Neural foundations of logical and mathematical cognition

Recurrence quantification analysis during a mental calculation task

The identification of brain dynamical changes under different cognitive conditions with noninvasive techniques such as electroencephalography (EEG) is relevant for the understanding of their underlying neural mechanisms. The comprehension of these mechanisms has applications in the early diagnosis of neurological disorders and asynchronous brain computer interfaces. In both cases, there are no reported features that could describe intersubject and intra subject dynamics behavior accurately enough to be applied on a daily basis. The present work proposes the use of three nonlinear features (recurrence rate, determinism, and recurrence times) extracted from recurrence quantification analysis (RQA) to describe central and parietal EEG power series complexity in continuous alternating episodes of mental calculation and rest state. Our results demonstrate a consistent mean directional change of determinism, recurrence rate, and recurrence times between conditions. Increasing values of determinism and recurrence rate were present from the rest state to mental calculation, whereas recurrence times showed the opposite pattern. The analyzed features in the present study showed statistically significant changes between rest and mental calculation states in both individual and population analysis. In general, our study described mental calculation EEG power series as less complex systems in comparison to the rest state. Moreover, ANOVA showed stability of RQA features along time.

An Eye-Tracking Study of Structural Priming from Abstract Arithmetic to Chinese Structure NP1 + You + NP2 + Hen + AP

The present study attempted to explore the abstract priming effects from mathematical equations to Mandarin Chinese structure NP₁ + You + NP₂ + Hen + AP in an on-line comprehension task with the aim to figure out the mechanism that underlying these effects. The results revealed that compared with baseline priming conditions, participants tended to choose more high-attachment options in high-attachment priming conditions and more low-attachment priming options in low-attachment priming conditions. Such difference had reached a significant level, which provided evidence for the shared structural representation across mathematical and linguistic domains. Additionally, the fixations sequences during arithmetic calculations reflected those equations were processed hierarchically and could be extracted in parallel instead of being scanned in a sequentially left-to-right order. Our results have provided some evidence for the Representational Account.

Intersubject Variability in Cerebrovascular Hemodynamics and Systemic Physiology during a Verbal Fluency Task under Colored Light Exposure: Clustering of Subjects by Unsupervised Machine Learning

There is large intersubject variability in cerebrovascular hemodynamic and systemic physiological responses induced by a verbal fluency task (VFT) under colored light exposure (CLE). We hypothesized that machine learning would enable us to classify the response patterns and provide new insights into the common response patterns between subjects. In total, 32 healthy subjects (15 men and 17 women, age: 25.5 ± 4.3 years) were exposed to two different light colors (red vs. blue) in a randomized cross-over study design for 9 min while performing a VFT. We used the systemic physiology augmented functional near-infrared spectroscopy (SPA-fNIRS) approach to measure cerebrovascular hemodynamics and oxygenation at the prefrontal cortex (PFC) and visual cortex (VC) concurrently with systemic physiological parameters. We found that subjects were suitably classified by unsupervised machine learning into different groups according to the changes in the following parameters: end-tidal carbon dioxide, arterial oxygen saturation, skin conductance, oxygenated hemoglobin in the VC, and deoxygenated hemoglobin in the PFC. With hard clustering methods, three and five different groups of subjects were found for the blue and red light exposure, respectively. Our results highlight the fact that humans show specific reactivity types to the CLE-VFT experimental paradigm.

Current and Potential Cognitive Development in Healthy Children: A New Approach to Raven Coloured Progressive Matrices

In clinical practice and research, Raven’s Coloured Progressive Matrices (RCPMs) continue to be used according to a single procedure that aims to evaluate a single overall score of the current general intelligence level. This study aimed to examine potential cognitive development in a sample of 450 typically developing children, aged from 6 to 10 years, by administering RCPMs according to the standard procedure followed immediately by a standardized interview on incorrect items. In addition, the study aimed to analyze how performance differed across age groups. The results analysis was examined on the basis of three different factors in which the items were grouped in previous factorial studies. The results found that performance improved markedly and significantly after the interview; however, the improvement was not homogeneous in the three factors across age groups or within each age group. The age groups showed a different development potential in relation to the nature of the task: the younger ones showed a greater increase on items requiring figure completion, and the older ones showed a greater increase on analogical reasoning items. Finally, the children who showed the greatest improvement were those with the best performance in standard RCPM administration. The procedure described in the present research could represent a useful tool in clinical practice and in the research for a broader cognitive assessment focused on potential cognitive development, as well as on real cognitive development, and to favor the planning of more adequate rehabilitation and educational treatments.

