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Siegler, Robert S.; Braithwaite, David W. – Grantee Submission, 2016
In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…
Descriptors: Numeracy, Numbers, Arithmetic, Fractions
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Siegler, Robert S. – Developmental Science, 2016
The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…
Descriptors: Numbers, Theories, Individual Development, Symbols (Mathematics)
Siegler, Robert S. – Grantee Submission, 2016
The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…
Descriptors: Numbers, Theories, Individual Development, Symbols (Mathematics)
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McNeil, Nicole M.; Rittle-Johnson, Bethany; Hattikudur, Shanta; Petersen, Lori A. – Journal of Cognition and Development, 2010
This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…
Descriptors: Equations (Mathematics), Arithmetic, Algebra, Problem Solving
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Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred – Neuropsychologia, 2010
Prodigies are individuals with exceptional mental abilities. How is it possible that some of these people mentally calculate exponentiations with high accuracy and speed? We examined CP, a mental calculation prodigy, and a control group of 11 normal calculators for moderate mental arithmetic tasks. CP has additionally been tested for exceptionally…
Descriptors: Control Groups, Mental Computation, Short Term Memory, Brain Hemisphere Functions
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Rousselle, Laurence; Noel, Marie-Pascale – Cognition, 2007
Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing…
Descriptors: Symbols (Mathematics), Reading Difficulties, Mathematics Education, Learning Disabilities
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Zhou, Xin; Wang, Yefang; Wang, Luodan; Wang, Bin – Early Child Development and Care, 2006
Two samples of kindergarten children's representation and understanding of written number symbols were examined in two time points in one academic year. About 85% of Chinese five year olds (mean = 5 years 10 months) were able to use conventional number symbols to represent the quantity of 30 or larger. At the end of the kindergarten year, 94% of…
Descriptors: Kindergarten, Mathematics, Arithmetic, Longitudinal Studies
Okazaki, Masakazu – International Group for the Psychology of Mathematics Education, 2003
If we consider the gap between mathematics at elementary and secondary levels, and the logical nature of the higher level, it is important that aspects of children's logical development in the latter grades in elementary school be clarified. We focused on 5th graders' learning "division with decimals" as it is known to be difficult to…
Descriptors: Childhood Attitudes, Grade 5, Elementary School Mathematics, Arithmetic
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Butterworth, Brian – Journal of Child Psychology and Psychiatry, 2005
Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…
Descriptors: Evidence, Neurology, Genetics, Arithmetic