Individual differences in children's understanding of inversion and arithmetical skill

British Journal of Educational Psychology

Volumn 76, Issue 2, 2006, Pages 309-331

  Gilmore, Camilla K ^a,b   Bryant, Peter ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AGE; ANALYSIS OF VARIANCE; ARTICLE; CHILD; CHILD DEVELOPMENT; COMPREHENSION; FEMALE; HUMAN; INDIVIDUALITY; LEARNING; MALE; MATHEMATICS; PROBLEM SOLVING;

AGE FACTORS; ANALYSIS OF VARIANCE; CHILD; CHILD DEVELOPMENT; COMPREHENSION; FEMALE; HUMANS; INDIVIDUALITY; LEARNING; MALE; MATHEMATICS; PROBLEM SOLVING;

EID: 33745663493     PISSN: 00070998     EISSN: None     Source Type: Journal    
DOI: 10.1348/000709905X39125     Document Type: Article

References (25)

1. Abnett, C. K., & Bryant, P. (2004, April). Children's understanding of the arithmetic principle of inversion. Poster session presented at the British Psychological Society Annual Conference, London.
2. Baroody, A. J., & Gannon, K. E. (1984). The development of the commutativity principle and economical addition strategies. Cognition and Instruction, 1, 321-339.
3. Bisanz, J., & LeFevre, J. A. (1990). Strategic and nonstrategic processing in the development of mathematical cognition. In D. F. Bjorklund (Ed.), Children's strategies: Contemporary views of cognitive development. Hillsdale, NJ: Lawrence Erlbaum Associates.
4. Bisanz, J., LeFevre, J. A., & Gilliland, S. (1989, April). Developmental changes in the use of logical principles in mental arithmetic. Poster session presented at the biennial meeting of the Society for Research in Child Development, Kansas City, MO.
5. 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.
6. Bryant, P., & Nunes, T. (2004). The results of a new mathematical reasoning task given to a large number of 8-year-old children. Manuscript in preparation.
7. Canobi, K. H. (2004). Individual differences in children's addition and subtraction knowledge. Cognitive Development, 19, 81-93.
8. Canobi, K. H., Reeve, R. A., & Pattison, P. E. (1998). The role of conceptual understanding in children's addition problem solving. Developmental Psychology, 34(5), 882-891.
9. Canobi, K. H., Reeve, R. A., & Pattison, P. E. (2002). Young children's understanding of addition concepts. Educational Psychology, 22(5), 513-532.
10. Canobi, K. H., Reeve, R. A., & Pattison, P. E. (2003). Patterns of knowledge in children's addition. Developmental Psychology, 39(3), 521-534.
11. Carpenter, T. P., & Moser, J. M. (1982). The development of addition and subtraction problem-solving skills. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 9-24). Hillsdale, NJ: Lawrence Erlbaum Associates.
12. Cowan, R., & Renton, M. (1996). Do they know what they are doing? Children's use of economical addition strategies and knowledge of commutativity. Educational Psychology, 16(4), 407-420.
13. Dowker, A. (2004). What works for difficulties in mathematics. London: DfES.
14. Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 243-275). New York: Macmillan.
15. Ireson, J., & Hallam, S. (2001). Ability grouping in education. London: Paul Chapman.
16. Klein, J. S., & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology, 54(2), 105-115.
17. Piaget, J. (1952). The child's conception of number. London: Routledge and Kegan Paul.
18. Piaget, J., & Moreau, A. (2001). The inversion of arithmetic operations. In J. Piaget (Ed.), Studies in reflecting adstraction (R. L. Campbell, Trans., pp. 69-86). Hove, UK: Psychology Press. (Original work published 1977).
19. Rasmussen, C., Ho, E., & Bisanz, J. (2003). Use of the mathematical principle of inversion in young children. Journal of Experimental Child Psychology, 85, 89-102.
20. Riley, M., 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. 153-196). New York: Academic Press.
21. Siegler, R. S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology - General, 127, 377-397.
22. Starkey, P., & Gelman, R. (1982). The development of addition and subtraction abilities prior to formal schooling in arithmetic. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds), Addition and subtraction: A cognitive perspective (pp. 99-116). Hillsdale, NJ: Erlbaum.
23. Stern, E. (1992). Spontaneous use of conceptual mathematical knowledge in elementary school children. Contemporary Educational Psychology, 17, 266-277.
24. Vilette, B. (2002). Do young children grasp the inverse relationship between addition and subtraction? Evidence against early arithmetic. Cognitive Development, 17, 1365-1383.
25. Wechsler, D. (1996). Wechsler objective numerical dimensions. London: Psychological Corporation.