A new method for training creativity: narrative as an alternative to divergent thinking

Creativity is a major source of innovation, growth, adaptability, and psychological resilience, making it a top priority of governments, global corporations, educational institutions, and other organizations that collectively invest hundreds of millions of dollars annually into training. The current foundation of creativity training is the technique known as divergent thinking; yet for decades, concerns have been raised about the adequacy of divergent thinking: it is incongruent with the creative processes of children and most adult creatives, and it has failed to yield expected downstream results in creative production. In this article, we present an alternative approach to creativity training, based in neural processes different from those involved in divergent thinking and drawing upon a previously unused resource for creativity research: narrative theory. We outline a narrative theory of creativity training; illustrate with examples of training and assessment from our ongoing work with the U.S. Department of Defense, Fortune 50 companies, and graduate and professional schools; and explain how the theory can help fill prominent lacunae and gaps in existing creativity research, including the creativity of children, the psychological mechanisms of scientific and technological innovation, and the failure of computer artificial intelligence to replicate human creativity.

The Raven's Coloured Progressive Matrices in Healthy Children: A Qualitative Approach

Studies on the structure of intelligence refer to two main theoretical models: the first one considers intelligence as a unitary construct, the second one assumes the involvement of a plurality of factors. Studies using Raven's Coloured Progressive Matrices (RCPM) tasks have often highlighted the involvement of different cognitive abilities and brain structures, but in the clinical setting, RCPM measurement continues to be used as a single score. The current study aimed to analyse the RCPM performance following qualitative clustering, in order to provide an interpretation of the intelligence assessment through a factorial criterion. The RCPM have been administered to a large group of typically developing children between 6 and 11 years of age. The sample was divided into twelve age groups, and the performance of each age group was shown. Three qualitative item clusters were identified through a factorial criterion. Data showed that performance on RCPM may arise from different cognitive abilities, starting from basic attentional skills up to the more complex ones that require perceptual or analogical reasoning. The qualitative parameters could provide more effective diagnostic and treatment suggestions than a single total score in the clinical setting, and may be crucial for focusing on strength and weakness in the intellectual functionality evaluation of children.

Left posterior prefrontal regions support domain-general executive processes needed for both reading and math

Substantial evidence has suggested that reading and math are supported by executive processes (EP). However, to date little is known about which portion of the neural system underpinning domain-general executive skills works to support reading and math. In this study, we aimed to answer this question using fMRI via two complementary approaches. First, imaging data were acquired whilst a sample of 231 adolescents performed each of three separate tasks designed to assess reading comprehension, numerical magnitude estimation, and EP in working memory (WM), respectively. With careful task designs and conjunction analyses, we were able to isolate cross-domain brain activity specifically related to EP, as opposed to lower-level domain-general processes (e.g., visual processing). Second, the meta-analytic tool Neurosynth was used to independently identify brain regions involved reading, math, and EP. Using a combination of forward and reverse statistical inference and conjunction analyses, we again isolated brain regions specifically supporting domain-general EP. Results from both approaches yielded overlapping activation for reading, math, and EP in the left ventrolateral prefrontal cortex, left inferior frontal junction, and left precentral gyrus. This pattern suggests that posterior regions of the prefrontal cortex, rather than more central regions such as mid-DLPFC, play a leading role in supporting domain-general EP utilized by both reading and math.

Asymmetrical interference between number and item size perception provides evidence for a domain specific impairment in dyscalculia

Dyscalculia, a specific learning disability that impacts arithmetical skills, has previously been associated to a deficit in the precision of the system that estimates the approximate number of objects in visual scenes (the so called 'number sense' system). However, because in tasks involving numerosity comparisons dyscalculics' judgements appears disproportionally affected by continuous quantitative dimensions (such as the size of the items), an alternative view linked dyscalculia to a domain-general difficulty in inhibiting task-irrelevant responses. To arbitrate between these views, we evaluated the degree of reciprocal interference between numerical and non-numerical quantitative dimensions in adult dyscalculics and matched controls. We used a novel stimulus set orthogonally varying in mean item size and numerosity, putting particular attention into matching both features' perceptual discriminability. Participants compared those stimuli based on each of the two dimensions. While control subjects showed no significant size interference when judging numerosity, dyscalculics' numerosity judgments were strongly biased by the unattended size dimension. Importantly however, both groups showed the same degree of interference from the unattended dimension when judging mean size. Moreover, only the ability to discard the irrelevant size information when comparing numerosity (but not the reverse) significantly predicted calculation ability across subjects. Overall, our results show that numerosity discrimination is less prone to interference than discrimination of another quantitative feature (mean item size) when the perceptual discriminability of these features is matched, as here in control subjects. By quantifying, for the first time, dyscalculic subjects' degree of interference on another orthogonal dimension of the same stimuli, we are able to exclude a domain-general inhibition deficit as explanation for their poor / biased numerical judgement. We suggest that enhanced reliance on non-numerical cues during numerosity discrimination can represent a strategy to cope with a less precise number sense.

