The codevelopment of skill at and preference for use of retrieval-based processes for solving addition problems: Individual and sex differences from first to sixth grades

Journal of Experimental Child Psychology

Volumn 113, Issue 1, 2012, Pages 78-92

  Bailey, Drew H ^a   Littlefield, Andrew ^a   Geary, David C ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Arithmetic; Mathematics achievement; Memory retrieval; Practice; Sex differences; Skill

Indexed keywords

AGE; APTITUDE; ARTICLE; CHILD; CHILD DEVELOPMENT; DECISION MAKING; EDUCATION; EXECUTIVE FUNCTION; FEMALE; HUMAN; INDIVIDUALITY; INTELLIGENCE TEST; LEARNING; LONG TERM MEMORY; MALE; MATHEMATICS; PROBLEM SOLVING; REACTION TIME; SEX DIFFERENCE; STATISTICS;

AGE FACTORS; APTITUDE; CHILD; CHILD DEVELOPMENT; CHOICE BEHAVIOR; EXECUTIVE FUNCTION; FEMALE; GENERALIZATION (PSYCHOLOGY); HUMANS; INDIVIDUALITY; INTELLIGENCE TESTS; MALE; MATHEMATICS; PRACTICE (PSYCHOLOGY); PROBLEM SOLVING; REACTION TIME; RETENTION (PSYCHOLOGY); SEX FACTORS; STATISTICS AS TOPIC;

EID: 84863783900     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2012.04.014     Document Type: Article

References (71)

1. Allan N.P., Lonigan C.J. Examining the dimensionality of effortful control in preschool children and its relation to academic and socioemotional indicators. Developmental Psychology 2011, 47:905-915.
2. Ashcraft M.H. The development of mental arithmetic: A chronometric approach. Developmental Review 1982, 2:213-236.
3. Baddeley A.D. Working memory 1986, Oxford University Press, Oxford, UK.
4. Baddeley A.D., Hitch G.J. Working memory. The psychology of learning and motivation: Advances in research and theory 1974, Vol. 8:47-90. Academic Press, New York.
5. Baron R.M., Kenny D.A. The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology 1986, 51:1173-1182.
6. Bates, D., & Maechler, M. (2010). lme4: Linear mixed-effects models using S4 classes (R package, Version 0.999375-33). Available at: http://CRAN.R-project.org/package=lme4.
7. 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 7years. Developmental Neuropsychology 2008, 33:205-228.
8. Byrnes J.P., Miller D.C., Schafer W.D. Gender differences in risk taking: A meta-analysis. Psychological Bulletin 1999, 125:367-383.
9. Carpenter T.P., Moser J.M. The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education 1984, 15:179-202.
10. Carr M., Alexeev N. Fluency, accuracy, and gender predict developmental trajectories of arithmetic strategies. Journal of Educational Psychology 2011, 103:617-631.
11. Carr M., Davis H. Gender differences in arithmetic strategy use: A function of skill and preference. Contemporary Educational Psychology 2001, 26:330-347.
12. Carr M., Jessup D.L. Gender differences in first-grade mathematics strategy use: Social and metacognitive influences. Journal of Educational Psychology 1997, 89:318-328.
13. Carroll J.B. Human cognitive abilities: A survey of factor-analytic studies 1993, Cambridge University Press, New York.
14. Cattell R.B. Theory of fluid and crystallized intelligence. A critical experiment. Journal of Educational Psychology 1963, 54:1-22.
15. Cho S., Ryali S., Geary D.C., Menon V. How do you solve 7+8? Decoding children's brain activity patterns during counting versus retrieval. Developmental Science 2011, 14:989-1001.
16. Colom R., Juan-Espinosa M., Abad F., García L.F. Negligible sex differences in general intelligence. Intelligence 2000, 28:57-68.
17. Cowan N. Attention and memory: An integrated framework 1995, Oxford University Press, New York.
18. 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.
19. Deary I.J., Strand S., Smith P., Fernandes C. Intelligence and educational achievement. Intelligence 2007, 35:13-21.
20. DeStefano D., LeFevre J.-A. The role of working memory in mental arithmetic. European Journal of Cognitive Psychology 2004, 16:353-386.
21. Embretson S.E. The role of working memory capacity and general control processes in intelligence. Intelligence 1995, 20:169-189.
22. Freedman D.A. As others see us: A case study in path analysis. Journal of Educational Statistics 1987, 12:101-128.
23. Geary D.C. A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology 1990, 49:363-383.
24. Geary D.C. Male, female: The evolution of human sex differences 2010, American Psychological Association, Washington, DC.
25. Geary D.C., Bow-Thomas C.C., Liu F., Siegler R.S. Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling. Child Development 1996, 67:2022-2044.
26. Geary D.C., Brown S.C., Samaranayake V.A. Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology 1991, 27:787-797.
27. Geary D.C., Burlingham-Dubree M. External validation of the strategy choice model for addition. Journal of Experimental Child Psychology 1989, 47:175-192.
28. Geary, D. C., Hoard, M. K., & Bailey, D. H. (in press). Fact retrieval deficits in low achieving children and children with mathematical learning disability. Journal of Learning Disabilities.
29. Geary D.C., Hoard M.K., Byrd-Craven J., DeSoto C.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.
30. 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.
31. Geary, D. C., Hoard, M. K., & Nugent, L. (in press). Different cognitive mechanisms contribute to the development of retrieval and procedural competencies in addition. Journal of Experimental Child Psychology.
32. Geary D.C., Hoard M.K., Nugent L., Bailey D.H. Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five year prospective study. Journal of Educational Psychology 2012, 104:206-223.
33. Geary D.C., Widaman K.F. Individual differences in cognitive arithmetic. Journal of Experimental Psychology: General 1987, 116:154-171.
34. Geary D.C., Widaman K.F. Numerical cognition: On the convergence of componential and psychometric models. Intelligence 1992, 16:47-80.
35. Gottfredson L. Why g matters: The complexity of everyday life. Intelligence 1997, 24:79-132.
36. Groen G.J., Parkman J.M. A chronometric analysis of simple addition. Psychological Review 1972, 79:329-343.
37. Jordan N.C., Hanich L.B., Kaplan D. Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology 2003, 85:103-119.
38. Jordan N.C., Montani T.O. Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities 1997, 30:624-634.
39. Klein J.S., Bisanz J. Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology 2000, 54:105-115.
40. Kline R.B. Principles and practice of structural equation modeling 2005, Guilford, New York. 2nd ed.
41. 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.
42. Littlefield A.K., Sher K.J., Wood P.K. Do changes in drinking motives mediate the relation between personality change and "maturing out" of problem drinking?. Journal of Abnormal Psychology 2010, 119:93-105.
43. Lynn R., Irwing P. Sex differences on the progressive matrices: A meta-analysis. Intelligence 2004, 32:481-498.
44. MacKinnon D.P., Lockwood C.M., Hoffman J.M., West S.G., Sheets V. A comparison of methods to test mediation and other intervening variable effects. Psychological Methods 2002, 7:83-104.
45. 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.
46. Muthén L.K., Muthén B.O. Mplus user's guide 1998-2010, Muthén & Muthén, Los Angeles. 6th ed.
47. National Council of Teachers of Mathematics Curriculum focal points for prekindergarten through Grade 8 mathematics: A quest for coherence 2006, Author, Reston, VA.
48. National Mathematics Advisory Panel Foundations for success: Final report of the National Mathematics Advisory Panel 2008, U.S. Department of Education, Washington, DC.
49. Noël M.-P. Counting on working memory when learning to count and to add: A preschool study. Developmental Psychology 2009, 45:1630-1643.
50. 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.
51. Peterson P.L., Fennema P. Effective teaching, student engagement in classroom activities, and sex-related differences in learning mathematics. American Educational Research Journal 1985, 22:309-335.
52. Pickering S., Gathercole S. Working Memory Test Battery for Children (WMTB-C) manual 2001, Psychological Corporation, London.
53. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Development Core Team. (2010). nlme: Linear and nonlinear mixed effects models [documentation for nlme package]. Available at: http://cran.r-project.org/web/packages/nlme/nlme.pdf.
54. Raven J.C., Court J.H., Raven J. Manual for Raven's Progressive Matrices and Vocabulary Scales 1993, H.K. Lewis, London.
55. Rivera S.M., Reiss A.L., Eckert M.A., Menon V. Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex 2005, 15:1779-1790.
56. Rogosa D. A critique of cross-lagged correlation. Psychological Bulletin 1980, 88:245-258.
57. Royer J.M., Tronsky L.N., Chan Y., Jackson S.J., Marchant H. Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemporary Educational Psychology 1999, 24:181-266.
58. Scollon C.N., Diener E. Love, work, and changes in extraversion and neuroticism over time. Journal of Personality and Social Psychology 2006, 91:1152-1165.
59. Foresman Scott Investigations in number, data, and space 1999, Author, Glenview, IL.
60. 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.
61. Siegler R.S. Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development 1988, 59:833-851.
62. Siegler R.S. Emerging minds: The process of change in children's thinking 1996, Oxford University Press, New York.
63. Siegler R.S., Shrager J. Strategy choices in addition and subtraction: How do children know what to do?. The origins of cognitive skills 1984, 229-293. Lawrence Erlbaum, Hillside, NJ. C. Sophian (Ed.).
64. 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.
65. 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.
66. 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.
67. Tofighi D., MacKinnon D.P. RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods 2011, 43:692-700.
68. Tomarken A.J., Waller N.G. Potential problems with "well fitting" models. Journal of Abnormal Psychology 2003, 112:578-598.
69. Walberg H.J. Improving the productivity of America's schools. Educational Leadership 1984, 41:19-27.
70. Wechsler D. Wechsler Abbreviated Scale of Intelligence 1999, PsychCorp, Harcourt Assessment, San Antonio, TX.
71. Wiebe S.A., Espy K.A., Charak D. Using confirmatory factor analysis to understand executive control in preschool children: I. Latent structure. Developmental Psychology 2008, 44:575-587.