Falsifying mental models: Testing the predictions of theories of syllogistic reasoning

Four experiments are reported that tested the claim, drawn from mental models theory, that reasoners attempt to construct alternative representations of problems that might falsify preliminary conclusions they have drawn. In Experiment 1, participants were asked to indicate which alternative conclusion(s) they had considered in a syllogistic reasoning task. In Experiments 2-4, participants were asked to draw diagrams consistent with the premises, on the assumption that these diagrams would provide insights into the mental representation being used. In none of the experiments was there any evidence that people constructed more models for multiple-model than for single-model syllogisms, nor was there any correlation between number of models constructed and overall accuracy. The results are interpreted as showing that falsification of the kind proposed by mental models theory may not routinely occur in reasoning.     

An experimental study of strategy development

Three experiments are reported in which the strategy usage for a compass point directions task was investigated. For this task, people may use either an efficient cancellation strategy or an inefficient spatial strategy (see Roberts, Gilmore, & Wood, 1997). Experiment 1, together with Experiment 2, showed that users of cancellation are unlikely to have explicit prior knowledge of this strategy; instead they discover it as a result of experience with the task. Experiment 1 also showed that strategy selection is unlikely to be based on stylistic preferences, and that reducing the cognitive demands of the task does not increase the discovery of cancellation. Experiment 3 showed that evaluation of strategy validity is also of importance: Unsuccessful evaluation may prevent the selection of a newly discovered strategy, even if it is the more efficient method.     

Perceptual selectivity is task dependent: The pop-out effect poops out

An attempt was made to determine why evidence for perceptual selectivity based on conceptual category (e.g., digits vs. letters) has been found in some experiments but not in others. Experiments using the partial-report paradigm find no partial-report superiority when the report is cued by category, whereas, in recent visual search studies, evidence for perceptual selectivity has been obtained for arrays containing a single item that was categorically different from the other items (e.g., a digit among letters). Using a search task, Experiment 1 investigated the possibility that the number of categorically different items in the arrays could be a determinant of selectivity. One, two, or three digits and a variable number of letters were presented on each trial, and subjects determined if a particular digit was present. No evidence of selectivity was obtained, even for the one-digit condition. Experiment 2 verified this result, and Experiment 3 extended the failure of selectivity to a search task in which the possible targets differed in color from the distractor items. In Experiment 4, subjects counted the number of digits or red letters in arrays in which black letters were the distractor items. The counting task was used to eliminate the requirement in our previous tasks that the subjects search forspecific items. Evidence was obtained in the counting task for selectivity based on the color difference but not on the categorical difference. The color stimuli used in the counting task were essentially the same as those that did not yield any evidence of selectivity in the search task. The results suggest that task demands are an important determinant of whether or not perceptual selectivity will occur.     

ROC parameters in item and context recognition

Conflicting theories argue that recognition is achieved either by familiarity exclusively, or by a mixture of familiarity and recollection. We explore in three experiments the goodness of fit of both positions to experimental data in which context information is manipulated. In Experiments 1 and 2, we explore the availability of context information in recognition, testing the focus stimulus, its context, and their associative relation. In Experiment 3, participants were confronted with a plurality task in an attempt to force them to use the peripheral information in recognition. The results show that people acquire specific associative information, and although overall recognition performance was not affected by the use of context, receiver operating characteristic (ROC) analysis showed that people use a duality of processes in recognition.     

Position Location on Topographical Maps: Effects of Task Factors,Training, and Strategies

There is little research on the ways people go about the very common task of extracting information from various forms of maps. In this study, we examined task factors, cognitive processes, and individual differences as determinants of performance differences when locating a position on a topographical map from a given position on the ground. Subjects for the study were 188 Australian Army personnel. Both spatial visualization ability and a visual learning style preference were found to be effective predictors of performance, whereas a form of verbal strategy training produced significantly improved performance. When no effective strategy was supplied, those subjects with a strong visual learning style preference performed dramatically better than their low-preference counterparts, suggesting that this form of processing preference may have a powerful impact on untrained performance. These results indicate that most subjects usually approach the task of map reading in a relatively passive way, without any coherent strategy, and then attempt to encode information using inefficient spatial codes. When a simple and effective verbal strategy was supplied, most subjects were able to adopt it, with uniformly beneficial, results. This suggests that performance on many spatial tasks could be improved by verbal strategy training.     

