Skip to main content
Log in

The Impact of Teacher Privileging on Learning Differentiation with Technology

  • Published:
International Journal of Computers for Mathematical Learning Aims and scope Submit manuscript

Abstract

This study examines how two teachers taught differentiation using a hand held computer algebra system, which made numerical,graphical and symbolic representations of the derivative readily available. The teachers planned the lessons together but taught their Year 11 classes in very different ways. They had fundamentally different conceptions of mathematics with associated teaching practices,innate ‘privileging’ of representations, and of technology use. This study links these instructional differences to the different differentiation competencies that the classes acquired. Students of the teacher who privileged conceptual understanding and student construction of meaning were more able to interpret derivatives. Students of the teacher who privileged performance of routines made better use of the CAS for solving routine problems. Comparison of the results with an earlier study showed that although each teacher's teaching approach was stable over two years, each used technology differently with further experience of CAS. The teacher who stressed understanding moved away from using CAS, whilst the teacher who stressed rules,adopted it more. The study highlights that within similar overall attainment on student tests, there can be substantial variations of what students know. New technologies provide more approaches to teaching and so greater variations between teaching and the consequent learning may become evident.

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.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Dick, T.P. (1996). Much more than a toy. Graphing calculators in secondary school calculus. In P. Gomez and B. Waits (Eds), Roles of Calculators in the Classroom (pp. 31-46). Una Empressa Docente, USA.

    Google Scholar 

  • Ellison, M. (1994). The Effect of Computer and Calculator Graphics on Students' Ability to Mentally Construct Calculus Concepts. (Doctoral dissertation, The University of Minnesota, 1993). Dissertation Abstracts International, 51/11, 4020.

  • Etlinger, L. (1974). The electronic calculator: A new trend in school mathematics. Educational Technology XIV(12): 43-45.

    Google Scholar 

  • Fennema, E. and Franke, M. (1992). Teachers' knowledge and its impact. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 147-164). New York: Macmillan.

    Google Scholar 

  • Heid, M.K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education 19(1): 3-25.

    Article  Google Scholar 

  • Hillel, J. (1993). Computer algebra systems as cognitive technologies: Implications for the practice of mathematics education. In C. Keitel and K. Ruthven (Eds), Learning from Computers: Mathematics Education and Technology (pp. 18-47). Berlin: Springer-Verlag.

    Google Scholar 

  • Hoyles, C. (1992). Mathematics teaching and mathematics teachers: A meta-case study. For the Learning of Mathematics 12(3): 32-44.

    Google Scholar 

  • Jost, K.L.E. (1992). The Implementation of Technology in the Calculus Classroom: An Examination of Teacher Beliefs, Practice and Curriculum Change. (Doctoral dissertation, Syracuse University, 1992). Dissertation Abstracts International, 53/06, 1876.

  • Keller, B., Russell, C. and Thompson, H. (1999). A large-scale study clarifying the roles of the TI-92 and instructional format on student success in calculus. International Journal of Computer Algebra in Mathematics Education 6(3): 191-207.

    Google Scholar 

  • Kendal, M. and Stacey, K. (1999a). CAS, calculus and classrooms. In O. Zaslavsky (Ed.), Proceedings of the 23rd Annual Conference of the International Group for the Psychology of Mathematics Education. PME, Haifa, Israel, 3, pp. 129-136.

    Google Scholar 

  • Kendal, M. and Stacey, K. (1999b) Varieties of teacher privileging for teaching calculus with computer algebra systems. International Journal of Computer Algebra in Mathematics Education 6(4): 233-247.

    Google Scholar 

  • Kendal, M. and Stacey, K. (2000). Tracing learning of three representations of differentiation with the derivative competency framework. Research in Computer Algebra Systems in Schools Collected Papers. DSME Preprint 4/2000 20-38.

  • Kuhn, T. and Ball, D. (1986). Approaches to Teaching Mathematics: Mapping the Domains of Knowledge, Skills and Dispositions. East Lansing: Michigan State University, Center on Teacher Education.

    Google Scholar 

  • Lagrange, J. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching precalculus. International Journal of Computers for Mathematical Learning 4: 51-81.

    Article  Google Scholar 

  • Noss, R. and Hoyles (1996). Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht, Netherlands: Kluwer Academic.

    Google Scholar 

  • Palmiter, J. (1991). Effects of computer algebra systems on concept and skill acquisition in calculus. Journal for Research in Mathematics Education 22(2): 151-156.

    Article  Google Scholar 

  • Penglase, M. and Arnold, S. (1996). The graphics calculator in mathematics education: A critical review of recent research. Mathematics Education Research Journal 8(1): 58-90.

    Google Scholar 

  • Repo, S. (1994). Understanding and reflective abstraction: Learning the concept of derivative in a computer environment. International DERIVE Journal 1(1): 97-113.

    Google Scholar 

  • Simmt, E. (1997). Graphing calculators in High School mathematics. Journal of Computers in Mathematics and Science Teaching 16(2/3): 269-289.

    Google Scholar 

  • Tall, D. (1996). Functions and Calculus (Vol. 1). Dordrecht, Netherlands: Kluwer Academic.

    Google Scholar 

  • Tharp, M., Fitzsimmons, J. and Brown Ayers, R. (1997). Negotiating a technological shift: Teacher perception of the implementation of graphing calculators. Journal of Computers in Mathematics and Science Teaching 16(4): 551-575.

    Google Scholar 

  • Thomas, M., Tyrrell, J. and Bullock, J. (1996). Using computers in the mathematics classroom: The role of the teacher. Mathematics Education Research Journal 8(1): 38-57.

    Google Scholar 

  • Thompson, A.G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 127-146). New York: Macmillan.

    Google Scholar 

  • Wertsch, J. (1990). The Voice of Rationality in a Sociocultural Approach to Mind. Cambridge: Cambridge University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kendal, M., Stacey, K. The Impact of Teacher Privileging on Learning Differentiation with Technology. International Journal of Computers for Mathematical Learning 6, 143–165 (2001). https://doi.org/10.1023/A:1017986520658

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017986520658

Navigation