The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades

Journal of Experimental Child Psychology

Volumn 79, Issue 2, 2001, Pages 192-227

  Hecht, Steven A ^a   Torgesen, Joseph K ^a   Wagner, Richard K ^a   Rashotte, Carol A ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Arithmetic; Mathematical achievement; Mathematical cognition; Mathematical computation; Phonological processing; Reading and mathematics

Indexed keywords

ARTICLE; CHILD; CHILD DEVELOPMENT; FACTORIAL ANALYSIS; FEMALE; HUMAN; LANGUAGE DEVELOPMENT; LONGITUDINAL STUDY; MALE; MATHEMATICS; MEMORY; PHONETICS; PSYCHOLOGICAL THEORY; READING; UNITED STATES;

CHILD; CHILD DEVELOPMENT; FACTOR ANALYSIS, STATISTICAL; FEMALE; HUMANS; LANGUAGE DEVELOPMENT; LONGITUDINAL STUDIES; MALE; MATHEMATICS; MEMORY; PHONETICS; PSYCHOLOGICAL THEORY; READING; UNITED STATES;

EID: 0035377229     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1006/jecp.2000.2586     Document Type: Article

References (90)

1. Ackerman, P. T., & Dykman, R. A. (1995). Reading-disabled students with and without comorbid arithmetic disability. Developmental Neuropsychology, 11, 351-371.
2. Adams, M. J. (1990). Beginning to read: Thinking & learning about print. Cambridge, MA: MIT Press.
3. Baddeley, A. D. (1986). Working memory. Oxford, UK: Oxford Univ. Press.
4. Baddeley, A. D. (1992). Working memory. Science, 255, 556-559.
5. Badian, N. A. (1983). Dyscalculia and nonverbal disorders of learning. In H. R. Myklebust (Ed.), Progress in learning disabilities (Vol. 5, pp. 235-264). New York: Stratton.
6. Bentler, P. M. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
7. Bisanz, J., Morrison, F. J., & Dunn, M. (1995). Effects of age and schooling on the acquisition of elementary quantitative skills. Developmental Psychology, 31, 221-236.
8. Blachman, B. A. (1997). Foundations of reading acquisition & dyslexia: Implications for early intervention. Mahwah, NJ: Erlbaum.
9. Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
10. Bowers, P. G., & Wolf, M. (1993). Theoretical links between naming speed, precise timing mechanisms, and orthographic skill in dyslexia. Reading & Writing, An Interdisciplinary Journal, 5, 69-85.
11. Bradley, L., & Bryant, P. (1985). Rhyme & reason in reading & spelling. Ann Arbor, MI: Univ. of Michigan Press.
12. Brady, S. A., & Shankweiler, D. P. (Eds.) (1991). Phonological processes in literacy. Hillsdale, NJ: Erlbaum.
13. Brainerd, C. J. (1983). Young children's mental arithmetic errors: A working memory analysis. Child Development, 54, 812-830.
14. Bryant, B. R., & Bryant, D. L. (1983). Test of articulation performance screen. Austin, TX: Pro-Ed.
15. Bryant, P. E., MacLean, M., Bradley, L. L., & Crossland, J. (1990). Rhyme and alliteration, phoneme detection, and learning to read. Developmental Psychology, 26, 429-438.
16. Buchner, A., Steffens, M. C., Innen, L., & Wender, K. F. (1998). Irrelevant auditory material affects counting. Journal of Experimental Psychology: Learning, Memory, & Cognition, 24, 48-67.
17. Bull, R., & 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.
18. Byrne, B. M. (1994). Structural equation modeling with EQS & EQS/Windows: Basic concepts, applications, & programming. Thousand Oaks, CA: Sage.
19. Byrnes, J. P. (1995). Domain specificity and the logic of using general ability as an independent variable or covariate. Merrill-Palmer Quarterly, 41, 1-24.
20. Campbell, J. I. D. (1998). Linguistic influences in cognitive arithmetic: Comment on Noel, Fias, and Brsybaert. Cognition, 67, 353-364.
21. Case, R. (1985). Intellectual development: Birth to adulthood. San Diego, CA: Academic Press.
22. Dark, V. J., & Benbow, C. P. (1991). Differential enhancement of working memory with mathematical versus verbal precocity. Journal of Educational Psychology, 83, 48-60.
23. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
24. Garnett, K., & Fleischner, J. E. (1983). Automatization and basic fact performance of normal and learning disabled children. Learning Disabilities Quarterly, 6, 223-230.
25. Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345-362.
26. 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.
27. Geary, D. C., Brown, S. C., & 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.
28. Geary, D. C., & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47, 175-192.
29. Geary, D. C., Fan, L., & Bow-Thomas, C. C. (1992). Numerical cognition: Loci of ability differences comparing children from China and the United States. Psychological Science, 3, 180-185.
30. Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for mathematical disability. Journal of Experimental Child Psychology, 74, 213-239.
31. Geary, D. C., & Widaman, K. F. (1992). Numerical cognition: On the convergence of componential and psychometric models. Intelligence, 16, 47-80.
32. Ginsburg, H. P. (1997). Mathematics learning disabilities: A view from developmental psychology. Journal of Learning Disabilities, 30, 20-33.