The role of short-term working memory in mental arithmetic

A series of experiments explored the role of information storage in working memory in performing mental arithmetic. Experiment 1 assessed the strategies people report for solving auditorily presented multidigit problems such as 325 + 46. As expected, all subjects reported breaking down the problems into a series of elementary stages, though there were considerable individual differences with regard to the order of their execution. Strategies of this type necessitate both the temporary storage of information and the mobilization of long-term knowledge. Experiments 2 and 3 examined the effects of delaying the output of individual partial results on calculation accuracy and showed that interim information is forgotten if it is not utilized immediately. Experiment 4 showed that forgetting the initial information is also a source of error and suggested that forgetting increases as a function of the number of calculation stages intervening between initial presentation and subsequent utilization of information. Two simple quantitative models were derived from a general task analysis, one of which assumed a decay process in working storage and the other no decay. The decay model gave a reasonable fit to data from Experiments 2–4, and in doing so it coped appreciably well with the effects of a large variety of task variables (e.g., carrying, the provision of written notes, calculation strategy, output order). The decay model is a tractable analysis of a complex task, and it is suggested that similar analyses may prove fruitful for other problem-solving activities which involve the use of working memory.     

Development of strategies for recalling letter sequences

Kindergarten, second-grade, and fourth-grade children (6, 8, and 10 years of age, respectively) were asked to recall letter sequences on a task that required the use of: (a) a verbal strategy; (b) a positional strategy; or (c) either strategy. Additional trials, allowing either strategy, were interspersed among those requiring a verbal or positional strategy; strategy use was determined from performance on these interspersed trials. The results show that children at all grade levels attempted to use a task-appropriate strategy. Performance on the verbal task showed a more marked developmental increase than did performance on the positional task. A second experiment replicated the first with the interspersed trials removed. A third experiment was designed to determine whether letter names interfered with older children's efficient use of a positional strategy. Even with this source of interference removed, the developmental pattern of Experiments 1 and 2 was replicated. There was a Sex by Condition interaction in Experiments 2 and 3 which showed that males do better in the condition requiring a positional strategy, and females do better in the condition requiring a verbal strategy.     

Causal structure learning over time: observations and interventions

Seven studies examined how people learn causal relationships in scenarios when the variables are temporally dependent - the states of variables are stable over time. When people intervene on X, and Y subsequently changes state compared to before the intervention, people infer that X influences Y. This strategy allows people to learn causal structures quickly and reliably when variables are temporally stable (Experiments 1 and 2). People use this strategy even when the cover story suggests that the trials are independent (Experiment 3). When observing variables over time, people believe that when a cause changes state, its effects likely change state, but an effect may change state due to an exogenous influence in which case its observed cause may not change state at the same time. People used this strategy to learn the direction of causal relations and a wide variety of causal structures (Experiments 4-6). Finally, considering exogenous influences responsible for the observed changes facilitates learning causal directionality (Experiment 7). Temporal reasoning may be the norm rather than the exception for causal learning and may reflect the way most events are experienced naturalistically.     

