ABSTRACTIn two experiments, we examined the resolution of confidence judgments in syllogistic reasoning and their heuristic bases. Based on the assumptions of Koriat's Self-Consistency Model of confidence, we expected the confidence judgments to be related to conclusion consensuality, reflecting the role of consistency as a heuristic cue to confidence. In Experiment 1, the participants evaluated 24 syllogisms with conclusions that varied with respect to validity and consensuality. In Experiment 2, the participants produced conclusions to 64 pairs of premises. The correlation (...) between confidence and reasoning accuracy was low. In both experiments confidence was related to the consensuality of the responses. For consensually correct items, correlation between confidence and accuracy was positive; however, for consensually incorrect items it was negative. In Experiment 2, confidence was lower for syllogisms with higher response cardinality, or syllogisms that elicited a greater variety of conclusions. (shrink)

ABSTRACTConditional inferences can be phrased with unspecific terms or specific terms. We investigate whether the specificity of terms affects people's acceptance of inferences. In Experiment 1, inferences with specific terms received higher acceptance ratings than inferences with unspecific terms. In Experiments 2 and 3, we used the same problems as in Experiment 1 but also problems with unspecific terms in the conditional and specific terms in the categorical and vice versa. When the conditional and the categorical had the same specificity, (...) results were as in Experiment 1. When the specificity of the conditional and the categorical mismatched, acceptance ratings were lower. Our results illustrate the importance of phrasing on reasoning. (shrink)

ABSTRACTStudies examining the interpretation that is given to if–then statementstypically use what are referred to as basic conditionals, which give contextless relations between two unrelated concrete terms. However, there is some evidence that basic conditionals require a more abstract form of representation. In order to examine this, we presented participants with truth-table tasks involving either basic conditionals or conditionals referring to imaginary categories, and standard conditional inference tasks with abstract and familiar premises. As expected, fewer typical defective conditional interpretations were (...) given to basic conditionals. In addition, partial correlations showed a unique relationship between the interpretation of basic conditionals and abstract inferential reasoning. Results suggest that people process basic conditionals as a form of abstract reasoning, and that the interpretation of conditionals... (shrink)

ABSTRACTTreating conditionals as probabilistic statements has been referred to as a defining feature of the “new paradigm” in cognitive psychology. Doing so is attractive for several reasons, but it complicates the problem of assessing the merits of conditional arguments. We consider several variables that relate to judging the persuasiveness of conditional arguments with uncertain premises. We also explore ways of judging the consistency of people's beliefs as represented by components of conditional arguments. Experimental results provide evidence that inconsistencies in beliefs (...) are more prevalent if the arguments’ components are spatially and temporally dispersed than if they are contiguous in space and time. This supports the idea that assuring the consistency among even a small number of beliefs is difficult to do, especially if the beliefs in question are not brought into consciousness at the same time; but consistency can be enhanced when beliefs are considered simultaneously or nea... (shrink)

ABSTRACTAdults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude comparison and estimation. Adults with higher mathematics anxiety had lower accuracy on the comparison task and greater percentage absolute error on the estimation task. Unexpectedly, mathematics anxiety was not related to variable strategy use. However, variable strategy use was linked to more accurate (...) magnitude comparisons, especially among adults with lower working memory performance or those who use mathematics less frequently, as well as lower PAE on the estimation task. These findings shed light on the role of strategy variability in fraction problem solving and demonstrate a link between mathematics anxiety and fraction magnitude reasoning, a key predictor of general mathematics achievement. (shrink)

ABSTRACTHumans are cognitive misers because their basic tendency is to default to processing mechanisms of low computational expense. Such a tendency leads to suboptimal outcomes in certain types of hostile environments. The theoretical inferences made from correct and incorrect responding on heuristics and biases tasks have been overly simplified, however. The framework developed here traces the complexities inherent in these tasks by identifying five processing states that are possible in most heuristics and biases tasks. The framework also identifies three possible (...) processing defects: inadequately learned mindware; failure to detect the necessity of overriding the miserly response; and failure to sustain the override process once initiated. An important insight gained from using the framework is that degree of mindware instantiation is strongly related to the probability of successful detection and override. Thus, errors on such tasks cannot be unambiguously attributed to miserly processing – and corre... (shrink)

ABSTRACTResearch has established that human thinking is often biased by intuitive judgement. The base-rate neglect effect provides such an example, so named because people often support their decisions in stereotypical individuating information, neglecting base-rates. Here, we test the hypothesis that reasoners acknowledge information provided by base-rates and may use individuating information in support of a “rational” decision process. Results from four experiments show that “base-rate neglecting” occurs when participants acknowledge sample distributions; participants who prefer individuating over base-rate information perceive base-rates (...) as less diagnostic and are more confident in their individuating-based responses; and that posterior probabilities predict more individuating-based responses for individuating-preference participants. However, data also show a deeper form of base-rate neglect: even when some partic... (shrink)

