Why People are Not Like Marbles in an Urn: An Effect of Context on Statistical Reasoning

The Role of Context in Developing Informal Statistical Inferential Reasoning: A Classroom Study

“…The conversations with different task-contexts (e.g., cell phone task, Orbital Express task) expanded and grew IIR learning for the data story in the contextual domain. As Schwartz and Goldman (1996) suggested, different task-contexts can improve student learning. But when developing learners' IIR using newly learnt theory-the data story in the statistical domain-the data-context or previously held theories may dominate if the theory has not been developed in a way that will transfer easily to the task under consideration.…”

“…The strong influence of task-context dependent reasoning has been noted by Schwartz and Goldman (1996) who believe that instruction needs to expose students' prototheories, give them opportunities to reconcile discrepancies, and provide new situations in which students can test and receive feedback on their current prototheories. Because the task learning-experience-context of the problem has a powerful effect they suggest that different task-contexts will bring forth different prototheories and hence students can "discover organizing principles that will align the prototheories and improve progress towards normative theories" (p. S110).…”

Statistical reasoning of middle school children engaged in survey inquiry

“…This way of reasoning was also found in studies involving the sampling of individuals. Schwartz and Goldman (1996) suggested that statistical rules for sampling are less evident when individuals as opposed to neutral objects, such as M&Ms, form a population because both characteristics (e.g., age, gender, political affiliation) and opinions/interests of that population are sampled. Students in our study focused on population interests in sampling categories by anticipating responses to a survey question based on their knowledge of the population.…”

“…Personal knowledge and beliefs seem to play a critical role in children's statistical reasoning (Jacobs, 1999;Schwartz & Goldman, 1996;Schwartz, Goldman, Vye, Barron, & CTGV, 1998). Similar findings are reported in studies involving inquiry situations (Zimmerman, 2000(Zimmerman, , 2005.…”

“…Studies with adults (Nisbett, 1993) and middle school children (Jacobs, 1999;Schwartz & Goldman, 1996;Schwartz et al, 1998) suggest that normative statistical reasoning about sampling is more likely elicited on formal statistical or chance problems involving random generating devices than on problems that are more social in nature, such as surveys, where individuals are selected to be in a sample. For example, when the hypothetical sampling context involved M&Ms (i.e., a chance context), Jacobs (1993) found that middle school students who had not received any formal statistical training were able to reason on statistical grounds.…”