Interactivity fosters Bayesian reasoning without instruction (original) (raw)
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People appear to be Bayesian when statistical information is presented in terms of natural frequencies and non-Bayesian when presented in terms of single-event probabilities, unless the probabilities resemble natural frequencies, for example, as chances. The isomorphic format of chances, however, does not always facilitate performance to the extent that the format of natural frequencies does. Prior research has not addressed the underlying mechanism that accounts for this gap despite its theoretical significance. The mechanism explaining this external format gap could lie in the interpretation of the problem as a setproblem, which cues relevant problem model and arithmetic operations (the problem interpretation hypothesis) and/or in the interpretation of the format as frequencies, which may be easier to process (the format interpretation hypothesis). In two parallel experiments, we found support for the problem interpretation hypothesis only: set representations mediated solely the isomorphic format gap (Experiment 1: part A) and accounted for the transfer effect to natural frequencies (Experiment 1: part B); priming set representations improved performance with chances (Experiment 2). We discuss how the supported explanation corroborates the nested-sets rather than the ecological rationality account of statistical reasoning and how it helps explain individual differences in Bayesian reasoning.
2002
The cognitive-theoretic instructional and assessment approaches described here represent our efforts to develop and measure students' abilities to reason spontaneously and flexibly with statistics in the context of complex real-world activity. We report results from two instructional projects based on situated cognition, in which students were taught statistical reasoning through guided participation in simulations of authentic professional activities requiring presentation and critique of statistical arguments. Although students' statistical reasoning improved in selected ways, the approach was costly and difficult to implement and sustain. In search of more practical and powerful approaches, current experiments are investigating whether instruction based on video technologies and Cognitive Flexibility Theory can speed development of ability to think flexibly with statistics while seeing interacting themes in real-world situations.
The effects of mental steps and compatibility on Bayesian reasoning
Four laboratory studies were conducted to test the hypothesis that correct Bayesian reasoning can be predicted by two factors of task complexity-the number of mental steps required to reach the normative solution, and the compatibility between the framing of data presented and the framing of the question posed. The findings show that participants performed better on frequency format questions only when one mental step was required to solve the task and when the data were in a compatible frequency format. By contrast, participants performed more poorly on more complicated tasks which required more mental steps (in a compatible frequency or probability format) or when the data and question formats were incompatible (Studies 1 and 2). Incompatibility between data and question formats was also associated with higher reaction times (Study 2b). Furthermore, on problems that incorporated incompatibility between the data sample size and the target (question) sample size, participants performed better on the probability question than the frequency question, regardless of data format (Study 3). The latter findings highlight the ecological advantage of translating data into probability terms, which are normalized in a range between 0 and 1, and thus can be transferred from one situation to another.
Wason cards were originally designed for an experiment evaluating subjects' reasoning abilities. Our claim is that they may be used as an educational tool in the classroom and their didactical value is enormous. Fourth graders can be trained in logical reasoning by playing not only with four Wason cards, as in the original experiment, but with samples of them and with various contexts, e.g., with sentences about daily life and with colours instead of symbols. The transition from logical to probabilistic reasoning can be made palpable to fourth graders through ritualized games with Wason cards. Yet Wason cards have limitations, which become apparent when several features are jointly to be taken into account. For these cases, tinker cubes and tinker towers can be, as we show subsequently, adequate tools for an enactive treatment of proportional and probabilistic reasoning in fourth grade.
The effect of experimentally contrived experience on reasoning performance
Psychological Research, 1983
Recent research on reasoning has shown that problem content is highly effective in mediating responses. This has been interpreted as support for the idea that reasoning responses are a function of the subjects' prior experience. However, although compelling, this interpretation is based on indirect evidence. When differential responses are observed, consideration of the (thematic) contents employed often reveals that subjects would be expected to have had differential experience of these contents. Two experiments are reported here that test directly whether such differential responses are produced by subjects' experience. They made use of symbolic content on the Wason selection task, and manipulated subjects' prior experience of this via probability learning tasks. In both cases, this contrived experience was effective, although to some extent in different ways. In the first experiment, run on an on-line computer terminal, subjects selected significantly more cards on 'false' rules. In the second, which controlled for matching bias by using rules with systematically negated components, subjects selected significantly more FA and FC but fewer TA and TC on 'false' rules. In addition, relationships were found between card selections and speed of (probability) learning. In general, the results are seen as providing strong evidence for the role of experience in determining responses.
In an ongoing debate about statistical reasoning competency, one view claims that pictorial representations help tap into the frequency coding mechanisms, whereas another view argues that pictorial representations simply help one to appreciate general subset relationships. The present experiments used Bayesian reasoning problems, expressed in an ambiguous numerical format (chances) and with different pictorial representations, to better understand influences on performance across these representation types. Although a roulette wheel diagram had some positive effect on performance, both abstract icons and pictographs improved performance markedly more. Furthermore, a frequency interpretation of the ambiguous numerical information was also associated with superior performance. These findings support the position that the human mind is more easily able to use frequency-based information, as opposed to grasping subset relations, as an explanation for improved statistical reasoning. These results also provide practical implications for how to present quantitative information to substantially improve public understanding.
Comprehension and computation in Bayesian problem solving
Frontiers in Psychology, 2015
Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on "transparent" Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point.
心理学报, 2007
What happens when format manipulations improve Bayesian reasoning? One view is that naturally sampled frequencies help induce a privileged representational system that is relatively specific in its operation. A contrasting view is that naturally sampled frequencies are but one way to induce a more general process of appreciating nested set relationships. This later view implies that fairly brief and immediate interventions (e.g., simple directives) should produce improvement, whereas the former view implies that more extensive interventions and/or more insightful understanding are necessary for improvement. The present research indicates that neither brief and immediate interventions nor pre-existing representational biases or representational flexibility facilitate performance. Some evidence emerged, on the other hand, that frequentist problem interpretation can improve statistical reasoning performance and increase confidence in responses at times. These results support the privileged representational system view.
Measures of Bayesian Reasoning Performance on 'Normal' and 'Natural' Frequency Tasks
The Journal of general psychology
While the majority of similar studies examining Bayesian reasoning investigate how participants avoid common errors such as base-rate neglect, the current research also examines whether different formats (frequency and probability) lead to a difference in levels of absolute accuracy. In Study One, older (≥60 years) and younger (18 to 29 years) participants completed tasks in probability and normalized frequency formats. In Study 2, participants completed tasks in probability and natural frequency formats. Findings are that frequencies lead to less over-estimation, particularly in natural frequency tasks, which also reveal an interaction between age and task format whereby older adults seem unaffected by format. There was no association found between format and the avoidance of errors such as base-rate neglect. Findings are discussed in the light of dual and multi-process theories of reasoning, having failed to support the theory that frequency formats elicit System 2 reasoning proce...
Applied Cognitive Psychology, 2009
In an ongoing debate between two visions of statistical reasoning competency, ecological rationality proponents claim that pictorial representations help tap into the frequency coding mechanisms of the mind, whereas nested sets proponents argue that pictorial representations simply help one to appreciate general subset relationships. Advancing this knowledge into applied areas is hampered by this present disagreement. A series of experiments used Bayesian reasoning problems with different pictorial representations (Venn circles, iconic symbols and Venn circles with dots) to better understand influences on performance across these representation types. Results with various static and interactive presentations of pictures all indicate a consistent advantage for iconic representations. These results are more consistent with an ecological rationality view of how these pictorial representations achieve facilitation in statistical task performance and provide more specific guidance for applied uses.