Numerical Cognition: Age-Related Differences in the Speed of Executing Biologically Primary and Biologically Secondary Processes

References

• Klahr , D. and Wallace , J. C. 1973 . The role of quantification operators in the development of conservation of quantity . Cognitive Psychology , 4 : 301 – 327 .
   Web of Science ®Google Scholar
• Saxe , G. B. 1985 . Effects of schooling on arithmetical understandings: Studies with Oksapmin children in Papua New Guinea . Journal of Educational Psychology , 77 : 503 – 513 .
   Web of Science ®Google Scholar
• Saxe , G. B. 1988 . The mathematics of child street vendors . Child Development , 59 : 1415 – 1425 .
   Web of Science ®Google Scholar
• Schacter , D. L. 1994 . “ Priming and multiple memory systems: Perceptual mechanisms of implicit memory ” . In Memory systems 1994 , Edited by: Schacter , D. L. and Tulving , E. 233 – 268 . Cambridge, MA : MIT Press .
   Google Scholar
• Schaie , K. W. 1996 . Intellectual development in adulthood: The Seattle longitudinal study , New York : Cambridge University Press .
   Google Scholar
• Shepard , R. N. 1994 . Perceptual-cognitive universals as reflections of the world . Psychonomic Bulletin & Review , 7 : 2 – 28 .
   Google Scholar
• Widaman , K. F. , Geary , D. C. , Cormier , P. and Little , T. D. 1989 . A componential model for mental addition . Journal of Experimental Psychology: Learning, Memory, and Cognition , 15 : 898 – 919 .
   PubMed Web of Science ®Google Scholar
• Wynn , K. 1992 . Addition and subtraction by human infants . Nature , 358 : 749 – 750 .
   PubMed Web of Science ®Google Scholar
• Dehaene , S. and Cohen , L. 1991 . Two mental calculation systems: A case study of severe acalculia with preserved approximation . Neuropsychologia , 29 : 1045 – 1074 .
   PubMed Web of Science ®Google Scholar
• Dehaene , S. and Cohen , L. 1994 . Dissociable mechanisms of subitizing and counting--Neuropsychological evidence from simultanagnosic patients . Journal of Experimental Psychology: Human Perception and Performance , 20 : 958 – 975 .
   PubMed Web of Science ®Google Scholar
• Eibl-Eibesfeldt , I. 1989 . Human ethology , New York : Aldine de Gruyter .
   Google Scholar
• Gallislel , C R. and Gelman , R. 1992 . Preverbal and verbal counting and computation . Cognition , 44 : 43 – 74 .
   PubMedGoogle 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. 1994 . Children's mathematical development: Research and practical applications , Washington, DC : American Psychological Association .
   Google Scholar
• Geary , D. C. 1995 . Reflection of evaluation and cultural in children's cognition: Implications for mathematical development and instruction . American Psychologist , SO : 24 – 37 .
   Google Scholar
• Geary , D. C. 1996a . The problem-size effect in mental addition: Developmental and cross-national trends . Mathematical Cognition , 2 : 63 – 93 .
   Google Scholar
• Geary , D. C. 1996b . Sexual selection and sex differences in mathematical abilities . Behavioral and Brain Sciences , 79 : 229 – 284 .
   Google Scholar
• Geary, D. C (1998). Functional organization of the human mind: Implications for behavioral genetic research. Human Biology
   Google Scholar
• Geary, D. C., Bow-Thomas, C. C., Liu, F., & Siegler, R. S. (1996). Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling Child Development, 67, 2022-2044.
   Google Scholar
• Geary , D. C. , Frensch , P.A. and Wiley , J. G. 1993 . Simple and complex mental subtraction: Strategy choice and speed-of-processing differences in younger and older adults . Psychology and Aging , 8 : 242 – 256 .
   PubMed Web of Science ®Google Scholar
• Geary, D. C., Hamson, C. O., Chen, G.-P., Liu, F., & Hoard, M. K. (in press). A biocultural model of academic development. In S. Paris & H. Wellman (Eds.), Global prospects for education: Development, culture and schooling. Washington, DC: American Psychological Association.
   Google Scholar
• Geary , D. C. , Hamson , C. O. , Chen , G.-R , Liu , F. , Hoard , M. K. and Salthouse , T. A. 1997 . Computational and reasoning abilities in arithmetic: Cross-generational change in China and the United States . Psychonomic Bulletin & Review , 4 : 425 – 430 .
   Web of Science ®Google Scholar
• Geary , D. C. , Salthouse , T. A. , Chen , G.-R and Fan , L. 1996 . Are East Asian versus American differences in arithmetical ability a recent phenomenon? . Developmental Psychology , 32 : 254 – 262 .
   Web of Science ®Google Scholar
• Geary , D. C. and Widaman , K. F. 1987 . Individual differences in cognitive arithmetic . Journal of Experimental Psychology: General , 116 : 154 – 171 .
   PubMed Web of Science ®Google Scholar
• Geary , D. C. and Wiley , J. G. 1991 . Cognitive addition: Strategy choice and speed-oh processing differences in young and elderly adults . Psychology and Aging , 6 : 474 – 483 .
   PubMed Web of Science ®Google Scholar
• Hale , S. and Myerson , J. 1996 . Experimental evidence for differential slowing in the lexical and nonlexical domains . Aging, Neuropsychology, and Cognition , 3 : 1 – 112 .
   Google Scholar
• Hale , S. , Myerson , J. , Faust , M. and Fristoe , N. 1995 . Converging evidence for domain-specific slowing from multiple nonlexical tasks and multiple analytic methods . Journal of Gerontology: Psychological Sciences , 50B : P202 – P211 .
   Google Scholar
• Hamilton , W. D. 1975 . “ Innate social aptitudes of man: An approach from evolutionary genetics ” . In Biosocial anthropology , Edited by: Fox , R. 133 – 155 . New York : Wiley .
   Google Scholar
• Hasher , L. and Zacks , R. T. 1979 . Automatic and effortful processes in memory . Journal of Experimental Psychology: General , 108 : 356 – 388 .
   Web of Science ®Google Scholar
• Hill , K. 1982 . Hunting and human evolution . Journal of Human Evolution , 11 : 521 – 544 .
   Web of Science ®Google Scholar
• Hill , K. and Hurtado , A. M. 1996 . Ache life history: The ecology and demography of a foraging people , New York : Aldine de Gruyter .
   Google Scholar
• Horn , J. L. and Cattell , R. B. 1966 . Refinement and test of the theory of fluid and crystallized general Intelligence . Journal of Educational Psychology , 57 : 253 – 270 .
   PubMed Web of Science ®Google Scholar
• Kotary , L. and Hoyer , W. J. 1995 . Age and the ability to inhibit distractor information in visual selective attention . Experimental Aging Research , 21 : 159 – 171 .
   PubMed Web of Science ®Google Scholar
• Landauer, T. K. (1962). Rate of implicit speech. Perceptual and Motor Skills, 75, 646.
   Google Scholar
• LeFevre , J.-A. , Sadesky , G. S. and Bisanz , J. 1996 . Selection procedures in mental addition: Reassessing the problem size effect in adults . Journal of Experimental Psychology: Learning, Memory, and Cognition , 22 : 216 – 230 .
   Web of Science ®Google Scholar
• Lima , S. D. , Hale , S and Myerson , J. 1991 . How general is general slowing? Evidence from the lexical domain . Psychology and Aging , 6 : 41 – 425 .
   Google Scholar
• Mandler , G. and Shebo , B. J. 1982 . Subitizing: An analysis of its component processes . Journal of Experimental Psychology: General , 111 : 1 – 22 .
   PubMed Web of Science ®Google Scholar
• Moyer , R. S. and Landauer , T. K. 1967 . Time required for judgments of numerical inequality . Nature , 215 : 1519 – 1520 .
   PubMed Web of Science ®Google Scholar
• Myerson , J. , Hale , S. , Wagstaff , D. , Poon , L. W. and Smith. , G. A. 1990 . The information loss model: A mathematical theory of age-related cognitive slowing . Psychological Review , 97 : 475 487
   Google Scholar
• Nebes , R. D. , Brady , C. B. and Reynolds , C. F. III. 1992 . Cognitive slowing in Alzheimer's disease and geriatric depression . Journal of Gerontology: Psychological Sciences , 47 : P331 – P336 .
   Google Scholar
• Pedhazur , E. J. 1982 . Multiple regression in behavioral research: Explanation and prediction , 2nd , New York : Holt, Rinehart, and Winston .
   Google Scholar
• Pepperberg , I. M. 1987 . Evidence for conceptual quantitative abilities in the African grey parrot: Labeling of cardinal sets . Ethology , 75 : 37 61
   Google Scholar
• Pinker , S. and Bloom , P. 1990 . Natural language and natural selection . Behavioral and Brain Sciences , 13 : 707 – 784 .
