Adults' Understanding of Inversion Concepts: How Does Performance on Addition and Subtraction Inversion Problems Compare to Performance on Multiplication and Division Inversion Problems?

Canadian Journal of Experimental Psychology

Volumn 57, Issue 4, 2003, Pages 321-330

  Robinson, Katherine M ^a   Ninowski, Jerilyn E ^a  

^a UNIVERSITY OF REGINA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347588516     PISSN: 11961961     EISSN: None     Source Type: Journal    
DOI: 10.1037/h0087435     Document Type: Article

References (18)

1. 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 (pp. 213-244). Hillsdale, NJ: Erlbaum.
2. Campbell, J. I. D. (1997). On the relationship between skilled performance of simple division and multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 920-929.
3. Campbell, J. I. D. (1999). Division by multiplication. Memory & Cognition, 27, 791-802.
4. Dixon, J. A., Deets, J. K., & Bangert, A. (2001). The representations of the arithmetic operations include functional relationships. Memory & Cognition, 29, 462-477.
5. Geary, D. C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
6. Geary, D. C., Frensch, P. A., & Wiley, J. G. (1993). Simple and complex mental subtraction: Strategy choice and speed-of-processing differences in young and elderly adults. Psychology and Aging, 8, 242-256.
7. 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, 105-116.
8. LeFevre, J.-A., & Morris, J. (1999). More on the relation between division and multiplication in simple arithmetic: Evidence for mediation of division solutions via multiplication. Memory & Cognition, 27, 803-812.
9. LeFevre, J.-A., Sadesky, G. S., & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem-size effect In adults. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 216-230.
10. Mauro, D. G., LeFevre, J.-A., & Morris, J. (2003). Effects of problem format on division and manipulation performance: Division facts are mediated via multiplication-based representations, Journal of Experimental Psychology: Learning, Memory, & Cognition, 29, 163-170.
11. Rittle-Johnson, B., Siegler, R.S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346-362.
12. Robinson, K. M. (2001). The validity of verbal reports in children's subtraction. Journal of Educational Psychology, 93, 211-222.
13. Robinson, K. M., Arbuthnott, K. D., & Gibbons, K. A. (2002). Adults' representations of division facts: A consequence of learning history? Canadian Journal of Experimental Psychology, 56, 302-309.
14. Robinson, K. M., Arbuthnott, K. D., Rose, D., McCarron, M. C., Globa, C. A., & Phonexay, S. D. (2003). Childrens' strategies for solving simple division problems. Manuscript submitted for publication.
15. Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 116, 250-264.
16. Siegler, R. S. (1989). Hazards of mental chronometry: An example from children's subtraction. Journal of Educational Psychology, 81, 497-506.
17. Siegler, R. S., & Crowley, K. (1991). The microgenetic method: A direct means for studying cognitive development. American Psychologist, 46, 606-620.
18. 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.