Concrete representations and the procedural analogy theory

Journal of Mathematical Behavior

Volumn 17, Issue 1, 1998, Pages 33-51

  Hall, Neil ^a  

^a LIVERPOOL JOHN MOORES UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032336888     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0732-3123(99)80060-1     Document Type: Article

References (32)

1. Andersen, J. R. (1983a). The architecture of cognition. Cambridge, MA: Harvard University Press.
2. Andersen, J. R. (1983b). Acquisition of proof skills in geometry. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.), Machine learning (pp. 191-219). Palo Alto, CA: Tioga.
3. Anderson, J. R. (1986). Knowledge compilation: The general learning mechanism. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.), Machine learning. Vol. II (pp. 289-310). Los Altos, CA: Kaufmann.
4. Bobis, J. (1992). Demands imposed on children by mathematics instructional material. In B. Southwell, B. Perry, & K. Owens (Eds.), Space - the first and final frontier (pp. 137-146). Proceedings of the 15th Annual Conference of the Mathematics Education Research Group of Australasia, Richmond, Australia.
5. Boulton-Lewis, G. M. (1992). The demands of some representations and strategies used in teaching mathematics to young children. Paper presented at the Annual Conference of the Australian Educational Research Association, Geelong, Australia.
6. Fennema, E. H. (1972). Models and mathematics. Arithmetic Teacher, 20(4), 635-640.
7. Freidman, M. (1978). The manipulative materials strategy: The latest pied piper? Journal for Research in Mathematics Education, 9, 78-80.
8. Fuson, K. C., & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21(3), 180-206.
9. Hall, N. (1992). Computers and information technologies: Programming and application, Book 2. Melbourne: Longman Cheshire.
10. Hall, N. (1993). Teaching mathematics using the procedural analogy theory. In B. Atweh, C. Kanes, M. Carss, & G. Booker (Eds.) Contexts in mathematics education (pp. 343-349), proceedings of the sixteenth annual conference of the Mathematics Education Research Group of Australasia (MERGA). Brisbane, Australia: MERGA.
11. Kaput, J. J. (1985). Representation and problem solving: Methodological issues related to modeling. In E. Silver (Ed.), Teaching and learning mathematical problem solving: multiple research perspectives {pp. 381-398). Hillsdale, NJ: Erlbaum.
12. Labinowicz, E. (1985). Learning from students: New beginnings for teaching numerical thinking. Menlo Park, CA: Addison-Wesley.
13. Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65-99.
14. Lesh, R., Post, T., & Behr, M. (1987a). Dienes revisited: Multiple embodiments in computer environments. In I. Wirzup & R. Streit (Eds.), Developments in school mathematics around the world (pp. 647-680). Reston, VA: National Council of Teachers of Mathematics.
15. Lesh, R., Post, T., & Behr, M. (1987b). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Erlbaum.
16. Millward, R. B. (1980). Models of concept formation. In R.E. Snow, P-A. Federico & W.E. Montague (Eds.), Aptitude, learning and instruction (pp. 245-275). Hillsdale, NJ: Erlbaum.
17. Mostow, D. J. (1983). Machine transformation of advice into heuristic search procedure. In R. S. Michalski, J. G. Carbonell & T. M. Mitchell (Eds.), Machine learning (pp. 367-403). Palo Alto, CA: Tioga.
18. Neves, D. M., & Anderson, J. R. (1981). Knowledge compilation: Mechanisms for the automatisation of cognitive skills. In J. R. Anderson, Cognitive skills and their acquisition (pp. 57-84). Hillsdale, NJ: Erlbaum.
19. Newell, A., & Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J.R. Anderson, Cognitive skills and their acquisition (pp. 1-55). Hillsdale, NJ: Erlbaum.
20. Ohlsson, S. (1991). Declarative and procedural knowledge. International Encyclopedia of Education (draft version).
21. Ohlsson, S., & Hall, N. (1990). The cognitive function of embodiments in mathematics instruction, (Technical Report No. KUL-90-02). Pittsburgh, PA: Learning Research & Development Center, University of Pittsburgh.
22. Resnick, L. B., & Omanson, S. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology, (Vol. 3, pp. 41-95). Hillsdale, NJ: Erlbaum.
23. Rosenbloom, P. S., & Newell, A. (1982a). Learning by chunking: A production system model of practice. Technical Report No. 82-135, Department of Computer Science, Carnegie-Mellon University, Pittsburgh.
24. Rosenbloom, P.S., & Newell, A. (1982b). Learning by chunking: Summary of a task and a model. Proceedings of AAAI-82 (pp. 255-257) Pittsburgh.
25. Rosenbloom, P. S., & Newell, A. (1986). The chunking of goal hierarchies: A generalised model of practice. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.), Machine learning. Vol. II. (pp. 247-288). Los Altos, CA: Kaufmann.
26. Schneider, W., & Fisk, A. D. (1983). Attention theory and mechanisms for skilled performance. In R. A. Magill, Memory and control of action (pp. 119-143). Amsterdam: North-Holland.
27. Scott, L. F., & Neufeld, H. (1976). Concrete instruction in elementary mathematics: Pictorial vs. manipulative. School Science and Mathematics, 76, 68-72.
28. Scott, P. B. (1983). A survey of perceived use of mathematics materials by elementary teachers in a large urban school district. School Science and Mathematics, 83 (1), 61-68.
29. Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498-505.
30. Suydam, M.N. & Higgins, J.L. (1976). Review and synthesis of studies of activity-based approaches to mathematics teaching (Final report, contract no. 400-75-0063). Washington, D.C.: National Institute of Education.
31. VanLehn, K., & Brown, J. S. (1980). Planning nets: A representation for formalising analogies and semantic models of procedural skills. In R. E. Snow, P-A. Federico, & W. E. Montague, (Eds.) Aptitude, learning and instruction (pp. 95-137). Hillsdale, NJ: Erlbaum.
32. Wearne, D., & Hiebert, J. (1988). A cognitive approach to meaningful mathematics instruction: Testing a local theory using decimal numbers. Journal for Research in Mathematics Education, 23(2), 123-147.