Counting Skills and Number Concepts of Students with Moderate Intellectual Disabilities

International Journal of Disability, Development and Education

Volumn 50, Issue 3, 2003, Pages 325-345

  Bashash, Laaya ^a   Outhred, Lynne ^b   Bochner, Sandra ^b  

^a SHIRAZ UNIVERSITY   (Iran)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344197681     PISSN: 1034912X     EISSN: None     Source Type: Journal    
DOI: 10.1080/1034912032000120480     Document Type: Article

References (60)

1. AMERICAN ASSOCIATION ON MENTAL RETARDATION. (2002). Mental retardation: Definition, classification, and systems of support (10th ed.). Washington, DC: Author.
2. BAROODY, A.J. (1986). Counting ability of moderately and mildly handicapped children. Education and Training of the Mentally Retarded, 21, 289-300.
3. BAROODY, A.J. (1987). Children's mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teachers College Press.
4. BAROODY, A.J. (1988). Number-comparison learning by children classified as mentally retarded. American Journal on Mental Retardation, 92, 461-471.
5. BAROODY, A.J. (1992). The development of preschoolers' counting skills and principles. In J. BIDEAUD, C. MELJAC, & J-P. FISCHER (Eds.), Pathways to number: Children's developing numerical abilities (pp. 99-126). Hillsdale, NJ: Laurence Erlbaum.
6. BAROODY, A.J. (1993). The relationship between the order-irrelevance principle and counting skill. Journal for Research in Mathematics Education, 24, 415-427.
7. BAROODY, A.J. (1995). The role of the number-after rule in the invention of computational shortcuts. Cognition and Instruction, 13, 189-219.
8. BAROODY, A.J. (1996). Self-invented addition strategies by children with mental retardation. American Journal of Mental Retardation, 101, 72-89.
9. BAROODY, A.J. (1999). The development of basic counting, number, and arithmetic knowedge among children classified as mentally handicapped. In I.M. GLIDDEN (Ed.), International review of research on mental retardation (pp. 51-103). San Diego, CA: Academic.
10. BAROODY, A.J., & PRICE, J. (1983). The development of the number-word sequence in the counting of three-year-olds. Journal of Research in Mathematics Education, 14, 361-368.
11. BAROODY, A.J., & SNYDER, P. (1983). A cognitive analysis of basic arithmetic abilities of TMR children. Education and Training of the Mentally Retarded, 18, 253-259.
12. BASHASH, L. (1997). Counting skills and concepts of number in children with moderate intellectual disabilities. Unpublished doctoral dissertation, Macquarie University, Sydney.
13. BASHASH, L., & OUTHRED, L. (1996). Number comparison skills of children with moderate intellectual disabilities. In P.C. CLARKSON (Ed.), Proceedings of the Nineteenth Annual Conference of the Mathematics Education Research Group of Australasia (pp. 72-79). Melbourne: Mathematics Education Research Group of Australasia.
14. BERRY, P., FRENEWEG, G., GIBSON, D., & BROWN, R.I. (1984). Mental development of adults with Down syndrome. American Journal of Mental Deficiency, 89, 252-256.
15. BOCHNER, S., OUTHRED, L., PIETERSE, M., & BASHASH, L. (2002). Numeracy and money management skills in young adults with Down syndrome. In M. CUSKELLY, A. JOBLING & S. BUCKLEY (Eds.), Down syndrome across the life span (pp. 93-106). London: Whurr.
16. BROWN, A.L., & DELOACHE, J.S. (1978). Skills, plans and self-regulation. In R. S. SIEGLER (Ed.), Children's thinking: What develops? (pp. 3-55). Hillsdale, NJ: Erlbaum.
17. CARR, J. (1995). Down's syndrome: Children growing up. Cambridge, UK: Cambridge University Press.
18. CASE, R. (1985). Intellectual development: Birth to adulthood. Orlando, FL: Academic Press.
19. CAYCHO, L., GUNN, P., & SIEGEL, M. (1991). Counting by children with Down syndrome. American Journal on Mental Retardation, 95, 575-583.
