id: 06458037
dt: j
an: 2015e.00838
au: Kuzmak, Sylvia
ti: A cognitive framework for normative reasoning under uncertainty, and
reasoning about risk, and implications for educational practice.
so: Math. Enthus. 12, No. 1-3, 140-156 (2015).
py: 2015
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: K70 K90 M40 C30 D70
ut: 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
ci:
li: http://www.math.umt.edu/tmme/vol12no1thru3/13_Kuzmak.pdf
ab: 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.
rv: