Understanding Risk through Board Games

Within our information-driven society, understanding and making decisions about risk has become important for personal and professional success. Each day individuals are bombarded by information from a host of organizations seeking to inform, influence, and persuade choices through the use of hypothetical situations involving risk, which I refer to as risk-laden (RL) situations. Here RL situations are defined as any situation that presents a perceived risk directly (e.g., men over the age of 25 have increased risk for gestational diabetes) or presents a risk indirectly by using probabilistic language (e.g., the odds of dying from heart disease are 1 in 7). Adults, in particular, are targeted by a host of groups (e.g., news organizations, advertisers, health professionals, financial planners, insurance companies) each of whom seeks to use RL situations to inform, influence, and motivate choices.RL situations can be differentiated using two criteria, which I will call (and later define) density and complexity. Density refers to the extent to which probabilistic information is incorporated into a RL situation. Low-density RL situations present simple probabilities whereas high-density situations use sophisticated probabilistic language that may be embedded or indirectly expressed. Complexity refers to the context of an RL situation. Everyday contexts have a relatively low complexity whereas specialized contexts have high complexity. These criteria are useful in comparing RL situations directly. For example, consider the following two situations: (a) A meteorologist reports that there is a 60% chance of rain this weekend; and, (b) Doctor John shows Kim the following finding from a medical study, "When used in primary prevention settings, aspirin has been shown to reduce serious vascular events among individuals at average/low risk by 12% (0.51% versus 0.57%/year, P = 0.0001)" (Cuzick et al., 2014, p. 5). The first situation has a low degree of density and complexity because it presents a simple probability within an everyday context. The second has a higher degree of complexity and density because it uses sophisticated mathematical language set within a more specific context. Thus, RL situations with high degrees of density and complexity embed sophisticated probabilistic information within specialized contexts.Although different in tenus of density and complexity, both of the previously mentioned situations present similar issues in decoding. For example, what does a 60% chance of rain mean? Does each day during the weekend have a 60% chance of rain? If it rains the first day, will the next day still have the same chance of rain? Similarly, what does it mean for an individual to be at average/low risk? What infonnation factors into this classification? What does a 12% reduction in serious vascular events amount to in terms of overall risk for these events? Additionally, the interpretation of each statement might change based upon the person making it. What if the meteorologist in the first situation worked for the National Weather Service? What if they worked for an insurance company? What if Dr. John were Kim's family doctor? What if he worked as a consultant for a retailer? These examples illustrate that, regardless of density and complexity, RL situations present similar challenges to individuals in terms of unpacking and understanding.Although mathematics education researchers have investigated a range of probabilistic concepts, RL situations present different challenges for several reasons. First, RL situations often require one to make sense of several different hypothetical outcomes and weigh competing possibilities against one another in order to make sense of the situation and determine the most beneficial decision. In some instances the best decision might yield a beneficial outcome, but in others the best decision might be the outcome with the least potential consequences. Second, in contrast to familiar contexts where the probability of an event does not change (e. …