Sources of difficulty in deductive reasoning: The THOG task

The THOG task presents four designs constructed from two shapes and two colours. Subjects are told that the experimenter has written down one of the shapes and one of the colours and are provided the rule that if, and only if, any design has either the shape or the colour, but not both, written down, then it is a THOG. Finally, they are given an exemplar and are asked to classify the remaining designs. Successful solution requires construction of hypotheses, reasoning under each hypothesis, and comparison of the results under each to reach a final conclusion. Few subjects are able to provide adequate responses on the standard version of the task. We present the results of four experiments, with 160 undergraduates each presented with one of eight versions of the task. Experiments 1 and 2 indicate that (1) some subjects think that the properties that are written down are identical to those of the exemplar, although these are not the same subjects who exhibit the modal error pattern, (2) many subjects correctly understand the disjunction of the rule but fail to consider the hypotheses, and (3) poor initial encoding of the problem is not easily corrected. Experiment 3 investigates the sufficiency of the claim of Griggs and Newstead (1982) that appropriate problem solution follows from explicit presentation of all problem information (including use of positive labels for properties that are not written down), and Experiment 4 investigates the necessity of the claim. The results of Experiments 3 and 4 show that presenting positive category labels does increase the frequency of correct solution; however, positive category labels are not necessary for such improvement. Separation of the labels of the THOG rule from those of the exemplar, or informing subjects that only one other design is a THOG, also increases the frequency of successful solution. The results suggest that many people have some fairly sophisticated reasoning skills. but application of these skills is easily discouraged when the features of the task lead to poor initial encoding.     

Predicting the difficulty of complex logical reasoning problems

The aim of the present research was to develop a difficulty model for logical reasoning problems involving complex ordered arrays used in the Graduate Record Examination. The approach used involved breaking down the problems into their basic cognitive elements such as the complexity of the rules used, the number of mental models required to represent the problem, and question type. Weightings for these different elements were derived from two experimental studies and from the reasoning literature. Based on these weights, difficulty models were developed which were then tested against new data. The models had excellent predictive validity and showed the relative influence of rule based factors and factors relating to the number of underlying models. Different difficulty models were needed for different question types, suggesting that people used a variety of approaches and, at a wider level, that both mental models and mental rules may be used in reasoning.     

Propositional reasoning: the differential contribution of "rules" to the difficulty of complex reasoning problems

In Experiment 1, complex propositional reasoning problems were constructed as a combination of several types of logical inferences: modus ponens, modus tollens, disjunctive modus ponens, disjunctive syllogism, and conjunction. Rule theories of propositional reasoning can account for how one combines these inferences, but the difficulty of the problems can be accounted for only if a differential psychological cost is allowed for different basic rules. Experiment 2 ruled out some alternative explanations for these differences that did not refer to the intrinsic difficulty of the basic rules. It was also found that part of the results could be accounted for by the notion of representational cost, as it is used in the mental model theory of propositional reasoning. However, the number of models as a measure of representational cost seems to be too coarsely defined to capture all of the observed effects.     

Formal reasoning in late adulthood: The role of semantic content and metacognitive strategy

Two experiments explored the availability of deductive or formal reasoning in late adulthood. In Experiment 1, fifty young (M=19.0 years) and 50 elderly adults (M=81.0 years) were assessed using adaptations of Wason's selection task and rated task content for familiarity, affect, and agreement. In Experiment 2, 100 young (M=21.0 years) and 100 elderly adults (M=81.0 years) were similarly assessed, with half of the subjects in each age group receiving a metacognitive strategy to facilitate reasoning. Results from Experiment 1 indicated equivalent reasoning among the groups on problems employed in earlier developmental research. In contrast, problems constructed to entail affect resulted in poorer performance by older adults. In Experiment 2, both young and older adults who used the metacognitive strategy reasoned equally acrossall problems. In both experiments, familiarity and agreement did not play a role in deductive reasoning performance, but affect seemed to be an interfering factor. Results are discussed in terms of competence-procedure and stability-decrement models of adult cognitive development.     

Overcoming the acting/reasoning dualism in intelligent behavior

In a paper that recently appeared in this journal, we proposed a model that aims at providing a comprehensive account of our ability to intelligently use tools, bridging sensorimotor and reasoning-based explanations of this ability. Central to our model is the notion of generalized motor programs for tool use, which we defined as a synthesis between classic motor programs, as described in the scientific literature, and Peircean habits. In his commentary, Osiurak proposes a critique of the notion of generalized motor program, and suggests that the limitations of our model can be solved by integrating it with the view that motor programs are generated by a previous mechanical reasoning, independent from sensorimotor knowledge. Here we reply that while on the one hand our reference to Peircean habits gets over the temptation to consider motor programs as fixed internal entities, it also rejects the view, endorsed by Osiurak, that intelligent practice is a mixture of antecedent abstract reasoning and subsequent motor execution.     

Why children have difficulty reasoning with three-term series problems

This study examined a number of hypotheses as to why children have difficulty in solving three-term series problems. No support was found for the hypothesis that their difficulties arise because of their inability to understand transitive relations. In addition, the problems were present throughout the task, so that poor memory for the premises was ruled out as a contributory factor in reasoning difficulty. The children's performance was found to improve, however, when they were provided with an aid to reduce the demands of the task on working memory, although this advantage was not maintained in a later test without a memory aid. There was also evidence that, overall, the children had greater difficulty in solving problems that imposed a higher load on working memory.     

Effects of perspective and belief on analytic reasoning in a scientific reasoning task

The purpose of these studies was to test the hypothesis that changing perspectives from one's own to another's promotes the engagement of analytic processing and, in turn, reduces the impact of beliefs. In two experiments participants evaluated research vignettes containing belief-consistent and belief-inconsistent conclusions, and indicated whether the data supported a correlation between two variables. Consistent with our hypothesis, the tendency to endorse correlations consistent with prior belief was reduced when participants evaluated the data from the researcher's perspective relative to their own. We also administered the Actively Open Minded Thinking (AOT) scale (Stanovich & West, 2007, 2008), which did not predict belief effects on our task. We did however observe that the AOT was reliably associated with different response strategies: high AOT scorers were more inclined to choose ambiguous response options, such as “no conclusion is warranted”, whereas low scorers evinced a preference for more determinate options (e.g., there is no relationship between the two variables). We interpret our findings in the context of dual process theories of reasoning and from a Bayesian perspective.     

The role of conscious reasoning and intuition in moral judgment: testing three principles of harm

Is moral judgment accomplished by intuition or conscious reasoning? An answer demands a detailed account of the moral principles in question. We investigated three principles that guide moral judgments: (a) Harm caused by action is worse than harm caused by omission, (b) harm intended as the means to a goal is worse than harm foreseen as the side effect of a goal, and (c) harm involving physical contact with the victim is worse than harm involving no physical contact. Asking whether these principles are invoked to explain moral judgments, we found that subjects generally appealed to the first and third principles in their justifications, but not to the second. This finding has significance for methods and theories of moral psychology: The moral principles used in judgment must be directly compared with those articulated in justification, and doing so shows that some moral principles are available to conscious reasoning whereas others are not.     

Shared and distinct cue utilization for metacognitive judgements during reasoning and memorisation

Metacognitive research is dominated by meta-memory studies; meta-reasoning research is nascent. Accessibility – the number of associations for a stimulus – is a reliable heuristic cue for Feeling of Knowing when answering knowledge questions. We used a similar cue, subjective accessibility, for exposing commonalities and differences between meta-reasoning and meta-memory. In Experiment 1, participants faced solvable Compound Remote Associate problems mixed with unsolvable random word triads. We collected initial Judgement of Solvability (iJOS), final JOS (fJOS) and confidence. Experiment 2 focused on confidence, controlling for potential interactions among judgements. In Experiment 3, the participants memorised the same triads and rated Ease of Learning and Judgement of Learning. sAccessibility was associated with all judgements. Notably, it reliably predicted memory judgements and confidence in the provided solutions. However, it was unreliable for judging solvability (iJOS and fJOS). The findings highlight the importance of studying meta-reasoning for exposing the biasing factors in reasoning processes and for getting a broad perspective on metacognitive processes.     

