Experimentation in Probability Teaching and Learning
This chapter explores the relationship between theoretical and empirical probability in experimentation-based teaching of probability. We examine previous research and a fresh small-scale teaching experiment in order to explore probability teaching, which
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Abstract This chapter explores the relationship between theoretical and empirical probability in experimentation-based teaching of probability. We examine previous research and a fresh small-scale teaching experiment in order to explore probability teaching, which involves students’ (12–13 years old) experimentation with data. The literature review and the teaching experiment point to several challenges for teaching probability through experimentations. Students emphasize absolute frequencies and part–part relationships, which makes it difficult for them to understand the principle of replacement and end up with numerical values to probability estimates. Students also find it hard to compare and make inferences if the samples are made up with different numbers of observations. According to teaching strategies, the teaching experiment shows how experimentation encourages students to engage in questions of chance and probability. Among other things, it is also shown how variation of meaning-contexts supports students understanding of unfamiliar situations and how comparison-oriented questions can be used to promote students understanding of the relationship between theoretical and empirical probability.
1 Introduction It is well known that both research and teaching in probability learning have had and largely still have their main focus on the theoretical, Laplace-oriented interpretation of probability (Jones et al. 2007). In recent years, however, this tradition has been questioned. Theoretical probability is based on the assumption of an equiprobable sample space and this is an assumption that can almost only be made in games of chance (Batanero et al. 2005). To act as conscious citizens of a modern society, we need to be able to express an opinion on the outcome of random events based on the observed frequencies of the event. However, there are also times when we must be able to express an opinion on the likelihood of an event when it is practically impossible to produce empirical evidence of the frequencies of a random event. We P. Nilsson (B) Linnaeus University, Växjö, Sweden e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_28, © Springer Science+Business Media Dordrecht 2014
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must be able to make predictions based on the composition of the random generator, although we cannot make assumptions about equiprobability. This dual nature of probability modeling supports a view of probability teaching that aims to develop an understanding of both theoretical and empirical (frequentist) probability and, in particular, the relationship between them (Nilsson 2009). This chapter provides a discussion on teaching and learning probability in the relationship between theoretical and empirical probability. We examine a smallscale teaching experiment, which involves acts of experimentation. In particular, the purpose of the experiment is to explore and illustrate critical aspects of probability teac
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