Skip to main content
Log in

Interweaving mathematics and pedagogy in task design: a tale of one task

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

In this article we introduce a usage-goal framework within which task design can be guided and analyzed. We tell a tale of one task, the Pentomino Problem, and its evolution through predictive analysis, trial, reflective analysis, and adjustment. In describing several iterations of the task implementation, we focus on mathematical affordances embedded in the design and also briefly touch upon pedagogical affordances.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. In strictly mathematical terms ‘orientation’ is part of ‘position’. However, as a theme emerging from the data the ‘orientation’ of the pentomino is distinct from its ‘position’.

References

  • Ball, D. (1996). Teacher learning and mathematical reform. Phi Delta Kappan, 77(1), 500–509.

    Google Scholar 

  • Ball, D. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.

    Google Scholar 

  • Feiman-Nemser, S., & Featherston, H. (1992). The student, the teacher, and the moon. In S. Feiman-Nemser, & H. Featherston (Eds.), Exploring teaching: Reinventing an introductory course (pp. 59–85). New York, NY: Teacher College Press.

    Google Scholar 

  • Fosnot, C. (1989). Enquiring teachers, enquiring learners: A constructivist approach for teaching. New York, NY: Teachers College Press.

    Google Scholar 

  • Liljedahl, P. (2007). Affecting affect: The re-education of preservice teachers’ beliefs about mathematics. In P. Elliot, G. Martin, & M. Strutchens (Eds.), 69th NCTM yearbook (2007)—The learning of mathematics.

  • Liljedahl, P. (2006). Pentominoes and AHA!’s. In R. Zazkis, & S. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects (pp. 141–172). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

    Google Scholar 

  • Liljedahl, P. (2005). AHA!: The effect and affect of mathematical discovery on undergraduate mathematics students. International Journal of Mathematical Education in Science and Technology, 36(2,3), 219–234.

    Article  Google Scholar 

  • Mosenthal, J., & Ball, D. (1992). Constructing new forms of teaching: Subject matter knowledge in inservice teacher education. Journal of Teacher Education, 43(5), 347–356.

    Article  Google Scholar 

  • Schoenfeld, A. (1982). Some thoughts on problem-solving research and mathematics education. In F. K. Lester, & J. Garofalo (Eds.), Mathematical problem solving: Issues in research (pp. 27–37). Philadelphia: Franklin Institute Press.

    Google Scholar 

  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter Liljedahl.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liljedahl, P., Chernoff, E. & Zazkis, R. Interweaving mathematics and pedagogy in task design: a tale of one task. J Math Teacher Educ 10, 239–249 (2007). https://doi.org/10.1007/s10857-007-9047-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-007-9047-7

Keywords

Navigation