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• W618539046 abstract "(ProQuest: ... denotes formulae omitted.)Obstacles for Teaching in SchoolsAlthough is understood as part of our everyday lives (Erickson, 2010) and is a hot (Spiegelhalter, 2014) that should be taught in school (cf. Gigerenzer, 2013), this hot topic seems to play at most minor role in school, particularly if mathematics teaching is regarded. We approach this only seemingly paradox with the following situation (Latten, Martignon, Monti, & Multmeier, 2011, p. 21) that was developed for mathematics teaching:Is it more risky to possess an Alsatian dog (German shepherd) than Chihuahua? It is known that four out of nine Chihuahuas and three out of ten Alsatian dogs bite their owner at most once.The specific task was to compare the risk of possessing an Alsatian dog or Chihuahua. The intended answer was that it is more risky to possess an Alsatian dog, because the result of bite from this dog breed is considerably worse than bite from Chihuahua, although the probability of Chihuahua's bite is bigger than that for bite from an Alsatian dog. This task includes first obstacle for teaching in school. The obstacle is not the dog-task itself, but the amount of different answers. Following different authors who work on issues, we found mainly three possible different answers:1. As mentioned above, the answer of the task developers is that the bite of the Alsatian dog represents the bigger risk. This answer is based on the of as the arithmetical product of measure of the dis-utility represented by random event and the probability p of this event, i.e. = p x measure of the dis-utility of an event (Latten et al., 2011). A disadvantage of this is the problem of measuring dis-utility (c.f. Kent, Pratt, Levinson, Yogui, & Kapadia, 2010). Of course bite from dog represents dis-utility. However it is not clear how to measure the loss of healthiness based on dog's bite. Further, the mentioned arithmetical product does not exist in certain cases. For example bite from the white killer shark (in Steven Spielberg's film Jaws) results in person's death. Thus, if we define the dis-utility of person's death as infinite the of bite from the killer shark is infinity. However, the of discussed above is often used in the literature and is close to the theory of the Subjective Expected Utility, theory of human decisions (Savage, 1954).2. In contrast, Gigerenzer (2013, pp. 39-40) defines as probability of an event that is measurable. The event could represent both good luck and bad luck or rather nice or nasty outcomes (Spiegelhalter, 2011). A disadvantage of this is the unclear distinction between and probability. Although Gigerenzer (2013) discusses lot of examples that intuitively could be assigned to the construct of (e.g. financial risks, diseases, games of chance), nearly every probability of random event could be understood as since nearly every random event represents in certain sense positive or negative outcome. For example, both the probability of bite from an Alsatian dog and the probability of 6 when throwing die represent risk. The of Gigerenzer (2013) is close to the (economical) of Keynes (1921), who defines the Laplacean probability and the frequentistic probability as risk, but subjective probability as (a person's) uncertainty.3. On first view, the third definition includes the demand not to define the term risk: Risk is strange concept. Different disciplines have tried to define it precisely, but perhaps it is better to be informal (Spiegelhalter, 2011, p. 17). On second view, is implicitly defined as situation's characteristic consisting of pair of probability and the related random event that mostly could be understood as bad event. Also this has the difficulty that there is no clear distinction between situation with and situation of uncertainty (without risk). …" @default.
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• W618539046 date "2015-06-01" @default.
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• W618539046 title "Teaching Risk in School" @default.
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