Numerical and Arithmetical Cognition: Performance of Low- and Average-IQ Children

References

• Ashcraft , M. H. 1995 . Cognitive psychology and simple arithmetic: A review and summary of new directions . Mathematical Cognition , 1 : 3 – 34 .
   Google Scholar
• Ashcraft , M. H. , Donley , R. D. , Halas , M. A. and & Vakali , M. 1992 . “ Working memory, automaticity, and problem difficulty ” . In The nature and origins of mathematical skills , Edited by: Campbell , J. I. D. 301 – 329 . Amsterdam : Elsevier .
   Google Scholar
• Baddeley , A. D. and & Hitch , G. J. 1974 . “ Working memory ” . In The psychology of learning and motivation, Vol 8: Advances in research and theory , Edited by: Bower , G. H. 47 – 89 . New York : Academic Press .
   Google Scholar
• Baroody , A. J. 1987 . Problem size and mentally retarded children's judgement of commutativity . American Journal of Mental Deficiency , 91 : 439 – 442 .
   PubMedGoogle Scholar
• Baroody , A. J. 1988 . Mental-addition development of children classified as mentally handicapped . Educational Studies in Mathematics , 19 : 369 – 388 .
   Google Scholar
• Baroody , A. J. 1996 . Self-invented addition strategies by children with mental retardation . American Journal of Mental Retardation , 101 : 72 – 89 .
   PubMedGoogle Scholar
• Baroody , A. 1999 . “ The development of basic counting, number, and arithmetic knowledge among children classified as mentally handicapped ” . In International Review of Research on Mental Retardation , Edited by: Glidden , L. M. 51 – 103 . San Diego, CA : Academic Press .
   Google Scholar
• Bow-Thomas , C. C. 1994 . Memory performance and addition strategy choice in mathematically disabled children , Columbia : University of Missouri . Doctoral dissertation
   Google Scholar
• Briars , D. and & Siegler , R. S. 1984 . A featural analysis of preschoolers' counting knowledge . Developmental Psychology , 20 : 607 – 618 .
   Web of Science ®Google Scholar
• Bull , R. and & Johnston , R. S. 1997 . Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory . Journal of Experimental Child Psychology , 65 : 1 – 24 .
   PubMed Web of Science ®Google Scholar
• Butterworth , B. , Cipolotti , L. and & Warrington , E. 1996 . Short-term memory impairment and arithmetical ability . Quarterly Journal of Experimental Psychology , 49A : 251 – 262 .
   Google Scholar
• Campbell , J. I. D. and & Clark , J. M. 1988 . An encoding-complex view of cognitive number processing: Comment on McCloskey, Sokol, and Goodman (1986) . Journal of Experimental Psychology , 117 : 204 – 214 .
   Google Scholar
• Cowan , N. 1986 . A matrix of consonant-cluster-free monosyllabic words in English . Behavior Research Methods, Instruments, & Computers , 18 : 434 – 446 .
   Google Scholar
• Cowan , N. , Keller , T. , Hulme , C. , Roodenrys , S. , McDougall , S. and & Rack , J. 1994 . Verbal memory span in children: Speech timing clues to the mechanisms underlying age and word length effects . Journal of Memory and Language , 33 : 234 – 250 .
   Web of Science ®Google Scholar
• Dark , V. J. and & Benbow , C. P. 1990 . Enhanced problem translation and short-term memory: Componentsof mathematical talent . Journal of Educational Psychology , 82 : 420 – 429 .
   Web of Science ®Google Scholar
• Dark , V. J. and & Benbow , C. P. 1991 . Differential enhancement of working memory with mathematical versus verbal precocity . Journal of Educational Psychology , 83 : 48 – 60 .
   Web of Science ®Google Scholar
• Dehaene , S. 1992 . Varieties of numerical abilities . Cognition , 44 : 1 – 42 .
   PubMed Web of Science ®Google Scholar
• Edwards , P. 1978 . Reading problems: Identification and treatment , London : Heinemann Educational Books .
   Google Scholar
• Fry , A. F. and & Hale , S. 1996 . Processing speed, working memory, and fluid intelligence: Evidence for a developmental cascade . Psychological Science , 7 : 237 – 241 .
   Web of Science ®Google Scholar
• Fuson , K. C. 1988 . Children's counting and concepts of number , New York : Springer-Verlag .
   Google Scholar
• Gallistel , C. R. and & Gelman , R. 1992 . Preverbal and verbal counting and computation . Cognition , 44 : 43 – 74 .
   PubMed Web of Science ®Google Scholar
• Gathercole , S. E. and & Adams , A. 1994 . Children's phonological working memory: Contributions of long-term knowledge and rehearsal . Journal of Memory and Language , 33 : 672 – 688 .
