TY - JOUR

T1 - Paradox, programming, and learning probability

T2 - A case study in a connected mathematics framework

AU - Wilensky, Uri

N1 - Funding Information:
The preparation of this article was supported by the National Science Foundation (Grant # MDR 875 1190),th e LEG0 Group, and Nintendo Inc., Japan. The ideas expressed here do not necessarily reflect the positions of the supporting agencies. I’d like to thank Seymour Papert, Mitchel Resnick, and David Chen for extensive feedback about this research. I’d also like to thank Donna Woods, Paul Whitmore, Ken Ruthven, Walter Stroup, David Rosenthal, Richard Noss, Yasmin Kafai, Wally Feurzeig, Laurie Edwards, Barbara Brizuela, and Aaron Brandes for helpful comments on drafts of this article. Finally, I’d like to thank Ellie and all the participants in the Connected Probability project. I have learned a lot from (and with) you.

PY - 1995/6

Y1 - 1995/6

N2 - Formal methods abound in the teaching of probability and statistics. In the Connected Probability project, we explore ways for learners to develop their intuitive conceptions of core probabilistic concepts. This article presents a case study of a learner engaged with a probability paradox. Through engaging with this paradoxical problem, she develops stronger intuitions about notions of randomness and distribution and the connections between them. The case illustrates a Connected Mathematics approach: that primary obstacles to learning probability are conceptual and epistemological; that engagement with paradox can be a powerful means of motivating learners to overcome these obstacles; that overcoming these obstacles involves learners making mathematics-not learning a "received" mathematics and that, through programming computational models, learners can more powerfully express and refine their mathematical understandings.

AB - Formal methods abound in the teaching of probability and statistics. In the Connected Probability project, we explore ways for learners to develop their intuitive conceptions of core probabilistic concepts. This article presents a case study of a learner engaged with a probability paradox. Through engaging with this paradoxical problem, she develops stronger intuitions about notions of randomness and distribution and the connections between them. The case illustrates a Connected Mathematics approach: that primary obstacles to learning probability are conceptual and epistemological; that engagement with paradox can be a powerful means of motivating learners to overcome these obstacles; that overcoming these obstacles involves learners making mathematics-not learning a "received" mathematics and that, through programming computational models, learners can more powerfully express and refine their mathematical understandings.

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U2 - 10.1016/0732-3123(95)90010-1

DO - 10.1016/0732-3123(95)90010-1

M3 - Article

AN - SCOPUS:58149319956

VL - 14

SP - 253

EP - 280

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

IS - 2

ER -