## Abstract

We investigated how students interpret linear and quadratic graphs on a graphics calculator screen. Clinical interviews were conducted with 25 Grade 10–11 students as they used graphics calculators to study graphs of straight lines and parabolas. Student errors were attributable to four main causes: a tendency to accept the graphic image uncritically, without attempting to relate it to other symbolic or numerical information; a poor understanding of the concept of scale; an inadequate grasp of accuracy and approximation; and a limited grasp of the processes used by the calculator to display graphs. Implications for teaching are discussed.

This is a preview of subscription content, access via your institution.

## References

Asp, G., Dowsey, J., & Stacey, K. (1993). Linear and quadratic graphs with the aid of technology. In B. Atweh, C. Kanes, & M. Carss (Eds.),

*Contexts in mathematics education*(Proceedings of the 16th annual conference of the Mathematics Education Research Group of Australasia, pp. 51–56). Brisbane: MERGA.Cavanagh, M., & Mitchelmore, M. C. (2000a). Students’ technical difficulties in operating a graphics calculator. In J. Bana & A. Chapman (Eds.),

*Mathematics education beyond 2000*(Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia, pp. 142–148). Perth: MERGA.Cavanagh, M., & Mitchelmore, M. C. (2000b).

*Student misconceptions in interpreting basic graphic calculator displays*. In N. Nakahara & M. Koyama (Eds.),*Proceedings of the 24th conference of the International Group for the Psychology of Mathematics*(Vol. 2, pp. 161–169). Hiroshima, Japan: Program Committee.Cavanagh, M., & Mitchelmore, M. C. (2000c). Graphics calculators in mathematics learning: Studies of student and teacher understanding. In M. O. J. Thomas (Ed.)

*Proceedings of TIME 2000, an International Conference on Technology in Mathematics Education*(pp. 112–119). Auckland, NZ.Demana, F., Schoen, H. L., & Waits, B. (1993). Graphing in the K-12 curriculum: The impact of the graphing calculator. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.),

*Integrating research on the graphical representation of functions*(pp. 11–40). Hillsdale, NJ: Lawrence Erlbaum.Dick, T. (1992). Super calculators: Implications for the calculus curriculum, instruction, and assessment. In J. T. Fey & C. R. Hirsch (Eds.),

*Calculators in mathematics education: 1992 yearbook*(pp. 145–157). Reston, VA: National Council of Teachers of Mathematics.Dion, G. S., & Fetta, I. B. (1993). Calculator graphs: Magic? or mathematics?

*Mathematics and Computer Education, 27*, 180–197.Dowsey, J., & Tynan, D. (1997). Making the most of the magic number.

*The Australian Mathematics Teacher, 53*(2), 42–46.Dugdale, S. (1993). Functions and graphs: Perspectives on student thinking. In T. A. Romberg, E. Fennema & T. P. Carpenter (Eds.),

*Integrating research on the graphical representation of functions*(pp. 101–130). Hillsdale, NJ: Lawrence Erlbaum.Dunham, P., & Dick, T. (1994). Research on graphing calculators.

*The Mathematics Teacher, 87*, 440–445.Giamati, C. M. (1991). The effect of graphing calculator use on students’ understanding of variations on a family of equations and the transformations of their graphs. (Doctoral dissertation, University of Michigan, 1990).

*Dissertation Abstracts International, 52/01*, 103.Goldenberg, E. P. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representation of functions.

*Journal of Mathematical Behaviour, 7*, 135–173.Goldenberg, E. P., & Kliman, M. (1988). Metaphors for understanding graphs: What you see is what you see (Report No. ETC-TR-88-22). Cambridge, MA: Harvard Graduate School of Education, Educational Technology Center. (ERIC Document Reproduction Service No. ED 303 369)

Kissane, B., Bradley, J., & Kemp, M. (1994). Graphics calculators, equity and assessment.

*Australian Senior Mathematics Journal, 8*(2), 31–43.Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching.

*Review of Educational Research, 60*, 1–64.Moschkovich, J., Schoenfeld, A. H., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. In T. A. Romberg, E. Fennema & T. P. Carpenter (Eds.),

*Integrating research on the graphical representation of functions*(pp. 69–100). Hillsdale, NJ: Lawrence Erlbaum.Mueller, D., & Forster, P. (1999). Graphics calculators in the public examination of calculus: Misuses and misconceptions. In J. M. Truran & K. M. Truran (Eds.),

*Making the difference*(Proceedings of the 22nd annual conference of the Mathematics Education Research Group of Australasia, pp. 396–403). Adelaide: MERGA.Penglase, M., & Arnold, S. (1996). The graphics calculator in mathematics education: A critical review of recent research.

*Mathematics Education Research Journal, 8*, 58–91.Ruthven, K. (1990). The influence of graphic calculator use on translation from graphic to symbolic forms.

*Educational Studies in Mathematics, 21*, 431–450.Steele, D. (1994).

*The Wesley College Technology Enriched Graphing Project*. (Unpublished Master’s thesis, University of Melbourne, 1994).Tuska, A. (1993). Students’ errors in graphing calculator-based precalculus classes. (Doctoral dissertation, The Ohio State University, 1992).

*Dissertation Abstracts International*, 53/08, 2725.Vonder Embse, C., & Engebretsen, A. (1996). Friendly windows for graphing calculators.

*The Mathematics Teacher, 89*, 508–511.Waits, B. K., & Demana, F. (2000). Calculators in mathematics teaching and learning: Past, present, and future. In M. J. Burke & F. R. Curcio (Eds.),

*Learning mathematics for a new century*(pp. 51–66). Reston, VA: National Council of Teachers of Mathematics.Williams, C. G. (1993). Looking over their shoulders: Some difficulties students have with graphing calculators.

*Mathematics and Computer Education, 27*, 198–202.

## Author information

### Authors and Affiliations

## Rights and permissions

## About this article

### Cite this article

Mitchelmore, M., Cavanagh, M. Students’ difficulties in operating a graphics calculator.
*Math Ed Res J* **12**, 254–268 (2000). https://doi.org/10.1007/BF03217088

Issue Date:

DOI: https://doi.org/10.1007/BF03217088

### Keywords

- Mathematic Teacher
- Mathematic Education Research
- Window Setting
- Tick Mark
- Pixel Grouping