Towards numerical cognition's origin: insights from day-old domestic chicks

Instead of the scepticism on animal numerical understanding that characterized the first half of the twentieth century, in recent decades, a large and increasing body of the literature has shown that adult animals can master a variety of non-symbolic (in the absence of symbols such as mathematical words) numerical tasks. Nonetheless, evidence proving early numerical abilities in non-human animals was sparse. In this paper, I report the ongoing work to investigate numerical cognition in the day-old domestic chick (Gallus gallus). Unlike previous studies on adult animals, chicks can be tested very early in life, which gives us the opportunity to discover the origins of numerical comprehension. Here, I discuss studies revealing that day-old domestic chicks can: (i) discriminate between different numbers of objects; (ii) solve rudimentary arithmetic operations; and (iii) use ordinal information, identifying a target element (e.g. the fourth) in a series of identical elements, on the basis of its serial-numerical position. Some of these abilities are number-specific, while others underlie the interplay between number and continuous extents (continuous-quantity cues that covary with number, such as area and perimeter). These data are discussed in terms of ontogenetic development of mathematical comprehension.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Neural correlates of free recall of "famous events" in a "hypermnestic" individual as compared to an age- and education-matched reference group

BACKGROUND

Memory performance of an individual (within the age range: 50-55 years old) showing superior memory abilities (protagonist PR) was compared to an age- and education-matched reference group in a historical facts ("famous events") retrieval task.

RESULTS

Contrasting task versus baseline performance both PR and the reference group showed fMRI activation patterns in parietal and occipital brain regions. The reference group additionally demonstrated activation patterns in cingulate gyrus, whereas PR showed additional widespread activation patterns comprising frontal and cerebellar brain regions. The direct comparison between PR and the reference group revealed larger fMRI contrasts for PR in right frontal, superior temporal and cerebellar brain regions.

CONCLUSIONS

It was concluded that PR generally recruits brain regions as normal memory performers do, but in a more elaborate way, and furthermore, that he applied a memory-strategy that potentially includes executively driven multi-modal transcoding of information and recruitment of implicit memory resources.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development.

WHAT THIS PAPER ADDS

This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models.

Neural circuitry governing anxious individuals' mis-allocation of working memory to threat

Dispositional anxiety is a trait-like phenotype that confers increased risk for a range of debilitating neuropsychiatric disorders. Like many patients with anxiety disorders, individuals with elevated levels of dispositional anxiety are prone to intrusive and distressing thoughts in the absence of immediate threat. Recent electrophysiological research suggests that these symptoms are rooted in the mis-allocation of working memory (WM) resources to threat-related information. Here, functional MRI was used to identify the network of brain regions that support WM for faces and to quantify the allocation of neural resources to threat-related distracters in 81 young adults. Results revealed widespread evidence of mis-allocation. This was evident in both face-selective regions of the fusiform cortex and domain-general regions of the prefrontal and parietal cortices. This bias was exaggerated among individuals with a more anxious disposition. Mediation analyses provided compelling evidence that anxious individuals’ tendency to mis-allocate WM resources to threat-related distracters is statistically explained by heightened amygdala reactivity. Collectively, these results provide a neurocognitive framework for understanding the pathways linking anxious phenotypes to the development of internalizing psychopathology and set the stage for developing improved intervention strategies.

How minimal executive feedback influences creative idea generation

The fixation effect is known as one of the most dominant of the cognitive biases against creativity and limits individuals' creative capacities in contexts of idea generation. Numerous techniques and tools have been established to help overcome these cognitive biases in various disciplines ranging from neuroscience to design sciences. Several works in the developmental cognitive sciences have discussed the importance of inhibitory control and have argued that individuals must first inhibit the spontaneous ideas that come to their mind so that they can generate creative solutions to problems. In line with the above discussions, in the present study, we performed an experiment on one hundred undergraduates from the Faculty of Psychology at Paris Descartes University, in which we investigated a minimal executive feedback-based learning process that helps individuals inhibit intuitive paths to solutions and then gradually drive their ideation paths toward creativity. Our results provide new insights into novel forms of creative leadership for idea generation.

Neurobiological mechanisms for nonverbal IQ tests: implications for instruction of nonverbal children with autism

Traditionally, the neurological correlates of IQ test questions are characterized qualitatively in terms of ‘control of attention’ and ‘working memory.’ In this report we attempt to characterize each IQ test question quantitatively by two factors: a) the number of disparate objects that have to be imagined in concert in order to solve the problem and, b) the amount of recruited posterior cortex territory. With such a classification, an IQ test can be understood on a neuronal level and a subject’s IQ score could be interpreted in terms of specific neurological mechanisms available to the subject.

Here we present the results of an analysis of the three most popular nonverbal IQ tests: Test of Nonverbal Intelligence (TONI-4), Standard Raven's Progressive Matrices, and Wechsler Intelligence Scale for Children (WISC-V). Our analysis shows that approximately half of all questions (52±0.02%) are limited to mental computations involving only a single object; these easier questions are found towards the beginning of each test. More difficult questions located towards the end of each test rely on mental synthesis of several disparate objects and the number of objects involved in computations gradually increases with question difficulty. These more challenging questions require the organization of wider posterior cortex networks by the lateral prefrontal cortex (PFC). This conclusion is in line with neuroimaging studies showing that activation level of the lateral PFC and the posterior cortex positively correlates with task difficulty. This analysis has direct implications for brain pathophysiology and, specifically, for therapeutic interventions for children with language impairment, most notably for children with Autism Spectrum Disorder (ASD) and other developmental disorders.

