
06458037
j
2015e.00838
Kuzmak, Sylvia
A cognitive framework for normative reasoning under uncertainty, and reasoning about risk, and implications for educational practice.
Math. Enthus. 12, No. 13, 140156 (2015).
2015
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
K70
K90
M40
C30
D70
risk
stochastics
statistics
probability theory
learning objectives
real life mathematics
risk management
reasoning under uncertainty
statistical reasoning
probabilistic reasoning
teaching
errors
misconceptions
statistics application
goals of mathematics education
stochastic thinking
http://www.math.umt.edu/tmme/vol12no1thru3/13_Kuzmak.pdf
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 nonmathematical 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, 11241131 (1974)], {\it G. Gigerenzer} [``On narrow norms and vague heuristics: a reply to Kahnemann and Tversky", Psychol. Rev. 103, 592596 (1996)], and others is related to and contrasted to the framework presented.