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.
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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’.
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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) doi:10.1007/s10857-007-9047-7
- Task design
- Teacher education
- Pentomino problem
- Task knowledge
- Pedagogical task knowledge
- Usage-goal framework