Basic Calculation Proficiency and Mathematics Achievement in Elementary School Children

Journal of Educational Psychology

Volumn 103, Issue 4, 2011, Pages 786-803

  Cowan, Richard ^a   Donlan, Chris ^b   Shepherd, Donna Lynn ^a   Cole Fletcher, Rachel ^a   Saxton, Matthew ^a   Hurry, Jane ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Mathematical achievement; Reading; Simple addition; Working memory; Young children

Indexed keywords

EID: 82155170665     PISSN: 00220663     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0024556     Document Type: Article

References (76)

1. Andersson U., Lyxell B. Working memory deficit in children with mathematical difficulties: A general or specific deficit. Journal of Experimental Child Psychology 2007, 96:197-228. doi: 10.1016/j.jecp.2006.10.001.
2. Askew M. Teaching primary mathematics: A guide for newly qualified and student teachers 1998, Hodder & Stoughton, London, England.
3. Baddeley A. Exploring the central executive. Quarterly Journal of Experimental Psychology Section A: Human Experimental Psychology 1996, 49:5-28. doi: 10.1080/027249896392784.
4. Baddeley A.D., Hitch G.J. Working memory. Recent advances in learning and motivation 1974, 8:47-90. Academic Press, New York, NY. G.A. Bower (Ed.).
5. Baroody A.J. Children's relational knowledge of addition and subtraction. Cognition and Instruction 1999, 17:137-175. doi: 10.1207/S1532690XCI170201.
6. Baroody A.J. The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. The development of arithmetic concepts and skills: Constructing adaptive expertise 2003, 1-33. Erlbaum, Mahwah, NJ. A.J. Baroody, A. Dowker (Eds.).
7. Baroody A.J. Why children have difficulty mastering the basic number combinations and how to help them. Teaching Children Mathematics 2006, 13:22-31.
8. Baroody A.J., Ginsburg H.P. The relationship between initial meaningful and mechanical knowledge of arithmetic. Conceptual and procedural knowledge: The case of mathematics 1986, 75-112. Erlbaum, Hillsdale, NJ. J. Hiebert (Ed.).
9. Bishop D.V.M. TROG-E: Test for Reception of Grammar, Version 2 (electronic) 2005, Harcourt Assessment, Oxford, England.
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. Cahan S., Cohen N. Age versus schooling effects on intelligence development. Child Development 1989, 60:1239-1249. doi: 10.2307/1130797.
12. Cahan S., Greenbaum C., Artman L., Deluy N., Gappel-Gilon Y. The differential effects of age and first grade schooling on the development of infralogical and logico-mathematical concrete operations. Cognitive Development 2008, 23:258-277. doi: 10.1016/j.cogdev.2008.01.004.
13. Campbell D.T., Kenny D.A. A primer on regression artifacts 1999, Guilford Press, New York, NY.
14. Canobi K.H., Reeve R.A., Pattison P.E. The role of conceptual understanding in children's addition problem solving. Developmental Psychology 1998, 34:882-891. doi: 10.1037/0012-1649.34.5.882.
15. Case R., Okamoto Y., Griffin S., McKeough A., Bleiker C., Henderson B., Stephenson K.M. The role of central conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development 1996, 61(1-2, Serial No. 246). doi: 10.1111/j.1540-5834.1996.tb00535.x.
16. Cowan R. Does it all add up? Changes in children's knowledge of addition facts, strategies, and principles. The development of arithmetic concepts and skills: Constructing adaptive expertise 2003, 35-74. Erlbaum, Mahwah, NJ. A.J. Baroody, A. Dowker (Eds.).
17. Cowan R., Donlan C., Newton E.J., Lloyd D. Number skills and knowledge in children with specific language impairment. Journal of Educational Psychology 2005, 97:732-744. doi: 10.1037/0022-0663.97.4.732.
18. Table 19: Maintained nursery and primary schools (1): School meal arrangements (2) January 2007 by Local Authority area and Government Office region in England 2007, Department for Children Schools and Families, Retrieved from http://www.dcsf.gov.uk/rsgateway/DB/SFR/s000744/index.shtml.
19. Table 7a: Pupils with statements of special educational needs (SEN) by type of school 2010, Department for Education, Retrieved from http://www.education.gov.uk/rsgateway/DB/SFR/s000925/index.shtml.
20. Table 7b: Pupils with special educational needs (SEN) without statements by type of school 2010, Department for Education, Retrieved from http://www.education.gov.uk/rsgateway/DB/SFR/s000925/index.shtml.
21. The National Numeracy Strategy: Framework for teaching mathematics from Reception to Year 6 1999, Department for Education and Employment, Cambridge University Press, Cambridge, England.
