Previous beliefs affect Bayesian reasoning in conditions fostering gist comprehension.

It has been shown that Bayesian reasoning is affected by the believability of the data, but it is unknown which conditions could potentiate or reduce such belief effect. Here, we tested the hypothesis that the belief effect would mainly be observed in conditions fostering a gist comprehension of the data. Accordingly, we expected to observe a significant belief effect in iconic rather than in textual presentations and, in general, when nonnumerical estimates were requested. The results of three studies showed more accurate Bayesian estimates, either expressed numerically or nonnumerically, for icons than for text descriptions of natural frequencies. Moreover, in line with our expectations, nonnumerical estimates were, in general, more accurate for believable rather than for unbelievable scenarios. In contrast, the belief effect on the accuracy of the numerical estimates depended on the format and on the complexity of the calculation. The present findings also showed that single-event posterior probability estimates based on described frequencies were more accurate when expressed nonnumerically rather than numerically, opening new avenues for the development of interventions to improve Bayesian reasoning.

Math anxiety and the shifting function: An event-related potential study of arithmetic task switching.

Why is math anxiety usually related to less efficient math processing? According to attentional control theory, anxiety leads to reduced attentional control, which often entails a greater investment of resources (e.g., more time or effort) to carry out a cognitive task. The executive functions mainly affected by anxiety are inhibition and shifting. Previous studies suggest that math anxiety may impair the inhibitory function. In the present study, the relationship between math anxiety and shifting efficiency when switching between two-digit additions and subtractions was examined. Twenty highly math-anxious and 20 low math-anxious individuals participated in an event-related potential (ERP) transition-cueing experiment. Math anxiety was expected to delay the shifting process, leading to a larger switch cost in response time and no centroparietal cue-locked switch-specific positivity registered in the electroencephalogram during the cue-target interval. Highly math-anxious individuals showed a larger switch cost than their low math-anxious peers. Asymmetrical switch effects between operations in response time were found in both groups, which might be due to larger sequential difficulty effects after subtractions than after additions. The cue-locked switch-specific positivity was present only in the low math-anxious group. The present results suggest that highly math-anxious individuals take longer to shift task sets. Additionally, the highly math-anxious group showed a more positive frontal P2 after the cue that announced a switch to subtraction, probably indicating stronger attentional capture by this cue, because the most threatening condition is anticipated. Taken together, these data suggest that math anxiety also impairs attentional control when switching between arithmetic tasks.

Proactive control of attention in math-anxious individuals.

Attentional control deficit has been proposed as one of the reasons for lower arithmetical performance in people with high math anxiety (HMA). Previous research trying to discern whether this deficit concerned proactive or reactive use of attentional control has been criticised because the methodologies used were mostly suited to investigating reactive control only. The aim of this study was to investigate proactive control in HMA individuals in a classical Stroop task. Twenty HMA and 20 low math-anxious individuals (LMA) named the ink colour in which congruent and incongruent colour words as well as X strings (neutral condition) were presented. The HMA group was slower than their LMA peers in the congruent and incongruent conditions only. Furthermore, HMA individuals showed a higher interference effect. Last, only LMA participants showed a facilitatory effect of the congruent condition. These results are interpreted as indicating the presence in the HMA individuals of a task conflict between the task to perform (ink naming) and an irrelevant task triggered by the stimuli (word reading). Task conflict is evident only when proactive control, responsible for maintaining the current goals, is too weak to solve the competition between tasks. Therefore, this study confirms that HMA individuals find it difficult to implement attention proactively.

Processing of Ordinal Information in Math-Anxious Individuals.

This study aimed to investigate whether the ordinal judgments of high math-anxious (HMA) and low math-anxious (LMA) individuals differ. Two groups of 20 participants with extreme scores on the Shortened Mathematics Anxiety Rating Scale (sMARS) had to decide whether a triplet of numbers was presented in ascending order. Triplets could contain one-digit or two-digit numbers and be formed by consecutive numbers (counting condition), numbers with a constant distance of two or three (balanced) or numbers with variable distances between them (neutral). All these triplets were also presented unordered: sequence order in these trials could be broken at the second (D2) or third (D3) number. A reverse distance effect (worse performance for ordered balanced than for counting trials) of equal size was found in both anxiety groups. However, HMA participants made more judgment errors than their LMA peers when they judged one-digit counting ordered triplets. This effect was related to worse performance of HMA individuals on a symmetry span test and might be related to group differences on working memory. Importantly, HMAs were less accurate than LMA participants at rejecting unordered D2 sequences. This result is interpreted in terms of worse cognitive flexibility in HMA individuals.

Spatial processing in a mental rotation task: Differences between high and low math-anxiety individuals.

Previous studies suggested that highly math-anxious (HMA) individuals invest more attentional resources than their low math-anxious (LMA) peers in numerical tasks, and have worse spatial skills. We aimed to explore whether they also need to apply more resources in spatial tasks. In this study, HMA and LMA individuals saw normal or mirror-reversed letters in six orientations and made mirror-normal decisions. In both groups, response times and errors increased with angular deviation from upright and the ERP mental rotation effect was found. However, HMAs were slower to respond than their LMA counterparts. Interestingly, the HMA group showed a larger P3b in greater deviations for normal letters and in all mirrored letters. Since P3b amplitude reflects the attentional resources invested in the categorization of relevant stimuli, HMA individuals may need to devote more processing effort than their LMA peers when performing mental rotation. This finding is consistent with the Attentional Control Theory.

Representation of numerical magnitude in math-anxious individuals.

Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed to further explore the relation between math anxiety and magnitude representation through three different tasks. HMA and low math-anxious individuals (LMA) performed a non-symbolic comparison, in which no group differences were found. Furthermore, we did not replicate previous findings in an Arabic digit comparison, in which HMA individuals showed equivalent distance effects to their LMA peers. Lastly, there were no group differences in a counting Stroop task. Altogether, an explanation of math anxiety differences in terms of less precise magnitude representation is not supported.

Number line estimation in highly math-anxious individuals.

In this study, we aimed to investigate the difficulties highly math-anxious individuals (HMA) may face when having to estimate a number's position in a number line task. Twenty-four HMA and 24 low math-anxiety (LMA) individuals were presented with four lines with endpoints 0-100, 0-1,000, 0-100,000, and 267-367 on a computer monitor on which they had to mark the correct position of target numbers using the mouse. Although no differences were found between groups in the frequency of their best-fit model, which was linear for all lines, the analysis of slopes and intercepts for the linear model showed that the two groups differed in performance on the less familiar lines (267-367 and 0-100,000). Lower values for the slope and higher values for the intercept were found in the HMA group, suggesting that they tended to overestimate small numbers and underestimate large numbers on these non-familiar lines. Percentage absolute error analyses confirmed that HMA individuals were less accurate than their LMA counterparts on these lines, although no group differences were found in response time. These results indicate that math anxiety is related to worse performance only in the less familiar and more difficult number line tasks. Therefore, our data challenge the idea that HMA individuals might have less precise numerical representations and support the anxiety-complexity effect posited by Ashcraft and colleagues.

From reading numbers to seeing ratios: a benefit of icons for risk comprehension.

Promoting a better understanding of statistical data is becoming increasingly important for improving risk comprehension and decision-making. In this regard, previous studies on Bayesian problem solving have shown that iconic representations help infer frequencies in sets and subsets. Nevertheless, the mechanisms by which icons enhance performance remain unclear. Here, we tested the hypothesis that the benefit offered by icon arrays lies in a better alignment between presented and requested relationships, which should facilitate the comprehension of the requested ratio beyond the represented quantities. To this end, we analyzed individual risk estimates based on data presented either in standard verbal presentations (percentages and natural frequency formats) or as icon arrays. Compared to the other formats, icons led to estimates that were more accurate, and importantly, promoted the use of equivalent expressions for the requested probability. Furthermore, whereas the accuracy of the estimates based on verbal formats depended on their alignment with the text, all the estimates based on icons were equally accurate. Therefore, these results support the proposal that icons enhance the comprehension of the ratio and its mapping onto the requested probability and point to relational misalignment as potential interference for text-based Bayesian reasoning. The present findings also argue against an intrinsic difficulty with understanding single-event probabilities.

Too Worried to Judge: On the Role of Perceived Severity in Medical Decision-Making.

Ideally, decisions regarding one's health should be made after assessing the objective probabilities of relevant outcomes. Nevertheless, previous beliefs and emotional reactions also have a role in decision-making. Furthermore, the comprehension of probabilities is commonly affected by the presentation format, and by numeracy. This study aimed to assess the extent to which the influence of these factors might vary between different medical conditions. A sample of university students were presented with two health scenarios containing statistical information on the prevalence of breast cancer and hypertension either through icon arrays (N = 71) or natural frequencies (N = 72). They also received information regarding a preventive measure (mammogram/low-sodium diet) and the likelihood of a positive mammogram or a rich-sodium diet either when suffering or not suffering from the disease. Before seeing the data, participants rated the severity of the disease and the inconvenience of the preventive measure. After reading the health scenario, participants had to rate its difficulty, and how worrisome it was. They had also to rate the prior probability of suffering from this medical condition, and the posterior probability of it, provided a positive mammogram or a rich-sodium diet. Finally, they rated the extent to which they would recommend the preventive measures. All the rates used the same 1 (little)-8 (a great deal) scale. Participants' numeracy was also assessed. The scenarios differed significantly in perceived severity and worry, with the cancer scenario obtaining higher scores. Importantly, regression analyses showed that the recommendations in the two health scenarios depended on different variables. A model taking into consideration severity and worry rates best explained decisions in the cancer scenario; in contrast, in the hypertension scenario the model that best explained the recommendations comprised both the posterior probability estimate and the severity rate. Neither numeracy nor presentation format affected recommendation but both affected difficulty, worrying and probability rates. We conclude that previous perceptions of the severity of a health condition modulate the use of probabilistic information for decision-making. The roles of presentation format and numeracy in enabling patients to understand statistical information are also discussed.

Math anxiety: A review of its cognitive consequences, psychophysiological correlates, and brain bases.

A decade has passed since the last published review of math anxiety, which was carried out by Ashcraft and Ridley (2005). Given the considerable interest aroused by this topic in recent years and the growing number of publications related to it, the present article aims to provide a full and updated review of the field, ranging from the initial studies of the impact of math anxiety on numerical cognition, to the latest research exploring its electrophysiological correlates and brain bases from a cognitive neuroscience perspective. Finally, this review describes the factors and mechanisms that have been claimed to play a role in the origins and/or maintenance of math anxiety, and it examines in detail the main explanations proposed to account for the negative effects of math anxiety on performance: competition for working memory resources, a deficit in a low-level numerical representation, and inhibition/attentional control deficit.

Attentional bias in high math-anxious individuals: evidence from an emotional Stroop task.

Attentional bias toward threatening or emotional information is considered a cognitive marker of anxiety, and it has been described in various clinical and subclinical populations. This study used an emotional Stroop task to investigate whether math anxiety is characterized by an attentional bias toward math-related words. Two previous studies failed to observe such an effect in math-anxious individuals, although the authors acknowledged certain methodological limitations that the present study seeks to avoid. Twenty high math-anxious (HMA) and 20 low math-anxious (LMA) individuals were presented with an emotional Stroop task including math-related and neutral words. Participants in the two groups did not differ in trait anxiety or depression. We found that the HMA group showed slower response times to math-related words than to neutral words, as well as a greater attentional bias (math-related - neutral difference score) than the LMA one, which constitutes the first demonstration of an attentional bias toward math-related words in HMA individuals.

Efficiency of Arithmetic Procedures Modulates the Problem-Size Effect in Subtraction.

