Sources of individual differences in fraction skills

Journal of Experimental Child Psychology

Volumn 86, Issue 4, 2003, Pages 277-302

  Hecht, Steven A ^a   Close, Linda ^a   Santisi, Mirtha ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Computation; Estimation; Fractions; Mathematical achievement; Mathematical cognition; Word problem solving

Indexed keywords

ARTICLE; CHILD; CHILD BEHAVIOR; COGNITION; FEMALE; HUMAN; MALE; MATHEMATICS; MEMORY; PROBLEM SOLVING;

CHILD; CHILD BEHAVIOR; COGNITION; FEMALE; HUMANS; MALE; MATHEMATICS; MEMORY; PROBLEM SOLVING;

EID: 0242635984     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2003.08.003     Document Type: Article

References (89)

1. Ackerman P.L. Traits and knowledge as determinants of learning and individual differences: Putting it all together In Ackerman P.L. Kyllonen P.C. Roberts R.D. (Eds.), Learning and individual differences: Process, trait, and content determinants 1999 437-460 American Psychological Association Washington, DC
2. Ashcraft M.H. Cognitive arithmetic: A review of data and theory Cognition 44 1992 75-106
3. Ashcraft M.H. Kirk E.P. The relationships among working memory, math anxiety, and performance Journal of Experimental Psychology: General 130 2001 224-237
4. Baddeley A.D. Working memory Science 255 1992 556-559
5. Barker T.A. Torgesen J.K. Wagner R.K. The role of orthographic processing skills on five different reading tasks Reading Research Quarterly 27 1992 334-345
6. Baron R.M. Kenny D.A. The mediator-moderator distinction in social psychology: Conceptual, strategic, and statistical considerations Journal of Personality and Social Psychology 51 1986 1173-1182
7. Bennett R.E. Gottesman R.L. Rock D.A. Cerullo F. Influence of behavior perceptions and gender on teachers' judgments of students' academic skill Journal of Educational Psychology 85 1993 347-356
8. Bisanz J. LeFevre J. Strategic and nonstrategic processing in the development of mathematical cognition In Bjorklund D.F. (Ed.), Children's strategies: Contemporary views of cognitive development 1990 213-244 Erlbaum Hillsdale, NJ
9. Bisanz J. LeFevre J.A. Understanding elementary mathematics In Campbell J.I.D. (Ed.), The nature and origins of mathematical skill 1992 113-136 Elsevier Amsterdam
10. Bisanz J. Morrison F.J. Dunn M. Effects of age and schooling on the acquisition of elementary quantitative skills Developmental Psychology 31 1995 221-236
11. Bollen K.A. Structural equations with latent variables 1989 John Wiley & Sons New York
12. Brady S.A. Shankweiler D.P. (Eds.), Phonological processes in literacy 1991 Erlbaum Hillsdale, NJ
13. Buchner A. Steffens M.C. Irmen L. Wender K.F. Irrelevant auditory material affects counting Journal of Experimental Psychology: Learning, Memory, & Cognition 24 1998 48-67
14. Bull R. Johnston R.S. Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory Journal of Experimental Child Psychology 65 1997 1-24
15. Byrne B.M. Structural equation modeling with EQS and EQS/Windows: Basic concepts, applications, and programming 1994 Sage Thousand Oaks
16. Byrnes J.P. Wasik B.A. Role of conceptual knowledge in mathematical and procedural learning Developmental Psychology 27 1991 777-786
17. Campbell J.I.D. Graham D.J. Mental multiplication skill: Structure, process, and acquisition Canadian Journal of Psychology 39 1985 338-366
18. Carpenter T.P. Conceptual knowledge as a foundation for procedural knowledge In Hiebert J. (Ed.), Conceptual and procedural knowledge 1986 1-27 Erlbaum Hillsdale, NJ
19. Carroll J.B. Human cognitive abilities: A survey of factor-analytic studies 1993 Cambridge University Press New York
20. Cawley J.C. Secondary school mathematics for the learning disabled 1985 Aspen Systems Corp Rockville, MD
21. Chen X. Rubin K.H. Li D. Relation between academic achievement and social adjustment: Evidence from Chinese children Developmental Psychology 33 1997 518-525
22. Cooney J.B. Swanson H.L. Individual differences in memory for mathematical story problem: Memory span and problem perception Journal of Educational Psychology 82 1990 570-577
23. Cramer K.A. Post T.R. delMas R.C. Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum Journal for Research in Mathematics Education 33 2002 111-144
24. Dark V. Benbow C.P. Enhanced problem translation and short term memory: Components of mathematical talent Journal of Educational Psychology 82 1990 420-429
25. Demaray M.K. Ruffalo S.L. Carlson J. Buss R.T. Olson A.E. McManus S.M. Leventhal A. Social skills assessment: A comparative evaluation of six published rating scales School Psychology Review 24 1995 648-671
26. English L.D. Halford G.S. Mathematics education: Models and processes 1995 Erlbaum Mahwah, NJ
27. Gagne R.M. Some issues in the psychology of mathematics instruction Journal for Research in Mathematics Education 14 1983 275-282
