Skip to main content
Log in

Visual, algebraic and mixed strategies in visually presented linear programming problems

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Linear programming problems were presented, in a predominantly visual setting, to high school students who were not acquainted with any specific methods for solving such problems. The strategies developed by the students for coping with these problems were identified and classified. Visual strategies were developed more frequently than either algebraic or mixed ones. In many cases, these visual strategies were unsophisticated. Providing the students with a visual solution tool (a level curve of the target function) did not lead to significant changes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bondesan, M. G. and Ferrari, P. L.: 1991, ‘The active comparison of strategies in problem solving: An exploratory study’, in F. Furinghetti (ed.),Proceedings of the Fifteenth International Conference on the Psychology of Mathematics Education, Assisi, Italy, Vol. I, pp. 168–175.

    Google Scholar 

  • Case, R.: 1978, ‘A developmentally based theory and technology of instruction’,Review of Educational Research 48(3), 439–463.

    Google Scholar 

  • Clements, M. A.: 1984, ‘Terence Tao’,Educational Studies in Mathematics 15(3), 213–238.

    Google Scholar 

  • Collis, K. F. and Watson, J. M.: 1991, ‘A mapping procedure for analyzing the structure of mathematics responses’,Journal of Structural Learning 11(1), 65–87.

    Google Scholar 

  • Dantzig, G. B.: 1963,Linear Programming and Extensions, Princeton University Press, Princeton, NJ.

    Google Scholar 

  • Eisenberg, T. and Dreyfus, T.: 1991, ‘On the reluctance to visualize in mathematics’, in W. Zimmermann and S. Cunningham (eds.),Visualization in Teaching and Learning Mathematics, Mathematical Association of America, pp. 25–38.

  • Noelting, G.: 1980, ‘The development of proportional reasoning and the ratio concept’,Educational Studies in Mathematics 11(2), 217–255 and 11(3), 331–363.

    Google Scholar 

  • Presmeg, N.: 1986, ‘Visualization and mathematical giftedness’,Educational Studies in Mathematics 17(3), 297–311.

    Google Scholar 

  • Shama, G. and Dreyfus, T.: 1991, ‘Spontaneous strategies for visually presented linear programming problems’, in F. Furinghetti (ed.),Proceedings of the Fifteenth International Conference on the Psychology of Mathematics Education, Assisi, Italy, Vol. III, pp. 262–269.

    Google Scholar 

  • Vinner, S.: 1989, ‘Avoidance of visual considerations in calculus students’,FOCUS on Learning Problems in Mathematics 11(2), 149–156.

    Google Scholar 

  • Wilkening, F. and Lange, K.: 1990, ‘When is children's perception holistic? Goals and styles in processing multidimensional stimuli’, in T. Globerson and T. Zelniker (eds.),Cognitive Style and Cognitive Development, Ablex, Norwood, NJ.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shama, G., Dreyfus, T. Visual, algebraic and mixed strategies in visually presented linear programming problems. Educ Stud Math 26, 45–70 (1994). https://doi.org/10.1007/BF01273300

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01273300

Keywords

Navigation