Deaf children's informal knowledge of multiplicative reasoning

Journal of Deaf Studies and Deaf Education

Volumn 14, Issue 2, 2009, Pages 260-277

  Nunes, Terezinha ^a   Bryant, Peter ^a   Burman, Diana ^a   Bell, Daniel ^a   Evans, Deborah ^a   Hallett, Darcy ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHILD; COGNITION; FEMALE; HEARING IMPAIRMENT; HUMAN; LEARNING; MALE; MATHEMATICS; PRESCHOOL CHILD; PROBLEM SOLVING;

CHILD; CHILD, PRESCHOOL; COGNITION; DEAFNESS; FEMALE; HUMANS; LEARNING; MALE; MATHEMATICS; PROBLEM SOLVING;

EID: 63349088527     PISSN: 10814159     EISSN: 14657325     Source Type: Journal    
DOI: 10.1093/deafed/enn040     Document Type: Article

References (67)

1. Ansell, E., & Pagliaro, C. M. (2006). The relative difficulty of signed arithmetic story problems for primary level deaf and hard-of-hearing students. Journal of Deaf Studies and Deaf Education, 11, 153-170.
2. Becker, J. (1993). Young children's numerical use of number words: Counting in many-to-one situations. Developmental Psychology, 19, 458-465.
3. Behr, M. J., Harel, G., Post, T., & Lesh, R. (1994). Units of quantity: A conceptual basis common to additive and multiplicative structures. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 121-176). Albany, NY: State University of New York Press.
4. Booth, L. R. (1981). Child-methods in secondary mathematics. Educational Studies in Mathematics, 12, 29-41.
5. Bradley, L., & Bryant, P. (1983). Categorising sounds and learning to read - A causal connection. Nature, 301, 419-421.
6. Bryant, P., Christie, C., & Rendu, A. (1999). Children's understanding of the relation between addition and subtraction: Inversion, identity and decomposition. Journal of Experimental Child Psychology, 74, 194-212.
7. Bryant, P., Nunes, T., Evans, D., Bell, D., & Burman, D. (2008). The number line as a teaching tool. Paper presented at the AERA (American Educational Research Association), New York.
8. Bovet, M. C. (1974). Cognitive processes among illiterate children and adults. In J. W. Berry & P. R. Dasen (Eds.), Culture and cognition: Readings in cross-cultural psychology (pp. 311-334). London: Methuen & Co.
9. Budoff, M. (1987). Measures for assessing learning potential. In C. S. Lidz (Ed.), Dynamic assessment: An interactional approach to evaluating learning potential (pp. 173-195). New York: Guilford.
10. Campione, J., & Brown, A. (1987). Linking dynamic assessment with school achievement. In C. S. Lidz (Ed.), Dynamic assessment: An interactional approach to evaluating learning potential (pp. 82-115). New York: Guilford.
11. Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem-solving processes. Journal for Research in Mathematics Education, 24, 428-441.
12. Carpenter, T. P., Hiebert, J., & Moser, J. M. (1981). Problem structure and first grade children's initial solution processes for simple addition and subtraction problems. Journal for Research in Mathematics Education, 12, 27-39.
13. Carraher, T. N. (1985). The decimal system: Understanding and notation. Proceedings of the 9th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 288-303). Utrecht, the Netherlands: Research Group on Mathematics Education and Educational Computer Centre, State University of Utrecht.
14. Confrey, J. (1994). Splitting, similarity and rate of change: A new approach to multiplication and exponential functions. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 293-332). Albany NY: State University of New York Press.
15. Elliott, C. D., Smith, P., & McCulloch, K. (1997). British Ability Scale-II Technical Manual. London: Nelson Publishing Company.
16. Feuerstein, R. (1979). The dynamic assessment of retarded performers: The learning potential assessment device, theory, instruments, and techniques. Baltimore, MD: University Park Press.
17. Frostad, P., & Ahlberg, A. (1999). Solving story-based arithmetic problems: Achievement of children with hearing impairment and their interpretation of meaning. Journal of Deaf Studies and Deaf Education, 4, 283-298.
