Abstract
Principles of task design should have both the fundamental function of a clear relation to the learner’s rules, learning powers or hypothetical learning trajectories and the practical function of easy evaluation of many similar tasks. Drawing on some theories and practical tasks in the literature, we developed a total of 11 principles of task design for learning mathematical conjecturing (4), transiting between conjecturing and proving (2), and proving (5). To further validate the functioning of those principles, more empirical research is encouraged.
With Contributors Jane-Jane Lo, Xuhua Sun, and Kahou Chan
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Notes
- 1.
Empirical arguments are arguments that purport to show the truth of a claim by validating the claim in a proper subset of all the possible cases it covers.
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NB: References marked with * are in F. L. Lin, F. J. Hsieh, G. Hanna, & M. de Villiers (Eds.) (2009). ICMI Study 19: Proof and proving in mathematics education. Taipei, Taiwan: The Department of Mathematics, National Taiwan Normal University.
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Lin, FL., Yang, KL., Lee, KH., Tabach, M., Stylianides, G. (2012). Principles of Task Design for Conjecturing and Proving. In: Hanna, G., de Villiers, M. (eds) Proof and Proving in Mathematics Education. New ICMI Study Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2129-6_13
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