Patterns of individual differences in conceptual understanding and arithmetical skill: A meta-analysis

Mathematical Thinking and Learning

Volumn 11, Issue 1-2, 2009, Pages 25-40

  Gilmore, Camilla K ^a   Papadatou Pastou, Marietta ^b  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67749133589     PISSN: 10986065     EISSN: 15327833     Source Type: Journal    
DOI: 10.1080/10986060802583923     Document Type: Article

References (41)

1. Baroody, A. J. (1992). The development of preschoolers' counting skills and principles. In J. Bideaud, C. Meljac, & J. P. Fischer (Eds.), Pathways to number (pp. 99-126). Hillsdale, NJ: Erlbaum.
2. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1-33). Mahwah, NJ: Erlbaum.
3. Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38(2), 115-131.
4. Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 75-112). Hillsdale, NJ: Erlbaum.
5. Baroody, A. J., & Lai, M. (2007). Preschoolers' understanding of the addition-subtraction inverse principle: A Taiwanese sample. Mathematics Thinking and Learning, 9, 131-171.
6. 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.
7. Bisanz, J., Sherman, J. L., Rasmussen, C., & Ho, E. (2005). Development of arithmetic skills and knowledge in preschool children. In J. I. D. Campbell (Ed.), Handbook of Mathematical Cognition. New York: Psychology Press.
8. Briars, D., & Siegler, R. S. (1984). A featural analysis of preschoolers' counting knowledge. Developmental Psychology, 20, 607-618.
9. 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.
10. Bryant, P., & Nunes, T. (2007, August). Children's understanding and use of the relation between addition and subtraction. Paper presented at the biennial meeting of the European Association for Research in Learning and Instruction, Budapest, Hungary.
11. Canobi, K. H. (2004). Individual differences in children's addition and subtraction knowledge. Cognitive Development, 19, 81-93.
12. Canobi, K. H. (2005). Children's profiles of addition and subtraction understanding. Journal of Experimental Child Psychology, 92, 220-246.
13. Canobi, K. H., Reeve, R. A., & Pattison, P. E. (1998). The role of conceptual understanding in children's addition problem solving. Developmental Psychology, 34, 882-891.
14. Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6, 81-89.
15. Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: Beginning with a coordinated process scheme. Journal of Mathematical Behavior, 15, 167-192.
16. Dehaene, S. (1997). The number sense. Oxford, UK: Oxford University Press.
17. Dowker, A. (1998). Individual differences in normal arithmetical development. In C. Donlan (Ed.), The development of mathematical skills. Hove, UK: Psychology Press.
18. Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Hove, UK: Psychology Press.
19. Gilmore, C. K. (2005). Children's understanding of the inverse relationship between addition and subtraction: Doctoral dissertation, University of Oxford, UK.
20. Gilmore, C. K. (2006). Investigating children's understanding of inversion using the missing number paradigm. Cognitive Development, 21, 301-316.
21. Gilmore, C. K., & Bryant, P. (2006). Individual differences in children's understanding of inversion and arithmetical skill. British Journal of Educational Psychology, 76, 309-331.
22. Gilmore, C. K., & Bryant, P. (2008). Can children construct inverse relations in arithmetic? Evidence for individual differences in the development of conceptual understanding and computational skill. British Journal of Developmental Psychology, 26, 301-316.
23. Gilmore, C. K., & Spelke, E. S. (2008). Children's understanding of the relationship between addition and subtraction. Cognition, 107, 932-945.
24. Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity, and flexibility: A "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25, 116-140.
25. Hecht, S. A., Close, L., & Santisi, M. (2003). Sources of individual differences in fraction skills. Journal of Experimental Child Psychology, 86, 277-302.
26. Hiebert, J., & Wearne, D. (1996). Instruction, understanding and skill in multidigit addition and subtraction. Cognition and Instruction, 14, 251-283.
27. Hughes, M. (1981). Can preschool children add and subtract? Educational Psychology, 1, 207-219.
28. Hunter, J. E., & Schmidt, F. L. (Eds.). (1990). Methods of meta-analysis. Newbury Park, California: Sage.
29. Imbo, I., & Vandierendonck, A. (2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96, 284-309.
30. Kerkman, D., & Siegler, R. (1997). Measuring individual differences in children's addition strategy choices. Learning and Individual Differences, 9, 1-18.
31. Klein, J. S., & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology-Revue Canadienne De Psychologie Experimentale, 54, 105-116.
32. 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.
33. 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.
34. Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skills. Studies in developmental psychology (pp. 75-110). Hove, UK: Psychology Press.
35. Robinson, K. M., Ninowski, J. E., & Gray, M. L. (2006). Children's understanding of the arithmetic concepts of inversion and associativity. Journal of Experimental Child Psychology, 94, 349-362.
36. Rose, S. (2002). The role of inversion, decomposition and the decimal structure in children's arithmetic. Unpublished manuscript, University of Oxford, UK.
37. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
38. Sherman, J., & Bisanz, J. (2007). Evidence for use of mathematical inversion by three-year-old children. Journal of Cognition and Development, 8, 333-344.
39. Stern, E. (1992). Spontaneous use of conceptual mathematical knowledge in elementary school children. Contemporary Educational Psychology, 17, 266-277.
40. Swanson, L., & Kim, K. (2007). Working memory, short-term memory, and naming speed as predictors of children's mathematical performance. Intelligence, 35, 151-168.
41. Watchorn, R., Bisanz, J., Fast, L., LeFevre, J.-A., Smith-Chant, B., Skwarchuk, S.-L., et al. (2007, March). Calculation skills and the use of conceptually advanced solution procedures. Paper presented at the Poster presented at the Biennial Meeting of the Society for Research in Child Development, Boston.