Working memory, metacognitive uncertainty, and belief bias in syllogistic reasoning

Studies of syllogistic reasoning have shown that the size of the belief bias effect varies with manipulations of logical validity and problem form. This paper presents a mental models-based account, which explains these findings in terms of variations in the working-memory demands of different problem types. We propose that belief bias may reflect the use of a heuristic that is applied when a threshold of uncertainty in one's processing-attributable to working-memory overload-is exceeded during reasoning. Three experiments are reported, which tested predictions deriving from this account. In Experiment 1, conclusions of neutral believability were presented for evaluation, and a predicted dissociation was observed in confidence ratings for responses to valid and invalid arguments, with participants being more confident in the former. In Experiment 2, an attempt to manipulate working-memory loads indirectly by varying syllogistic figure failed to produce predicted effects upon the size of the belief bias effect. It is argued that the employment of a conclusion evaluation methodology minimized the effect of the figural manipulation in this experiment. In Experiment 3, participants' articulatory and spatial recall capacities were calibrated as a direct test of working-memory involvement in belief bias. Predicted differences in the pattern of belief bias observed between highand lowspatial recall groups supported the view that limited working memory plays a key role in belief bias.     

Why some surprises are more surprising than others: Surprise as a metacognitive sense of explanatory difficulty

Early theories of surprise, including Darwin’s, argued that it was predominantly a basic emotion. Recently, theories have taken a more cognitive view of surprise, casting it as a process of “making sense of surprising events”. The current paper advances the view that the essence of this sense-making process is explanation; specifically, that people’s perception of surprise is a metacognitive estimate of the cognitive work involved in explaining an abnormal event. So, some surprises are more surprising because they are harder to explain. This proposal is tested in eight experiments that explore how (i) the contents of memory can influence surprise, (ii) different classes of scenarios can retrieve more/less relevant knowledge from memory to explain surprising outcomes, (iii) how partial explanations constrain the explanation process, reducing surprise, and (iv) how, overall, any factor that acts to increase the cognitive work in explaining a surprising event, results in higher levels of surprise (e.g., task demands to find three rather than one explanations). Across the present studies, using different materials, paradigms and measures, it is consistently and repeatedly found that the difficulty of explaining a surprising outcome is the best predictor for people’s perceptions of the surprisingness of events. Alternative accounts of these results are considered, as are future directions for this research.     

Heuristic and analytic processes in propositional reasoning with negatives

The authors report 4 studies on heuristic and analytic processes in conditional reasoning with negations and show that a heuristic negative conclusion bias cannot account for the effects observed on problem-solving latencies derived from eye-movement measures (Experiment 1) and a novel mouse-tracking methodology (Experiment 2). A double negation elimination process can account for both the latency and response-frequency effects of a negation in the clause about which an inference is made. It is further shown that other negation effects cannot be explained by an affirmative premise bias proposed in the literature. Experiments 3 and 4 demonstrate that a novel availability hypothesis provides a viable alternative. It is argued that extant analytic theories need to be extended to incorporate a validating search for counter examples and need to specify how pragmatic and comprehension processes influence such a search.     

A dual-process account of the development of scientific reasoning: The nature and development of metacognitive intercession skills

Metacognitive knowledge of the dual-processing basis of judgment is critical to resolving conflict between analytic and experiential processing responses [Klaczynski, P. A. (2004). A dual-process model of adolescent development: Implications for decision making, reasoning, and identity. In R. V. Kail (Ed.), Advances in child development and behavior, Vol. 31 (pp. 73–123). San Diego, CA: Academic Press]. Such conflict is ubiquitous when reasoning scientifically. Three studies explored the nature, development, and stability of this metacognitive knowledge. In each study, participants completed the ratio-bias judgment task, which assessed their tendency to make analytically based responses, and the ratio-bias evaluation task, which assessed their metacognitive knowledge of the processing basis of judgments on the task (Metacognitive Status). In Study 1, college students’ judgment performance was related to metacognitive status but not to general cognitive ability. In Study 2, metacognitive status was related to age and mathematics-related changes. Metacognitive status again predicted participants’ tendency to make analytically based judgments. In Study 3, college students’ judgments, but not metacognitive status, were affected by task conditions. The evidence suggests that assessing metacognitive knowledge is important for understanding how conflict between analytically and experientially based judgments is resolved.     

