Probabilistic Thinking: Analyses from a Psychological Perspective
In this paper, we describe the major lines of debate that run through the research on probabilistic understanding from a psychological perspective. A first line deals with the question whether humans can be considered as unbiased, natural-born statisticia
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A sophisticated understanding of probability and risk seems evident to become a must in various specialized areas such as medics, economics, logistics, or insurance. But it is equally important in many other domains of modern science such as subatomic physics and in the study of evolution, so that one can easily argue that it is crucial to scientific literacy. Nowadays, however, the ability to interpret and critically evaluate stochastic phenomena that people encounter in diverse contexts is considered essential not only for scientists but for everyone. Being statistically literate (Gal 2002) seems necessary in order to act as an informed and critical citizen in modern society (Rumsey 2002; Utts 2003). Not only its societal importance turned probabilistic reasoning into a rich domain of research. Probability received interest by researchers from a variety of fields for several other reasons. From a curricular point of view, it is a field having strong links to other areas of mathematics (such as proportional reasoning, combinatorics, multiplicative reasoning, and being closely linked to formal logic as well) while not completely defined by them: Probability is additionally characterized by a focus on situations in which the result is variable and characterized by randomness, uncertainty and outcomes being independent of previous outcomes. Altogether, these characteristics lead to unpredictability, particularly of specific outcomes. So, unlike in other mathematical domains (for instance, I can easily and convincingly show that the area of a circle is not doubled if its diameter is doubled) it is often much more difficult to validate one’s assumptions of a probabilistic situation (for instance, the idea that the chance of getting at least one six is doubled if the number of die rolls is doubled). Besides mathematical challenges, probabilistic situations often also pose emotional challenges. Very often, probabilistic situations are not merely neutral to the problem solver, as the outcomes have a particular personal relevance and emotional, societal or material value: One strategy of playing a game may lead to a larger W. Van Dooren (B) Centre for Instructional Psychology and Technology, University of Leuven, Leuven, Belgium e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_7, © Springer Science+Business Media Dordrecht 2014
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chance of success of winning a valuable prize, the implementation of a certain diagnostic screening may lead to the early detection of a rare disease, but with a risk of showing false positives (and sometimes even more false than true positives). A final characteristic that makes probability interesting as a domain is that people apparently perform notoriously badly in a wide variety of tasks that require probabilistic thinking to arrive at a normatively correct answer. Systematic errors have been observed in a variety of ages and expertise levels, and also hist
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