   Web of Science ®Google Scholar
• Salthouse , T. A. 1991 . Mediation of adult age differences in cognition by reductions in working memory and speed of processing . Psychological Science , 2 : 179 – 183 .
   Web of Science ®Google Scholar
• Salthouse , T. A. 1992 . Working-memory mediation of adult age differences in integrative reasoning . Memory & Cognition , 20 : 413 – 423 .
   PubMed Web of Science ®Google Scholar
• Salthouse , T. A. I . 1996 . The processing speed theory of adult age difference in cognition . Psychological Review , 103 : 403 – 428 .
   PubMed Web of Science ®Google Scholar
• Salthouse , T. A. and Babcock , R. L. 1991 . Decomposing adult age differences in working memory . Developmental Psychology , 27 : 763 – 776 .
   Web of Science ®Google Scholar
• Salthouse , T. A.. and Coon , V. E. 1994 . Interpretation of differential deficits: The case of aging and mental arithmetic . Journal of Experimental Psychology: Learning, Memory, and Cognition , 20 : 1172 – 1182 .
   PubMed Web of Science ®Google Scholar
• Saxe , G. B. 1982 . Developing forms of arithmetical thought among the Oksapmin of Papua New Guinea . Developmental Psychology , 18 : 583 – 594 .
   Web of Science ®Google Scholar
• Wynn , K . 1996 . Infants' individuation and enumeration of actions . Psychological Science , 7 : 164 – 169 .
   Web of Science ®Google Scholar
• Zhrodoff , J. N. and Logan , G. D. 1990 . On the relation between production and verification tasks in the psychology of simple arithmetic . Journal of Experimental Psychology: Learning, Memory! and Cognition , 16 : 83 – 97 .
   Google Scholar
• Siegler , R. S. 1989 . Hazards of mental chronometry: An example from children's subtraction . Journal of Educational Psychology , 81 : 497 – 506 .
   Web of Science ®Google Scholar
• Siegler , R. S. and Crowley , K. 1994 . Constraints on learning in nonprivileged domains . Cognitive Psychology , 27 : 194 – 226 .
   PubMed Web of Science ®Google Scholar
• Simon , T. J. , Hespos , S. J. and Rochat , P. 1995 . Do infants understand simple arithmetic? A replication of Wynn (1992) . Cognitive Development , 10 : 253 – 269 .
   Web of Science ®Google Scholar
• Simon , T. and Vaishnavi , S. 1996 . Subitizing and counting depend on different attentional mechanisms: Evidence from visual enumeration in afterimages . Perception and Psychophysics , 58 : 915 – 926 .
   PubMed Web of Science ®Google Scholar
• Sliwinski , M. 1997 . Aging and counting speed: Evidence for process-specific slowing . Psychology and Aging , 12 : 38 – 49 .
   PubMed Web of Science ®Google Scholar
• Sliwinski , M. , Buschke , H. , Kuslansky , G. , Senior. , G. and Scarisbrick , D. 1994 . Proportional slowing and addition speed in old and young adults . Psychology and Aging , 9 : 72 – 80 .
   PubMedGoogle Scholar
• Starkey , P. 1992 . The early development of numerical reasoning . Cognition , 43 : 93 – 126 .
   PubMed Web of Science ®Google Scholar
• Sternberg , R. J. 1977 . Intelligence, information processing, and analogical reasoning: The componential analysis of human abilities , Hillsdale, NJ : Erlbaum .
   Google Scholar
• Allen , P. A. , Ashcraft , M. H. and Weber , T. A. 1992 . On menial multiplication and age . Psychology and Aging , 7 : 536 – 545 .
   PubMed Web of Science ®Google Scholar
• Allen , P. A. , Smith , A. F. , Jerge , K. A. and Vires-Collins , H. 1997 . Age differences in mental multiplication: Evidence for peripheral but not central decrements . Journal of Gerontology: Psychological Sciences , 52 : 81 – 90 .
   Google Scholar
• Anderson , J. R. and Schooler , L. J. 1991 . Reflections of the environment in memory . Psychological Science , 2 : 396 – 408 .
   Web of Science ®Google Scholar
• Anstey , K. , Stankov , L. and Lord , S. 1993 . Primary aging, secondary aging, and intelligence . Psychology and Aging , 8 : 562 – 570 .
   PubMed Web of Science ®Google Scholar
• Antell , S. E. and Keating , D. P. 1983 . Perception of numerical invariance in neonates . Child Development , 54 : 695 – 701 .
