the development of mathematical knowledge from the perspective of the framework theory approach to conceptual change: Lessons for mathematics education
- Abstract
- Introduction
- Continuities between natural and rational number knowledge
- The framework theory approach to conceptual change
- Empirical research on the development of rational number knowledge guided by the framework theory approach
- The coexistence of framework and scientific theories
- The framework theory approach and the natural number bias
- Implications for instruction
- Chapter 6: Subtraction by addition: A remarkably natural and clever way to subtract?
- Abstract
- Two vignettes
- Introduction
- Mental subtraction up to 20
- Multidigit mental subtraction
- Written multidigit subtraction
- Word problem solving
- Conceptual underpinnings of subtraction by addition
- Conclusion and discussion
- Chapter 7: Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations
- Abstract
- Acknowledgments
- Rational numbers beyond the classroom
- Deconstructing “whole number bias”
- Implicit understanding of number systems
- Behavioral evidence for the role of inhibitory control in rational number processing
- Magnitude representations of symbolic rational number quantities
- Nonsymbolic rational numbers and inhibitory control
- Brain imaging of rational number processing
- Conclusions and directions for future research
- Chapter 8: Learning and education in numerical cognition: We do need education
- Abstract
- Acknowledgments
- Introduction
- The complexity of basic symbolic number processing
- How is numerical cognition related to classroom learning?
- Classroom learning changes its (neuro)cognitive predictors
- The possibilities of experimental studies
- Using the educational context as a natural experiment
- Conclusion
- Section III: Intervention studies
- Chapter 9: Supporting early numeracy: The role of spontaneous mathematical focusing tendencies in learning and instruction
- Abstract
- Introduction
- Cultural activities and formal teaching in the development of numeracy
- Spontaneous focusing on numerosity and other numerical aspects
- How to enhance SFON and SFOR?
- Mathematical knowledge, transfer, and spontaneous mathematical focusing tendencies
- Conclusions
- 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
- Abstract
- Introduction
- How to predict which child will develop dyscalculia
- Is prevention of dyscalculia possible?
- Persisting character of developmental dyscalculia
- Summary
- Chapter 11: Neurocognitive mechanisms of numerical intervention studies: The case of brain stimulation
- Abstract
- Introduction
- Conclusion and future directions
- Chapter 12: Intervention studies in math: A metareview
- Abstract
- Acknowledgments
- Introduction
- Methodology
- Results
- Conclusion
- Appendix
- Section IV: Math deficiencies and difficulties
- Chapter 13: The complex pathways toward the development of math anxiety and links with achievements
- Abstract
- Introduction
- The antecedents of math anxiety
- Assessment of math anxiety: Methods and difficulties
- The role of low math achievements
- The current framework
- Conclusions
- 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?
- Abstract
- Introduction
- Purpose and research questions
- Results
- Discussion
- Conclusion
- Chapter 15: Early neurocognitive development of dyscalculia
- Abstract
- Introduction
- Interplay of domain-specific and domain-general factors in math development
- Domain-general factors
- Neurobiological evidence
- Summary and future outlook
- Chapter 16: Early difficulties in numerical cognition
- Abstract
- Number conservation
- Piaget’s error?
- The development of numerical cognition
- Density and experimental control
- Attention to numerosity
- Inhibition, education, and numerical cognition
- Conclusions
- Index
- Edition: 1
- Published: May 27, 2021
- No. of pages (Hardback): 422
- No. of pages (eBook): 422
- Imprint: Academic Press
- Language: English
- Hardback ISBN: 9780128174142
- eBook ISBN: 9780128174159
WF
Wim Fias
Dr. Fias is a Professor of Experimental Psychology at Ghent University. He is currently editor-in-chief of the Journal of Numerical Cognition and has been consulting editor for Journal of Experimental Psychology: Learning Memory and Cognition and was an editorial board member of the journal Cognition. He serves regularly as an ad hoc reviewer for all major journals in the domain of Cognitive Psychology and Cognitive Neuroscience. Dr. Fias has over 100 publications on the topics of numerical cognition, working memory and cognitive control. His research uses behavioral and neuroimaging techniques in a complementary way.
Affiliations and expertise
Professor of Experimental Psychology, Faculty of Psychology and Educational Sciences, Department of Experimental Psychology, Ghent University, Ghent, BelgiumAH
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, IsraelRead Heterogeneous Contributions to Numerical Cognition on ScienceDirect