About the Book
How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding?
Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling).
While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties.
This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.
Table of Contents:
Section I: Introduction
1: Chris J. Budd: Promoting maths to the general public
2: Marcus Giaquinto: Philosophy of math
Section II: human cognition
3: Oliver Lindemann and Martin H. Fischer: Cognitive Foundations of Human Number Representations and Mental Arithmetic
4: Joseph Tzelgov, Dana Ganor-Stern, Arava Kallai, and Michal Pinhas: Primitives and non-primitives of numerical representations
5: Michael Andres and Mauro Pesenti: Finger-based representation of mental arithmetic
6: Jean-Philippe van Dijck, Véronique Ginsburg, Luisa Girelli and Wim Gevers: Linking Numbers to Space: From the Mental Number Line towards a Hybrid Account
7: Hans-Christoph Nuerk, H.-C., Moeller, and Klaus Willmes: Multi-digit Number Processing: Overview, Conceptual Clarifications, and Language Influences
8: Jamie I.D. Cambell: How Abstract is Arithmetic?
9: Catherine Thevenot and Pierre Barrouillet: Arithmetic Word Problem Solving and Mental Representations
10: Kinga Morsanyi and Denes Szucs: Intuition in mathematical and probabilistic reasoning
Section III: Phylogeny and Ontogeny of Mathematical and Numerical understanding
11: Elizabeth M. Brannon and Joonkoo Park: Phylogeny and Ontogeny of Mathematical and Numerical Understanding
12: Christian Agrillo: Numerical and Arithmetic abilities in non-primate species
13: Michael J. Beran, Bonnie M. Perdue, and Theodore A. Evans: Monkey Mathematical Abilities
14: Koleen McCrink and Wesley Birdsall: Numerical Abilities and Arithmetic in Infancy
15: Minna M. Hannula-Sormunen: Spontaneous focusing on numerosity and its relation to counting and arithmetic
16: Barbara W. Sarnecka, Meghan C. Goldman, Emily B. Slusser: How Counting Leads to Children's First Representations of Exact, Large Numbers
17: Camilla Gilmore: Approximate arithmetic abilities in childhood
18: Titia Gebuis and Bert Reynvoet: Numerosity and mathematical development
19: Kim Uittenhove and Patrick Lemaire: Numerical Cognition during Cognitive Aging
Section IV: Culture and Language
20: Geoffrey B. Saxe: Culture, Language, and Number
21: John N. Towse, Kevin Muldoon, Victoria Simms: Cross-cultural differences in numerical competence
22: Yukari Okamoto: Mathematics learning in the USA and Japan: influences of language
23: Linda Sturman: What international comparisons such as TIMSS have shown about national differences in mathematics, and how these might be explained
Section V: Neuroscience of Mathematics
24: Roi Cohen Kadosh: Neuroscience
25: Andreas Nieder: Single-cell neurophysiology in monkeys
26: Liane Kaufmann, Karin Kucian, and Michael von Aster: The development of the numerical brain
27: Vinod Menon: Arithmetic in the child and adult brain
28: Ian D. Holloway and Daniel Ansari: Numerical Symbols: An Overview of Their Cognitive and Neural Underpinnings
29: Vincent Walsh: A theory of magnitude (ATOM) re-evaluated
30: Tom Verguts: Basic number representations: From computational modelling to neuroimaging
31: Elena Salillas and Carlo Semenza: Mapping the Brain for Math: Reversible Inactivation by Direct Cortical Electrostimulation and Transcranial Magnetic Stimulation
32: 1. Bert De Smedt and Roland H. Grabner: Applications of Neuroscience to Mathematics Education
Section VI: Numerical Impairments, co-morbidity, and rehabilitation
33: Marie-Pascale Noël: When Number Processing and Calculation Is Not Your Cup of Tea
34: Brian Butterworth, Sashank Varma, and Diana Laurillard: Dyscalculia: From Brain to Education
35: Avishai Henik, Orly Rubinsten, and Sarit Ashkenazi: Developmental Dyscalculia as a heterogeneous disability
36: Silke M. Göbel: Number Processing and Arithmetic in Children and Adults with Reading Difficulties