The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies.

Efficiency of arithmetic procedures modulates the problem-size effect in subtraction

The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies (AU)

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Reactive recruitment of attentional control in math anxiety: an ERP study of numeric conflict monitoring and adaptation.

This study uses event-related brain potentials (ERPs) to investigate the electrophysiological correlates of numeric conflict monitoring in math-anxious individuals, by analyzing whether math anxiety is related to abnormal processing in early conflict detection (as shown by the N450 component) and/or in a later, response-related stage of processing (as shown by the conflict sustained potential; Conflict-SP). Conflict adaptation effects were also studied by analyzing the effect of the previous trial's congruence in current interference. To this end, 17 low math-anxious (LMA) and 17 high math-anxious (HMA) individuals were presented with a numerical Stroop task. Groups were extreme in math anxiety but did not differ in trait or state anxiety or in simple math ability. The interference effect of the current trial (incongruent-congruent) and the interference effect preceded by congruence and by incongruity were analyzed both for behavioral measures and for ERPs. A greater interference effect was found for response times in the HMA group than in the LMA one. Regarding ERPs, the LMA group showed a greater N450 component for the interference effect preceded by congruence than when preceded by incongruity, while the HMA group showed greater Conflict-SP amplitude for the interference effect preceded by congruence than when preceded by incongruity. Our study showed that the electrophysiological correlates of numeric interference in HMA individuals comprise the absence of a conflict adaptation effect in the first stage of conflict processing (N450) and an abnormal subsequent up-regulation of cognitive control in order to overcome the conflict (Conflict-SP). More concretely, our study shows that math anxiety is related to a reactive and compensatory recruitment of control resources that is implemented only when previously exposed to a stimuli presenting conflicting information.

Abnormal error monitoring in math-anxious individuals: evidence from error-related brain potentials.

This study used event-related brain potentials to investigate whether math anxiety is related to abnormal error monitoring processing. Seventeen high math-anxious (HMA) and seventeen low math-anxious (LMA) individuals were presented with a numerical and a classical Stroop task. Groups did not differ in terms of trait or state anxiety. We found enhanced error-related negativity (ERN) in the HMA group when subjects committed an error on the numerical Stroop task, but not on the classical Stroop task. Groups did not differ in terms of the correct-related negativity component (CRN), the error positivity component (Pe), classical behavioral measures or post-error measures. The amplitude of the ERN was negatively related to participants' math anxiety scores, showing a more negative amplitude as the score increased. Moreover, using standardized low resolution electromagnetic tomography (sLORETA) we found greater activation of the insula in errors on a numerical task as compared to errors in a non-numerical task only for the HMA group. The results were interpreted according to the motivational significance theory of the ERN.

One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers.

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also measured by asking the children to assess the correctness of a cartoon character's counting in both contexts. In general, the children performed cardinal tasks significantly better than ordinal ones. Tasks requiring the production of the number for a given quantity or position were solved more accurately than those testing the ability to select a set of n objects or the object in the nth position. Different profiles were obtained for the principles; those principles shared by the two contexts were mastered earlier in the cardinal context. Regarding order (ir)relevance, older children adhered to rigid ways of counting, producing better results in the ordinal context and incorrect rejections in the cardinal trials. Altogether, our data indicate that the acquisitions of cardinal and ordinal meanings of numbers are related, and cardinality precedes the development of ordinality.

Getting to the source: a questionnaire on the learning and use of arithmetical operations