   Web of Science ®Google Scholar
• Geary , D. C. 1990 . A componential analysis of an early learning deficit in mathematics . Journal of Experimental Child Psychology , 49 : 363 – 383 .
   PubMed Web of Science ®Google Scholar
• Geary , D. C. 1993 . Mathematical disabilities: Cognitive, neuropsychological, and genetic components . Psychological Bulletin , 114 : 345 – 362 .
   PubMed Web of Science ®Google Scholar
• Geary , D. C. 1995 . Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction . American Psychologist , 50 : 24 – 37 .
   PubMed Web of Science ®Google Scholar
• Geary , D. C. 1998 . Male, female: The evolution of human sex differences , Washington, DC : American Psychological Association .
   Google Scholar
• Geary , D. C. , Bow-Thomas , C. C. , Fan , L. and & Siegler , R. S. 1993 . Even before formal instruction, Chinese children outperform American children in mental addition . Cognitive Development , 8 : 517 – 529 .
   Web of Science ®Google Scholar
• Geary , D. C. , Bow-Thomas , C. C. and & Yao , Y. 1992 . Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children . Journal of Experimental Child Psychology , 54 : 372 – 391 .
   PubMed Web of Science ®Google Scholar
• Geary , D. C. and & Brown , S. C. 1991 . Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children . Developmental Psychology , 27 : 398 – 406 .
   Web of Science ®Google Scholar
• Geary , D. C. , Brown , S. C. and & Samaranayake , V. A. 1991 . Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children . Developmental Psychology , 27 : 787 – 797 .
   Web of Science ®Google Scholar
• Geary , D. C. and & Burlingham-Dubree , M. 1989 . External validation of the strategy choice model for addition . Journal of Experimental Child Psychology , 47 : 175 – 192 .
   Web of Science ®Google Scholar
• Geary , D. C. and & Widaman , K. F. 1992 . Numerical cognition: On the convergence of componential and psychometric models . Intelligence , 16 : 47 – 80 .
   Web of Science ®Google Scholar
• Gelman , R. 1990 . First principles organize attention to and learning about relevant data: Number and the animate-inanimate distinction as examples . Cognitive Science , 14 : 79 – 106 .
   Web of Science ®Google Scholar
• Gelman , R. and & Gallistel , C. R. 1978 . The child's understanding of number , Cambridge, MA : Harvard University Press .
   Google Scholar
• Gelman , R. and & Meek , E. 1983 . Preschooler' counting: Principles before skill . Cognition , 13 : 343 – 359 .
   PubMed Web of Science ®Google Scholar
• Gottfredson , L. 1997a . Mainstream science on intelligence: An editorial with 52 signatories, history, and bibliography . Intelligence , 24 : 13 – 23 .
   Web of Science ®Google Scholar
• Gottfredson , L. 1997b . Why g matters: The complexity of everyday life . Intelligence , 24 : 79 – 132 .
   Web of Science ®Google Scholar
• Groen , G. J. and & Parkman , J. M. 1972 . A Chronometrie analysis of simple addition . Psychological Review , 79 : 329 – 343 .
   Web of Science ®Google Scholar
• Hitch , G. J. 1978 . The role of short-term working memory in mental arithmetic . Cognitive Psychology , 10 : 302 – 323 .
   Web of Science ®Google Scholar
• Hitch , G. J. and & McAuley , E. 1991 . Working memory in children with specific arithmetical learning difficulties . British Journal of Psychology , 82 : 375 – 386 .
   PubMed Web of Science ®Google Scholar
• Hunt , E. 1978 . Mechanisms of verbal ability . Psychological Review , 85 : 109 – 130 .
   Web of Science ®Google Scholar
• Jensen , A. R. 1998 . The g factor: The science of mental ability , Westport, CT : Praeger .
   Google Scholar
• Kail , R. 1991 . Developmental change in speed of processing during childhood and adolescence . Psychological Bulletin , 109 : 490 – 501 .
   PubMed Web of Science ®Google Scholar
• Keating , D. P. and & Bobbit , B. L. 1978 . Individual and developmental differences in cognitive processing components of mental ability . Child Development , 49 : 155 – 167 .
   Web of Science ®Google Scholar
• Logie , R. H. , Gilhooly , K. J. and & Wynn , V. 1994 . Counting on working memory in arithmetic problem solving . Memory and Cognition , 22 : 395 – 410 .
   PubMed Web of Science ®Google Scholar
• McCloskey , M. 1992 . Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia . Cognition , 44 : 107 – 157 .
