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.
Similar content being viewed by others
Notes
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.
Ball, D. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.
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.
Fosnot, C. (1989). Enquiring teachers, enquiring learners: A constructivist approach for teaching. New York, NY: Teachers College Press.
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.
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.
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.
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.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Author information
Authors and Affiliations
Corresponding author
Rights 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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10857-007-9047-7