- Individual differences in non-verbal number acuity correlate with maths achievement
Justin Halberda
Johns Hopkins University, Ames Hall, 3400 North Charles Street, Baltimore, Maryland 21218, USA
Nature 455:665-8. 2008
Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching...
- Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations
Marie Arsalidou
Diagnostic Imaging and Research Institute, Hospital for Sick Children, University of Toronto, Toronto, ON, Canada
Neuroimage 54:2382-93. 2011
Most of us use numbers daily for counting, estimating quantities or formal mathematics, yet despite their importance our understanding of the brain correlates of these processes is still evolving...
- Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia
Manuela Piazza
INSERM CEA Cognitive Neuroimaging Unit, Gif sur Yvette, France
Cognition 116:33-41. 2010
..These results establish for the first time a clear association between dyscalculia and impaired "number sense", and they may open up new horizons for the early diagnosis and rehabilitation of mathematical learning deficits...
- Core systems of number
Lisa Feigenson
Department of Psychological and Brain Sciences, 3400 North Charles Street, Johns Hopkins University, Baltimore, MD 21218, USA
Trends Cogn Sci 8:307-14. 2004
..These systems account for our basic numerical intuitions, and serve as the foundation for the more sophisticated numerical concepts that are uniquely human...
- Preschoolers' precision of the approximate number system predicts later school mathematics performance
Michele M M Mazzocco
Kennedy Krieger Institute, Baltimore, Maryland, United States of America
PLoS ONE 6:e23749. 2011
..These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the ..
- Exact and approximate arithmetic in an Amazonian indigene group
Pierre Pica
Unité Mixte de Recherche 7023 Formal Structures of Language, CNRS and Paris VIII University, Paris, France
Science 306:499-503. 2004
..However, they fail in exact arithmetic with numbers larger than 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic...
- Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing
Laurence Rousselle
Unité Cognition et Développement CODE, Catholic University of Louvain, 10 Place C Mercier, 1348 Louvain la Neuve, Belgium
Cognition 102:361-95. 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...
- Interactions between number and space in parietal cortex
Edward M Hubbard
INSERM Unit 562 Cognitive Neuroimaging, Service Hospitalier Frederic Joliot, 4 Place du General Leclerc, F94101 Orsay, France
Nat Rev Neurosci 6:435-48. 2005
....
- Sources of mathematical thinking: behavioral and brain-imaging evidence
S Dehaene
Unité INSERM 334, Service Hospitalier Frederic Joliot, CEA DSV, 91401 Orsay Cedex, France
Science 284:970-4. 1999
..Mathematical intuition may emerge from the interplay of these brain systems...
- Non-verbal number acuity correlates with symbolic mathematics achievement: but only in children
Matthew Inglis
Loughborough University, Leicestershire, England
Psychon Bull Rev 18:1222-9. 2011
The process by which adults develop competence in symbolic mathematics tasks is poorly understood...
- When brightness counts: the neuronal correlate of numerical-luminance interference
Roi Cohen Kadosh
Department of Psychology and Zlotowski Center for Neuroscience, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
Cereb Cortex 18:337-43. 2008
..The current results support the idea that the parietal lobe might be equipped with neuronal substrates for magnitude processing even for nonspatial dimensions...
- Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement
Ian D Holloway
Numerical Cognition Laboratory, Department of Psychology, University of Western Ontario, Ontario N6A 5C2, Canada
J Exp Child Psychol 103:17-29. 2009
..To address these questions, we collected mathematics achievement measures from 6- to 8-year-olds as well as reaction times from a numerical comparison task...
- Recruitment of an area involved in eye movements during mental arithmetic
Andre Knops
INSERM, Cognitive Neuroimaging Unit, F 91191 Gif sur Yvette, France
Science 324:1583-5. 2009
Throughout the history of mathematics, concepts of number and space have been tightly intertwined. We tested the hypothesis that cortical circuits for spatial attention contribute to mental arithmetic in humans...
- Large number discrimination in 6-month-old infants
F Xu
125 NI, Department of Psychology, Northeastern University, Boston, MA 02155, USA
Cognition 74:B1-B11. 2000
..16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting...
- Cross-national patterns of gender differences in mathematics: a meta-analysis
Nicole M Else-Quest
Villanova University, Department of Psychology, 800 Lancaster Avenue, Villanova, PA 19085, USA
Psychol Bull 136:103-27. 2010
A gender gap in mathematics achievement persists in some nations but not in others...
