Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study

Developmental Psychology

Volumn 47, Issue 6, 2011, Pages 1539-1552

  Geary, David C ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Achievement growth; Longitudinal study; Mathematical cognition; Mathematics; Reading

Indexed keywords

ACHIEVEMENT; ARTICLE; CHILD; CHILD DEVELOPMENT; COGNITION; EXECUTIVE FUNCTION; FEMALE; HUMAN; INDIVIDUALITY; INTELLIGENCE; KNOWLEDGE; LONGITUDINAL STUDY; MALE; MATHEMATICS; NEUROPSYCHOLOGICAL TEST; PHYSIOLOGY; PREDICTIVE VALUE; PROBLEM SOLVING; READING; SHORT TERM MEMORY;

ACHIEVEMENT; CHILD; CHILD DEVELOPMENT; COGNITION; EXECUTIVE FUNCTION; FEMALE; HUMANS; INDIVIDUALITY; INTELLIGENCE; KNOWLEDGE; LONGITUDINAL STUDIES; MALE; MATHEMATICS; MEMORY, SHORT-TERM; NEUROPSYCHOLOGICAL TESTS; PREDICTIVE VALUE OF TESTS; PROBLEM SOLVING; READING;

EID: 82755187521     PISSN: 00121649     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0025510     Document Type: Article

References (101)

1. Ackerman P.L., Beier M.E., Boyle M.O. Working memory and intelligence: The same or different constructs?. Psychological Bulletin 2005, 131:30-60. doi: 10.1037/0033-2909.131.1.30.
2. Ashenfelter O., Krueger A. Estimates of the economic return to schooling from a new sample of twins. American Economic Review 1994, 84:1157-1173.
3. Baddeley A.D. Working memory 1986, Oxford University Press, Oxford, England.
4. Baddeley A., Gathercole S., Papagno C. The phonological loop as a language learning device. Psychological Review 1998, 105:158-173. doi: 10.1037/0033-295X.105.1.158.
5. Baddeley A.D., Hitch G.J. Working memory. The psychology of learning and motivation: Advances in research and theory 1974, 8:47-90. Academic Press, New York, NY. G.H. Bower (Ed.).
6. Booth J.L., Siegler R.S. Developmental and individual differences in pure numerical estimation. Developmental Psychology 2006, 42:189-201. doi: 10.1037/0012-1649.41.6.189.
7. Bradley L., Bryant P.E. Categorizing sounds and learning to read: A causal connection. Nature 1983, February 3, 301:419-421. doi: 10.1038/301419a0.
8. Briars D., Siegler R.S. A featural analysis of preschoolers' counting knowledge. Developmental Psychology 1984, 20:607-618. doi: 10.1037/0012-1649.20.4.607.
9. Bull R., Espy K.A., Wiebe S.A. Short-term memory, working memory, and executive functions in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology 2008, 33:205-228. doi: 10.1080/87565640801982312.
10. Bull R., Johnston R.S. Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology 1997, 65:1-24. doi: 10.1006/jecp.1996.2358.
11. Carroll J.B. Human cognitive abilities: A survey of factor-analytic studies 1993, Cambridge University Press, New York, NY, doi: 10.1017/CBO9780511571312.
12. Conway A.R.A., Cowan N., Bunting M.F., Therriault D.J., Minkoff S.R.B. A latent variable analysis of working memory capacity, short-term memory capacity, processing speed, and general fluid intelligence. Intelligence 2002, 30:163-184. doi: 10.1016/S0160-2896(01)00096-4.
13. Cormier P., Dea S. Distinctive patterns of relationship of phonological awareness and working memory with reading development. Reading and Writing 1997, 9:193-206. doi: 10.1023/A:1007932721290.
14. Cowan N. Attention and memory: An integrated framework 1995, Oxford University Press, New York, NY.
15. Crosnoe R., Morrison F., Burchinal M., Pianta R., Keating D., Friedman S.L. Instruction, teacher-student relations, and math achievement trajectories in elementary school. Journal of Educational Psychology 2010, 102:407-417. The Eunice Kennedy Shriver National Institute of Child Health and Human Development Early Child Care Research Network, doi: 10.1037/a0017762.
16. Dark V.J., Benbow C.P. Differential enhancement of working memory with mathematical versus verbal precocity. Journal of Educational Psychology 1991, 83:48-60. doi: 10.1037/0022-0663.83.1.48.
17. Deary I.J., Der G., Ford G. Reaction times and intelligence differences: A population-based cohort study. Intelligence 2001, 29:389-399. doi: 10.1016/S0160-2896(01)00062-9.
18. Deary I.J., Strand S., Smith P., Fernandes C. Intelligence and educational achievement. Intelligence 2007, 35:13-21. doi: 10.1016/j.intell.2006.02.001.
19. Denckla M.B., Rudel R. Rapid automatized naming (RAN): Dyslexia differentiated from other learning disabilities. Neuropsychologia 1976, 14:471-479. doi: 10.1016/0028-3932(76)90075-0.
20. Der G., Deary I.J. IQ, reaction time and the differentiation hypothesis. Intelligence 2003, 31:491-503. doi: 10.1016/S0160-2896(02)00189-7.
21. De Smedt B., Janssen R., Bouwens K., Verschaffel L., Boets B., Ghesquière P. Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade. Journal of Experimental Child Psychology 2009, 103:186-201. doi: 10.1016/j.jecp.2009.01.004.
22. Desoete A., Stock P., Schepens A., Baeyens D., Roeyers H. Classification, seriation, and counting in Grades 1, 2, and 3 as two-year longitudinal predictors for low achieving in numerical facility and arithmetical achievement?. Journal of Psychoeducational Assessment 2009, 27:252-264. doi: 10.1177/0734282908330588.
23. DeStefano D., LeFevre J.-A. The role of working memory in mental arithmetic. European Journal of Cognitive Psychology 2004, 16:353-386. doi: 10.1080/09541440244000328.
