The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

How do we deal with unlikely witness testimonies? Whether in legal or everyday reasoning, corroborative evidence is generally considered a strong marker of support for the reported hypothesis. However, questions remain regarding how the prior probability, or base rate, of that hypothesis interacts with corroboration. Using a Bayesian network…

Previous research has shown that people who endorse conspiracy theories are more prone to the conjunction fallacy: the tendency to perceive conjunct events as more probable than constituent events. The present study examined the relationship between specific beliefs (belief in conspiracy theories, religiosity) and the susceptibility to conjunction…

In this paper, we develop a personal synthesis of the most outstanding research on the teaching and learning of probability in the past years. We conducted a systematic search to examine publications on this topic in mathematics education, statistics education, education, and psychology journals. This exploration was complemented by additional…

Findings on children's proportional reasoning abilities strongly vary across studies. This might be due to the different contexts that can be used in proportional problems: fair-sharing, mixtures, and probability. A review of the scientific literature suggests that the context of proportional problems may not only impact the difficulty of the…

Mental model (Johnson-Laird, 2001) and probabilistic theories (Oaksford & Chater, 2009) claim to provide distinct explanations of human reasoning. However, the dual strategy model of reasoning suggests that this distinction corresponds to different reasoning strategies, termed "counterexample" and "statistical,"…

It is increasingly recognised that to be informed citizens and to participate fully in the workforce requires an understanding of statistical data and risk. Such understanding is underpinned by statistical reasoning. It has been shown, however, that students have difficulty moving from concrete representations and procedural mathematical…

The theory of mental models postulates that conditionals and disjunctions refer to possibilities, real or counterfactual. Factual conditionals, for example, "If there's an apple, there's a pear," parallel counterfactual ones, for example, "If there had been an apple, there would have been a pear." A similar parallel underlies…

When physicians are asked to determine the positive predictive value from the a priori probability of a disease and the sensitivity and false positive rate of a medical test (Bayesian reasoning), it often comes to misjudgments with serious consequences. In daily clinical practice, however, it is not only important that doctors receive a tool with…

Children and adults appreciate that physical action is typically the conduit between individuals' desires and the fulfillment of those desires. However, certain forms of petitionary thought -- e.g., wishing and praying -- are believed by many people to influence the external world and fulfill desires without direct physical action. We examine…

We consider the proposition that reasoners represent causal conditionals such as "if John studies hard, he will do well in the test" as a causal model in which the antecedent ("John studies hard") is a potential cause of the consequent ("John does well in the test"). Some studies suggest that reasoners ignore…

Problems teaching probability in Tonga (in the South Pacific) led to the question on how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to identify the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan…

Research on teaching and learning quantum physics (QP) frequently explores students' conceptual difficulties to identify common patterns in their reasoning. The abstractness of QP is often found to be at the origin of students' conceptual difficulties. Due to this abstract nature students resort to common sense reasoning or classical thinking when…

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an…

Hinterecker, Knauff, and Johnson-Laird (2016) compared the adequacy of the probabilistic new paradigm in reasoning with the recent revision of mental models theory (MMT) for explaining a novel class of inferences containing the modal term "possibly." For example, "the door is closed or the window is open or both," therefore,…