- Contribution of hand motor circuits to counting
Michael Andres
Universite Catholique de Louvain, Belgium
J Cogn Neurosci 19:563-76. 2007
..This finding suggests that hand motor circuits are involved whenever items have to be put in correspondence with the elements of any ordered series...
- Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students
Karin Landerl
Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London WC1N 3AR, UK
Cognition 93:99-125. 2004
..We conclude that dyscalculia is the result of specific disabilities in basic numerical processing, rather than the consequence of deficits in other cognitive abilities...
- Mathematics of quantitative kinetic PCR and the application of standard curves
R G Rutledge
Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre, 1055 du P E P S, PO Box 3800, Sainte Foy, Quebec G1V 4C7, Canada
Nucleic Acids Res 31:e93. 2003
..In this study, the mathematics of quantitative PCR are examined in detail, from which several fundamental aspects of the threshold method and ..
- Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling
Camilla K Gilmore
Learning Sciences Research Institute, University of Nottingham, Nottingham, UK
Cognition 115:394-406. 2010
..Do children harness these abilities when they begin to learn school mathematics? In two experiments in different schools, kindergarten children from diverse backgrounds were tested on their ..
- Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties
Bert De Smedt
Centre for Parenting, Child Welfare and Disabilities, Katholieke Universiteit, Leuven, 3000 Leuven, Belgium
J Exp Child Psychol 108:278-92. 2011
..magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively...
- Brain damage: neglect disrupts the mental number line
Marco Zorzi
Dipartimento di Psicologia Generale, Universita di Padova, Via Venezia 8, 35131 Padova, Italy
Nature 417:138-9. 2002
..This new form of representational neglect constitutes strong evidence that the mental number line is more than simply a metaphor, and that its spatial nature renders it functionally isomorphic to physical lines...
- Developmental change in the acuity of the "Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults
Justin Halberda
Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD 21218, USA
Dev Psychol 44:1457-65. 2008
..We show that the resolution of this system continues to increase throughout childhood, with adultlike levels of acuity attained surprisingly late in development...
- Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study
David C Geary
University of Missouri, Columbia, MO 65211 2500, USA
Dev Psychol 47:1539-52. 2011
The study's goal was to identify the beginning of 1st grade quantitative competencies that predict mathematics achievement start point and growth through 5th grade...
- The predictive value of numerical magnitude comparison for individual differences in mathematics achievement
Bert De Smedt
Center for Parenting, Child Welfare, and Disabilities, Katholieke Universiteit Leuven, Leuven, Belgium
J Exp Child Psychol 103:469-79. 2009
Although it has been proposed that the ability to compare numerical magnitudes is related to mathematics achievement, it is not clear whether this ability predicts individual differences in later mathematics achievement...
- Preschool executive functioning abilities predict early mathematics achievement
Caron A C Clark
Canterbury Child Development Research Group, Department of Psychology, University of Canterbury, Christchurch, NewZealand
Dev Psychol 46:1176-91. 2010
..between children's developing executive function abilities at age 4 and children's subsequent achievement in mathematics at age 6, 1 year after school entry...
- Exact and approximate judgements of visual and auditory numerosity: an fMRI study
Manuela Piazza
Institute of Cognitive Neuroscience, University College London, London, UK
Brain Res 1106:177-88. 2006
..Counting activates additional left prefrontal, parietal, and bilateral premotor areas, again independently from stimulus modality. These results dissociate two neuronal systems that underlie different numerosity judgements...
- Reading habits for both words and numbers contribute to the SNARC effect
Samuel Shaki
Ariel University Center of Samaria, Ariel, Israel
Psychon Bull Rev 16:328-31. 2009
..These results suggest that reading habits for both words and numbers contribute to the spatial representation of numbers...
- The brain locus of interaction between number and size: a combined functional magnetic resonance imaging and event-related potential study
Roi Cohen Kadosh
Ben Gurion University of the Negev, Beer Sheva, Israel
J Cogn Neurosci 19:957-70. 2007
..We concluded that the processing of magnitude can be subserved by shared or distinct neural substrates, depending on task requirements...
- Foundational numerical capacities and the origins of dyscalculia
Brian Butterworth
Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London WC1N 3AR, UK
Trends Cogn Sci 14:534-41. 2010
..Nevertheless, critical tests should involve both longitudinal studies and intervention, and these have yet to be carried out...