22. De Vaus D. Surveys in social research 2002, Routledge, London, England. 5th ed.
23. Donlan C., Cowan R., Newton E.J., Lloyd D. The role of language in mathematical development: Evidence from children with specific language impairments. Cognition 2007, 103:23-33. doi: 10.1016/j.cognition.2006.02.007.
24. Dowker A. Individual differences in arithmetic 2005, Psychology Press, Hove, England, doi: 10.4324/9780203324899.
25. Dunn L.M., Dunn L.M., Whetton C., Burley J. The British Picture Vocabulary Scale 1997, NFER-Nelson, London, England. 2nd ed.
26. Durand M., Hulme C., Larkin R., Snowling M. The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds. Journal of Experimental Child Psychology 2005, 91:113-136. doi: 10.1016/j.jecp.2005.01.003.
27. Field A. Discovering statistics using SPSS 2009, Sage, London, England. 3rd ed.
28. 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.
29. Gathercole S.E., Pickering S.J. Assessment of working memory in 6- and 7-year-old children. Journal of Educational Psychology 2000, 92:377-390. doi: 10.1037/0022-0663.92.2.377.
30. Geary D.C. Mathematical disabilities: Cognitive, neuropsychological and genetic components. Psychological Bulletin 1993, 114:345-362. doi: 10.1037/0033-2909.114.2.345.
31. Geary D.C. Mathematics and learning disabilities. Journal of Learning Disabilities 2004, 37:4-15. doi: 10.1177/00222194040370010201.
32. Geary D.C., Brown S.C. Cognitive addition: Strategy choice, and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology 1991, 27:398-406. doi: 10.1037/0012-1649.27.3.398.
33. Geary D.C., Burlingham-Dubree M. External validation of the strategy choice model of addition. Journal of Experimental Child Psychology 1989, 47:175-192. doi: 10.1016/0022-0965(89)90028-3.
34. Geary D.C., Hoard M.K., Byrd-Craven J., DeSoto M.C. 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.
35. 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.
36. Gersten R., Jordan N.C., Flojo J.R. Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities 2005, 38:293-304. doi: 10.1177/00222194050380040301.
37. Griffin, S. (1997). Building conceptual bridges: Creating more powerful models to improve mathematics learning and teaching. Year 2 report submitted to the James S. McDonnell Foundation. Unpublished manuscript.
38. Griffin S. Fostering the development of whole-number sense: Teaching mathematics in the primary grades. How students learn: History, mathematics, and science in the classroom 2005, 257-308. The National Academies Press, Washington, DC. M.S. Donovan, J.D. Bransford (Eds.).
39. Hanich L.B., Jordan N.C., Kaplan D., Dick J. Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology 2001, 93:615-626. doi: 10.1037/0022-0663.93.3.615.
40. Hecht S.A. Group differences in adult simple arithmetic: Good retrievers, not-so-good retrievers, and perfectionists. Memory & Cognition 2006, 34:207-216. doi: 10.3758/BF03193399.
41. Hecht S.A., Torgesen J.K., Wagner R.K., Rashotte C.A. 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 2001, 79:192-227. doi: 10.1006/jecp.2000.2586.
42. Hitch G.J. The numerical abilities of industrial trainee apprentices. Journal of Occupational Psychology 1978, 51:163-176.
43. Hitch G.J., Towse J.N., Hutton U. What limits children's working memory span? Theoretical accounts and applications for scholastic development. Journal of Experimental Psychology: General 2001, 130:184-198. doi: 10.1037/0096-3445.130.2.184.
44. 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. doi: 10.1016/S0022-0965(03)00032-8.
45. Jordan N.C., Hanich L.B., Kaplan D. A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development 2003, 74:834-850. doi: 10.1111/1467-8624.00571.
46. Jordan N.C., Kaplan D., Locuniak M.N., Ramineni C. Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice 2007, 22:36-46. doi: 10.1111/j.1540-5826.2007.00229.x.
47. Jordan N.C., Kaplan D., Ramineni C., Locuniak M.N. Development of number combination skill in the early school years: When do fingers help?. Developmental Science 2008, 11:662-668. doi: 10.1111/j.1467-7687.2008.00715.x.
48. 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. doi: 10.1177/002221949703000606.
49. Kail R., Hall L.K. Sources of developmental change in children's word-problem performance. Journal of Educational Psychology 1999, 91:660-668. doi: 10.1037/0022-0663.91.4.660.
50. Kline P. The handbook of psychological testing 1999, Routledge, London, England. 2nd ed.