33. Goldman, S. R., Mertz, D. L., & Pellegrino, J. W. (1989). Individual differences in extended practice functions and solution strategies for basic addition facts. Journal of Educational Psychology, 81, 481-496.
34. Goldman, S. R., Pellegrino, J. W., & Mertz, D. L. (1988). Extended practice of basic addition facts: Strategy changes in learning disabled students. Cognition & Instruction, 5, 223-265.
35. Gollob, H. F., & Reichardt, C. S. (1987). Taking account of time lags in causal models. Child Development, 58, 80-92.
36. Hartje, W. (1987). The effect of spatial disorders on arithmetical skills. In G. Deloche & X. Seron (Eds.), Mathematical disabilities: A cognitive neuropsychological perspective (pp. 121-135). Hillsdale, NJ: Erlbaum.
37. Healy, A. F., & Nairne, J. S. (1985). Short-term memory processes in counting. Cognitive Psychology, 17, 417-444.
38. Hecht, S. A. (1998). Toward an information processing account of individual differences in fraction skills. Journal of Educational Psychology, 90, 545-559.
39. Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults. Memory & Cognition, 1097-1107.
40. Hecht, S. A. (2001). Working memory and individual solution processes while solving addition simple arithmetic problems. Manuscript submitted for publication.
41. Hecht, S. A., Burgess, S. R., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2000). Explaining social class differences in growth of reading skills from beginning kindergarten through fourth-grade: The role of phonological awareness, rate of access, and print knowledge. Reading & Writing: An Interdisciplinary Journal, 12, 99-127.
42. Hitch, G. J., & McAuley, E. (1991). Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 82, 375-386.
43. Howell, R., Sidorenko, E., & Jurica, J. (1987). The effects of computer use on the acquisition of multiplication facts by a student with learning disabilities. Journal of Learning Disabilities, 20, 336-341.
44. Kail, R., & Hall, L. K. (1999). Sources of developmental change in children's word-problem performance. Journal of Educational Psychology, 4, 660-668.
45. Kaye, D. B. (1986). The development of mathematical cognition. Cognitive Development, 1, 157-170.
46. Kulak, A. G. (1993). Parallels between math and reading disability: Common issues and approaches. Journal of Learning Disabilities, 26, 666-673.
47. Lemaire, P., Abdi, H., & Fayol, M. (1996). The role of working memory resources in simple cognitive arithmetic. European Journal of Cognitive Psychology, 8, 73-103.
48. Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124, 83-97.
49. Logie, R. H., & Baddeley, A. D. (1987). Cognitive processes in counting. Journal of Experimental Psychology: Learning, Memory, & Cognition, 13, 310-326.
50. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory & Cognition, 22, 395-410.
51. Marsh, R. L., & Hicks, J. L. (1998). Event-based prospective memory and executive control of working memory. Journal of Experimental Psychology: Learning, Memory, & Cognition, 24, 336-349.
52. McLeod, D. B. (1990). Information processing theories and mathematics learning: The role of affect. International Journal of Educational Research, 14, 13-29.
53. McBride-Chang, C., Wagner, R. K., & Chang, L. (1997). Growth modeling of phonological awareness. Journal of Educational Psychology, 89, 621-630.
54. Miura, I. T., Okamoto, Y., Vlahovic-Stetic, V., Kim, C. C., & Han, J. H. (1999). Language supports for children's understanding of numerical fractions: Cross national comparisons. Journal of Experimental Child Psychology, 74, 356-365.
55. Perfetti, C. A., Beck, I., Bell, L., & Hughes, C. (1987). Phonemic knowledge and learning to read are reciprocal: A longitudinal study of first grade children. Merrill-Palmer Quarterly, 33, 283-319.
56. Pressley, M. (1986). The relevance of the good strategy user model to the teaching of mathematics. Educational Psychologist, 21, 139-161.
57. Rasanen, P., & Ahonen, T. (1995). Arithmetic disabilities with and without reading difficulties: A comparison of arithmetic errors. Developmental Neuropsychology, 11, 275-295.
58. Rourke, B. P. (1989). Nonverbal learning disabilities: The syndrome & the model. New York: Guilford.
59. Rourke, B. P. (1993). Arithmetic disabilities, specific and otherwise: A neuropsychological perspective. Journal of Learning Disabilities, 26, 214-226.
60. Rourke, B. P., & Conway, J. A. (1997). Disabilities of arithmetic and mathematical reasoning: Perspectives from neurology and neuropsychology. Journal of Learning Disabilities, 30, 34-46.
61. Sattler, J. M. (1988). Assessment of children (3rd ed.). San Diego, CA: Academic Press.
62. Share, D. L., Moffitt, T. E., & Silva, P. A. (1988). Factors associated with arithmetic-and-reading disability and specific arithmetic disability. Journal of Learning Disabilities, 21, 313-320.
63. Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60, 973-980.
64. Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 116, 250-264.
65. Siegler, R. S. (1988). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development, 59, 833-851.