- To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving
Roland H Grabner
Institute for Behavioral Sciences, Swiss Federal Institute of Technology, Zurich, Universitaetsstrasse 6, CH 8092 Zurich, Switzerland
Neuropsychologia 47:604-8. 2009
..These data directly link the left angular gyrus with arithmetic fact retrieval and show that strategy self-reports can be used to predict differential patterns of brain activation...
- Calibrating the mental number line
Veronique Izard
Department of Psychology, Harvard University, 33 Kirkland Street, Cambridge, MA 02138, USA
Cognition 106:1221-47. 2008
..Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line...
- Reading aloud and arithmetic calculation improve frontal function of people with dementia
Ryuta Kawashima
NICHe, Tohoku University, Aramaki Aza Aoba, Aobaku Sendai 980 8579, Japan
J Gerontol A Biol Sci Med Sci 60:380-4. 2005
..The purpose of this study was to measure the effect of reading aloud and arithmetic calculation, by elderly people who were clinically diagnosed with dementia Alzheimer type, on their brain functions and activities of daily living...
- Does subitizing reflect numerical estimation?
Susannah K Revkin
INSERM, U562, Cognitive Neuroimaging Unit, Gif Yvette, France
Psychol Sci 19:607-14. 2008
....
- School readiness and later achievement
Greg J Duncan
School of Education and Social Policy, Northwestern University, Evanston, IL 60208, USA
Dev Psychol 43:1428-46. 2007
..Patterns of association were similar for boys and girls and for children from high and low socioeconomic backgrounds...
- The development of numerical estimation: evidence for multiple representations of numerical quantity
Robert S Siegler
Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Psychol Sci 14:237-43. 2003
....
- The mental representation of numerical fractions: real or integer?
Mario Bonato
Dipartimento di Psicologia Generale, University of Padova, Italy
J Exp Psychol Hum Percept Perform 33:1410-9. 2007
..e., integers) rather than real numbers and that the well-known difficulties of children in mastering fractions are circumvented by skilled adults through a flexible use of strategies based on the integer components...
- Origins of number sense. Large-number discrimination in human infants
Jennifer S Lipton
Massachusetts Institute of Technology, MA, USA
Psychol Sci 14:396-401. 2003
....
- Dyslexia and dyscalculia: two learning disorders with different cognitive profiles
Karin Landerl
Department of Psychology, University of Tuebingen, Tuebingen, Germany
J Exp Child Psychol 103:309-24. 2009
..These findings suggest that dyslexia and dyscalculia have separable cognitive profiles, namely a phonological deficit in the case of dyslexia and a deficient number module in the case of dyscalculia...
- Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: findings from a 3-year longitudinal study
Kristin Krajewski
German Institute of International Educational Research, Frankfurt, Germany
J Exp Child Psychol 103:516-31. 2009
..e., when number words were isolated from quantities [QNC Level I]), explaining the moderate relationship between early literacy development and the development of mathematical competencies...
- Impact of high mathematics education on the number sense
Julie Castronovo
Department of Psychology, University of Hull, Hull, United Kingdom
PLoS ONE 7:e33832. 2012
..the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement...
- ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control
Mary Wagner Fuhs
Department of Psychology, University of Notre Dame, USA
Dev Sci 16:136-48. 2013
..that there is an association between the acuity of young children's approximate number system (ANS) and their mathematics ability before exposure to instruction in formal schooling...
- Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic
S Dehaene
INSERM, CNRS, Laboratoire de Sciences Cognitives et Psycholinguistique, Paris, France
Cortex 33:219-50. 1997
..We suggest that a left subcortical network contributes to the storage and retrieval of rote verbal arithmetic facts, while a bilateral inferior parietal network is dedicated to the mental manipulation of numerical quantities...
- Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?
Delphine Sasanguie
Laboratory of Experimental Psychology, KU Leuven, B 3000 Leuven, Belgium Subfaculty of Psychology and Educational Sciences, KU Leuven Kulak, B 8500 Kortrijk, Belgium
J Exp Child Psychol 114:418-31. 2013
..address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used...
