Cognitive complexity of suppositional reasoning: An application of the relational complexity metric to the knight-knave task

An application of the Method of Analysis of Relational Complexity (MARC) to suppositional reasoning in the knight—knave task is outlined. The task requires testing suppositions derived from statements made by individuals who either always tell the truth or always lie. Relational complexity (RC) is defined as the number of unique entities that need to be processed in parallel to arrive at a solution. A selection of five ternary and five quaternary items were presented to 53 psychology students using a pencil and paper format. A computer-administered version was presented to 50 students. As predicted, quaternary problems were associated with higher error rates and longer response times than ternary problems. The computer-administered form was more difficult than the pencil and paper version of the test. These differences are discussed in terms of RC theory and alternative processing accounts. Together, they indicate that the relational complexity metric is a useful and parsimonious way to quantify complexity of reasoning tasks.     

A comparison of backward and forward spatial spans

The standard Corsi blocks task is frequently used to measure the capacity of visuospatial working memory, but the implications of the use of both forward and backward recall are still unclear. In the present study, we showed that the backward Corsi task is particularly powerful in discriminating between low- and high-spatial-ability individuals and involves different processes from those involved in the forward task. From a sample of 425 participants we selected one group of 20 high-spatial-ability participants and one of 20 low-spatial-ability participants. The results demonstrated that a backward spatial span offers specific information not available from a forward spatial span, and that there was no facilitation due to a descending format. In particular, in the low-spatial-ability group, performance was generally poorer, but backward Corsi recall was lower than forward recall, and participants did not show any advantage following the descending presentation format—which in some contexts is considered to reduce proactive interference. We conclude that the backward Corsi task has specific value and that the assumption of fully parallel verbal and visuospatial working-memory systems can lead to a variety of misunderstandings.     

How to support learning from multiple hypertext sources

In the present study, we investigated three factors that were assumed to have a significant influence on the success of learning from multiple hypertexts, and on the construction of a documents model in particular. These factors were task (argumentative vs. narrative), available text material (with vs. without primary sources), and presentation format (active vs. static). The study was conducted with the help of the combination of three tools (DEWEX, Chemnitz LogAnalyzer, and SummTool) developed for Web-based experimenting. The results show that the task is the most important factor for successful learning from multiple hypertexts. Depending on the task, the participants were either able or unable to apply adequate strategies, such as considering the source information. It was also observed that argumentative tasks were supported by an active hypertext presentation format, whereas performance on narrative tasks increased with a passive presentation format. No effect was shown for the type of texts available.     

Measuring the ability of transitive reasoning,using product and strategy information

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having different characteristics with respect to presentation form, task format, and task content. Both product and strategy information were analyzed to measure the performance of 6- to 13-year-old children. Three methods (MSP, DETECT, and Improved DIMTEST) were used to determine the number of abilities involved and to test the assumptions imposed on the data by item response models. Nonparametric IRT models were used to construct a scale for transitive reasoning. Multiple regression was used to determine the influence of task characteristics on the difficulty level of the tasks. It was concluded that: (1) the qualitatively distinct abilities predicted by Piaget's theory could not be distinguished by means of different dimensions in the data structure; (2) transitive reasoning could be described by one ability, and some task characteristics influenced the difficulty of a task; and (3) strategy information provided a stronger scale than product information.     

Explaining inappropriate strategy selection in a simple reasoning task

People's strategy selections appear to reflect attempts to maximize performance by selecting the most effective option for a particular task or format. Theories that account for such behaviour will be named rational models of strategy selection. However, it is possible to find instances where people are apparently biased towards using less effective strategies, and such behaviour appears to go against these models. Two experiments are reported in which participants were instructed to use first one, and then the other of two possible strategies for solving a compass point directions task (the instructed phase), and were subsequently permitted to use any strategy (the free‐choice phase). A substantial minority of participants selected the less effective spatial strategy during the free‐choice phase. Overall, it was found that people who rely on the spatial strategy when given a free‐choice tend to be those who: (1) have not been given particular incentive to perform as well as possible; (2) have difficulty executing the better alternative, cancellation and (3) are particularly prone to making errors at the spatial strategy. Hence, although evidence was found in support of rational models of strategy selection, it is also suggested that these must additionally take account of the motivational and conceptual difficulties that people may have with a task.     

Individual differences and task format in sentence verification

This study examined the effects of task format and individual differences in cognitive ability on performance of the sentence-picture verification task. Four groups of subjects were selected on the basis of their scores on psychometric tests of verbal and spatial ability: low verbal/low spatial, high verbal/high spatial, low verbal/high spatial, and high verbal/low spatial. Subjects completed four different versions of the sentence verification task, each version differing in terms of the interval between sentence and picture presentation. The results confirmed the importance of both task format and spatial ability in determining the cognitive strategy employed by subjects in carrying out the task. The finding of principal interest, however, was that spatial ability was the most significant determinant of strategy choice, and that low spatial subjects made substantial use of linguistic strategies under task formats designed to encourage imaginal strategies.     