   PubMed Web of Science ®Google Scholar
• 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. and Christy , K. S. 1995 . The frequency of arithmetic facts in elementary texts: Addition and multiplication in Grades 1-6 . Journal of Research in Mathematics Education , 26 : 396 – 421 .
   Web of Science ®Google Scholar
• Bahrick , H. P. and Hall , L. K. 1991 . Lifetime maintenance of high school mathematics content . Journal of Experimental Psychology: General , 120 : 22 – 33 .
   Google Scholar
• Baltes , P. B. 1993 . The aging mind: Potential and limits . Gerontologist , 33 : 580 – 594 .
   PubMed Web of Science ®Google Scholar
• Baltes , P. B. and Kliegl , R. 1992 . Further testing of limits of cognitive plasticity: Negative age differences in a mnemonic skill are robust . Developmental Psychology , 28 : 121 – 125 .
   Web of Science ®Google Scholar
• Birren, J. E., & Fisher, L. M. (1992). Aging and slowing of behavior. Consequences for cognition and survival. In T. B. Sonderegger (Ed.), Nebraska symposium on motivation 7997 (Vol. 39, pp. 1-37). Lincoln: University of Nebraska Press.
   Google Scholar
• Boysen , S. T. and Berntson , G. G. 1989 . Numerical competence in a chimpanzee (Pan troglodytes) . Journal of Comparative Psychology , 103 : 23 – 31 .
   PubMed Web of Science ®Google Scholar
• Campbell , J. I. D. 1995 . Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation . Mathematical Cognition , 7 : 121 – 164 .
   Google Scholar
• Campbell , J. I. D. and Charness , N. 1990 . Age-related declines in working memory skills: Evidence from a complex calculation task . Developmental Psychology , 26 : 879 – 888 .
   Web of Science ®Google Scholar
• Campbell , J. I. D. and Tarling , D. P.M. 1996 . Retrieval processes in arithmetic production and verification . Memory & Cognition , 24 : 156 172
   Google Scholar
• Cerella, J. (1990). Age and information-processing rate. In J. E. Birren & K. W. Schaie (Eds.), Handbook of the psychology of aging (3rd ed.. pp. 201-233). San Diego, CA: Academic Press.
   Google Scholar
• Cerella , J. and Fozard , J. L. 1984 . Lexical access and age . Developmental Psychology , 20 : 235 – 243 .
   Web of Science ®Google Scholar
• Charness , N. 1981 . Aging and skilled problem solving . Journal of Experimental Psychology: General , 170 : 21 – 38 .
   Google Scholar
• Charness , N. 1987 . Component processes in bridge bidding and novel problem solving tasks . Canadian Journal of Psychology , 41 : 223 – 243 .
   PubMed Web of Science ®Google Scholar
• Charness , N. and Campbell , J. I. D. 1988 . Acquiring skill at mental calculation in adulthood: A task decomposition . Journal of Experimental Psychology: General , 777 : 115 – 129 .
   Google Scholar
• Darwin , C. 1859 . The origin of species by means of natural selection , London : John Murray .
   Google Scholar
• Darwin , C. 1871 . The descent of man, and selection in relation to sex , London : John Murray .
   Google Scholar
• Davis , H. and Perusse , R. 1988 . Numerical competence in animals: Definitional issues, current evidence, and a new research agenda . Behavioral and Brain Sciences , 7 7 : 561 – 615 .
   Google Scholar
• Dehaene , S. 1489 . The psychophysics of numerical comparison: A re-examination of apparently incompatible data . Perception and Psychophysics , 45 : 557 – 566 .
   Google Scholar
• Sternberg , R. J. and Gardner , M. K. 1983 . Unities in inductive reasoning . Journal of Experimental Psychology: General , 112 : 80 – 116 .
   Google Scholar
• Symons , D. 1979 . The evolution of human sexuality , New York : Oxford University Press .
   Google Scholar
• Trick , L. M. , Enns , J. T. and Brodeur , D. A. 1996 . Life span changes in visual enumeration: The number discrimination task . Developmental Psychology , 32 : 925 – 932 .
   Web of Science ®Google Scholar
• Uttl , B. and Graf , P. 1993 . Episodic spatial memory in adulthood . Psychology and Aging , 8 : 257 – 273 .
   PubMed Web of Science ®Google Scholar
• Wechsler , D. 1981 . Wechsler Adult intelligence Scale--Revised New YorkPsychological Corporation
   Google Scholar