28. Geary D.C. Mathematical disabilities: Cognitive, neuropsychological, and genetic components Psychological Bulletin 114 1993 345-362
29. 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 27 1991 787-797
30. Geary D.C. Hoard M.K. Hamson C.O. Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for mathematical disability Journal of Experimental Child Psychology 74 1999 213-239
31. Gelman R. Meck E. Preschoolers' counting: Principles before skill Cognition 13 1983 343-359
32. Ginsburg H.P. Mathematics learning disabilities: A view from developmental psychology Journal of Learning Disabilities 30 1997 20-33
33. Goldman S.R. Hasselbring T.S. Achieving meaningful mathematics literacy for students with LD Journal of Learning Disabilities 30 1997 198-208
34. Goldman S.R. Mertz D.L. Pelligrino J.W. Individual differences in extended practice functions and solution strategies for basic addition facts Journal of Educational Psychology 81 1989 481-496
35. Goodman L.A. On the exact variance of products Journal of the American Statistical Association 55 1960 708-713
36. Green K.D. Forehand R.L. Beck S.J. Vosk B. An assessment of the relationship among measures of children's social competence and children's academic achievement Child Development 51 1980 1149-1156
37. Graham J.D. Campbell J.L. Network interference and number-fact retrieval: Evidence from children's alphaplication Canadian Journal of Psychology 46 1992 65-91
38. Gresham F.M. Elliott S.N. Social skills rating system 1990 American Guidance Service Circle Pines, MN
39. Hamann M.S. Ashcraft M.H. Textbook presentations of the basic addition facts Cognition and Instruction 3 1986 173-192
40. Hecht S.A. Toward an information processing account of individual differences in fraction skills Journal of Educational Psychology 90 1998 545-559
41. Hecht S.A. Individual solution processes while solving addition and multiplication math facts in adults Memory & Cognition 1999 1097-1107
42. Hecht S.A. Counting on working memory in simple arithmetic when counting is used for problem solving Memory & Cognition 30 2002 447-455
43. Hecht S.A. Greenfield D.B. Comparing the predictive validity of first grade teacher ratings and reading related tests on third grade levels of reading skills in young children exposed to poverty School Psychology Review 30 2001 50-69
44. Hecht S.A. Torgesen J.K. Wagner R.K. Shotte C.A. The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second- to fifth-grade Journal of Experimental Child Psychology 79 2001 192-227
45. Hegarty M. Mayer R.E. Monk C.A. Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers Journal of Educational Psychology 87 1995 18-32
46. Hiebert J. LeFevre P. Conceptual and procedural knowledge in mathematics: An introductory analysis In Hiebert J. (Ed.), Conceptual and procedural knowledge 1986 1-27 Erlbaum Hillsdale, NJ
47. Hiebert J. Wearne D. Procedures over concepts: the acquisition of decimal number knowledge In: Hiebert J. (Ed.), Conceptual and procedural knowledge: The case of mathematics 1986 199-223 LEA Hillsdale, NJ
48. Hitch G.J. McAuley E. Working memory in children with specific arithmetical learning difficulties British Journal of Psychology 82 1991 375-386
49. Jordan N.C. Hanich L.B. Kaplan D. Arithmetic fact mastery in young children: A longitudinal investigation Journal of Experimental Child Psychology 85 2003 103-119
50. Just M.A. Carpenter P.A. A capacity theory of comprehension: Individual differences in working memory Psychological Review 99 1992 122-149
51. Kail R. Hall L.K. Sources of developmental change in children's word-problem performance Journal of Educational Psychology 4 1999 660-668
52. Kenny, D. A., Kashy, D. A., & Bolger, N. (1998). Data analysis in social psychology. In D. Gilbert, S. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 1, 4th ed., pp. 233-265). Boston, MA: McGraw-Hill
53. Kieran T.E. Personal knowledge of rational numbers: Its intuitive and formal development In Hiebert J. Behr M. (Eds.), Number concepts and operations in the middle grades 1988 162-181 National Council of Teachers of Mathematics Reston, VA
54. Kilpatrick J. Swafford J. Findell B. Adding it up: Helping children learn mathematics 2001 National Academy Press Washington, DC
55. Kintsch W. Greeno J.G. Understanding and solving word arithmetic problems Psychological Review 92 1985 109-129
56. Koshmider J.W. Ashcraft M.H. Emergence of information-retrieval strategies in numerical cognition: A developmental study Cognition & Instruction 3 1991 127-150
57. Kulak A.G. Parallels between math and reading disability: Common issues and approaches Journal of Learning Disabilities 26 1993 666-673