Numbers and functional lateralization: A visual half-field and dichotic listening study in proficient bilinguals

Potential links between language and numbers and the laterality of symbolic number representations in the brain are still debated. Furthermore, reports on bilingual individuals indicate that the language-number interrelationships might be quite complex. Therefore, we carried out a visual half-field (VHF) and dichotic listening (DL) study with action words and different forms of symbolic numbers used as stimuli to test the laterality of word and number processing in single-, dual-language and mixed -task and language- contexts. Experiment 1 (VHF) showed a significant right visual field/left hemispheric advantage in response accuracy for action word, as compared to any form of symbolic number processing. Experiment 2 (DL) revealed a substantially reversed effect - a significant right ear/left hemisphere advantage for arithmetic operations as compared to action word processing, and in response times in single- and dual-language contexts for number vs. action words. All these effects were language independent. Notably, for within-task response accuracy compared across modalities significant differences were found in all studied contexts. Thus, our results go counter to findings showing that action-relevant concepts and words, as well as number words are represented/processed primarily in the left hemisphere. Instead, we found that in the auditory context, following substantial engagement of working memory (here: by arithmetic operations), there is a subsequent functional reorganization of processing single stimuli, whether verbs or numbers. This reorganization - their weakened laterality - at least for response accuracy is not exclusive to processing of numbers, but the number of items to be processed. For response times, except for unpredictable tasks in mixed contexts, the "number problem" is more apparent. These outcomes are highly relevant to difficulties that simultaneous translators encounter when dealing with lengthy auditory material in which single items such as number words (and possibly other types of key words) need to be emphasized. Our results may also shed a new light on the "mathematical savant problem".

Fear and anger have opposite effects on risk seeking in the gain frame

Emotions strongly influence our decisions, particularly those made under risk. A classic example of the effect of emotion on decision making under risk is the “framing effect,” which involves predictable shifts in preferences when the same problem is formulated in different ways. According to dual process theories, this bias could stem from an affective heuristic belonging to an intuitive type of reasoning. In this study, we examined whether specific incidental negative emotions (i.e., fear and anger) influence framing susceptibility and risk-taking identically. In each trial, participants received an initial amount of money, and pictures of angry or fearful faces were presented to them. Finally, participants chose between a sure option and a gamble option of equally expected value in a gain or loss frame. Risk-taking was modulated by emotional context: fear and anger influenced risk-taking specifically in the gain frame and had opposite effects. Fear increased risk-averse choices, whereas anger decreased risk-averse choices, leading to a suppression of the framing effect. These results confirm that emotions play a key role in framing susceptibility.

Worry is associated with impaired gating of threat from working memory

Dispositional anxiety is a well-established risk factor for the development of anxiety and other emotional disorders. These disorders are common, debilitating, and challenging to treat, pointing to the need to understand the more elementary neurocognitive mechanisms that confer elevated risk. Importantly, many of the maladaptive behaviors characteristic of anxiety, such as worry, occur when threat is absent. This raises the possibility that worry reflects difficulties gating threat-related information from working memory--a limited capacity workspace that supports the maintenance, recall, and manipulation of information--and facilitates goal-directed thoughts and actions. Here, we tested, for the first time, whether trait-like individual differences in worry, a key facet of the anxious phenotype, reflect difficulties gating threat and neutral-related distracters from working memory. Results indicated that both dispositional worry and anxiety individually predicted the combined filtering cost of threat and neutral distracters. Importantly, worry was associated with inefficient filtering of threat-related, but not neutral, distracters from working memory. In contrast, dispositional anxiety was related to a similar level of threat and neutral filtering cost. Furthermore, dispositional anxiety's relationship to filtering of threat was predominantly driven by differences in worry. These results suggest that the propensity to worry is characterized by a failure to gate task-irrelevant threat from working memory. These results provide a framework for understanding the mechanisms underlying chronic worry and, more broadly, the cognitive architecture of dispositional anxiety.

Measuring inhibitory control in children and adults: brain imaging and mental chronometry

Jean Piaget underestimated the cognitive capabilities of infants, preschoolers, and elementary schoolchildren, and overestimated the capabilities of adolescents and even adults which are often biased by illogical intuitions and overlearned strategies (i.e., “fast thinking” in Daniel Kahneman’s words). The crucial question is now to understand why, despite rich precocious knowledge about physical and mathematical principles observed over the last three decades in infants and young children, older children, adolescents and even adults are nevertheless so often bad reasoners. We propose that inhibition of less sophisticated solutions (or heuristics) by the prefrontal cortex is a domain-general executive ability that supports children’s conceptual insights associated with more advanced Piagetian stages, such as number-conservation and class inclusion. Moreover, this executive ability remains critical throughout the whole life and even adults may sometimes need “prefrontal pedagogy” in order to learn inhibiting intuitive heuristics (or biases) in deductive reasoning tasks. Here we highlight some of the discoveries from our lab in the field of cognitive development relying on two methodologies used for measuring inhibitory control: brain imaging and mental chronometry (i.e., the negative priming paradigm). We also show that this new approach opens an avenue for re-examining persistent errors in standard classroom-learning tasks.