20. CLEMENTS, D.H. (1984). Training effects on the development and generalisation of Piagetian logical operations and knowledge of number. Journal of Educational Psychology, 76, 766-776.
21. CORNWELL, A.C. (1974). Development of language, abstraction and numerical concept formation in Down's syndrome children. American Journal of Mental Deficiency, 79, 179-190.
22. COWAN, R., FOSTER, C.M., & AL-SUBAIDI, A.S. (1993). Encouraging children to count. British Journal of Developmental Psychology, 11, 411-420.
23. FREDERICK-DUGAN, A., TEST, D.W., & VARN, L. (1991). Acquisition and generalisation of purchasing skills using a calculator by students who are mentally retarded. Education and Training in Mental Retardation, 26, 381-387.
24. FUSON, K.C. (1988). Children's counting and concepts of number. New York: Springer-Verlag.
25. FUSON, K.C. (1992). Relationships between counting and cardinality from age 2 to age 8. In J. BIDEAUD, C. MELJAC, & J-P. FISCHER (Eds.), Pathways to number: Children's developing numerical abilities (pp. 127-149). Hillsdale, NJ: Lawrence Erlbaum.
26. FUSON, K.C., BRIARS, D., & SECADA, W. (1988). Correspondence errors in children's counting. In K.C. FUSON, Children's counting and concepts of number (pp. 64-91). New York: Springer-Verlag.
27. FUSON, K.C., & HALL, J.W. (1983). The acquisition of early number word meanings. In H. GINSBURG (Ed.), The development of student's mathematical thinking (pp. 49-107). New York: Academic Press.
28. FUSON, K.C., RICHARDS, J., & BRIARS, D.J. (1982). The acquisition and elaboration of the number word sequence. In C. BRAINERD (Ed.), Progress in cognitive development research: Vol 1. Children's logical and mathematical cognition (pp. 33-92). New York: Springer-Verlag.
29. FUSON, K.C., & SECADA, W.G. (1983). The development of number word sequence skills. In J. BERGERON & N. HERSCOVICS (Eds.), Proceedings of the Fifth Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 266-274). Montreal: University of Montreal.
30. GEARY, D.C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
31. GEARY, D.C., BOW-THOMAS, C.C., & YAO, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically-disabled children. Journal of Experimental Child Psychology, 54, 372-391.
32. GELMAN, R. (1972). The nature and development of early number concepts. In H.W. REESE (Ed.), Advances in child development and behavior (Vol. 7, pp. 115-167). New York: Academic Press.
33. GELMAN, R. (1982). Basic numerical abilities. In R.J. STERNBERG (Ed.), Advances in the psychology of human intelligence (pp. 181-205). Hillsdale, NJ: Erlbaum.
34. GELMAN, R. (1993). A rational-constructivist account of early learning about numbers and objects. The Psychology of Learning, 30, 61-96.
35. GELMAN, R., & COHEN, M. (1988). Qualitative differences in the way Down's syndrome children solve a novel counting problem. In L. NADEL (Ed.), The psychobiology of Down's syndrome (pp. 51-99). Cambridge, MA: MIT Bradford Press.
36. GELMAN, R., & GALLISTEL, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
37. GELMAN, R., & GREENO, J.G. (1989). On the nature of competence: Principles for understanding in a domain. In L.B. RESNICK (Ed.), Knowing, learning and instruction: Essays in honor of Robert Glaser (pp. 125-186). Hillsdale, NJ: Erlbaum.
38. GELMAN, R., & MECK, E. (1983). Preschoolers' counting: Principles before skill. Cognition, 13, 343-359.
39. GINSBURG, H.P., & RUSSELL, R.L. (1981). Social class and racial influences on early mathematical thinking. Monographs of the Society for Research in Child Development, 46(6, Serial No. 193).
40. HOARD, M.K., GEARY, D.C., & HAMSON, C.O. (1999). Numerical and arithmetical cognition: Performance of low- and average-IQ children. Mathematical Cognition, 5, 65-91.