18. Frydman, O., & Bryant, P. (1994). Children's understanding of multiplicative relationships in the construction of quantitative equivalence. Journal of Experimental Child Psychology, 58, 489-509.
19. Frydman, O., & Bryant, P. E. (1988). Sharing and the understanding of number equivalence by young children. Cognitive Development, 3, 323-339.
20. Garrison, W., Long, G., & Dowaliby, F. (1997). Working memory capacity and comprehension processes in deaf readers. Journal of Deaf Studies and Deaf Education, 2, 78-94.
21. Good III, R. H., & Kaminski, R. A. (1996). Assessment for instructional decisions: Toward a proactive/prevention model of decision-making for early literacy skills. School Psychology Quarterly, 11, 326-336.
22. Gravemeijer, K. (1997). Mediating between concrete and abstract. In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 315-346). Hove, UK: Psychology Press.
23. Gregory, S. (1998). Mathematics and deaf children. In S. Gregory, P. Knight, W. McCracken, S. Powers, & L. Watson (Eds.), Issues in deaf education (pp. 119-126). London: David Fulton.
24. Gresham, F. K. (2002). Responsiveness to intervention: An alternative approach to the identification of learning disabilities. In R. Bradley, L. Danielson, & D. Hallahan (Eds.), Identification of learning disabilities: Research to practice (pp. 467-519). Mahwah, NJ: Erlbaum.
25. Hitch, G. J., Arnold, P., & Philips, L. J. (1983). Cognitive processes in deaf children's arithmetic. British Journal of Psychology, 74, 429-437.
26. Hyde, M., Zevenbergen, R., & Power, D. (2003). Deaf and hard of hearing students' performance on arithmetic word problems. American Annals of the Deaf, 148, 56-64.
27. Inhelder, B., Sinclair, H., & Bovet, M. (1974). Learning and the development of cognition. London: Routledge and Kegan Paul.
28. Kamii, M. (1981). Children's ideas about written number. Topics in Learning and Learning Disabilities, 1, 47-59.
29. Kaminski, R. A., & Good, R. H. (1996). Towards a technology for assessing basic early literacy skills. School Psychology Review, 25 215-227.
30. Kaput, J. (1985). Multiplicative word problems and intensive quantities: An integrated software response. (Technical Report 85-19). Cambridge, MA: Harvard University, Educational Technology Center.
31. Kaput, J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 237-292). Albany, NY: State University of New York Press.
32. Kelly, R. R., Lang, H. G., & Pagliaro, C. M. (2003). Mathematics word problem solving for deaf students: A survey of practices in Grades 6-12. Journal of Deaf Studies and Deaf Education, 8, 104-119.
33. Kouba, V. (1989). Children's solution strategies for equivalent set multiplication and division word problems. Journal for Research in Mathematics Education, 20, 147-158.
34. Lidz, C. S. (1995). Dynamic assessment and the legacy of L.S. Vygotsky. School Psychology International, 16, 143-153.
35. Lidz, C. S. (2002). Mediated learning experience (MLE) as a basis for an alternative approach to assessment. School Psychology International, 23, 68-84.
36. Moreno, C. (2000). Predictors of mathematics attainment in hearing impaired children. Unpublished PhD Thesis. London: Institute of Education, University of London.
37. Newman, D., Griffin, P., & Cole, M. (1989). The construction zone: Working for cognitive change in school. Cambridge: Cambridge University Press.
38. Nunes, T. (2004). Teaching mathematics to deaf children. London: Whurr.
39. Nunes, T., Bryant, P., Burman, D., Bell, D., Evans, D., Hallett, D., et al. (2008). Deaf children's understanding of inverse relations. In M. Marschark & P. C. Hauser (Eds.), Cognitive underpinnings of learning by deaf and hard-of-hearing students (pp. 201-225). Oxford: Oxford University Press.
40. Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., et al. (2007). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology, 25, 147-166.
41. Nunes, T., Bryant, P., & Pretzlik, U. (2006). Using deaf children's visual skills to promote mathematics learning. Poster presented at the ISSBD Biennial Meeting, 1-5 August 2006. Melbourne, Australia.
42. Nunes, T., & Moreno, C. (1997). Solving word problems with different ways of representing the task. Equals Mathematics and Special Educational Needs, 2, 15-17.