- Sex differences in intrinsic aptitude for mathematics and science?: a critical review
Elizabeth S Spelke
Department of Psychology, Harvard University, 1130 William James Hall, 33 Kirkland Street, Cambridge, MA 02138, USA
Am Psychol 60:950-8. 2005
..cognitive sex differences account for the differential representation of men and women in high-level careers in mathematics and science: (a) males are more focused on objects from the beginning of life and therefore are predisposed to ..
- Arithmetic and the brain
Stanislas Dehaene
Institut National de la Santé et de la Recherche Médicale unit 562 Cognitive neuroimaging, Service Hospitalier Frederic Joliot, Commissariat à L Energie Atomique DRM DSV, 4 Place du General Leclerc, 91401 Orsay Cedex, France
Curr Opin Neurobiol 14:218-24. 2004
..Finally, pathologies of this system, leading to acalculia in adults or to developmental dyscalculia in children, are beginning to be understood, thus paving the way for brain-oriented intervention studies...
- Spatial attention and the mental number line: evidence for characteristic biases and compression
Matthew R Longo
Department of Psychology, University of Chicago, Chicago, IL, USA
Neuropsychologia 45:1400-7. 2007
....
- Beyond the mental number line: A neural network model of number-space interactions
Qi Chen
Ghent University, Belgium
Cogn Psychol 60:218-40. 2010
..These results suggest that number-space interactions are emergent properties resulting from the interaction between different brain areas...
- Neuroanatomical substrates of arabic number processing, numerical comparison, and simple addition: a PET study
M Pesenti
Universite Catholique de Louvain, Belgium
J Cogn Neurosci 12:461-79. 2000
..Implications for current anatomo-functional models of numerical cognition are drawn...
- Internet cognitive testing of large samples needed in genetic research
Claire M A Haworth
Social, Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, King s College London, London, United Kingdom
Twin Res Hum Genet 10:554-63. 2007
..We developed Internet versions of reading, language, mathematics and general cognitive ability tests and investigated their reliability and validity for 10- and 12-year-old ..
- Executive functioning as a predictor of children's mathematics ability: inhibition, switching, and working memory
R Bull
Department of Psychology, University ofAberdeen, Scotland
Dev Neuropsychol 19:273-93. 2001
..Furthermore, regression analyses revealed that each executive function measure predicted unique variance in mathematics ability...
- Representation of number in animals and humans: a neural model
Tom Verguts
Department of Experimental Psychology, Ghent University, 9000 Ghent, Belgium
J Cogn Neurosci 16:1493-504. 2004
..This finding presents a concrete proposal on the linkage between higher order numerical cognition and more primitive numerical abilities and generates specific predictions on the neural substrate of number processing...
- Beyond the number domain
Jessica F Cantlon
Center for Cognitive Neuroscience, Duke University, Durham, NC 27708, USA
Trends Cogn Sci 13:83-91. 2009
....
- Spatial representation of pitch height: the SMARC effect
Elena Rusconi
Institute of Cognitive Neuroscience, University College London, 17 Queen Square, WC1N 3AR, London, UK
Cognition 99:113-29. 2006
..Both the basic elements of mathematical cognition (i.e. numbers) and the basic elements of musical cognition (i.e. pitches), appear to be mapped onto a mental spatial representation in a way that affects motor performance...
- The development of ordinal numerical knowledge in infancy
Elizabeth M Brannon
Center for Cognitive Neuroscience, Duke University, Box 90999, Durham, NC 27708 0999, USA
Cognition 83:223-40. 2002
..These data raise many questions about how infants represent number and what happens between 9 and 11 months to support ordinal numerical judgments...
- Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability
David C Geary
Department of Psychological Sciences, University of Missouri Columbia 65211 2500, USA
Child Dev 78:1343-59. 2007
Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n=15) and low achieving (LA, n=44) were identified...
- Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin
Nicolas Molko
INSERM U 562, Cognitive Neuroimaging, Service Hospitalier Frederic Joliot, CEA DSV, IFR 49 Orsay, France
Neuron 40:847-58. 2003
..Thus, a genetic form of developmental dyscalculia can be related to both functional and structural anomalies of the right intraparietal sulcus, suggesting a crucial role of this region in the development of arithmetic abilities...
- Short-term memory, working memory, and executive functioning in preschoolers: longitudinal predictors of mathematical achievement at age 7 years
Rebecca Bull
School of Psychology, University of Aberdeen, Aberdeen, United Kingdom
Dev Neuropsychol 33:205-28. 2008
..Children were tested in preschool (M age = 4 years, 6 months) on a battery of cognitive measures, and mathematics and reading outcomes (from standardized, norm-referenced school-based assessments) were taken on entry to ..
- Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten
Clancy Blair
Human Development and Family Studies, The Pennsylvania State University, University Park 16802 6504, USA
Child Dev 78:647-63. 2007
..Findings suggest that curricula designed to improve self-regulation skills as well as enhance early academic abilities may be most effective in helping children succeed in school...
- Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta)
E M Brannon
Department of Psychology, Columbia University, New York, New York 10027, USA
J Exp Psychol Anim Behav Process 26:31-49. 2000
..S. Moyer & T. K. Landaeur, 1967). Collectively these studies show that monkeys represent the numerosities 1-9 on at least an ordinal scale...
- Representational change and children's numerical estimation
John E Opfer
The Ohio State University, Columbus, OH, USA
Cogn Psychol 55:169-95. 2007
..The findings indicated that cognitive change can occur at the level of an entire representation, rather than always involving a sequence of local repairs...
- Effects of development and enculturation on number representation in the brain
Daniel Ansari
Numerical Cognition Laboratory, Department of Psychology and Graduate Program in Neuroscience, University of Western Ontario, Ontario N6G 2K3, Canada
Nat Rev Neurosci 9:278-91. 2008
..This Review provides an evaluation of this contention and proposes hypotheses to guide investigations into the neural mechanisms that constrain the acquisition of cultural representations of numerical magnitude...
- The relationship between the shape of the mental number line and familiarity with numbers in 5- to 9-year old children: evidence for a segmented linear model
Mirjam Ebersbach
University of Leuven, Belgium
J Exp Child Psychol 99:1-17. 2008
..Findings are discussed in terms of the accumulator model, assuming a linear mental representation with scalar variability...
- The relationships among working memory, math anxiety, and performance
M H Ashcraft
Department of Psychology, Cleveland State University, Cleveland, Ohio 44115, USA
J Exp Psychol Gen 130:224-37. 2001
....
- Quantity discrimination in female mosquitofish
Christian Agrillo
Department of General Psychology, University of Padova, Via Venezia 8, 35131, Padova, Italy
Anim Cogn 10:63-70. 2007
....
- Numerical cognition without words: evidence from Amazonia
Peter Gordon
Department of Biobehavioral Sciences, Columbia University, 525 West 120th Street, New York, NY 10027, USA
Science 306:496-9. 2004
..Performance with quantities greater than three was remarkably poor, but showed a constant coefficient of variation, which is suggestive of an analog estimation process...
- Core information processing deficits in developmental dyscalculia and low numeracy
Teresa Iuculano
Institute of Cognitive Neuroscience, University College London, London, UK
Dev Sci 11:669-80. 2008
..Low numeracy was related not to a poor grasp of exact numerosities, but to a poor understanding of symbolic numerals...
- Number sense in human infants
Fei Xu
Northeastern University, Boston, USA
Dev Sci 8:88-101. 2005
..In contrast, infants may fail to represent small numerosities in visual-spatial arrays with continuous quantity controls, consistent with the thesis that separate systems serve to represent large versus small numerosities...
- Are subitizing and counting implemented as separate or functionally overlapping processes?
Manuela Piazza
Institute of Cognitive Neuroscience, London, United Kingdom
Neuroimage 15:435-46. 2002
..Results speak against the idea of the two processes being implemented in separable neural systems...
- Number processing pathways in human parietal cortex
Seppe Santens
Department of Experimental Psychology, Ghent University, Henri Dunantlaan 2, Ghent, Belgium
Cereb Cortex 20:77-88. 2010
..The preferred pathway for processing nonsymbolic quantities included the number-sensitive area in superior parietal cortex, whereas the pathway for processing symbolic quantities did not...
- Different components of working memory have different relationships with different mathematical skills
Fiona R Simmons
School of Natural Sciences and Psychology, Liverpool John Moores University, Liverpool L3 3AF, UK
J Exp Child Psychol 111:139-55. 2012
..06). The results are consistent with the VSSP having a role in the development of number writing and magnitude judgments but a lesser role in early arithmetic...
- Gender, culture, and sex-typed cognitive abilities
David Reilly
School of Applied Psychology, Griffith University, Southport, Queensland, Australia
PLoS ONE 7:e39904. 2012
..Furthermore, when gender gaps in reading, mathematics and science literacy are reported they are often attributed to innate, biological differences rather than ..
- A generalized fraction: an entity smaller than one on the mental number line
Arava Y Kallai
Learning Research and Development Center, Department of Psychology, University of Pittsburgh, PA, USA
J Exp Psychol Hum Percept Perform 35:1845-64. 2009
....
- Men and things, women and people: a meta-analysis of sex differences in interests
Rong Su
Department of Psychology, University of Illinois at Urbana Champaign, IL 61820, USA
Psychol Bull 135:859-84. 2009
..Prediger's (1982) Things-People and Data-Ideas dimensions, and the STEM (science, technology, engineering, and mathematics) interest areas. Technical manuals for 47 interest inventories were used, yielding 503,188 respondents...
- An integrated theory of whole number and fractions development
Robert S Siegler
Carnegie Mellon University, 331 Baker Hall, 5000 Forbes Ave, Pittsburgh, PA 15213, USA
Cogn Psychol 62:273-96. 2011
..of fraction magnitude representations is closely related to both fractions arithmetic proficiency and overall mathematics achievement test scores, that fraction magnitude representations account for substantial variance in ..
- Physical fitness and academic achievement in third- and fifth-grade students
Darla M Castelli
Department of Kinesiology and Community Health, University of Illinois, Urbana, IL, USA
J Sport Exerc Psychol 29:239-52. 2007
..Associations were demonstrated in total academic achievement, mathematics achievement, and reading achievement, thus suggesting that aspects of physical fitness may be globally related ..
- Numerical magnitude representations influence arithmetic learning
Julie L Booth
Human Computer Interaction Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Child Dev 79:1016-31. 2008
..Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning...
- Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills
Minna M Hannula
Department of Education, University of Turku, FIN 20014 Turku, Finland
J Exp Child Psychol 107:394-406. 2010
..In addition, the relationship between SFON and number sequence skills in kindergarten is not explained by children's individual differences in their focusing on a non-numerical aspect that is, spatial locations...
- Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?
Lynn S Fuchs
Department of Special Education, Peabody College, Vanderbilt University, Nashville, TN 37203, USA
Dev Psychol 46:1731-46. 2010
..between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5...
- Digits affect actions: the SNARC effect and response selection
Marwan Daar
Department of Psychology, University of Toronto, Toronto, ON, Canada
Cortex 44:400-5. 2008
..Thus, the SNARC effect not only affects how fast responses can be initiated but also affects what responses will be selected...
- Number-space mapping in human infants
Maria Dolores de Hevia
Laboratory for Developmental Studies, William James Hall, 11th Floor, Harvard University, 33 Kirkland St, Cambridge, MA 02138, USA
Psychol Sci 21:653-60. 2010
..A central foundation of mathematics, science, and technology therefore emerges prior to experience with language, symbol systems, or measurement ..
- The role of visual information in numerosity estimation
Titia Gebuis
Laboratory of Experimental Psychology, University of Leuven, Leuven, Belgium
PLoS ONE 7:e37426. 2012
..Instead, we propose that humans estimate numerosity by weighing the different visual cues present in the stimuli...
- A magnitude code common to numerosities and number symbols in human intraparietal cortex
Manuela Piazza
Institut National de la Sante et de la Recherche Medicale INSERM, Cognitive Neuroimaging Unit, Service Hospitalier Frederic Joliot, F 91401 Orsay, France
Neuron 53:293-305. 2007
..They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities...
- The contributions of numerosity and domain-general abilities to school readiness
Lynn S Fuchs
Vanderbilt University, Nashville, TN 37203, USA
Child Dev 81:1520-33. 2010
..Results suggest that development of NC and WP depends on different constellations of numerical versus more general cognitive abilities...
- Association between basic numerical abilities and mathematics achievement
Delphine Sasanguie
Department of Psychology, University of Leuven, Belgium
Br J Dev Psychol 30:344-57. 2012
..these different measures of number representation are related to performance on a curriculum-based standardized mathematics achievement test in kindergarteners, first, second, and sixth graders...
- Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals
Stephanie Bugden
Numerical Cognition Laboratory, Department of Psychology, The University of Western Ontario, Canada
Cognition 118:32-44. 2011
....