66. Siegler, R. S., & Shipley, E. (1995). Variation, selection, and cognitive change. In G. Halford & T. Simon (Eds.), Developing cognitive competence: New approaches to process modeling (pp. 31-76). Hillsdale, NJ: Erlbaum.
67. Siegler, R. S., & Shrager, J. (1984). Strategy choice in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229-293). Hillsdale, NJ: Erlbaum.
68. Silver, C. H., Pennett, H. D., Black, J. L., Fair, G. W., & Balise, R. R. (1999). Stability of arithmetic disability subtypes. Journal of Learning Disabilities, 32, 108-120.
69. Stanovich, K. E. (1986). Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. Reading Research Quarterly, 21, 360-407.
70. Stanovich, K. E., Cunningham, A. E., & Cramer, B. B. (1984). Assessing phonological awareness in kindergarten children: Issues of task comparability. Journal of Experimental Child Psychology, 38, 175-190.
71. Stevenson, H. W., Parker, T., Wilkinson, A., Hegion, A., & Fish, E. (1976). Longitudinal study of individual differences in cognitive development and scholastic achievement. Journal of Educational Psychology, 68, 377-400.
72. Swanson, H. L., Ashbaker, M. H., & Lee, C. (1996). Learning disabled readers' working memory as a function of processing demands. Journal of Experimental Child Psychology, 61, 242-275.
73. Thorndike, R. L., Hagen, E. P., & Sattler, J. M. (1986a). Guide for administering & scoring the Stanford-Binet intelligence scale (4th ed.). Chicago, IL: Riverside.
74. Thorndike, R. L., Hagen, E. P., & Sattler, J. M. (1986b). Stanford-Binet intelligence scale (4th ed.). Chicago, IL: Riverside.
75. Torgesen, J. K. (1993). Variations on theory in learning disabilities. In G. R. Lyon, D. B. Gray, J. F. Kavanagh, & N. A. Krasnegor (Eds.), Better understanding learning disabilities (pp. 153-170). Baltimore, MD: Paul H. Brookes.
76. Torgesen, J. K. (1996). A model of memory from an information processing perspective: The special case of phonological memory. In G. R. Lyon & N. A. Krasnegor (Eds.), Attention, memory, & executive function (pp. 157-184). Baltimore, MD: Paul H. Brookes.
77. Torgesen, J. K., & Houck, G. (1980). Processing deficiencies in learning disabled children who perform poorly on the digit span task. Journal of Educational Psychology, 72, 141-160.
78. Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (1994). Longitudinal studies of phonological processing and reading. Journal of Learning Disabilities, 27, 276-286.
79. Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (1999). Prevention and remediation of severe reading disabilities: Keeping the end in mind. Scientific Studies of Reading, 3, 217-234.
80. Torgesen, J. K., Wagner, R. K., Rashotte, C. A., Burgess, S. R., & Hecht, S. A. (1997). The contributions of phonological awareness and rapid automatic naming ability to the growth of word reading skills in second- to fifth-grade children. Scientific Studies of Reading, 1, 161-185.
81. Torgesen, J. K., Wagner, R. K., Simmons, K., & Laughon, P. (1990). Identifying phonological coding problems in disabled readers: Naming, counting, or span measures. Learning Disability Quarterly, 13, 236-243.
82. Wagner, R. K., & Torgesen, J. K. (1987). The nature of phonological processing and its causal role in the acquisition of reading skills. Psychological Bulletin, 101, 192-212.
83. Wagner, R. K., Torgesen, J. K., Laughon, P., Simmons, K., & Rashotte, C. (1993). The development of young readers' phonological processing abilities. Journal of Educational Psychology, 85, 83-103.
84. Wagner, R. K., Torgesen, J. K., & Rashotte, C. A. (1994). Development of reading-related phonological processing abilities: New evidence of bidirectional causality from a latent variable longitudinal study. Developmental Psychology, 30, 73-87.
85. Wagner, R. K., Torgesen, J. K., Rashotte, C. A., Hecht, S. A., Barker, T. A., Burgess, S. R., Donahue, J., & Garon, T. (1997). Changing relations between phonological processing abilities and word-level reading as children develop from beginning to skilled readers: A five year longitudinal study. Developmental Psychology, 33, 468-479.
86. Widaman, K. F., & Little, T. D. (1992). The development of skill in mental arithmetic: An individual differences approach. In J. I. D. Campbell (Ed.), The nature & origins of mathematical skills. Amsterdam: Elsevier.
87. Widaman, K. F., Little, T. D., Geary, D. C., & Cormier, P. (1992). Individual differences in the development of skill in mental addition: Internal and external validation of chronometric models. Learning & Individual Differences, 4, 167-213.
88. Woodcock, R. W (1987). Woodcock reading mastery tests - revised. Circle Pines, MN: American Guidance Service.
89. Woodcock, R. W., & Johnson, M. B. (1977). Woodcock-Johnson Psycho-Educational Battery. Circle Press, MN: American Guidance Service Inc.
90. Zentall, S. S. (1990). Fact-retrieval and math problem solving by learning disabled, attention-disordered, and normal adolescents. Journal of Educational Psychology, 82, 856-865.