The effects of metacognitive training versus worked‐out examples on students' mathematical reasoning

Background: The present study is rooted in a cognitive‐metacognitive approach. The study examines two ways to structure group interaction: one is based on worked‐out examples (WE) and the other on metacognitive training (MT). Both methods were implemented in cooperative settings, and both guided students to focus on the problem's essential parts and on appropriate problem‐solving strategies. Aims: The aim of the present study is twofold: (a) to investigate the effects of metacognitive training versus worked‐out examples on students' mathematical reasoning and mathematical communication; and (b) to compare the long‐term effects of the two methods on students' mathematical achievement. Sample: The study was conducted in two academic years. Participants for the first year of the study were 122 eighth‐grade Israeli students who studied algebra in five heterogeneous classrooms with no tracking. In addition, problem‐solving behaviours of eight groups (N = 32) were videotaped and analysed. A year later, when these participants were ninth graders, they were re‐examined using the same test as the one administered in eighth grade. Method: Three measures were used to assess students' mathematical achievement: a pretest, an immediate post‐test, and a delayed post‐test. ANOVA was carried out on the post‐test scores with respect to the following criteria: verbal explanations, algebraic representations and algebraic solution. In addition, chi‐square and Mann‐Whitney procedures were used to analyse cooperative, cognitive, and metacognitive behaviours. Results: Within cooperative settings, students who were exposed to metacognitive training outperformed students who were exposed to worked‐out examples on both the immediate and delayed post‐tests. In particular, the differences between the two conditions were observed on students' ability to explain their mathematical reasoning during the discourse and in writing. Lower achievers gained more under the MT than under WE condition. Conclusions: The findings indicate that the kind of task and the way group interaction is structured are two important variables in implementing cooperative learning, each of which is likely to have different effects on mathematical communication and achievement outcomes.     

Effects of training and instruction on analytic and belief-based reasoning processes

Two studies are reported which demonstrate that analytic responding on everyday reasoning problems can be increased and bias eliminated after training on the law of large numbers (Fong, Krantz, & Nisbett, 1986 Fong, G. T., Krantz, D. H. and Nisbett, R. E. 1986. The effects of statistical training on thinking about everyday problems. Cognitive Psychology, 18: 253–292. [Crossref], [Web of Science ®] , [Google Scholar]). Critical thinking problems involving belief-consistent, neutral, and inconsistent conclusions were presented. Belief bias was eliminated when a written justification of argument strength was elicited. However, belief-based responding was still evident when evaluations of the arguments were elicited using rating scales. This finding demonstrates a dissociation between analytic and belief-based responding as a function of response format. In Experiment 2 an instructional condition designed to foster decontextualised reasoning was included but was ineffective in reducing the degree to which judgements were biased by beliefs. It was concluded that training which makes available the analytic strategies necessary to evaluate a problem has the potential to facilitate performance only if the requested response triggers conscious deliberation of the evidence.     

Belief-based and analytic processing in transitive inference depends on premise integration difficulty

Three experiments investigated belief-based versus analytic processing in transitive inference. Belief-based and analytic processing were inferred from conclusion acceptance rates for problems with conclusions that were either valid or invalid and believable or unbelievable. Premise integration difficulty was manipulated by varying premise integration time (Experiment 1), premise presentation order (Experiment 2), and the markedness of the relational terms in the premises (Experiment 3). In all the conditions, reasoning accuracy and rated confidence were lower on conflict problems, where belief-based and analytic processes yielded different responses. Participants relied more on analytic processing and less on belief-based processing in conditions in which premise integration was easier. Fluid intelligence and premise integration ability predicted analytical reasoning on conflict problems after reasoning on the no-conflict problems was controlled for. The findings were related to three dual-process models of belief bias. They provide the first evidence of belief bias in transitive inference.     

Formal reasoning in Japanese older adults: The role of metacognitive strategy,task content,and social factors

This study investigated the availability of deductive reasoning competence in late adulthood. Forty-six Japanese older (mean age =71 years) and 58 Japanese young adults (mean age =19.6 years) were assessed for formal or deductive reasoning using Overton's (1990) revision of the four-card selection task. For older adults, metacognitive strategy—operating as a procedure designed to access reasoning competence—resulted in enhanced performance levels. When the semantic content of the reasoning task involved emotional issues, however, the metacognitive strategy failed to facilitate reasoning performance. This suggests that reasoning competence is available in late adulthood but that performance is susceptible to contextual variables. Social factors were not significantly related to older adults' reasoning performance. Thus, assessment of these factors may have been based on too broad a definition to describe adequately the status of the older adults. For the young, only semantic task content was related to reasoning performance.