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.
Dr. Avishai Henik is a Distinguished Professor of Psychology at Ben-Gurion University of the Negev and Chair of the recently established Inter-Faculty Brain Sciences School. Prior to this he held visiting scientist positions at U.C. Davis, U.C. Berkeley, and the University of Utah. He holds a position on the Board of the journal Neuropsychologia, was recently guest editor for Developmental Neuropsychology on the topic of Numerical Cognition, and serves regularly as an ad hoc reviewer for various journals in the field and granting agencies. Dr. Henik has over 200 publications of which most are in peer reviewed journals. A leader in the field, he has been awarded a prestigious European Research Council (ERC) advanced grant to continue his cutting-edge research on the contribution of non-countable dimensions to the development and understanding of numerical cognition. Dr. Henik is also the coordinator of an Israeli Science Foundation (ISF) Center of Excellence, which aims to study the neurocognitive basis of numerical cognition, and currently holds the Zlotowski Chair of Cognitive Neuropsychology.
SECTION I. DEVELOPMENT 1. Development of quantitative thinking across correlated dimensions Kelly S. Mix, Susan C. Levine and Nora S. Newcombe 2. Link between numbers and spatial extent from birth to adulthood Maria Dolores de Hevia 3. Catching math problems early: Findings from the number sense intervention project Nancy C. Jordan and Nancy Dyson 4. Contextual sensitivity and the large number word bias: When is bigger really more? Michele M. Mazzocco, Jenny Yun-Chen Chan and Maria Sera 5. Learning, ageing, and the number brain Marinella Cappelletti 6. The development of counting ability - An evolutionary computation point of view Gali Katz, Amit Benbassat and Moshe Sipper SECTION II. ANIMAL STUDIES 7. Number vs. continuous quantities in lower vertebrates Christian Agrillo, Maria Elena Miletto Petrazzini and Angelo Bisazza 8. Going for more: Discrete and continuous quantity judgments by nonhuman animals Michael J. Beran and Audrey E. Parrish SECTION III. PROCESSES AND MECHANISMS 9. Number sense: What's in a name and why should we bother? Bert Reynvoet, Karolien Smets and Delphine Sasanguie 10. The distribution game: evidence for discrete numerosity coding in preschool children Alain Content and Julie Nys 11. Magnitudes in the coding of visual multitudes: Evidence from adaptation Frank H. Durgin 12. The ordinal instinct: A neurocognitive perspective and methodological issues Orly Rubinstein 13. Discrete and continuous presentation of quantities in science and mathematics education Ruth Stavy and Reuven Babai 14. The interaction of numerical and non-numerical parameters in magnitude comparison tasks with children and their relation to arithmetic performance Swiya Nath and Denes Szucs SECTION IV. MODELS 15. Symbolic and nonsymbolic representation of number in the human parietal cortex Moriah Sokolowski and Daniel Ansari 16. What do we measure when we measure magnitudes? Tali Leibovich, Arava Y. Kallai and Shai Itamar 17. How do humans represent numerical and non-numerical magnitudes? Evidence for an integrated system of magnitude representation across development Stella F. Lourenco 18. The sensory integration theory: An alternative to the approximate number system Wim Gevers, Roi Cohen Kadosh and Titia Gebuis