24. Dettmers S., Trautwein U., Lüdtke O., Kunter M., Baumert J. Homework works if homework quality is high: Using multilevel modeling to predict the development of achievement in mathematics. Journal of Educational Psychology 2010, 102:467-482. doi: 10.1037/a0018453.
25. Duncan G.J., Dowsett C.J., Claessens A., Magnuson K., Huston A.C., Klebanov P., Japel C. School readiness and later achievement. Developmental Psychology 2007, 43:1428-1446. doi: 10.1037/0012-1649.43.6.1428.
26. Embretson S.E. The role of working memory capacity and general control processes in intelligence. Intelligence 1995, 20:169-189. doi: 10.1016/0160-2896(95)90031-4.
27. Engle R.W., Tuholski S.W., Laughlin J.E., Conway A.R.A. Working memory, short-term memory, and general fluid intelligence: A latent-variable approach. Journal of Experimental Psychology: General 1999, 128:309-331. doi: 10.1037/0096-3445.128.3.309.
28. Every Child a Chance Trust. The long-term costs of numeracy difficulties 2009, Retrieved from http://www.everychildachancetrust.org/counts/index.cfm.
29. Feigenson L., Dehaene S., Spelke E. Core systems of number. Trends in Cognitive Sciences 2004, 8:307-314. doi: 10.1016/j.tics.2004.05.002.
30. Foresman S. Investigations in number, data, and space 1999, Author, Glenview, IL.
31. Fuchs L.S., Fuchs D., Compton D.L., Powell S.R., Seethaler P.M., Capizzi A.M., Fletcher J.M. The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology 2006, 98:29-43. doi: 10.1037/0022-0663.98.1.29.
32. Fuchs L.S., Geary D.C., Compton D.L., Fuchs D., Hamlett C.L. The contributions of numerosity and domain-general abilities for school readiness. Child Development 2010, 81:1520-1533. doi: 10.1111/j.1467-8624.2010.01489.x.
33. Gallistel C.R., Gelman R. Preverbal and verbal counting and computation. Cognition 1992, 44:43-74. doi: 10.1016/0010-0277(92)90050-R.
34. Geary D.C. A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology 1990, 49:363-383. doi: 10.1016/0022-0965(90)90065-G.
35. Geary D.C. Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin 1993, 114:345-362. doi: 10.1037/0033-2909.114.2.345.
36. Geary D.C. Children's mathematical development: Research and practical applications 1994, American Psychological Association, Washington, DC, doi: 10.1037/10163-000.
37. Geary D.C. Sexual selection and sex differences in mathematical abilities. Behavioral and Brain Sciences 1996, 19:229-284. doi: 10.1017/S0140525X00042400.
38. Geary D.C. The origin of mind: Evolution of brain, cognition, and general intelligence 2005, American Psychological Association, Washington, DC, doi: 10.1037/10871-000.
39. Geary D.C., Bailey D.H., Hoard M.K. Predicting mathematical achievement and mathematical learning disability with a simple screening tool: The Number Sets Test. Journal of Psychoeducational Assessment 2009, 27:265-279. doi: 10.1177/0734282908330592.
40. Geary D.C., Bow-Thomas C.C., Yao Y. Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology 1992, 54:372-391. doi: 10.1016/0022-0965(92)90026-3.
41. Geary D.C., Hoard M.K., Byrd-Craven J., Desoto M. Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology 2004, 88:121-151. doi: 10.1016/j.jecp.2004.03.002.
42. Geary D.C., Hoard M.K., Byrd-Craven J., Nugent L., Numtee C. Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development 2007, 78:1343-1359. doi: 10.1111/j.1467-8624.2007.01069.x.
43. Geary D.C., Saults S.J., Liu F., Hoard M.K. Sex differences in spatial cognition, computational fluency, and arithmetical reasoning. Journal of Experimental Child Psychology 2000, 77:337-353. doi: 10.1006/jecp.2000.2594.
44. Gelman R., Gallistel C.R. The child's understanding of number 1978, Harvard University Press, Cambridge, MA.
45. Gelman R., Meck E. Preschooler's counting: Principles before skill. Cognition 1983, 13:343-359. doi: 10.1016/0010-0277(83)90014-8.
46. Ginsburg H.P., Baroody A.J. Test of Early Mathematics Ability 2003, Western Psychological Services, Los Angeles, CA. 3rd ed.
47. Gottfredson L. Why g matters: The complexity of everyday life. Intelligence 1997, 24:79-132. doi: 10.1016/S0160-2896(97)90014-3.
48. Groen G.J., Parkman J.M. A chronometric analysis of simple addition. Psychological Review 1972, 79:329-343. doi: 10.1037/h0032950.
49. Halberda J., Feigenson L. Developmental change in the acuity of the "number sense": The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology 2008, 44:1457-1465. doi: 10.1037/a0012682.
