From personal to conventional probabilities: from sample set to sample space |
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| Authors: | Egan J Chernoff and Rina Zazkis |
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| Institution: | (1) College of Education, University of Saskatchewan, 28 Campus Drive, Saskatoon, SK S7N 0X1, Canada;(2) Faculty of Education, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada |
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| Abstract: | This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that
reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with
learners’ initial ways of reasoning. We suggest a “desirable pedagogical approach” in which the solution builds on the set
of outcomes as identified by learners and serves as a bridge towards mathematical convention. To explore prospective high
school mathematics teachers’ ideas related to addressing a potential learner’s mistake and their reactions towards the suggested
approach, we presented them with two tasks. In Task I, participants (n = 30) were asked to suggest a pedagogical remedy to a frequent mistake found in dealing with a standard probability problem,
whereas in Task II, they were asked to solve a probabilistic problem, which they had not encountered previously. We discuss
participants’ mathematical solutions to Task II in reference to their pedagogical approaches to Task I. The presented disparity
serves in extending the convincing power of the suggested pedagogical approach. |
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