Effects of problem presentation durations on arithmetic strategies: a study in young and older adults

Young and older adults were asked toaccomplish a computational estimation task (i.e. provide approximate sums to two-digit addition problems like 38 + 74) under a short versusa longer presentation duration condition. In a choice condition, participants selected the better strategy more often under a long than undera short presentation duration and after an easier than after a harder problem. In the no-choice condition, influence of presentation durationon strategy execution depended on the preceding problems, as participants showed sequence poorer strategy effects. That is, participantswere slower while executing the poorer than while executing the better strategy on current problems following better strategy problems (butequally fast after poorer strategy problems) only under short presentation duration condition. These findings have important theoreticalimplications, as current assumptions of computational models of strategies cannot explain how problem presentation durations influencestrategy selection and strategy execution.     

Comparing eye movements during position tracking and identity tracking: No evidence for separate systems

There is an ongoing debate as to whether people track multiple moving objects in a serial fashion or with a parallel mechanism. One recent study compared eye movements when observers tracked identical objects (Multiple Object Tracking—MOT task) versus when they tracked the identities of different objects (Multiple Identity Tracking—MIT task). Distinct eye-movement patterns were found and attributed to two separate tracking systems. However, the same results could be caused by differences in the stimuli viewed during tracking. In the present study, object identities in the MIT task were invisible during tracking, so observers performed MOT and MIT tasks with identical stimuli. Observer were able to track either position and identity depending on the task. There was no difference in eye movements between position tracking and identity tracking. This result suggests that, while observers can use different eye-movement strategies in MOT and MIT, it is not necessary.     

十文钱问题再探

本研究设计了三个实验,探讨了被试在经典的十文钱问题以及与其异质同构的组团旅游问题中的推理情况。实验1通过调查法发现,被试在十文钱异质同构问题中表现出了与十文钱问题同样高的错误率,属于推理错觉问题。在此基础上,实验二、三就其推理错误的可能原因进行了实证探究,结果发现：（1）题目表面特征的弱化能显著提高被试的推理成绩。（2）批判性思维意识与批判性思维技巧的线索提示能显著提高被试的推理成绩。     

Keep or trade? An experimental study of the exchange paradox

The “exchange paradox”—also referred to in the literature by a variety of other names, notably the “two-envelopes problem”—is notoriously difficult, and experts are not all agreed as to its resolution. Some of the various expressions of the problem are open to more than one interpretation; some are stated in such a way that assumptions are required in order to fill in missing information that is essential to any resolution. In three experiments several versions of the problem were used, in each of which the information given was sufficient to determine an optimal choice strategy when it exists or to justify indifference regarding keeping or trading when such a strategy does not exist. College students who were presented with the various versions of the problem tended to base their choices on simple heuristics and to give little evidence of understanding the probabilistic implications of the differences in the problem statements.     

Influences of task concreteness upon transitive responding in humans

The derivation of the conclusion Anna is bigger than Mary from the premises Anna is bigger than Paul and Mary is smaller than Paul is considered an instance of transitive deduction. For a non-verbal presentation, the premise statements were here transformed into a multiple operant discrimination task. Adult subjects were trained with overlapping pairs of a six-member stimulus series (A+B–, A+C–, C+D–, D+E–, E+F–; +: choice rewarded, choice penalized). A computer game-type presentation that hid the actual problem structure from the subjects was employed. The effects of varying the presentation style of the task on the objective performance and the structure awareness of subjects were investigated. A first experiment used random polygons as stimuli and the relations between them were only signalled by the above reinforcement allocations. In a second experiment the stimuli were cartoon figures additionally involved in a dominance hierarchy that was suggested graphically. A third experiment used named items that were related through visible size differences in addition to the reinforcement allocations but was otherwise like an experiment using an abstract format reported by Werner et al. (1992). In all experiments a similar proportion of subjects responded transitively when subsequently tested with the pairs BD, BE and CE by preferentially choosing stimulus B or C. Each subject subsequently filled in a questionnaire, completed a stimulus ordering exercise, and was interviewed to find out whether they were explicitly aware of the stimulus hierarchy underlying each of the tasks. Although the proportion of subjects revealing an explicit transitive responding increased together with the concreteness of the stimuli and their relations across the experiments, the objective performance in terms of choice accuracy did not vary. The accuracy performance on tests could be accurately simulated with a modification of a simple conditioning model. It is concluded that an implicit mode of processing may underlie many instances of transitive responding in humans even when explicit task understanding is reported.     