The role of number words: the phonological length effect in multidigit addition

We explored the role of phonological representations of number words in exact calculation. The reaction times and accuracy of responses in multidigit addition problems were compared across three groups of participants (young healthy, older healthy, and 3 patients with severe aphasia) and two types of addition problems: phonologically long in English (containing the bisyllabic number word "seven") and short in English (monosyllabic number words-e.g., "six"). Older healthy participants were significantly faster and more accurate in calculation than younger healthy participants. The older participants showed no evidence of a phonological length effect. However this effect was apparent in the younger adults, with longer reaction times on phonologically long problems. Furthermore, there was an association between the presence of a phonological length effect and the overall speed of response, suggesting that less proficient calculators were more reliant on phonological mediation of performance. The aphasic participants retained the ability to complete multidigit additions and were as accurate as the younger healthy group, although the response times of two of the 3 patients were slow. The aphasic participants varied with regard to the presence of a phonological length effect. Two participants showed no evidence of phonological mediation, while 1 displayed a phonological length effect. The results suggest that language resources are not mandatory for exact addition, although they may be used to scaffold math performance in less competent calculators. Evidence of phonological mediation of performance in aphasic participants may provide insight into the integrity or otherwise of inner speech in severe aphasia.

Lateralized mechanisms for encoding of object. Behavioral evidence from an animal model: the domestic chick (Gallus gallus)

In our previous research we reported a leftward-asymmetry in domestic chicks required to identify a target element, on the basis of its ordinal position, in a series of identical elements. Here we re-coded behavioral data collected in previous studies from chicks tested in a task involving a different kind of numerical ability, to study lateralization in dealing with an arithmetic task. Chicks were reared with a set of identical objects representing artificial social companions. On day 4, chicks underwent a free-choice test in which two sets, each composed of a different number of identical objects (5 vs.10 or 6 vs. 9, Experiment 1), were hidden behind two opaque screens placed in front of the chick, one on the left and one on the right side. Objects disappeared, one by one, behind either screen, so that, for example, one screen occluded 5 objects and the other 10 objects. The left-right position of the larger set was counterbalanced between trials. Results show that chicks, in the attempt to rejoin the set with the higher number of social companions, performed better when this was located to the right. However, when the number of elements in the two sets was identical (2 vs. 2, in Experiment 2) and they differed only in the coloration of the objects, this bias was not observed, suggesting a predisposition to map the numerical magnitude from left to right. Future studies should be devoted to the direct investigation of this phenomenon, possibly employing an identical number of mono-chromatic imprinting stimuli in both conditions involving a numerical discrimination and conditions not involving any numerosity difference.

Toward a cultural-historical perspective on the selection task

Independently of their age, individuals produce weak logical responses when they solve the Wason selection task. Many studies describe conditional reasoning, focusing on intra-individual and general processes. The role of meaning attributed to the situation or the linguistic interpretation of the rules have nevertheless been stressed by pragmatic studies. Few scattered studies show the role of collective situations, of subjects' prior knowledge and of objects in solving the selection task. This paper goes back to the questions raised by the selection task and attempts to place past results into a cultural-historical theoretical framework, which defines a complex and evolving cognitive system, where human beings rely on social exchanges, equip themselves with cultural instruments, create intellectual tools, and give meaning to their experiences. Taking into account such a system is necessary to shed light upon the possibilities for the development of human thinking processes in order to solve selection tasks.

Frequency-dependent enhancement of fluid intelligence induced by transcranial oscillatory potentials

Everyday problem solving requires the ability to go beyond experience by efficiently encoding and manipulating new information, i.e., fluid intelligence (Gf) [1]. Performance in tasks involving Gf, such as logical and abstract reasoning, has been shown to rely on distributed neural networks, with a crucial role played by prefrontal regions [2]. Synchronization of neuronal activity in the gamma band is a ubiquitous phenomenon within the brain; however, no evidence of its causal involvement in cognition exists to date [3]. Here, we show an enhancement of Gf ability in a cognitive task induced by exogenous rhythmic stimulation within the gamma band. Imperceptible alternating current [4] delivered through the scalp over the left middle frontal gyrus resulted in a frequency-specific shortening of the time required to find the correct solution in a visuospatial abstract reasoning task classically employed to measure Gf abilities (i.e., Raven's matrices) [5]. Crucially, gamma-band stimulation (γ-tACS) selectively enhanced performance only on more complex trials involving conditional/logical reasoning. The present finding supports a direct involvement of gamma oscillatory activity in the mechanisms underlying higher-order human cognition.