41. HUNTING, R.P. (1999). Rational number learning in the early years: What is possible? In J.V. COPLEY (Ed.), Mathematics in the early years (pp. 80-87). Reston, VA: National Council for Teachers of Mathematics. (ERIC Document Reproduction Service No. ED 437 162)
42. IRWIN, K.C. (1991). Teaching children with Down syndrome to add by counting-on. Education and Treatment of Children. 14, 128-141.
43. IRWIN, K. C. (1996). Young children's formation of numerical concepts: Or 8 = 9 + 7. In H. MANSFIELD, N.A. PATEMAN, & N. BEDNARZ (Eds.), Mathematics for tomorrow's young children: International perspectives on curriculum (pp. 137-150). Dordrecht, The Netherlands: Kluwer Academic Publishers.
44. KIRK, S.A. (1957). Public school provisions for moderately retarded children: A survey of practices in the United States. Albany, NY: New York State Interdepartmental Health Resources Board.
45. KLAHR, D., & WALLACE, J.G. (1976). Cognitive development: An information-processing view. Hills-dale, NJ: Lawrence Erlbaum.
46. PIAGET, J. (1965). The child's conception of number. New York: Norton.
47. PORTER, J. (1993). What do pupils with moderate learning difficulties understand about counting? British Journal of Special Education, 20, 72-75.
48. RESNICK, L.B. (1983). A developmental theory of number understanding. In H.P. GINSBURG (Ed.), The development of mathematical thinking (pp. 109-151). New York: Academic Press.
49. RESNICK, L.B., & FORD, W.W. (1981). The psychology of mathematics for instruction. Hillsdale, NJ: Erlbaum.
50. RYNDERS, J.E., SCHLEIEN, S.J., & MATSON, S.I. (1996). One foot in school, one in a community recreational setting. In J.E. RYNDERS & J.M. HORROBIN (Eds.), Down syndrome: Birth to adulthood - Giving families an EDGE (pp. 193-210). Denver, CO: Love.
51. SCHAEFFER, B., EGGELSTON, V.H., & SCOTT, J.L. (1974). Number development in young children. Cognitive Psychology, 6, 357-379.
52. SECADA, W.G., FUSON, K.C., & HALL, J.W. (1983). The transition from counting-all to counting-on in addition. Journal for Research in Mathematics Education, 14, 47-57.
53. SIEGEL, L.S. (1982). The development of quantity concepts: Perceptual and linguistic factors. In C.J. BRAINERD (Ed.), Children's logical and mathematical cognition (pp. 123-155). New York: Springer-Verlag.
54. SIEGLER, R.S., & ROBINSON, M. (1982). The development of numerical understandings. In H.W. REESE & L.P. LIPITT (Eds.), Advances in child development and behaviour (Vol. 16, pp. 242-312). New York: Academic Press.
55. SOPHIAN, C. (1992). Learning about numbers: Lessons for mathematics education from preschool number development. In J. BIDEAUD, C. MELJAC, & J-P. FISCHER (Eds.), Pathways to number: Children's developing numerical abilities (pp. 19-40). Hillsdale, NJ: Lawrence Erlbaum.
56. STEFFE, L. P. (1992). Learning stages in the construction of the number sequence. In J. BIDEAUD, C. MELJAC, & J-P. FISCHER (Eds.), Pathways to number: Children's developing numerical abilities (pp. 83-98). Hillsdale, NJ: Lawrence Erlbaum.
57. STEFFE, L.P., VON GLASERSFELD, E., RICHARDS, J., & COBB, P. (1983). Children's counting types: Philosophy, theory, and application. New York: Praeger Scientific.
58. WOHLHUETER, M.J., & SINDBERG, R.M. (1972). Longitudinal development of object performance in mentally retarded children: An exploratory study. American Journal of Mental Deficiency, 79, 513-515.
59. WRIGHT, R.J. (1996). Problem-centred mathematics in the first year of school. In J. MULLIGAN & M. MICHELMORE (Eds.), Children's number learning (pp. 35-54). Adelaide, South Australia: Mathematics Education Research Group of Australasia.
60. WYNN, K. (1990). Children's understanding of counting. Cognition, 36, 155-193.