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A cognitive framework for normative reasoning under uncertainty, and reasoning about risk, and implications for educational practice. (English)
Math. Enthus. 12, No. 1-3, 140-156 (2015).
Summary: Clarifying what is normative or appropriate reasoning under various circumstances provides a valuable reference for guiding what should be taught, and, in contrast, what should not be. This paper proposes a cognitive framework for viewing normative reasoning and behavior under uncertainty, including the applying of knowledge of probability and statistics in real world situations; and identifies implications for educational practice. Factors relevant to normative reasoning under uncertainty that are addressed within the framework include: risk of misapplying statistics knowledge, involvement of mathematical and non-mathematical reasoning, knowledge of real world domains and situation/application detail, and existence of expert consensus. The cognitive framework is illustrated using examples of reasoning about risk, including industry standards for risk management. The work of {\it A. Tversky} and {\it D. Kahneman} [“Judgment and uncertainty: heuristics and biases", Science 185, 1124‒1131 (1974)], {\it G. Gigerenzer} [“On narrow norms and vague heuristics: a reply to Kahnemann and Tversky", Psychol. Rev. 103, 592‒596 (1996)], and others is related to and contrasted to the framework presented.
Classification: K70 K90 M40 C30 D70
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