   PubMed Web of Science ®Google Scholar
• McCloskey , M. , Alminosa , D. and & Macaruso , P. 1991 . Theory-based assessment of acquired dyscalculia . Brain and Cognition , 17 : 285 – 308 .
   PubMed Web of Science ®Google Scholar
• McCloskey , M. , Caramazza , A. and & Basili , A. 1985 . Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia . Brain and Cognition , 4 : 171 – 196 .
   PubMed Web of Science ®Google Scholar
• Miller , K. , Smith , C. , Zhu , J. and & Zhang , H. 1995 . Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems . Psychological Science , 6 : 56 – 60 .
   Web of Science ®Google Scholar
• Sattler , J. M. 1982 . Assessment of children's intelligence and special abilities , 2nd ed. , Boston : Allyn & Bacon .
   Google Scholar
• Seron , X. and & Fayol , M. 1994 . Number transcoding in children: A functional analysis . British Journal of Developmental Psychology , 12 : 281 – 300 .
   Web of Science ®Google Scholar
• Shalev , R. S. , Manor , O. and & Gross-Tsur , V. 1993 . The acquisition of arithmetic in normal children: Assessment by a cognitive model of dyscalculia . Developmental Medicine and Child Neurology , 35 : 593 – 601 .
   PubMed Web of Science ®Google Scholar
• Siegel , L. S. and & Ryan , E. B. 1989 . The development of working memory in normally achieving and subtypes of learning disabled children . Child Development , 60 : 973 – 980 .
   PubMed Web of Science ®Google Scholar
• Siegler , R. S. 1987 . Some general conclusions about children's strategy choice procedures. Special Issue: The neo-Piagetian theories of cognitive development: Toward an integration . International Journal of Psychology , 22 : 729 – 749 .
   Web of Science ®Google Scholar
• Siegler , R. S. 1988 . Individual differences in strategy choices: Good students, not-so-good students, and perfectionists . Child Development , 59 : 833 – 851 .
   PubMed Web of Science ®Google Scholar
• Siegler , R. S. 1993 . “ Adaptive and non-adaptive characteristics of low-income children's mathematical strategy use ” . In The challenge of mathematics and science education: Psychology's response , Edited by: Penner , L. A. , Batsche , G. M. , Knoff , H. M. and Nelson , D. L. 341 – 366 . Washington, DC : American Psychological Association .
   Google Scholar
• Siegler , R. S. and & Kotovsky , K. 1986 . “ Two levels of giftedness: Shall ever the twain meet? ” . In Conceptions of giftedness , Edited by: Sternberg , R. J. and Davidson , J. E. 417 – 435 . Cambridge : Cambridge University Press .
   Google Scholar
• Siegler , R. S. and & Shrager , J. 1984 . “ Strategy choice in addition and subtraction: How do children know what to do? ” . In Origins of cognitive skills , Edited by: Sophian , C. 229 – 293 . Hillsdale, NJ : Erlbaum .
   Google Scholar
• Swanson , H. L. 1993 . Working memory in learning disability subgroups . Journal of Experimental Child Psychology , 56 : 87 – 114 .
   PubMed Web of Science ®Google Scholar
• Temple , C. M. 1991 . Procedural dyscalculia and number fact dyscalculia: Double dissociation in developmental dyscalculia . Cognitive Neuropsychology , 8 : 155 – 176 .
   Web of Science ®Google Scholar
• Thorndike , R. L. , Hagen , E. P. and & Sattler , J. M. 1986 . The Stanford-Binet Intelligence Scale: Fourth Edition , Chicago, IL : Riverside Publishing Company .
   Google Scholar
• Vernon , P. A. 1983 . Speed of information processing and general intelligence . Intelligence , 7 : 53 – 70 .
   Web of Science ®Google Scholar
• Wagner , R. K. and & Torgesen , J. K. 1987 . The nature of phonological processing and its causal role in the acquisition of reading skills . Psychological Bulletin , 101 : 192 – 212 .
   Web of Science ®Google Scholar
• Wechsler , D. 1991 . Wechsler Intelligence Scale for Children , 3rd ed. , San Antonio, TX : Psychological Corporation, Harcourt Brace .
   Google Scholar
• Wechsler , D. 1992 . Wechsler Individual Achievement Test , San Antonio, TX : Psychological Corporation, Harcourt Brace .
   Google Scholar
• Woodcock , R. W. and Johnson , M. B. 1989/1990 . Woodcock-Johnson Psycho-Educational Battery—Revised , Alien, TX : DLM Teaching Resources .
   Google Scholar
• Wynn , K. 1996 . Infants' individuation and enumeration of actions . Psychological Science , 7 : 164 – 169 .
   Web of Science ®Google Scholar