Abstract
This study reports on how instruction that is based on engaging students in practical experiments can create challenges and opportunities in the teaching of the relationship between a classical a priori and a frequentist model in estimating the probability of random outcomes. Knowledge is assumed to lie in the inferentialist relationships within the game of giving and asking for reasons (GoGAR). We report on dilemmas (challenges vs. opportunities) faced by the teachers and the researchers who co-designed the tasks: (i) whether it is effective to avoid the elicitation of deterministic reasons for random behaviour or to invite students to reflect on the lack of power of such reasons; (ii) whether the GoGAR is best served by accepting any responses from students or by challenging responses in order to clarify what is normative; (iii) whether the sample space that generates random outcomes should be revealed or not.
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Notes
- 1.
Henceforth, we will refer to a classical a priori model simply as a ‘classical model ’. It is an a priori approach in that it allows for modelling probabilities before any trial is made, based on the assumption of equally likely elementary events in the sample space (Borovcnik and Kapadia 2014).
- 2.
The idea of using transparent and covered bottles filled with marbles as random devices was borrowed from Brousseau et al. (2001).
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Nilsson, P., Eckert, A., Pratt, D. (2018). Challenges and Opportunities in Experimentation-Based Instruction in Probability. In: Batanero, C., Chernoff, E. (eds) Teaching and Learning Stochastics. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-72871-1_4
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