ABSTRACTInitial acts of self-control can reduce effort and performance on subsequent tasks – a phenomenon known as ego depletion. Ego depletion is thought to undermine the capacity or willingness to engage executive control, an important determinant of success for many tasks. We examined whether ego depletion improves performance on a task that favours less executive control: insight problem solving. In two experiments, participants completed an ego-depletion manipulation or a non-depleting control condition followed by an insight problem-solving task. Participants in the (...) depleting condition demonstrated greater insight problem-solving accuracy than those in the non-depleting control condition. Priming theories of willpower did not impact these results. Although ego depletion is widely regarded as a “state of impairment”, attendant decreases in executive control may foster insightful thinking. (shrink)

ABSTRACTPeople accept conclusions of valid conditional inferences less, the more disablers exist. We investigated whether rules that through their phrasing exclude disablers evoke higher acceptance ratings than rules that do not exclude disablers. In three experiments we re-phrased content-rich conditionals from the literature as either universal or existential rules and embedded these rules in Modus Ponens and Modus Tollens inferences. In Experiments 2 and 3, we also used abstract rules. The acceptance of conclusions increased when the rule was phrased with (...) “all” instead of “some” and the number of disablers had a higher impact on existential rules than on universal rules. Further, the effect of quantifier was more pronounced for abstract rules and when tested within subjects. We discuss the relevance of phrasing, quantifiers and knowledge on reasoning. (shrink)

ABSTRACTTo build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: the conditional event interpretation in the coherencebased probability logic, the discourse processingtheory of Hans Kamp, and the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, (...) a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction. (shrink)

ABSTRACTThree experiments examined how people reason about what is possible or necessary when a conditional is true. Participants were asked to indicate whether it was necessary, possible or impossible for a specific instance to conform to one of the truth-table cases, given the truth of the conditional. It was found that most participants, inconsistently, judged the pq case as necessary but the ¬pq or ¬p¬q cases as possible. Logically, these two kinds of judgments are contradictory. Moreover, a true conditional doesn’t (...) imply that a specific instance under the conditional must be pq. Therefore, people demonstrate a necessity illusion for pq cases which contradicts their commitment to the possibility of ¬pq or ¬p¬q cases. Existing accounts of conditionals are unable to explain the contradiction and the necessity illusion. We propose an inference dissociation account and explore the theoretical implications of this necessity illusion. (shrink)

The present study examined whether a dissociation among formats for rational numbers can be obtained in tasks that require comparing a number to a non-symbolic quantity. In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude task was performed more quickly (...) using decimals, whereas the relation task was performed more accurately with fractions. The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display. (shrink)

Decades of research have focused on children's reasoning about math equivalence problems for both practical and theoretical insights. Not only are math equivalence problems foundational in arithmetic and algebra, they also represent a class of problems on which children's thinking is resistant to change. Feedback is one instructional tool that can serve as a key trigger of cognitive change. In this paper, we review all experimental studies on the effects of feedback on children's understanding of math equivalence. Meta-analytic results indicate (...) that feedback has positive effects for low-knowledge learners and negative effects for high-knowledge learners, and these effects are stronger for procedural outcomes than conceptual outcomes. Findings highlight the variable influences of feedback on math equivalence understanding and suggest that models of thinking and reasoning need to consider learner characteristics, learning outcomes, and learning materials, as well as the dynamic interactions among them. (shrink)

Recent studies have shown that deductive reasoning skills are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive (...) reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions. (shrink)

Research into mathematics often focuses on basic numerical and spatial intuitions, and one key property of numbers: their magnitude. The fact that mathematics is a system of complex relationships that invokes reasoning usually receives less attention. The purpose of this special issue is to highlight the intricate connections between reasoning and mathematics, and to use insights from the reasoning literature to obtain a more complete understanding of the processes that underlie mathematical cognition. The topics that are discussed range from the (...) basic heuristics and biases to the various ways in which complex, effortful reasoning contributes to mathematical cognition, while also considering the role of individual differences in mathematics performance. These investigations are not only important at a theoretical level, but they also have broad and important practical implications, including the possibility to improve classroom practices and educational outcomes, to facilitate people's decision-making, as well as the clear and accessible communication of numerical information. (shrink)

Cognitive reflection is recognized as an important skill, which is necessary for making advantageous decisions. Even though gender differences in the Cognitive Reflection test appear to be robust across multiple studies, little research has examined the source of the gender gap in performance. In Study 1, we tested the invariance of the scale across genders. In Study 2, we investigated the role of math anxiety, mathematical reasoning, and gender in CRT performance. The results attested the measurement equivalence of the Cognitive (...) Reflection Test – Long, when administered to male and female students. Additionally, the results of the mediation analysis showed an indirect effect of gender on CRT-L performance through mathematical reasoning and math anxiety. The direct effect of gender was no longer statistically significant after accounting for the other variables. The current findings suggest that cognitive reflection is affected by numerical skills and related feelings. (shrink)

Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems but reverse OM with non-zero problems. In a third experiment, we tested (...) the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. (shrink)

Three-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever children's hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, (...) but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section. (shrink)

Solutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities are aligned with addition, whereas certain functional relations between entities are aligned with division. Similarly, discreteness vs. continuity of quantities is aligned with different formats for rational numbers. These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. Textbook analyses (...) revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations. (shrink)

Many investigations of moral decision-making employ hypothetical scenarios in which each participant has to choose between two options. One option is usually deemed “utilitarian” and the other either “non-utilitarian” or “deontological”. Very little has been done to establish the validity of such measures. It is unclear what they measure, let alone how well they do so. In this exploratory study, participants were asked about the reasons for their decisions in six hypothetical scenarios. Various concerns contributed to each decision. Action decisions (...) occurred when utilitarian concerns dominated. Bystanding decisions resulted from different concerns or combinations of concerns dominating in different situations, with utilitarianism usually among participants’ concerns. None of the labels usually used for either decision therefore seems entirely appropriate. Five concerns were identified as necessary and sufficient to predict over 85% of participants’ decisions. This suggests great promise for future research, particularly in investigation of real-world moral decisions. (shrink)

ABSTRACTIn everyday situations, people regularly receive information from large groups of people and from single experts. Although lay opinions and expert opinions have been studied extensively in isolation, the present study examined the relationship between the two by asking how many laypeople are needed to counter an expert opinion. A Bayesian formalisation allowed the prescription of this quantity. Participants were subsequently asked to assess how many laypeople are needed in different situations. The results demonstrate that people are sensitive to the (...) relevant factors identified for determining how many lay opinions are required to counteract a single expert opinion. People's assessments were fairly good in line with Bayesian predictions. (shrink)

Why does discourse so often seem shallow, with people arguing past one another more than with one another? Might contributing causes be individual and logical rather than only dialogical? We consider here whether there exist errors in reasoning that could be particularly damaging in their effects on argumentive discourse. In particular, we examine implications for discourse of two such errors – explanation as a replacement for evidence and neglecting the likelihood of multiple causes contributing to an outcome. In Studies 1 (...) and 2, we show these errors to be prevalent in a cross section of adults, as well as samples of community college students and young adolescents, with minimal age-related improvement. They also occur, although less frequently, among a sample of highly educated adults, and in Study 3, we examine their role in the discourse of college-educated adults. We point finally to evidence that these individual reasoning errors are potentially addressable through education. (shrink)

Participants acting as mock jurors made inferences about whether a person was a suspect in a murder based on an expert's testimony about the presence of objects at the crime scene and the disclosure that the testimony was true or false. Experiment 1 showed that participants made more correct inferences, and made inferences more quickly, when the truth or falsity of the expert's testimony was disclosed immediately after the testimony rather than when the disclosure was delayed. Experiment 2 showed no (...) advantage for prior disclosure over immediate disclosure. Experiment 3 showed that the pattern of inferences when there was no disclosure mirrored the pattern when it was disclosed that the expert's testimony was true rather than false. Participants made more correct inferences from true conjunctions than disjunctions, and from false disjunctions than conjunctions. We discuss the implications for theories of the mental representations and cognitive processes that underlie human reasoning. (shrink)

Actively open-minded thinking is often used as a proxy for reflective thinking in research on reasoning and related fields. It is associated with less biased reasoning in many types of tasks. However, few studies have examined its psychometric properties and criterion validity. We developed a shortened, 17-item version of the AOT for quicker administration. AOT17 is highly correlated with the original 41-item scale and has highly similar relationships to other thinking dispositions, social competence and supernatural beliefs. Our analyses revealed that (...) the AOT is not a unitary construct, but comprises four distinct dimensions, some of which concern attitudes towards knowledge, and others concern attitudes towards people. This factor structure was replicated in another data-set, and correlations with other measures in four data-sets support the criterion validity of these dimensions. Different dimensions were responsible for the AOT's relationships with other thinking dispositions. (shrink)

Can ownership status influence probability judgements under condition of uncertainty? In three experiments, we presented our participants with a recording of a real horse race. We endowed half of our sample with a wager on a single horse to win the race, and the other half with money to spend to acquire the same wager. Across three large studies, we found the endowment effect – owners demanded significantly more for the wager than buyers were willing to pay to acquire it. (...) However, we also found that probability estimates of each horse winning the race did not differ between owners and non-owners of the betting slip. Our results demonstrate that distorted perception of probability is unlikely to be a mechanism explaining the endowment effect. (shrink)