When theories don't add up: Disentangling the manipulatives debate

Theory into Practice

Volumn 46, Issue 4, 2007, Pages 309-316

  McNeil, Nicole M ^a   Jarvin, Linda ^b  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b TUFTS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36448934541     PISSN: 00405841     EISSN: None     Source Type: Journal    
DOI: 10.1080/00405840701593899     Document Type: Article

References (38)

1. Amaya, M. M., Uttal, D. H., O'Doherty, K. D., Liu, L. L., & DeLoache, J. S. (2007). Two-digit subtraction: Examining the link between concrete and abstract representations of knowledge. Manuscript under revision.
2. Baranes, R., Perry, M., & Stigler, J. W. (1989). Activation of real-world knowledge in the solution of word problems. Cognition and Instruction, 6, 287-318.
3. Boulton-Lewis, G. M. (1998). Children's strategy use and interpretations of mathematical representations. Journal of Mathematical Behavior, 17, 219-237.
4. Bruner, J. S. (1966). Towards a theory of instruction. Cambridge, MA: Harvard University Press.
5. Burns, M. (1996, April). How to make the most of math manipulatives. Instructor, 105, 45-51.
6. Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21-29.
7. DeLoache, J. S. (1995). Early symbol understanding and use. In D. L. Medin (Ed.), The psychology of learning and motivation (Vol. 33, pp. 65-114). New York: Academic Press.
8. Empson, S. B. (1999). Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17, 283-342.
9. Fennema, E. (1972). Models and mathematics. Arithmetic Teacher, 18, 635-640.
10. Friedman, M. (1978). The manipulatives materials strategy: The latest pied piper? Journal for Research in Mathematics Education, 9, 78-80.
11. Fuson, K. C., & Briars, D. J. (1990). Using a baseten blocks learning/teaching approach for first-and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21, 180-206.
12. Glenberg, A. M., Gutierrez, T., Levin, J. R., Japuntich, S., & Kaschak, M. P. (2004). Activity and imagined activity can enhance young children's reading comprehension. Journal of Educational Psychology, 96, 424-436.
13. Goldstone, R. L., & Sakamoto, Y. (2003). The transfer of abstract principles governing complex adaptive systems. Cognitive Psychology, 46, 414-466.
14. Greeno, J. G. (1989). Situations, mental models, and generative knowledge. In D. Klahr & K. Kotovsky (Eds.), Complex information processing: The impact of Herbert Simon (pp. 285-318). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
15. Jarvin, L., McNeil, N. M., & Sternberg, R. J. (2006, June). Understanding students' mathematical competencies: An exploration of the impact of contextualizing math problems. Paper presented at the Institute of Education Sciences Research Conference, Washington, DC.
16. Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from the tower of Hanoi. Cognitive Psychology, 17, 248-294.
17. Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26, 422-441.
18. Martin, T., & Schwartz, D. L. (2005). Physically distributed learning: Adapting and reinterpreting physical environments in the development of fraction concepts. Cognitive Science, 29, 587-625.
19. McNeil, N. M., & Alibali, M. W. (2005). Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 1-17.
20. McNeil, N. M., Uttal, D. H., Jarvin, L., & Sternberg, R. J. (2007). Should you show me the play money? Concrete objects both hurt and help performance on math problems.
21. Meehl, P. E. (1978). Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of Consulting and Clinical Psychology, 4, 806-834.
22. Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29, 121-142.
23. Mix, K. S. (2003). Spatial tools for mathematical thought. In L. B. Smith, M. Gasser, & K. S. Mix (Eds.), The spatial foundations of cognition and language. Manuscript submitted for publication.
24. Moch, P. L. (2001). Manipulatives work. The Educational Forum, 66, 81-87.
25. Montessori, M. (1964). The Montessori method. New York: Schocken.
26. Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197.
27. Piaget, J., & Szeminska, A. (1995). The child's conception of number (C. Gattegno & F. M. Hodgson, Trans.). In H. E. Gruber & J. J. Voneche (Eds.), The essential Piaget (pp. 298-341). Northvale, NJ: Jason Aronson. (Original work published 1941).
28. Resnick, L. B., & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 3, pp. 41-96). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
29. Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 175-189.
30. Rittle-Johnson, B., & Koedinger, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23, 313-349.
31. Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well taught" mathematics courses. Educational Psychologist, 23, 145-166.
32. Sloutsky, V. M., Kaminski, J. A., & Heckler, A. F. (2005). The advantage of simple symbols for learning and transfer. Psychonomic Bulletin and Review, 12, 508-513.
33. Smith, J. P. (1996). Efficacy and teaching mathematics by telling: A challenge for reform. Journal for Research in Mathematics Education, 27, 387-402.
34. Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20, 498-505.
35. Sternberg, R. J., & Grigorenko, E. L. (2004). Successful intelligence in the classroom. Theory Into Practice, 43, 274-280.
36. Thompson, P. W. (1992). Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics. Journal for Research in Mathematics Education, 23, 123-147.
37. Uttal, D. H. (2003). On the relation between play and symbolic thought: The case of mathematics manipulatives. In O. Saracho & B. Spodek (Eds.), Contemporary perspectives in early childhood (pp. 97-114). Greenwich, CT: Information Age.
38. Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18, 37-54.