51. LeFevre J., Sadesky G.S., Bisanz J. Selection of procedures in mental addition: Reassessing the problem-size effect in adults. Journal of Experimental Psychology: Learning, Memory, and Cognition 1996, 22:216-230. doi: 10.1037/0278-7393.22.1.216.
52. Meyer M.L., Salimpoor V.N., Wyu S.S., Geary D.C., Menon V. Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders. Learning & Individual Differences 2010, 20:101-109. doi: 10.1016/j.lindif.2009.08.004.
53. Montgomery J.W., Magimairaj B.M., Finney M.C. Working memory and specific language impairment: An update on the relation and perspectives on assessment and treatment. American Journal of Speech-Language Pathology 2010, 19:78-94. doi: 10.1044/1058-0360(2009/09-0028).
54. Mullis I.V.S., Martin M.O., Foy P. TIMSS 2007 international mathematics report: Findings from IEA's Trends in International Mathematics and Science Study at the fourth and eighth grades 2009, TIMSS & PIRLS International Study Center, Boston College, Chestnut Hill, MA. Rev. ed.
55. Noble M., McLennan D., Wilkinson K., Whitworth A., Barnes H., Dibben C. The English Indices of Deprivation 2007 2008, Communities and Local Government, London, England.
56. Pickering S.J., Gathercole S.E. Working Memory Test Battery for Children (WMTB-C) 2001, The Psychological Corporation, London, England.
57. Preacher K.J., Hayes A.F. Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods 2008, 40:879-891. doi: 10.3758/BRM.40.3.879.
58. Reddick M. Behaviour and alternative education review: Executive summary and recommendations 2010, Retrieved from http://www.rbwm.gov.uk/public/meetings_100705_cslosp_behaviour_review_appendix.pdf.
59. Reys R.E., Suydam M.N., Lindquist M.M., Smith N.L. Helping children learn mathematics 1998, Allyn & Bacon, Boston, MA. 5th ed.
60. Rittle-Johnson B., Siegler R.S. The relation between conceptual and procedural knowledge in learning mathematics: A review. The development of mathematical skills 1998, 75-110. Psychology Press, Hove, England. C. Donlan (Ed.).
61. Russell R.L., Ginsburg H.P. Cognitive analysis of children's mathematical difficulties. Cognition and Instruction 1984, 1:217-244. doi: 10.1207/s1532690xci0102_3.
62. Savage R., Lavers N., Pillay V. Working memory and reading difficulties: What we know and what we don't know about the relationship. Educational Psychology Review 2007, 19:185-221. doi: 10.1007/s10648-006-9024-1.
63. 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.
64. Siegler R.S. Strategy choices in subtraction. Cognitive processes in mathematics 1987, 81-106. Clarendon, Oxford, England. J.A. Sloboda, D. Rogers (Eds.).
65. Siegler R.S. Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development 1988, 59:833-851. doi: 10.2307/1130252.
66. Siegler R.S. Emerging minds: The process of change in children's thinking 1996, Oxford University Press, Oxford, England.
67. Siegler R.S. Implications of cognitive science research for mathematics education. A research companion to skills and standards for school mathematics 2003, 219-233. NCTM, Reston, VA. J. Kilpatrick, W.B. Martin, D.E. Schifter (Eds.).
68. Siegler R.S., Shipley C. Variation, selection, and cognitive change. Developing cognitive competence: New approaches to process modeling 1995, 31-76. Erlbaum, Hillsdale, NJ. T. Simon, G. Halford (Eds.).
69. Siegler R.S., Shrager J. Strategy choices in addition and subtraction: How do children know what to do?. Origins of cognitive skills 1984, 229-293. Erlbaum, Hillsdale, NJ. C. Sophian (Ed.).
70. Siegler R.S., Stern E. Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General 1998, 127:377-397. doi: 10.1037/0096-3445.127.4.377.
71. Stanovich K.E. Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. Reading Research Quarterly 1986, 21:360-406. doi: 10.1598/RRQ.21.4.1.
72. Swanson H.L. Generality and modifiability of working memory among skilled and less skilled readers. Journal of Educational Psychology 1992, 84:473-488. doi: 10.1037/0022-0663.84.4.473.
73. Torgesen J.K., Wagner R.K., Rashotte C.A. Test of Word Reading Efficiency 1999, Pro-Ed, Austin, TX.
74. Wechsler D. Wechsler Intelligence Scale for Children-Third UK edition 1992, The Psychological Corporation, London, England.
75. Wechsler D. Wechsler Individual Achievement Test-Second UK Edition 2005, Harcourt Assessment, Oxford, England.
76. Woodcock R.W., McGrew K.S., Mather N. Woodcock-Johnson III Tests of Cognitive Abilities 2001, Riverside, Itasca, IL.