Algunos modelos actuales sobre la cognición matemática (Dehaene, 1992; Campbell & Clark, 1992) hacen sus predicciones sobre el código en que se resuelven las operaciones aritméticas basándose en cómo se aprendieron dichas operaciones o en cómo se utilizan habitualmente. Sin embargo, los datos de adquisición y uso a menudo se han derivado de informes anecdóticos y nunca se han recogido datos de modo sistemático. En este estudio se diseñó un cuestionario para investigar cómo habían aprendido las tablas de multiplicar los participantes, así como el código en que las operaciones de una y de varias cifras se resuelven habitualmente. El cuestionario se pasó a dos grupos de estudiantes universitarios, uno español (Estudio 1) y otro belga (Estudio 2). Los resultados mostraron que las multiplicaciones de una cifra se aprenden básicamente a través de la repetición en voz alta, pero los participantes adultos prefieren resolverlas visualizando mentalmente números arábicos. Éste es el código preferido también para calcular las sumas, restas y divisiones. La preferencia por el código arábico aumenta cuando deben calcularse operaciones de más de una cifra(AU)

Some current models of mathematical cognition (Dehaene, 1992; Campbell & Clark, 1992) make strong claims about the code in which arithmetical operations are solved, basing themselves on how these operations were originally acquired or are most frequently employed. However, data on acquisition and use are often derived from anecdotic reports and no systematic figures have ever been collected. In this study a questionnaire was devised to investigate how participants learned multiplication tables, as well as the code in which one-digit and multi-digit operations are usually solved. The questionnaire was administered to two groups of university students, one Spanish (Study 1) and the other Belgian (Study 2). The results show that multiplication tables are mainly learnt by oral rehearsal, but adults solve multiplications more frequently by visualizing Arabic digits. This is also their preferred code for calculating additions, subtractions, and divisions. The preference for the Arabic code increases when subjects have to solve multidigit operations(AU)

Which words are activated during bilingual word production?

Whether words are or are not activated within the lexicon of the nonused language is an important question for accounts of bilingual word production. Prior studies have not led to conclusive results, either because alternative accounts could be proposed for their findings or because activation could have been artificially induced by the experimental paradigms. Moreover, previous data only involved target translations, and nothing is known about the activation of nontarget words in the nonused language. The picture-picture interference paradigm was used here, since it allowed the activation of nontarget words to be determined without showing stimuli that could artificially activate the nonused language. Proficient Spanish-Catalan speakers were presented with pairs of partially overlapping colored pictures and were instructed to name the green picture and ignore the red picture. In Experiment 1, distractor pictures with cognate names interfered more than distractor pictures with noncognate names. In Experiment 2, facilitation was observed when the names of the distractor pictures in the nonused language were phonologically related to the names of the target pictures. Overall, these results indicate that nontarget words are activated in the nonused language, at least in the case of proficient bilingual speakers. These results help researchers to constrain theories of bilingual lexical access. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

Language effects in addition: How you say it counts.

This study aimed to investigate the role of language in calculation. Two populations were compared, one with a base-10 language, and another (Basque) in which number words are constructed by combining multiples of 20 and units or teens (e.g., "35" is said "twenty and fifteen"). Experiment 1 asked participants to verbally solve additions presented as Arabic digits. Basque participants solved the additions that consisted of a multiple of 20 and a teen (e.g., 20 + 15) faster than controls with identical answers (e.g., 25 + 10). No differences were found in the base-10 language group. Experiment 2 replicated this result even if participants had to type the answer on a numerical keypad, instead of saying it. Hence, the structure of number words in each of the languages influenced the way additions were solved, even if language was not necessary for conducting the task. Finally, in Experiment 3, both language groups performed a numerical comparison task in which no effects of the structure of number words were obtained. Results of the three experiments are discussed in light of current models of numerical cognition.

Acceso léxico en producción del lenguaje: el caso bilingüe / Lexical Access in Speech Production: the Bilingual Case

En este artículo se revisan modelos de acceso léxico en producción de lenguaje en hablantes bilingües. Nos centramos en dos aspectos fundamentales del acceso léxico: a) cómo se alcanza la selección léxica , y b) si el acceso léxico implica estadios de procesamiento discretos o en cascada.Comenzamos considerando supuestos importantes sobre el funcionamiento?A. Costa et al. 432 del acceso léxico en monolingües, para después discutirlos en el contexto de los hablantes bilingües. Se describen los modelos teóricos y la evidencia empírica reciente acorde a estos supuestos (AU)