43. Nunes, T., & Moreno, C. (1998a). Is hearing impairment a cause of difficulties in learning mathematics? In C. Donlan (Ed.), The development of mathematical skills (pp. 227-254). Hove, UK: Psychology Press.
44. Nunes, T., & Moreno, C. (1998b). The signed algorithm and its bugs. Educational Studies in Mathematics, 35, 85-92.
45. Nunes, T., & Schliemann, A. D. (1990). Knowledge of the numeration system among pre-schoolers. In L. S. T. Wood (Ed.), Transforming early childhood education: International perspectives (pp. 135-141). Hillsdale, NJ: Lawrence Erlbaum.
46. Olive, J., & Steffe, L. P. (2002). The construction of an iterative fractional scheme: The case of Joe. Journal of Mathematical Behavior, 20, 413-437.
47. Park, J., & Nunes, T. (2001). The development of the concept of multiplication. Cognitive Development, 16, 763-773.
48. Piaget, J. (1952). The child's conception of number. London: Routledge & Kegan Paul.
49. Piaget, J. (1954). The construction of reality in the child. London: Routledge and Kegan Paul.
50. Pickering, S., & Gathercole, S. (2001). Working Memory Test Battery for Children (WMTB-C) Manual. London: The Psychological Corporation.
51. Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 110-152). New York: Academic Press.
52. Riley, N. S., Greeno, J. G., & Heller, J. I. (1983). Development of children's problem-solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153-200). New York: Academic Press.
53. Secada, W. (1984). Counting in sign: The number string, accuracy and use. Unpublished PhD Thesis. Evanston, IL: Northwestern University.
54. Serrano Pau, C. (1995). The deaf child and solving problems in arithmetic: The importance of comprehensive reading. American Annals of the Deaf, 140, 287-290.
55. Siegler, R. S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General, 127, 377-397.
56. Smedslund, J. (1961). The acquisition of conservation of substance and weight in children: II. External reinforcement of conservation of weight and of the operations of addition and subtraction. Scandinavian Journal of Psychology, 2, 71-84.
57. Steffe, L. (1994). Children's multiplying schemes. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3-40). Albany, NY: State University of New York Press.
58. Streefland, L. (1985). Search for the roots of ratio: Some thoughts on the long term learning process (Towards... A Theory): Part II: The outline of the long term learning process. Educational Studies in Mathematics, 16, 75-94.
59. Traxler, C. B. (2000). The Stanford Achievement Test, 9th Edition: National norming and performance standards for deaf and hard-of-hearing students. Journal of Deaf Studies and Deaf Education, 5, 337-348.
60. Tymms, P., Brien, D., Merrell, C., Collins, J., & Jones, P. (2003). Young deaf children and the prediction of reading and mathematics. Journal of Early Childhood Research, 1, 197-202.
61. Vellutino, F. R., Scanlon, D. M., Small, S., & Fanuele, D. P. (2006). Response to intervention as a vehicle for distinguishing between children with and without reading disabilities: Evidence for the role of kindergarten and first-grade interventions. Journal of Learning Disabilities, 38, 157-169.
62. Vergnaud, G. (1982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 60-67). Hillsdale, NJ: Lawrence Erlbaum.
63. Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 128-175). London: Academic Press.
64. Vergnaud, G. (1994). Multiplicative conceptual field: What and why? In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 41-60). Albany, NY: State University of New York Press.
65. Wollman, D. C. (1965). The attainments in English and arithmetic of secondary school pupils with impaired hearing. The Teacher of the Deaf, 159, 121-129.
66. Wood, D., Wood, H., & Howarth, P. (1983). Mathematical abilities of deaf school leavers. British Journal of Developmental Psychology, 1, 67-73.
67. Zarfaty, Y., Nunes, T., & Bryant, P. (2004). The performance of young deaf children in spatial and temporal number tasks. Journal of Deaf Studies and Deaf Education, 9, 315-326.