37: Jo Van Herwegen and Annette Karmiloff-Smith: Genetic developmental disorders and numerical competence across the lifespan
38: Karin Kucian, Liane Kaufmann, and Michael von Aster: Brain Correlates of Numerical Disabilities
39: Pekka Räsänen: Computer-assisted Interventions on Basic Number
40: David C. Geary: The Classification and Cognitive Characteristics of Mathematical Disabilities in Children
41: Julie Castronovo: Numbers in the Dark: Numerical cognition and blindness
42: Marinella Cappelletti: The Neuropsychology of Acquired Number and Calculation Disorders
43: L. Zamarian and Margarete Delazer: Arithmetic Learning in Adults - Evidence from Brain Imaging
Section VII: Individual Differences
44: Chris Donlan: Individual Differences
45: Ann Dowker: Individual Differences in Arithmetical Abilities: The Componential Nature of Arithmetic
46: Jo-Anne LeFevre, Emma Wells, and Carla Sowinski: Individual Differences in Basic Arithmetical Processes in Children and Adults
47: Annemie Desoete: Cognitive predictors of mathematical abilities and disabilities
48: Alex M. Moore, Nathan O. Rudig, and Mark H. Ashcraft: Affect, Motivation, Working Memory, and Mathematics
49: L. Verschaffel, F. Depaepe, and W. Van Dooren: Individual differences in word problem solving
50: Julie Ann Jordan: Individual Differences in Children's Paths to Arithmetical Development
51: Maria G. Tosto, Claire M. A. Haworth, and Yulia Kovas: Behavioural Genomics of Mathematics
Section VIII: Education
52: Richard Cowan: Education
53: Karen C. Fuson, Aki Murata, and Dor Abrahamson: Using Learning Path Research to Balance Mathematics Education: Teaching/Learning for Understanding and Fluency
54: Herbert P. Ginsburg, Rachael Labrecque, Kara Carpenter, and Dana Pagar: New Possibilities for Early Mathematics Education: Cognitive Guidelines for Designing High-Quality Software to Promote Young Children's Meaningful Mathematics Learning
55: Nancy C. Jordan, Lynn S. Fuchs, Nancy Dyson: Early Number Competencies and Mathematical Learning: Individual Variation, Screening, and Intervention
56: Nick Dowrick: Every Child Counts: effects of intervention for children struggling with mathematics
57: Bethany Rittle-Johnson and Michael Schneider: Developing Conceptual and Procedural Knowledge of Mathematics: An Updated Review
58: Geetha B. Ramani, Robert S. Siegler: What experiences can improve mathematical performance?
About the Author :
Roi Cohen Kadosh is a Wellcome RCD Fellow at the University of Oxford. His work combines basic and applied science, with focus on high level cognitive abilities and cognitive enhancement. At the theoretical level, his work challenges and revises previous theories in mathematical cognition with implications to psychology, neuroscience and education. At the translational level his work is in the forefront in integrating brain stimulation with enhancement of
high-level and complex cognitive functions, such as mathematical abilities. His work does not only focus on research but also discusses the ethical implications of his research. He is actively involved in
policy making. His pioneering work has received prestigious awards in the fields of neuroscience and psychology, and coverage by leading media channels (e.g., BBC, CNN, Science Magazine, Nature, Scientific American, Time Magazine). Ann Dowker is a University Research Lecturer at the Department of Experimental Psychology, University of Oxford, UK. She has carried out extensive research on developmental psychology and individual differences, especially with regard to mathematical learning. Her
interests include the effects of culture and language on mathematics; mathematics anxiety; links between neuroscience and education; and the development of intervention programs for children with
mathematical difficulties. She is the lead researcher on the Catch Up Numeracy Intervention project.
