Reconceptualizing procedural knowledge

Journal for Research in Mathematics Education

Volumn 36, Issue 5, 2005, Pages 404-411

  Star, Jon R ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Algorithm; Conceptual knowledge; Flexibility; Heuristic; Procedural knowledge

Indexed keywords

EID: 27744470274     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (29)

1. Anderson, J. R. (1982). Acquisition of cognitive skill. Psychological Review, 89, 369-406.
2. Anderson, J. R. (1992). Automaticity and the ACT* theory. American Journal of Psychology, 105, 165-180.
3. Anderson, J. R., Fincham, J. M., & Douglass, S. (1997). The role of examples and rules in the acquisition of a cognitive skill. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 932-945.
4. Ballheim, C. (1999, October). Readers respond to what's basic. Mathematics Education Dialogues, 3, 11.
5. Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4, 379-426.
6. Brown, S., Seidelmann, A., & Zimmermann, G. (n.d.). In the trenches: Three teachers' perspectives on moving beyond the math wars. Retrieved June 1, 2005, from the Mathematically Sane Web site: http://mathematicallysane.com/ analysis/trenches.asp
7. Brownell, W. A. (1945). When is arithmetic meaningful? Journal of Educational Research, 38, 481-498.
8. Budd, K., Carson, E., Garelick, B., Klein, D., Milgram, R. J., Raimi, R. A., et al. (2005). Ten myths about math education and why you shouldn't believe them. Retrieved June 1, 2005, from the New York City HOLD Web site: http://www.nychold.com/myths-050504.html
9. Davis, R. B. (1983). Complex mathematical cognition. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 253-290). New York: Academic Press.
10. De Jong, T., & Ferguson-Hessler, M. (1996). Types and qualities of knowledge. Educational Psychologist, 31, 105-113.
11. Gelman, S. A., Star, J. R., & Flukes, J. (2002). Children's use of generics in inductive inferences. Journal of Cognition and Development, 3, 179-199.
12. Glaser, R. (1991). The maturing of the relationship between the science of learning and cognition and educational practice. Learning and Instruction, 1, 129-144.
13. Hiebert, J. (Ed.). (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.
14. Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.
15. Mathematically correct, (n.d.). Retrieved June 1, 2005, from the Mathematically Correct Web site: http://www.mathematicallycorrect.com/
16. Matz, M. (1980). Towards a computational theory of algebraic competence. Journal of Mathematical Behavior, 3, 93-166.
17. Medin, D. L. (1989). Concepts and conceptual structure. American Psychologist, 44, 1469-1481.
18. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Washington, DC: National Academy Press.
19. Ohlsson, S., & Rees, E. (1991). The function of conceptual understanding in the learning of arithmetic procedures. Cognition and Instruction, 8, 103-179.
20. Pesek, D. D., & Kirschner, D. (2000). Interference of instrumental instruction in subsequent relational learning. Journal for Research in Mathematics Education, 31, 524-540.
21. 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.
22. Schoenfeld, A. H. (1979). Explicit heuristic training as a variable in problem-solving performance. Journal for Research in Mathematics Education, 10, 173-187.
23. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
24. Sowder, J. T. (1998). What are the "math wars" in California all about? Reasons and perspectives. Retrieved June 1, 2005, from the Mathematically Sane Web site: http://mathematicallysane.com/analysis/mathwars. asp
25. Star, J. R. (2000). On the relationship between knowing and doing in procedural learning. In B. Fishman & S. O'Connor-Divelbiss (Eds.), Proceedings of the Fourth International Conference of the Learning Sciences (pp. 80-86). Mahwah, NJ: Erlbaum.
26. Star, J. R. (2002a). Re-conceptualizing procedural knowledge: The emergence of "intelligent" performances among equation solvers. In D. Mewborn, P. Sztajn, D. White, H. Wiegel, R. Bryant, & K. Nooney (Eds.), Proceedings of the Twenty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 999-1007). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
27. Star, J. R. (2002b). Re-conceptualizing procedural knowledge: Innovation and flexibility in equation solving (Doctoral dissertation, University of Michigan, 2001). Dissertation Abstracts International, 62, 3327A.
28. Star, J. R., & Seifert, C. (in press). The development of flexibility in equation solving. Contemporary Educational Psychology.
29. VanLehn, K. (1990). Mind bugs: The origins of procedural misconceptions. Cambridge, MA: MIT Press.