Failure to filter: anxious individuals show inefficient gating of threat from working memory

Dispositional anxiety is a well-established risk factor for the development of psychiatric disorders along the internalizing spectrum, including anxiety and depression. Importantly, many of the maladaptive behaviors characteristic of anxiety, such as anticipatory apprehension, occur when threat is absent. This raises the possibility that anxious individuals are less efficient at gating threat's access to working memory, a limited capacity workspace where information is actively retained, manipulated, and used to flexibly guide goal-directed behavior when it is no longer present in the external environment. Using a well-validated neurophysiological index of working memory storage, we demonstrate that threat-related distracters were difficult to filter on average and that this difficulty was exaggerated among anxious individuals. These results indicate that dispositionally anxious individuals allocate excessive working memory storage to threat, even when it is irrelevant to the task at hand. More broadly, these results provide a novel framework for understanding the maladaptive thoughts and actions characteristic of internalizing disorders.

Deduction electrified: ERPs elicited by the processing of words in conditional arguments

This study investigates the ERP components associated with the processing of words that are critical to generating and rejecting deductive conditional Modus Ponens arguments (If P then Q; P//Therefore, Q). The generation of a logical inference is investigated by placing a verb in the minor premise that matches the one used in the antecedent of the conditional premise so that the inference can be carried out (If John is sleeping then he is snoring; John is sleeping). Rejections are examined by placing verbs that are associates of the verb that would make the conclusion valid (Conclusion 'therefore John is dreaming' in the example above). The inference generation phase was characterized by two ERP components, namely the P3b and the PSW. Rejections were associated with an N2 and a late positive component. The implications of these results regarding the processing of words in an inferential context are discussed.

A hybrid model for the neural representation of complex mental processing in the human brain

In the present conceptual review several theoretical and empirical sources of information were integrated, and a hybrid model of the neural representation of complex mental processing in the human brain was proposed. Based on empirical evidence for strategy-related and inter-individually different task-related brain activation networks, and further based on empirical evidence for a remarkable overlap of fronto-parietal activation networks across different complex mental processes, it was concluded by the author that there might be innate and modular organized neuro-developmental starting regions, for example, in intra-parietal, and both medial and middle frontal brain regions, from which the neural organization of different kinds of complex mental processes emerge differently during individually shaped learning histories. Thus, the here proposed model provides a hybrid of both massive modular and holistic concepts of idiosyncratic brain physiological elaboration of complex mental processing. It is further concluded that 3-D information, obtained by respective methodological approaches, are not appropriate to identify the non-linear spatio-temporal dynamics of complex mental process-related brain activity in a sufficient way. How different participating network parts communicate with each other seems to be an indispensable aspect, which has to be considered in particular to improve our understanding of the neural organization of complex cognition.

Sentence processing in Lewy body spectrum disorder: the role of working memory

Prior work has related sentence processing to executive deficits in non-demented patients with Parkinson's disease (PD). We extended this investigation to patients with dementia with Lewy bodies (DLB) and PD dementia (PDD) by examining grammatical and working memory components of sentence processing in the full range of patients with Lewy body spectrum disorder (LBSD). Thirty-three patients with LBSD were given a two-alternative, forced-choice sentence-picture matching task. Sentence type, working memory, and grammatical structure were systematically manipulated in the sentences. We found that patients with PDD and DLB were significantly impaired relative to non-demented PD patients and healthy controls. The deficit in PDD/DLB was most pronounced for sentences lengthened by the strategic placement of an additional prepositional phrase and for sentences with an additional proposition due to a center-embedded clause. However, there was no effect for subject-relative versus object-relative grammatical structure. An MRI voxel-based morphometry analysis in a subset of patients showed significant gray matter thinning in the frontal lobe bilaterally, and this extended to temporal, parietal and occipital regions. A regression analysis related sentence processing difficulty in LBSD to frontal neocortex, including inferior prefrontal, premotor, and dorsolateral prefrontal regions, as well as right superior temporal cortex. These findings are consistent with the hypothesis that patients with PDD and DLB have difficulty processing sentences with increased working memory demands and that this deficit is related in part to their frontal disease.

Epistemic normativity from the reasoner's viewpoint

Elqayam & Evans (E&E) are focused on the normative judgments used by theorists to characterize subjects' performances (e.g. in terms of logic or probability theory). They ignore the fact, however, that subjects themselves have an independent ability to evaluate their own reasoning performance, and that this ability plays a major role in controlling their first-order reasoning tasks.

The neural architecture of expert calendar calculation: a matter of strategy?

Savants and prodigies are individuals with exceptional skills in particular mental domains. In the present study we used functional magnetic resonance imaging to examine neural correlates of calendar calculation in two individuals, a savant with Asperger's disorder and a self-taught mathematical prodigy. If there is a modular neural organization of exceptional performance in a specific mental domain, calendar calculation should be reflected in a considerable overlap in the recruitment of brain circuits across expert individuals. However, considerable individual differences in activation patterns during calendar calculation were noted. The present results indicate that activation patterns produced by complex mental processing, such as calendar calculation, seem to be influenced strongly by learning history and idiosyncratic strategy usage rather than a modular neural organization. Thus, well-known individual differences in complex cognition play a major role even in experts with exceptional abilities in a particular mental domain and should in particular be considered when examining the neural architecture of complex mental processes and skills.

