Academic journal article The Mathematics Enthusiast

Teaching Risk in School

Academic journal article The Mathematics Enthusiast

Teaching Risk in School

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Obstacles for Teaching Risk in Schools

Although risk is understood as a "part of our everyday lives" (Erickson, 2010) and risk is "a hot topic" (Spiegelhalter, 2014) that should be taught in school (cf. Gigerenzer, 2013), this hot topic seems to play at most a 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 a 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 a Chihuahua. The intended answer was that it is more risky to possess an Alsatian dog, because the result of a bite from this dog breed is considerably worse than a bite from a Chihuahua, although the probability of a Chihuahua's bite is bigger than that for a bite from an Alsatian dog. This task includes a first obstacle for teaching risk in school. The obstacle is not the dog-task itself, but the amount of different answers. Following different authors who work on risk 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 definition of risk as the arithmetical product of a measure of the dis-utility represented by a random event and the probability p of this event, i.e. risk = p x measure of the dis-utility of an event (Latten et al., 2011). A disadvantage of this definition is the problem of measuring a dis-utility (c.f. Kent, Pratt, Levinson, Yogui, & Kapadia, 2010). Of course a bite from a dog represents a dis-utility. However it is not clear how to measure the loss of healthiness based on a dog's bite. Further, the mentioned arithmetical product does not exist in certain cases. For example a bite from the white killer shark (in Steven Spielberg's film Jaws) results in a person's death. Thus, if we define the dis-utility of a person's death as infinite the risk of a bite from the killer shark is infinity. However, the definition of risk discussed above is often used in the literature and is close to the theory of the Subjective Expected Utility, a theory of human decisions (Savage, 1954).

2. In contrast, Gigerenzer (2013, pp. 39-40) defines risk as a 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 definition is the unclear distinction between risk and probability. Although Gigerenzer (2013) discusses a lot of examples that intuitively could be assigned to the construct of risk (e.g. financial risks, diseases, games of chance), nearly every probability of a random event could be understood as a risk since nearly every random event represents in a certain sense a positive or a negative outcome. For example, both the probability of a bite from an Alsatian dog and the probability of a 6 when throwing a die represent a risk. The definition of Gigerenzer (2013) is close to the (economical) risk definition of Keynes (1921), who defines the Laplacean probability and the frequentistic probability as risk, but a subjective probability as (a person's) uncertainty.

3. On a first view, the third "definition" includes the demand not to define the term risk: "Risk is a strange concept. Different disciplines have tried to define it precisely, but perhaps it is better to be informal" (Spiegelhalter, 2011, p. 17). On a second view, risk is implicitly defined as a situation's characteristic consisting of a pair of a probability and the related random event that mostly could be understood as a bad event. Also this definition has the difficulty that there is no clear distinction between a situation with risk and a situation of uncertainty (without risk). …

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