Audio-visual speech perception off the top of the head

The study examined whether people can extract speech related information from the talker's upper face that was presented using either normally textured videos (Experiments 1 and 3) or videos showing only the outlined of the head (Experiments 2 and 4). Experiments 1 and 2 used within- and cross-modal matching tasks. In the within-modal task, observers were presented two pairs of short silent video clips that showed the top part of a talker's head. In the cross-modal task, pairs of audio and silent video clips were presented. The task was to determine the pair in which the talker said the same sentence. Performance on both tasks was better than chance for the outline as well as textured presentation suggesting that judgments were primarily based on head movements. Experiments 3 and 4 tested if observing the talker's upper face would help identify speech in noise. The results showed the viewing the talker's moving upper head produced a small but reliable improvement in speech intelligibility, however, this effect was only secure for the expressive sentences that involved greater head movements. The results suggest that people are sensitive to speech related head movements that extend beyond the mouth area and can use these to assist in language processing.     

Children's Understanding of the Natural Numbers’ Structure

When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010 ; Siegler & Opfer, 2003 ). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011 ; Cantlon, Cordes, Libertus, & Brannon, 2009 ; Cohen & Blanc‐Goldhammer, 2011 ). We show here that children prefer linear number lines over logarithmic lines when they do not have to deal with the meanings of individual numerals (i.e., number symbols, such as “5” or “80”). In Experiments 1 and 2, when 5‐ and 6‐year‐olds choose between number lines in a forced‐choice task, they prefer linear to logarithmic and exponential displays. However, this preference does not persist when Experiment 3 presents the same lines without reference to numbers, and children simply choose which line they like best. In Experiments 4 and 5, children position beads on a number line to indicate how the integers 1–100 are arranged. The bead placement of 4‐ and 5‐year‐olds is better fit by a linear than by a logarithmic model. We argue that previous results from the number‐line task may depend on strategies specific to the task.     

Subitizing and its subprocesses

 When people are presented with small sets of elements such as dots they can very easily determine their number. This ability has been called subitizing. The present paper reports results from four experiments. The discussion focuses on the question whether one or two psychological processes have to be assumed for this task of subitizing. Taken together our results support the two-process theories. In particular, a distinction between a process of separation and a process of enumeration is suggested. Experiments 3 and 4 support the canonical pattern hypothesis. Canonical patterns are processed substantially faster than noncanonical patterns. Furthermore, if a complex pattern can be broken down into small canonical patterns, then participants follow a partition and add strategy. Accepted: 22 December 1999     

Working memory components of the Corsi blocks task

A computerized version of the Corsi blocks task (Milner, 1971) was assessed for standard forward‐recall order (Experiments 1 and 3) and for reversed‐recall order (Experiments 2 and 3) either in a single‐task or in a dual‐task design combined with articulatory suppression, matrix‐tapping, random‐interval generation or fixed‐interval generation as concurrent tasks during the encoding stage. Concurrent performance of the matrix‐tapping task impaired memory performance for short as well as for longer block sequences. The random‐interval generation task, which loads executive processes, impaired memory performance mainly at intermediate‐ and longer‐sequence lengths, while fixed‐interval generation, which is presumed to put no load on executive processing, did not show any effect. Articulatory suppression did not impair memory performance on forward‐recall order, but it impaired memory for longer sequences in the backward‐recall condition in Experiment 2, but not in Experiment 3. The results are discussed within the context of the working‐memory model of Baddeley and Hitch (1974).     

Two meanings of “if”? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.     

Two meanings of "if"? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.     

Effect of visual perspective on memory and interpretation in dysphoria

When engaging in self-reflection, the visual perspective one adopts has important effects on emotional reactivity. Specifically, adopting a distanced stance, or viewing oneself from a third-person perspective, has been found to reduce emotional reactivity to negative autobiographical memories. The effect of adopting this perspective is moderated by depression such that reactivity is not reduced for individuals with particularly low levels of depressive symptoms. In the current study, we examine the effects of visual perspective on two forms of mental imagery in dysphoric and nondysphoric individuals. We attempt to replicate previous findings for recall of sad autobiographical memories and extend this research to interpretation of ambiguous situations. The results suggest that the effects of adopting a distanced stance are not moderated by depressive symptoms and do not extend from memories to interpretations of ambiguous situations.     