50. Jensen A.R. The g factor: The science of mental ability 1998, Praeger, Westport, CT.
51. Johnson E.S. Sex differences in problem solving. Journal of Educational Psychology 1984, 76:1359-1371. doi: 10.1037/0022-0663.76.6.1359.
52. Johnson W., Deary I.J., Iacono W.G. Genetic and environmental transactions underlying educational attainment. Intelligence 2009, 37:466-478. doi: 10.1016/j.intell.2009.05.006.
53. Jordan N.C., Kaplan D., Ramineni C., Locuniak M.N. Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology 2009, 45:850-867. doi: 10.1037/a0014939.
54. Kovas Y., Harlaar H., Petrill S.A., Plomin R. "Generalist genes" and mathematics in 7-year-old twins. Intelligence 2005, 33:473-489. doi: 10.1016/j.intell.2005.05.002.
55. Krajewski K., Schneider W. 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. Journal of Experimental Child Psychology 2009, 103:516-531. doi: 10.1016/j.jecp.2009.03.009.
56. Kyllonen P.C., Christal R.E. Reasoning ability is (little more than) working-memory capacity?!. Intelligence 1990, 14:389-433. doi: 10.1016/S0160-2896(05)80012-1.
57. Lachance J., Mazzocco M.M.M. A longitudinal analysis of sex differences in math and spatial skills in primary school age children. Learning and Individual Differences 2006, 16:195-216. doi: 10.1016/j.lindif.2005.12.001.
58. Landerl K., Bevan A., Butterworth B. Developmental dyscalculia and basic numerical capacities: A study of 8- to 9-year-old students. Cognition 2004, 93:99-125. doi: 10.1016/j.cognition.2003.11.004.
59. LeFevre J.-A., Smith-Chant B.L., Fast L., Skwarchuk S.-L., Sargla E., Arnup J.S., Kamawar D. What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2. Journal of Experimental Child Psychology 2006, 93:285-303. doi: 10.1016/j.jecp.2005.11.002.
60. Levine S.C., Jordan N.C., Huttenlocher J. Development of calculation abilities in young children. Journal of Experimental Child Psychology 1992, 53:72-103. doi: 10.1016/S0022-0965(05)80005-0.
61. Lewis A.B. Training students to represent arithmetic word problems. Journal of Educational Psychology 1989, 81:521-531. doi: 10.1037/0022-0663.81.4.521.
62. Locuniak M.N., Jordan N.C. Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities 2008, 41:451-459. doi: 10.1177/0022219408321126.
63. Logie R.H. Visuo-spatial working memory 1995, Erlbaum, Hove, England.
64. Luke D.A. Multilevel modeling 2004, Sage, Thousand Oaks, CA.
65. MacMillan N.A. Signal detection theory. H. Stevens' handbook of experimental psychology, 3rd ed. Vol. 4: Methodology in experimental psychology 2002, 43-90. Wiley, New York, NY. J. Wixted, H. Pashler (Eds.).
66. Mazzocco M.M.M., Kover S.T. A longitudinal assessment of executive function skills and their association with math performance. Child Neuropsychology 2007, 13:18-45. doi: 10.1080/09297040600611346.
67. Mazzocco M.M.M., Myers G. Complexities in identifying and defining mathematics learning disability in the primary school-age years. Annals of Dyslexia 2003, 53:218-253. doi: 10.1007/s11881-003-0011-7.
68. Mazzocco M.M.M., Thompson R.E. Kindergarten predictors of math learning disability. Learning Disabilities Research & Practice 2005, 20:142-155. doi: 10.1111/j.1540-5826.2005.00129.x.
69. McLean J.F., Hitch G.J. Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology 1999, 74:240-260. doi: 10.1006/jecp.1999.2516.
70. Foundations for success: Final report of the National Mathematics Advisory Panel 2008, National Mathematics Advisory Panel, United States Department of Education, Washington, DC, Retrieved from http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.
71. Paglin M., Rufolo A.M. Heterogeneous human capital, occupational choice, and male-female earning differences. Journal of Labor Economics 1990, 8:123-144. doi: 10.1086/298239.
72. Passolunghi M.C., Vercelloni B., Schadee H. The precursors of mathematics learning: Working memory, phonological ability and numerical competence. Cognitive Development 2007, 22:165-184. doi: 10.1016/j.cogdev.2006.09.001.
73. Pickering S., Gathercole S. Working Memory Test Battery for Children (WMTB-C) manual 2001, Psychological Corporation, London, England.
74. Raftery A.E. Bayesian model selection in social research. Sociological Methodology 1995, 25:111-196. doi: 10.2307/271063.