58. LeFevre J.A. Bisanz J. Daley K.E. Buffone L. Sadesky G.S. Multiple solution routes to solution of single-digit multiplication problems Journal of Experimental Psychology: General 125 1996 284-306
59. LeFevre J.A. Greenham S.L. Waheed N. The development of procedural and conceptual knowledge in computational estimation Cognition & Instruction 11 1993 95-132
60. Mack N.K. Learning fractions with understanding: Building on informal knowledge Journal for Research in Mathematics Education 21 1990 16-32
61. 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 7 2002 83-104
62. McKinney J.D. Speece D.L. Academic consequences and longitudinal stability of behavioral subtypes of learning disabled children Journal of Educational Psychology 78 1986 369-372
63. McLeod D.B. Information processing theories and mathematics learning: The role of affect International Journal of Educational Research 14 1990 13-29
64. National Assessment of Educational Progress. (1990). The fifth national mathematics assessment. Denver, CO: Author
65. Ni Y. How valid is it to use number lines to measure children's conceptual knowledge about rational number? Educational Psychology 20 2000 139-152
66. Ni Y. Semantic domains of rational numbers and the acquisition of fraction equivalence Contemporary Educational Psychology 26 2001 400-417
67. Peck D.M. Jencks S.M. Conceptual issues in the teaching and learning of fractions Journal for Research in Mathematics Education 12 1981 339-348
68. Pressley M. The relevance of the good strategy user model to the teaching of mathematics Educational Psychologist 21 1986 139-161
69. Putnam R.T. Heaton R.M. Prewat R.S. Remillard J. Teaching mathematics for understanding Elementary School Journal 93 1992 213-228
70. Rittle-Johnson B. Alibali M.W. Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology 91 1999 175-189
71. Rittle-Johnson B. Siegler R.S. Alibali M.W. Developing conceptual understanding and procedural skill in mathematics: An iterative process Journal of Educational Psychology 93 2001 346-362
72. Rittle-Johnson B. Siegler R.S. The relations between conceptual and procedural knowledge in learning mathematics: A review In Donlan C. (Ed.), The development of mathematical skill 1998 75-110 Psychology Press Hove, England
73. Siegler R.S. The perils of averaging data over strategies: An example from children's addition Journal of Experimental Psychology: General 116 1987 250-264
74. Siegler R.S. Strategy choice procedures and the development of multiplication skill Journal of Experimental Psychology: General 117 1988 258-275
75. Siegler R.S. Shipley E. Variation, selection, and cognitive change In Halford G. Simon T. (Eds.), Developing cognitive competence: New approaches to process modeling 1995 31-76 Erlbaum Hillsdale, NJ
76. Silver E.A. Using conceptual and procedural knowledge: A focus on relationships In Hiebert J. (Ed.), Conceptual and procedural knowledge 1986 181-198 Erlbaum Hillsdale, NJ
77. Smith J.P. Competent reasoning with rational numbers Cognition & Instruction 13 1995 3-50
78. Stanovich K. A model for studies of reading disability Developmental Review 13 1993 225-245
79. Stern E. What makes certain arithmetic word problems involving the comparison of sets so difficult for children? Journal of Educational Psychology 85 1993 7-23
80. Stevenson H. Lee S.S. Stigler J. The mathematics achievement of Chinese, Japanese, and American children Science 56 1986 693-699
81. 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 79 2001 294-321
82. Torgesen J.K. Cognitive and behavioral characteristics of children with learning disabilities 1990 Pro-ed Austin, TX
83. Torgesen J.K. Variations on theory in learning disabilities In Lyon G.R. Gray D.B. Kavanagh J.F. Krasnegor N.A. (Eds.), Better understanding learning disabilities 1993 153-170 Paul H. Brookes Publishing Co Baltimore, MD
84. Torgesen J.K. A model of memory from an information processing perspective: The special case of phonological memory In Lyon G.R. Krasnegor N.A. (Eds.), Attention, memory, and executive function 1996 157-184 Paul H. Brookes Publishing Co Baltimore, MD
85. Torgesen J.K. Wagner R.K. Rashotte C.A. Burgess S.R. Hecht S.A. 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 1997 161-185
86. Traub R.E. Reliability for the social sciences: Theory and applications 1994 Sage Thousand Oaks, CA
87. Wearne D. Hiebert J. Cognitive changes during conceptually based instruction on decimal fractions Journal of Educational Psychology 81 1989 507-513
88. Wearne D. Kouba V.L. Rational numbers In Silver E.A. Kenney P.A. (Eds.), Results from the seventh mathematics assessment of the National Assessment of Educational Progress 2000 163-191 National Council of Teachers of Mathematics Reston, VA
89. Wentzel K.R. Relations between social competence and academic achievement in early adolescence Child Development 62 1991 1066-1078