Unmixing the mixing cost: contributions from dimensional relevance and stimulus-response suppression

When participants repeat the same task in a context in which the task may also switch (a mixed block), performance deteriorates compared to when there is only one task repeating (a pure block). Three experiments were designed to assess how perceptual and motor transitions influenced this mixing cost. Experiment 1 provided three pure block baselines for perceptual and motor transitions. Experiments 2 and 3 examined these transitions in a mixed block. Results show that most of the mixing cost comes from two factors: (a) episodic interference in the mixed block when the stimulus changes and the response repeats, and (b) increased suppression in mixed blocks affecting trials where stimulus-response mappings repeat. We propose that these mechanisms are strategically applied when adopting a sustained "switching set" in mixed blocks. The purpose of this set would be to avoid perseveration errors in the most demanding trials (the task-switching trials), but remaining active during task-repetitions. Results regarding the mixing cost are thus relevant to the assessment of models of task-switching, which at present mainly rely on data from task switch trials.     

Individual differences in motivated social cognition: the case of self-serving information processing

Three experiments examined the hypothesis that people show consistency in motivated social cognitive processing across self-serving domains. Consistent with this hypothesis, Experiment 1 revealed that people who rated a task at which they succeeded as more important than a task at which they failed also cheated on a series of math problems, but only when they could rationalize their cheating as unintentional. Experiment 2 replicated this finding and demonstrated that a self-report measure of self-deception did not predict this rationalized cheating. Experiment 3 replicated Experiments 1 and 2 and ruled out several alternative explanations. These experiments suggest that people who show motivated processing in ego-protective domains also show motivated processing in extrinsic domains. These experiments also introduce a new measurement procedure for differentiating between intentional versus rationalized cheating.     

Exhaustive memory-scanning and familiarity discrimination: Separate mechanisms in recognition memory tasks

Experiment I was a yes-no recognition task with lists of one, two or four items to remember. Each item in the experiment appeared in only one list, and each list was presented only once. One group of subjects performed the task with complex pictures. Their results were incompatible with the hypothesis of exhaustive memory scanning, since the function relating “yes” response latency to list length was not parallel to but steeper than the function for “no” responses. Another group performed the task with words. Their results were consistent with exhaustive memory-scanning. Experiment II was a similar task in which the familiarity was varied of the test items to which the subjects had to respond “no”. That variation affected response latency with pictures but not with words. From these results and from a consideration of relevant neurological data, the hypothesis is advanced that familiarity discrimination and exhaustive memory-scanning are separate mechanisms.     

Individual differences in Sternberg’s memory scanning task

This study provides a new perspective on both the cognitive processes actually implemented and the effect of a simple experimental control - the recall constraint - in Sternberg’s memory scanning task. These findings were highlighted by adopting a new approach based on the comparison of qualitative and quantitative results.The analysis of individual processing, on 72 adults, each participating in one of two experimental conditions (with or without sequence recall), highlighted a large variability in quantitative results as well as qualitative procedures. Based on the participants’ retrospective verbalisations, two categories of strategies were identified: (1) the procedures used to memorize the sequence of digits, and (2) the procedures used to compare this sequence with the test digit, which includes strategies for coding the items and processes for searching them in memory. The analysis of the strategies shows that their frequencies of use depend not only on the experimental condition, but also on the participants, the level of task difficulty and the interaction between participants and level of difficulty. This variability questions the accuracy of Sternberg’s mean model. Furthermore, this approach suggests some answers to the old debate concerning the exhaustive search pattern for the yes response. Indeed, our results show three types of strategies that can be identified according to the different models of search suggested in the literature. The “exhaustive” search, that would only be involved in the recall condition and only for some of the participants, the “self-terminating” search and the “immediate” strategy, which can be identified with a model of parallel search with limited resources. Thus our study suggests that the different search models are appropriate but depend on both the specific experimental conditions and participant’s strategy. Our results should help to improve the interpretation of data collected with this paradigm in cognitive and neuroscientific studies of memory.