75. Rivera-Batiz F. Quantitative literacy and the likelihood of employment among young adults in the United States. Journal of Human Resources 1992, 27:313-328. doi: 10.2307/145737.
76. Rousselle L., Noël M.-P. Basic numerical skills in children with mathematical learning disabilities: A comparison of symbolic vs. non-symbolic number magnitude processing. Cognition 2007, 102:361-395. doi: 10.1016/j.cognition.2006.01.005.
77. Statistical Analysis System 7.5 2004, SAS Institute, Author, Cary, NC.
78. Siegler R.S. The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General 1987, 116:250-264. doi: 10.1037/0096-3445.116.3.250.
79. Siegler R.S., Booth J.L. Development of numerical estimation in young children. Child Development 2004, 75:428-444. doi: 10.1111/j.1467-8624.2004.00684.x.
80. Siegler R.S., Opfer J. The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science 2003, 14:237-243. doi: 10.1111/1467-9280.02438.
81. Siegler R.S., Ramani G.B. Playing board games promotes low-income children's numerical development. Developmental Science 2008, 11:655-661. doi: 10.1111/j.1467-7687.2008.00714.x.
82. Siegler R.S., Shrager J. Strategy choice in addition and subtraction: How do children know what to do?. Origins of cognitive skills 1984, 229-293. Erlbaum, Hillsdale, NJ. C. Sophian (Ed.).
83. Spelke E.S. Core knowledge. American Psychologist 2000, 55:1233-1243. doi: 10.1037/0003-066X.55.11.1233.
84. Starkey P. The early development of numerical reasoning. Cognition 1992, 43:93-126. doi: 10.1016/0010-0277(92)90034-F.
85. Starkey P., Cooper R.G. Perception of numbers by human infants. Science 1980, November 28, 210:1033-1035. doi: 10.1126/science.7434014.
86. Starkey P., Spelke E.S., Gelman R. Numerical abstraction by human infants. Cognition 1990, 36:97-127. doi: 10.1016/0010-0277(90)90001-Z.
87. Stevenson H.W., Parker T., Wilkinson A., Hegion A., Fish E. Longitudinal study of individual differences in cognitive development and scholastic achievement. Journal of Educational Psychology 1976, 68:377-400. doi: 10.1037/0022-0663.68.4.377.
88. Swanson H.L., Ashbaker M.H. Working memory, short-term memory, speech rate, word recognition and reading comprehension in learning disabled readers: Does the executive system have a role?. Intelligence 2000, 28:1-30. doi: 10.1016/S0160-2896(99)00025-2.
89. Swanson H.L., Jerman O., Zheng X. Growth in working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology 2008, 100:343-379. doi: 10.1037/0022-0663.100.2.343.
90. Swanson H.L., Sachse-Lee C. Mathematical problem solving and working memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology 2001, 79:294-321. doi: 10.1006/jecp.2000.2587.
91. Swanson H.L., Trainin G., Necoechea D.M., Hammill D.D. Rapid naming, phonological awareness and reading: A meta-analysis of the correlation evidence. Review of Educational Research 2003, 73:407-440. doi: 10.3102/00346543073004407.
92. Taub G.E., Floyd R.G., Keith T.Z., McGrew K.S. Effects of general and broad cognitive abilities on mathematics achievement. School Psychology Quarterly 2008, 23:187-198. doi: 10.1037/1045-3830.23.2.187.
93. Wagner R.K., Torgesen J.K. The nature of phonological processing and its causal role in the acquisition of reading skills. Psychological Bulletin 1987, 101:192-212. doi: 10.1037/0033-2909.101.2.192.
94. Walberg H.J. Improving the productivity of America's schools. Educational Leadership 1984, 41:19-27.
95. Wechsler D. Wechsler Individual Achievement Test 1992, The Psychological Corporation, Harcourt Brace, San Antonio, TX.
96. Wechsler D. Wechsler Abbreviated Scale of Intelligence 1999, PsychCorp, Harcourt Assessment, San Antonio, TX.
97. Wechsler D. Wechsler Individual Achievement Test-II-Abbreviated 2001, The Psychological Corporation, Harcourt Brace, San Antonio, TX.
98. Wolf M., Bowers P.G., Biddle K. Naming-speed processes, timing, and reading: A conceptual review. Journal of Learning Disabilities 2000, 33:387-407. doi: 10.1177/002221940003300409.
99. Wynn K. Addition and subtraction by human infants. Nature 1992, August 27, 358:749-750.
100. Wynn K., Bloom P., Chiang W.-C. Enumeration of collective entities by 5-month-old infants. Cognition 2002, 83:B55-B62. doi: 10.1016/S0010-0277(02)00008-2.
101. Xu F., Spelke E.S. Large number discrimination in 6-month-old infants. Cognition 2000, 74:B1-B11. doi: 10.1016/S0010-0277(99)00066-9.