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)