- Do fish count? Spontaneous discrimination of quantity in female mosquitofish
Christian Agrillo
Department of General Psychology, University of Padova, Via Venezia 8, 35131, Padua, Italy
Anim Cogn 11:495-503. 2008
....
- rTMS over the intraparietal sulcus disrupts numerosity processing
Marinella Cappelletti
Center for Non Invasive Brain Stimulation, Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, MA 02215, USA
Exp Brain Res 179:631-42. 2007
....
- Neural correlates of arithmetic and language comprehension: a common substrate?
Juliana V Baldo
VA Northern California Health Care System, Martinez, CA 94553, USA
Neuropsychologia 45:229-35. 2007
..These findings are discussed in light of previous work on the neural basis of arithmetic ability and its relationship to language...
- Salamanders ( Plethodon cinereus) go for more: rudiments of number in an amphibian
Claudia Uller
Institute of Cognitive Science, University of Louisiana at Lafayette, Lafayette, LA 70504 3772, USA
Anim Cogn 6:105-12. 2003
..The findings indicate that salamanders "go for more," just like human babies and monkeys. This rudimentary capacity is a type of numerical discrimination that is spontaneously present in this amphibian...
- Adolescents' functional numeracy is predicted by their school entry number system knowledge
David C Geary
Department of Psychological Sciences, University of Missouri, Columbia, Missouri, USA
PLoS ONE 8:e54651. 2013
....
- Diversity. Culture, gender, and math
Luigi Guiso
European University Institute, Villa San Paolo, Via della Piazzuola 43, 50133 Florence, Italy
Science 320:1164-5. 2008
- Numerical bias in bounded and unbounded number line tasks
Dale J Cohen
Department of Psychology, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403 5612, USA
Psychon Bull Rev 18:331-8. 2011
....
- Counting on neurons: the neurobiology of numerical competence
Andreas Nieder
Primate NeuroCognition Laboratory, Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research, University of Tubingen, Hoppe Seyler Strasse 3, 72076 Tubingen, Germany
Nat Rev Neurosci 6:177-90. 2005
..Neural representations of numerical information can engage extensive cerebral networks, but the posterior parietal cortex and the prefrontal cortex are the key structures in primates...
- Costs and benefits of representational change: effects of context on age and sex differences in symbolic magnitude estimation
Clarissa A Thompson
Department of Psychology, The Ohio State University, Columbus, OH 43206, USA
J Exp Child Psychol 101:20-51. 2008
..Finally, both before and after training that eliminated age differences in estimation accuracy, complementary sex differences were observed across the two estimation contexts...
- A supramodal number representation in human intraparietal cortex
Evelyn Eger
Cognitive Neurology Unit, Department of Neurology, Johann Wolfgang Goethe University, Frankfurt a M, Germany
Neuron 37:719-25. 2003
..This stimulus-driven number-specific intraparietal response supports the idea of a supramodal number representation that is automatically accessed by presentation of numbers and may code magnitude information...
- A genome-wide association study identifies multiple loci associated with mathematics ability and disability
S J Docherty
Social, Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, King s College London, UK
Genes Brain Behav 9:234-47. 2010
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- The development of ordinal numerical competence in young children
E M Brannon
Center for Cognitive Neuroscience, Duke University, Durham, NC 27708 0999, USA
Cogn Psychol 43:53-81. 2001
..Number may become a salient dimension as children begin to learn to count. An analog magnitude representation of number may underlie success on the ordinal task...
- Infants' discrimination of number vs. continuous extent
Lisa Feigenson
Department of Psychology, New York University, New York, NY 10003, USA
Cogn Psychol 44:33-66. 2002
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- Moving along the number line: operational momentum in nonsymbolic arithmetic
Koleen McCrink
Department of Psychology, Harvard University, Cambridge, Massachusetts 02138, USA
Percept Psychophys 69:1324-33. 2007
..The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum...
- Linking visual attention and number processing in the brain: the role of the temporo-parietal junction in small and large symbolic and nonsymbolic number comparison
Daniel Ansari
Dartmouth College, USA
J Cogn Neurosci 19:1845-53. 2007
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- Grey parrot numerical competence: a review
Irene M Pepperberg
Department of Psychology, Brandeis University, Waltham, MA 02454, USA
Anim Cogn 9:377-91. 2006
..His success shows that he understands number symbols as abstract representations of real-world collections, and that his sense of number compares favorably to that of chimpanzees and young human children...