Presentation procedures in lineups and mug books: a direct comparison

The purpose of this research was to replicate and to extend past findings that the best procedure for presenting lineup pictures is not the best procedure for presenting mug book pictures. Participants witnessed a videotape of a simulated crime that was followed by a lineup task for half the participants or a mug book task for the other half. The task factor was crossed with two other factors: (a) a presentation procedure factor—pictures presented one‐at‐a‐time or grouped 12 per page and (b) a presence of the perpetrator factor—perpetrator present or absent in the viewed pictures. For perpetrator‐absent conditions, the one‐at‐a time lineup procedure produced more correct rejections than the grouped lineup procedure replicating past results; however, for the mug book task the two presentation procedures did not differ. For perpetrator‐present conditions, the grouped presentation procedure produced more correct identifications than the one‐at‐a time procedure in both lineups and mug books. The different pattern of results for lineups and mug books was explained in terms of differences in response criterion. Copyright © 2007 John Wiley & Sons, Ltd.     

IGT-Open: An open-source,computerized version of the Iowa Gambling Task

The Iowa Gambling Task (IGT) is commonly used to understand the processes involved in decision-making. Though the task was originally run without a computer, using a computerized version of the task has become typical. These computerized versions of the IGT are useful, because they can make the task more standardized across studies and allow for the task to be used in environments where a physical version of the task may be difficult or impossible to use (e.g., while collecting brain imaging data). Though these computerized versions of the IGT have been useful for experimentation, having multiple software implementations of the task could present reliability issues. We present an open-source software version of the Iowa Gambling Task (called IGT-Open) that allows for millisecond visual presentation accuracy and is freely available to be used and modified. This software has been used to collect data from human subjects and also has been used to run model-based simulations with computational process models developed to run in the ACT-R architecture.     

The effect of judges' attitudes on ratings of attitude statements. A theoretical analysis

Judgments of attitude statements with the method of equal-appearing intervals have been found to vary as a function of the judges' attitudes. In this paper explanations of the relationship between judges' attitudes and judgments of attitude statements in terms of models of psychophysical judgment are discussed. It is argued that psychophysical models such as adaptation-level theory, the range-frequency model, and the ‘rubber-band’ model and its derivations, cannot account satisfactorily for judges' performance of the attitude rating task in a great number of studies. The reason for this failure, it is argued, is that the stimulus series employed in the psychophysical judgment research on which these models are based typically varied only on the dimension being judged. The sets of statements judged in attitude rating studies, however, vary not only on the dimension of interest (favourability—Unfavourability) but also on a number of other dimensions. It is suggested that this incidental stimulus variation of attitude statements may account for the failure of psychophysical models to predict accurately the performance of judges in the attitude rating task. It is argued that if principles which could account for the effects of this incidental stimulus variation on attitude ratings could be incorporated into psychophysical models, the predictive qualities of these models could be improved considerably. One such model is discussed.     

Children's use of addition to solve two‐digit subtraction problems

Subtraction problems of the type M ? S = ? can be solved with various mental calculation strategies. We investigated fourth‐ to sixth‐graders' use of the subtraction by addition strategy, first by fitting regression models to the reaction times of 32 two‐digit subtractions. These models represented three different strategy use patterns: the use of direct subtraction, subtraction by addition, and switching between the two strategies based on the magnitude of the subtrahend. Additionally, we compared performance on problems presented in two presentation formats, i.e., a subtraction format (81 ? 37 = .) and an addition format (37 + . = 81). Both methods converged to the conclusion that children of all three grades switched between direct subtraction and subtraction by addition based on the combination of two features of the subtrahend: If the subtrahend was smaller than the difference, direct subtraction was the dominant strategy; if the subtrahend was larger than the difference, subtraction by addition was mainly used. However, this performance pattern was only observed when the numerical distance between subtrahend and difference was large. These findings indicate that theoretical models of children's strategy choices in subtraction should include the nature of the subtrahend as an important factor in strategy selection.     

Handling mathematical objects: representations and context

This article takes as a starting point the current popular anti realist position, Fictionalism, with the intent to compare it with actual mathematical practice. Fictionalism claims that mathematical statements do purport to be about mathematical objects, and that mathematical statements are not true. Considering these claims in the light of mathematical practice leads to questions about how mathematical objects are handled, and how we prove that certain statements hold. Based on a case study on Riemann’s work on complex functions, I propose that mathematicians deal with systems of representations and that truth—or what we can prove—depends on available representations in some context where the problem can be solved.     

Catalog of scaled verbal material

Atotal of 172 studies presenting informationon scaledverbal material (letters, CVCs, words, ete.) were summarized and indexed. For each study, the following information was abstracted: kind of materials, type and number of subjects, task, and data presentation format. These studies were indexed accordingto the type of materials sealed and, within material type, by type of seale information (objective information, subjective rating, or subject production). All studies were from a readily accessible English language source.     

Catalog of scaled verbal material

Atotal of 172 studies presenting informationon scaledverbal material (letters, CVCs, words, ete.) were summarized and indexed. For each study, the following information was abstracted: kind of materials, type and number of subjects, task, and data presentation format. These studies were indexed accordingto the type of materials sealed and, within material type, by type of seale information (objective information, subjective rating, or subject production). All studies were from a readily accessible English language source.