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Abstract Interactive computer simulations are commonly used as pedagogical tools to support students’ statistical reasoning. This paper examines whether and how these simulations enable their intended effects. We begin by contrasting two theoretical frameworks—dual processes and grounded cognition—in the context of people’s conceptions about statistical sampling, setting the stage for the potential benefits of simulations in learning such conceptions. Then, we continue with reviewing the educational literature on statistical sampling simulations. Our review tentatively suggests benefits of the simulations for building statistical habits of mind. However, challenges seem to persist when more specific concepts and skills are investigated. With and without simulations, students have difficulty forming an aggregate view of data, interpreting sampling distributions, showing a process-based understanding of the law of large numbers, making statistical inferences, and context-independent reasoning. We propose that grounded cognition offers a framework for understanding these findings, highlighting the bidirectional relationship between perception and conception, perceptual design features, and guided perceptual routines for supporting students’ meaning making from simulations. Finally, we propose testable instructional strategies for using simulations in statistics education.

Abstract We analyze the visual perception task that home plate umpires (N = 121) perform calling balls and strikes (N = 3,001,019) in baseball games, focusing on the topics of perceptual learning and bias in decision-making. In the context of perceptual learning, our results show that monitoring, training, and feedback improve skill over time. In addition, we document two other aspects of umpires’ improvement that are revealing with respect to the nature of their perceptual expertise. First, we show that biases in umpires’ decision-making persist even as their overall accuracy improves. This suggests that bias and accuracy are orthogonal and that reduction of bias in decision-making requires interventions aimed specifically at this goal. Second, we measure a distinct difference in the rate of skill improvement between older and younger umpires. Younger umpires improve more quickly, suggesting that the decision task umpires engage in becomes routinized over time.

In the present exploratory study we investigate whether cognitive flexibility is a unitary mechanism underlying flexible behaviours across many domains or a domain-specific capacity. The literature on cognitive flexibility is divided into several research lines that do not converge. The most prominent one considers flexibility an executive function that represents the ability to switch among rules or tasks. In other research traditions it is associated with distinct components, such as the capacity to place an item into many categories (in creativity tests) or a characteristic of different cognitive or perceptual processes (e.g., flexible language use, flexibility in mathematics, perceptual flexibility). To determine whether flexibility in different domains relies on a general shared mechanism, 221 subjects from two countries (The United States and Romania, mean age 19.52 years) were tested online with several measurements from four different domains of investigation: language, mathematics, perception, and executive functions (specifically, set shifting). All tasks required some form of cognitive flexibility. In addition, we measured math anxiety to see how this relates to mathematical flexibility. The results show very few and small significant partial correlations among the tasks. They also highlight that there is no unitary overarching “executive” factor. The most prominent common factor was speed of processing for mathematical and language response times. Shifting does not seem to be a mechanism that underlies flexibility in all the investigated domains. While we acknowledge the need for replication of this study, the data suggest that the construct of shifting does not exhaust the notion of flexibility as it arises across cognitive domains.

Abstract In peer instruction, instructors pose a challenging question to students, students answer the question individually, students work with a partner in the class to discuss their answers, and finally students answer the question again. A large body of evidence shows that peer instruction benefits student learning. To determine the mechanism for these benefits, we collected semester-long data from six classes, involving a total of 208 undergraduate students being asked a total of 86 different questions related to their course content. For each question, students chose their answer individually, reported their confidence, discussed their answers with their partner, and then indicated their possibly revised answer and confidence again. Overall, students were more accurate and confident after discussion than before. Initially correct students were more likely to keep their answers than initially incorrect students, and this tendency was partially but not completely attributable to differences in confidence. We discuss the benefits of peer instruction in terms of differences in the coherence of explanations, social learning, and the contextual factors that influence confidence and accuracy.

In visual search tasks, physically large target stimuli are more easily identified among small distractors than are small targets among large distractors. The present study extends this finding by presenting preliminary evidence of a new search asymmetry: stimuli that symbolically represent larger magnitude are identified more easily among featurally equivalent distractors that represent smaller magnitude. Participants performed a visual search task using line-segment digits representing the numbers 2 and 5, and the numbers 6 and 9, as well as comparable non-numeric control stimuli. In three experiments, we found that search times are faster when the target is a digit that represents a larger magnitude than the distractor, although this pattern was not evident in one additional experiment. The results provide suggestive evidence that the magnitude of a number symbol can affect perceptual comparisons between number symbols, and that the semantic meaning of a target stimulus can systematically affect visual search.

This paper uses laboratory experiments to examine the effect of an endogenous rule change from open access to private property as a potential solution to overharvesting in commons dilemmas. A novel, spatial, real-time renewable resource environment was used to investigate whether participants were willing to invest in changing the rules from an open access situation to a private property system. We found that half of the participants invested in creating private property arrangements. Groups who had experienced private property in the second round of the experiment, made different decisions in the third round when open access was reinstituted in contrast to groups who experienced three rounds of open access. At the group level, earnings increased in Round 3, but this was at a cost of more inequality. No significant differences in outcomes occurred between experiments where rules were imposed by the experimental design or chosen by participants.

Studying different concepts by frequently alternating between them (i.e., interleaving), improves discriminative contrast between different categories, while studying each concept in separate blocks emphasizes the similarities within each category. Interleaved study has been shown to improve learning of high similarity categories by increasing between-category comparison, while blocked study improves learning of low similarity categories by increasing within-category comparison. In addition, interleaved study presents greater temporal spacing between repetitions of each category compared to blocked study, which might present long-term memory benefits. In this study we asked if the benefits of temporal spacing would interact with the benefits of sequencing for making comparisons when testing was delayed, particularly for low similarity categories. Blocked study might be predicted to promote noticing similarities across members of the same category and result in short-term benefits. However, the increase in temporal delay between repetitions inherent to interleaved study might benefit both types of categories when tested after a longer retention interval. Participants studied categories either interleaved or blocked and were tested immediately and 24 hours after study. We found an interaction between schedule of study and the type of category studied, which is consistent with the differential emphasis promoted by each sequential schedule. However, increasing the retention interval did not modulate this interaction or resulted in improved performance for interleaved study. Overall, this indicates that the benefit of interleaving is not primarily due to temporal spacing during study, but rather due to the cross-category comparisons that interleaving facilitates. We discuss the benefits of temporal spacing of repetitions in the context of sequential study and how it can be integrated with the attentional bias hypothesis proposed by Carvalho and Goldstone (2014).