# Some cognitive factors relevant to mathematics instruction

- 62 Downloads
- 4 Citations

## Abstract

Our understanding of cognitive processes has progressed sufficiently in the last few years to enable us to generate novel instructional techniques that can enhance substantially learning of subjects such as mathematics. This paper will review briefly some research intended to contribute to this process. There are two relevant aspects. Firstly, recent work has thrown light on schema acquisition while learning mathematics, and on techniques for detecting schemas in mathematics learners. Secondly, other research has assessed the distribution of cognitive resources while learning mathematics and other related subjects leading to the design of instructional techniques to facilitate schema acquisition.

## Keywords

Cognitive Load Educational Psychology Irrelevant Information Schema Acquisition Cognitive Load Theory## Preview

Unable to display preview. Download preview PDF.

## References

- Ayres, P., & Sweller, J. (1990). Locus of difficulty in multi-stage mathematics problems.
*American Journal of Psychology, 103*, 167–193.CrossRefGoogle Scholar - Chase, W.G., & Simon, H.A. (1973). Perception in chess.
*Cognitive Psychology, 4*, 55–81.CrossRefGoogle Scholar - Chi, M., Glaser, R., & Rees, E. (1982). Expertise in problem solving. In R. Sternberg (Ed.),
*Advances in the psychology of human intelligence*(pp. 7–75). Hillsdale, NJ: Erlbaum.Google Scholar - Chi, M.T., & Glaser, R. (1985). Problem solving ability. In R.J. Sternberg (Ed.),
*Human abilities: An information-processing approach*(pp. 227–250). NY: Freeman.Google Scholar - Cooper, G., & Sweller, J. (1987). The effects of schema acquisition and rule automation on mathematical problem-solving transfer.
*Journal of Educational Psychology, 79*, 347–362.CrossRefGoogle Scholar - De Jong, T., & Ferguson-Hessler, M.G.M. (1986). Cognitive structures of good and poor novice problem solvers in physics.
*Journal of Educational Psychology, 78*, 279–288.CrossRefGoogle Scholar - Hinsley, D.A., Hayes, J.R., & Simon, H.A. (1977). From words to equations. In M.A. Just & P.A. Carpenter (Eds.),
*Cognitive processes in comprehension*(pp. 89–106). Hillsdale: Erlbaum.Google Scholar - Lawson, M. (1990). The case for instruction in use of general problem-solving strategies in mathematics: A comment on Owen and Sweller (1989).
*Journal for Research in Mathematics Education, 21*, 403–410.CrossRefGoogle Scholar - Low, R., & Over, R. (1990). Text editing of algebraic word problems.
*Australian Journal of Psychology, 42*, 63–73.CrossRefGoogle Scholar - Low, R., & Over, R. (1992a).
*Sex differences in solution of algebraic word problems containing irrelevant information*. Unpublished manuscript, University of New South Wales.Google Scholar - Low, R., & Over, R. (1992b). Hierarchical ordering of schematic knowledge relating to the area-of-rectangle problems.
*Journal of Educational Psychology, 84*, 62–69.CrossRefGoogle Scholar - Marshall, S.P., & Smith, J.D. (1987). Sex differences in learning mathematics: A longitudinal study with item and error analyses.
*Journal of Educational Psychology, 79*, 372–383.CrossRefGoogle Scholar - Mayer, R. (1981). Frequency norms and structural analysis of algebra story problems into families, categories and templates.
*Instructional Science, 10*, 135–175.CrossRefGoogle Scholar - Mayer, R. (1982). Memory for algebra story problems,
*Journal of Educational Psychology, 74*, 199–216.CrossRefGoogle Scholar - Mayer, R.E. (1987).
*Educational psychology: A cognitive approach*. Boston: Little, Brown.Google Scholar - Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems?
*Journal of Educational Psychology, 77*, 272–284.CrossRefGoogle Scholar - Owen, E., & Sweller, J. (1989). Should problem solving be used as a learning device in mathematics?
*Journal for Research in Mathematics Education, 20*, 322–328.CrossRefGoogle Scholar - Silver, E. (1990). Contributions of research to practice: Applying findings, methods and perspectives. In T. Cooney (Ed.),
*Teaching and Learning Mathematics in the 1990s: 1990 Yearbook*(pp. 1–11). Reston: National Council of Teachers of Mathematics.Google Scholar - Sweller, J. (1988). Cognitive load during problem solving: Effects on learning.
*Cognitive Science, 12*, 257–285.CrossRefGoogle Scholar - Sweller, J. (1989). Cognitive technology: Some procedures for facilitating learning and problem solving in mathematics and science.
*Journal of Educational Psychology, 81*, 457–466.CrossRefGoogle Scholar - Sweller, J. (1990). On the limited evidence for the effectiveness of teaching general problem solving strategies.
*Journal for Research in Mathematics Education, 21*, 411–415.CrossRefGoogle Scholar - Sweller, J., Chandler, P., Tierney, P., & Cooper, M. (1990). Cognitive load and selective attention as factors in the structuring of technical material.
*Journal of Experimental Psychology: General, 119*, 176–192.CrossRefGoogle Scholar - Sweller, J., & Cooper, G.A. (1985). The use of worked examples as a substitute for problem solving.
*Journal of Experimental Psychology; General, 112*, 634–656.Google Scholar - Sweller, J., Mawer, R., & Ward, M. (1983). Development of expertise in mathematical problem solving.
*Journal of Experimental Psychology: General, 112*, 634–656.CrossRefGoogle Scholar - Tarmizi, R., & Sweller, J. (1988). Guidance during mathematical problem solving.
*Journal of Educational Psychology, 80*, 424–436.CrossRefGoogle Scholar - Ward, M., & Sweller, J. (1990). Structuring effective worked examples.
*Cognition and Instruction, 7*, 1–39.CrossRefGoogle Scholar