[The neural impact of cognitive training]

Tracing the connections from brain functions to education is a major goal of modern neuroscience. By providing insights into the abilities and constraints of the learning brain, neuroscience can help to explain why some learning environments work while others fail. The results presented here provide the first insights into neuropedagogy of reasoning.

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

Approximate processing of numerosities is a universal and preverbal skill, while exact number processing above 4 involves the use of culturally acquired number words and symbols. The authors first review core concepts of numerical cognition, including number representation in the brain and the influential view that numbers are associated with space along a “mental number line.” Then, they discuss how cultural influences, such as reading direction, finger counting, and the transparency of the number word system, can influence the representation and processing of numbers. Spatial mapping of numbers emerges as a universal cognitive strategy. The authors trace the impact of cultural factors on the development of number skills and conclude that a cross-cultural perspective can reveal important constraints on numerical cognition.

Memory maintenance and inhibitory control differentiate from early childhood to adolescence

Existing evidence suggests that the organization of cognitive functions may differentiate during development. We investigated two key components of executive functions, memory maintenance and inhibitory control, by applying latent factor models appropriate for examining developmental differences in functional associations among aspects of cognition. Two-hundred and sixty-three children (aged 4 to 14 years) were administered tasks that required maintaining rules in mind or inhibiting a prepotent tendency to respond on the same side as the stimulus. Memory maintenance and inhibitory control were not separable in children of 4-7 or 7-9.5 years, but were differentiated in an older group (9.5-14.5 years).

Mapping numerical processing, reading, and executive functions in the developing brain: an fMRI meta-analysis of 52 studies including 842 children

Tracing the connections from brain functions to children's cognitive development and education is a major goal of modern neuroscience. We performed the first meta-analysis of functional magnetic resonance imaging (fMRI) data obtained over the past decade (1999-2008) on more than 800 children and adolescents in three core systems of cognitive development and school learning: numerical abilities, reading, and executive functions (i.e. cognitive control). We ran Activation Likelihood Estimation (ALE) meta-analyses to obtain regions of reliable activity across all the studies. The results indicate that, unlike results usually reported for adults, children primarily engage the frontal cortex when solving numerical tasks. With age, there may be a shift from reliance on the frontal cortex to reliance on the parietal cortex. In contrast, the frontal, temporo-parietal and occipito-temporal regions at work during reading in children are very similar to those reported in adults. The executive frontal regions are also consistent with the imaging literature on cognitive control in adults, but the developmental comparison between children and adolescents demonstrates a key role of the anterior insular cortex (AIC) with an additional right AIC involvement in adolescents.

Two- vs. three-dimensional presentation of mental rotation tasks: Sex differences and effects of training on performance and brain activation

The well-documented sex difference in mental rotation favoring males has been shown to emerge only for 2-dimensional presentations of 3-dimensional objects, but not with actual 3-dimensional objects or with virtual reality presentations of 3-dimensional objects. Training studies using computer games with mental rotation-related content have demonstrated training effects on mental rotation performance. Here, we studied the combined effect of a two-week mental rotation (MR) training on 2-dimensional vs. 3-dimensional presentations of a classic Shepard–Metzler task (presented in a pretest–training–posttest design) and their accompanying cortical activation patterns assessed via EEG in a sample of 38 male and 39 female adolescents of about 15 years of age. Analysis of one performance parameter (reaction times) displayed only main effects of dimensionality (with shorter RTs on the 3D vs. 2D version of the MR task) and of training (significant shortening of RTs), but no significant sex difference. Analysis of the other performance parameter (scores) in the MR task revealed a sex difference favoring males that first, appeared only in the 2D version, but not in the 3D version of the MR task and, secondly, diminished after training. Neurophysiologically we observed a complex sex × dimensionality × training × hemisphere interaction showing that the hypothesized decrease of brain activation (increase in neural efficiency) with training emerged for males in both 2D and 3D conditions, whereas for females this decrease was found only in the 3D but not with the 2D version of the MR task.

Neural Correlates of Species-typical Illogical Cognitive Bias in Human Inference

The ability to think logically is a hallmark of human intelligence, yet our innate inferential abilities are marked by implicit biases that often lead to illogical inference. For example, given AB (“if A then B”), people frequently but fallaciously infer the inverse, BA. This mode of inference, called symmetry, is logically invalid because, although it may be true, it is not necessarily true. Given pairs of conditional relations, such as AB and BC, humans reflexively perform two additional modes of inference: transitivity, whereby one (validly) infers AC; and equivalence, whereby one (invalidly) infers CA. In sharp contrast, nonhuman animals can handle transitivity but can rarely be made to acquire symmetry or equivalence. In the present study, human subjects performed logical and illogical inferences about the relations between abstract, visually presented figures while their brain activation was monitored with fMRI. The prefrontal, medial frontal, and intraparietal cortices were activated during all modes of inference. Additional activation in the precuneus and posterior parietal cortex was observed during transitivity and equivalence, which may reflect the need to retrieve the intermediate stimulus (B) from memory. Surprisingly, the patterns of brain activation in illogical and logical inference were very similar. We conclude that the observed inference-related fronto-parietal network is adapted for processing categorical, but not logical, structures of association among stimuli. Humans might prefer categorization over the memorization of logical structures in order to minimize the cognitive working memory load when processing large volumes of information.

