A Cognitive Framework for Normative Reasoning under Uncertainty, and Reasoning about Risk, and Implications for Educational Practice

Kuzmak, Sylvia
June 2015
Mathematics Enthusiast;Jun2015, Vol. 12 Issue 1-3, p140
Academic Journal
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 Kahneman and Tversky, G. Gigerenzer, and others is related to and contrasted to the framework presented.


Related Articles

  • Scale construction from a decisional viewpoint. Smithson, Michael // Minds & Machines;Aug2006, Vol. 16 Issue 3, p339 

    Many quantitative scales are constructed using cutoffs on a continuum with scores assigned to the cutoffs. This paper develops a framework for using or constructing such scales from a decision-making standpoint. It addresses questions such as: How many distinct thresholds or cutoffs on a scale...

  • Taming chance: Risk and the quantification of uncertainty. Kadvany, John // Policy Sciences;Feb96, Vol. 29 Issue 1, p1 

    The quantification of uncertainty through probability is central to definitions of risk used in environmental policy analysis. This essay explores the translation of unquantified uncertainty into probability and the expression of allied philosophical problems in the practice of environmental...

  • The Role of Probabilistic Reasoning Abilities on Adolescent Risk Taking. Donati, Maria Anna; Chiesi, Francesca; Primi, Caterina // Mathematics Enthusiast;Jun2015, Vol. 12 Issue 1-3, p262 

    The aim of this work was to investigate the role of the cognitive system and the affective system on adolescents’ risk taking in gambling tasks characterized as different on the basis of information given to decision makers. In Study 1, we explored the role of probabilistic reasoning and...

  • Risk as an Explanatory Factor for Researchers’ Inferential Interpretations. Hoekstra, Rink // Mathematics Enthusiast;Jun2015, Vol. 12 Issue 1-3, p103 

    Logical reasoning is crucial in science, but we know that this is not something that humans are innately good at. It becomes even harder to reason logically about data when there is uncertainty, because there is always a chance of being wrong. Dealing with uncertainty is inevitable, for example,...

  • Uncertainty, credal sets and second order probability. Mork, Jonas // Synthese;Feb2013, Vol. 190 Issue 3, p353 

    The last 20 years or so has seen an intense search carried out within Dempster-Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory-another generalization of the traditional...

  • Uncertainty in Lagrangian pollutant transport simulations due to meteorological uncertainty at mesoscale. Angevine, W. M.; Brioude, J.; McKeen, S.; Holloway, J. S. // Geoscientific Model Development Discussions;2014, Vol. 7 Issue 4, p4603 

    Lagrangian particle dispersion models require meteorological fields as input. Uncertainty in the driving meteorology is one of the major uncertainties in the results. The propagation of uncertainty through the system is not simple, and has not been thoroughly explored. Here, we take an ensemble...

  • System of management of uncertainty and risk of renewable resources. Ščurek, Radomír; Stoniš, Ondřej; Konečný, Martin; Maršálek, Daniel // Advanced Materials Research;2014, Vol. 1001, p492 

    The article deals mainly with the risk analysis and uncertainty of a risk of renewable resources. It also mentions the importance of managing the risks associated with the uncertainty of a risk of renewable resources. Specifically, in the paper addressed the relationship between risk and...

  • Comparision of a Case Study of Uncertainty Propagation using Possibility - Probability Transformation. Ali, Tazid; Dutta, Palash; Boruah, Hrishikesh // International Journal of Computer Applications;Dec2011, Vol. 35, p47 

    Uncertainty parameters in risk assessment can be modeled by different ways viz. probability distribution, possibility distribution, belief measure, depending upon the nature and availability of the data. Different transformations exist for converting expression of one form of uncertainty to...

  • Entropic Uncertainty Relation and Information Exclusion Relation for multiple measurements in the presence of quantum memory. Zhang, Jun; Zhang, Yang; Yu, Chang-shui // Scientific Reports;7/3/2015, p11701 

    The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics