caa a22 4500 445882085 CHVBK 20180317145546.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s10649-010-9288-8 doi (NATIONALLICENCE)springer-10.1007/s10649-010-9288-8 From personal to conventional probabilities: from sample set to sample space [Elektronische Daten] [Egan Chernoff, Rina Zazkis] 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. Springer Science+Business Media B.V., 2010 Sample space nationallicence Sample set nationallicence Classical probability nationallicence Subjective probability nationallicence The problem of points nationallicence Chernoff Egan College of Education, University of Saskatchewan, 28 Campus Drive, SK S7N 0X1, Saskatoon, Canada aut Zazkis Rina Faculty of Education, Simon Fraser University, 8888 University Drive, BC V5A 1S6, Burnaby, Canada aut Educational Studies in Mathematics Springer Netherlands 77/1(2011-05-01), 15-33 0013-1954 77:1<15 2011 77 10649 https://doi.org/10.1007/s10649-010-9288-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10649-010-9288-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chernoff Egan College of Education, University of Saskatchewan, 28 Campus Drive, SK S7N 0X1, Saskatoon, Canada aut NATIONALLICENCE 700 1- Zazkis Rina Faculty of Education, Simon Fraser University, 8888 University Drive, BC V5A 1S6, Burnaby, Canada aut NATIONALLICENCE 773 0- Educational Studies in Mathematics Springer Netherlands 77/1(2011-05-01), 15-33 0013-1954 77:1<15 2011 77 10649 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer