Interactivity fosters Bayesian reasoning without instruction.

Successful statistical reasoning emerges from a dynamic system including: a cognitive agent, material artifacts with their actions possibilities, and the thoughts and actions that are realized while reasoning takes place. Five experiments provide evidence that enabling the physical manipulation of the problem information (through the use of playing cards) substantially improves statistical reasoning, without training or instruction, not only with natural frequency statements (Experiment 1) but also with single-event probability statements (Experiment 2). Improved statistical reasoning was not simply a matter of making all sets and subsets explicit in the pack of cards (Experiment 3), it was not merely due to the discrete and countable layout resulting from the cards manipulation, and it was not mediated by participants' level of engagement with the task (Experiment 5). The positive effect of an increased manipulability of the problem information on participants' reasoning performance was generalizable both over problems whose numeric properties did not map perfectly onto the cards and over different types of cards (Experiment 4). A systematic analysis of participants' behaviors revealed that manipulating cards improved performance when reasoners spent more time actively changing the presentation layout "in the world" as opposed to when they spent more time passively pointing at cards, seemingly attempting to solve the problem "in their head." Although they often go unnoticed, the action possibilities of the material artifacts available and the actions that are realized on those artifacts are constitutive of successful statistical reasoning, even in adults who have ostensibly reached cognitive maturity.