Two experiments examined predictions from two separate explanations for previously observed display effects for communicating low-probability risks: foreground:background salience and proportional reasoning. According to foreground:background salience, people's risk perceptions are based on the relative salience of the foreground (number of people harmed) versus the background (number of people at risk), such that calling attention to the background makes the risk seem smaller. Conversely, the proportional reasoning explanation states that what matters is whether the respondent attends to the proportion, which conveys how small the risk is. In Experiment 1, we made the background more salient via color and bolding; in contrast to the foreground:background salience prediction, this manipulation did not influence participants' risk aversion. In Experiment 2, we separately manipulated whether the foreground and the background were displayed graphically or numerically. In keeping with the proportional reasoning hypothesis, there was an interaction whereby participants given formats that displayed the foreground and background in the same modality (graphs or numbers, thereby making the proportion easier to form) saw the probability as smaller and were less risk averse than participants given the information in different modalities. There was also a main effect of displaying the background graphically, providing some support for foreground:background salience. In total, this work suggests that the proportional reasoning account provides a good explanation of many display effects related to communicating low-probability risks, although there is some role for foreground:background salience as well.questions did not influence their response to that question. Next, they filled out a packet containing the rest of the measures listed above and some other items included for exploratory purposes. Figure 4. Experiment 2 risk magnitude information displaying (a) the background information numerically and the foreground information graphically and (b) the background information graphically and the foreground information numerically 480 Journal of Behavioral Decision Making

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A literate person must have a basic understanding of how science works. One important component of scientific literacy is understanding that the ability to identify causal relations between variables is central to explaining scientific phenomena and, in turn, that isolating causal relations depends on being able to control irrelevant variables. Indeed, an understanding of the logic of controlling variables is a landmark goal of early science education (National Research Council, 1996; Zimmerman, 2005). Instruction in strategies to control variables (CVS) has been the focus of a great deal of education research (Ross, 1988; Schwichow, Croker, Zimmerman, Hoffler, & Hartig, 2016) and the subject of a long debate in the literature. There continues to be much discussion of the relative merits of embedding instruction of CVS in an authentic, complex scientific context (Allchin, 2014; Kuhn, Ramsey, & Arvidsson, 2015) as opposed to teaching CVS in a simpler and relatively isolated scientific context (Klahr & Chen, 2011; Lorch et al., 2014). This discussion should and will continue; however, there is now substantial empirical evidence that a rudimentary understanding of CVS can be effectively taught to many 4 th-grade students using a relatively brief intervention that emphasizes direct instruction of the key concepts. A protocol first developed by Chen and Klahr (1999) has proven effective at teaching CVS in lab studies. The basic teaching intervention uses a simplified, concrete domain to illustrate the logic of experimentation. For example, a commonly used domain investigates the effects of different variables on how far a ball rolls