Over the last decades, understanding the sources of the difficulty of Bayesian problem solving has been an important research goal, with the effects of numerical format and individual numeracy being widely studied. However, the focus on the comprehension of probability numbers has overshadowed the relational reasoning demand of the Bayesian task. This is particularly the case when the statistical data are verbally described since the requested quantitative relation (posterior ratio) is misaligned with the presented ones (prior and likelihood ratios). In (...) this regard, here I develop the proposal that research on Bayesian reasoning might improve by considering the notational alignment framework of mathematical problem-solving. Specifically, this framework can help to understand the sources of the main difficulties underlying Bayesian inferences based on verbal descriptions. In essence, the present proposal supports the general claim in math education regarding the need to foster relational comprehension to avoid misleading alignments and improve problem solving. (shrink)

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 reasoning 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 versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

The presence of general intelligence poses a major evolutionary puzzle, which has led to increased interest in its presence in nonhuman animals. The aim of this review is to critically evaluate this question and to explore the implications for current theories about the evolution of cognition. We first review domain-general and domain-specific accounts of human cognition in order to situate attempts to identify general intelligence in nonhuman animals. Recent studies are consistent with the presence of general intelligence in mammals. However, (...) the interpretation of a psychometricgfactor as general intelligence needs to be validated, in particular in primates, and we propose a range of such tests. We then evaluate the implications of general intelligence in nonhuman animals for current theories about its evolution and find support for the cultural intelligence approach, which stresses the critical importance of social inputs during the ontogenetic construction of survival-relevant skills. The presence of general intelligence in nonhumans implies that modular abilities can arise in two ways, primarily through automatic development with fixed content and secondarily through learning and automatization with more variable content. The currently best-supported model, for humans and nonhuman vertebrates alike, thus construes the mind as a mix of skills based on primary and secondary modules. The relative importance of these two components is expected to vary widely among species, and we formulate tests to quantify their strength. (shrink)

In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically (...) explaining people’s faulty thinking, or proposing and experimentally implementing measures to foster insight and to make these problems accessible to the human mind. Yet these problems have thus far usually been empirically analyzed on an individual-item level only (e.g., by experimentally comparing participants’ performance on various versions of one of these problems). In this paper, by contrast, we examine these illusions as a group and look at the ability to solve them as a psychological construct. Based on an sample ofN= 2,643 Luxembourgian school students of age 16–18 we investigate the internal psychometric structure of these illusions (i.e., Are they substantially correlated? Do they form a reflexive or a formative construct?), their connection to related constructs (e.g., Are they distinguishable from intelligence or mathematical competence in a confirmatory factor analysis?), and the question of which of a person’s abilities can predict the correct solution of these brain teasers (by means of a regression analysis). (shrink)

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant’s performance against the normatively correct answer provided by Bayes’ theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated that the use (...) of frequencies in a natural sampling framework —as opposed to single-event probabilities—can improve participants’ Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally-sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained “camps” organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying “siloed” within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration. (shrink)