Neural basis of repetition priming during mathematical cognition: repetition suppression or repetition enhancement?

We investigated the neural basis of repetition priming (RP) during mathematical cognition. Previous studies of RP have focused on repetition suppression as the basis of behavioral facilitation, primarily using word and object identification and classification tasks. More recently, researchers have suggested associative stimulus-response learning as an alternate model for behavioral facilitation. We examined the neural basis of RP during mathematical problem solving in the context of these two models of learning. Brain imaging and behavioral data were acquired from 39 adults during novel and repeated presentation of three-operand mathematical equations. Despite wide-spread decreases in activation during repeat, compared with novel trials, there was no direct relation between behavioral facilitation and the degree of repetition suppression in any brain region. Rather, RT improvements were directly correlated with repetition enhancement in the hippocampus and the posteromedial cortex [posterior cingulate cortex, precuneus, and retrosplenial cortex; Brodmann's areas (BAs) 23, 7, and 30, respectively], regions known to support memory formation and retrieval, and in the SMA (BA 6) and the dorsal midcingulate ("motor cingulate") cortex (BA 24d), regions known to be important for motor learning. Furthermore, improvements in RT were also correlated with increased functional connectivity of the hippocampus with both the SMA and the dorsal midcingulate cortex. Our findings provide novel support for the hypothesis that repetition enhancement and associated stimulus-response learning may facilitate behavioral performance during problem solving.

Pedagogical Effect of Action on Arithmetic Performances in Wynn-Like Tasks Solved by 2-Year-Olds

Previous studies have provided evidence of interference due to a language-default mode (i.e., the singular/plural opposition) in 2-year-old children when solving arithmetic problems using a traditional onlooker method. However, an action-based method could help to bypass this language bias. In particular, when an arithmetic problem is presented to the children by the experimenter (onlooker mode) or realized by the children themselves (actor mode), performances are better with the latter. Thus, an experimental procedure based on “math in action” allows a brain-and-mind shift from a global language-bias (singular/plural) strategy to an exact numerical strategy. In this framework, we examined whether the exact numerical strategy induced by the actor method remains operational when children had to subsequently solve the same arithmetic problem using the traditional onlooker method. Results from 112 children suggest that this pedagogical effect of action bypasses the interference from language in onlooker mode after an initial confrontation of the problem in actor mode. This enduring embodiment effect has important implications for cognitive and preschool assessment in toddlers.

How to explain receptivity to conjunction-fallacy inhibition training: evidence from the Iowa gambling task

Intuitive predictions and judgments under conditions of uncertainty are often mediated by judgment heuristics that sometimes lead to biases. Using the classical conjunction bias example, the present study examines the relationship between receptivity to metacognitive executive training and emotion-based learning ability indexed by Iowa Gambling Task (IGT) performance. After completing a computerised version of the IGT, participants were trained to avoid conjunction bias on a frequency judgment task derived from the works of Tversky and Kahneman. Pre- and post-test performances were assessed via another probability judgment task. Results clearly showed that participants who produced a biased answer despite the experimental training (individual patterns of the biased --> biased type) mainly had less emotion-based learning ability in IGT. Better emotion-based learning ability was observed in participants whose response pattern was biased --> logical. These findings argue in favour of the capacity of the human mind/brain to overcome reasoning bias when trained under executive programming conditions and as a function of emotional warning sensitivity.

Abstract after all? Abstraction through inhibition in children and adults

I challenge two points in Cohen Kadosh & Walsh's (CK & W) argument: First, the definition of abstraction is too restricted; second, the distinction between representations and operations is too clear-cut. For example, taking Jean Piaget's “conservation of number task,” I propose that another way to avoid orthodoxy in the field of numerical cognition is to consider inhibition as an alternative idea of abstraction.

Overlapping and distinct neural representations of numbers and verbal transitive series

It is a familiar and intuitive notion that human numerical and logical reasoning skills are tightly related. However, very little is known about the interaction between numerical knowledge and logical reasoning in the brain. Using functional magnetic resonance imaging in healthy subjects, we investigated ordered relations as they are expressed in number (4 is greater than 2) and in transitive reasoning (A is to the left of C after receiving; A is to the left of B; B is to the left of C) in order to determine the extent to which the same neural substrates support both. We found that representing an ordered series verbally learned by transitive reasoning draws on the representations of numbers in the anterior intraparietal sulcus. We further observed that, unlike numbers, transitive series are additionally encoded in the basal ganglia-dopamine system. Intraparietal and basal ganglia mechanisms are not active to the same extent at the same time. Although the intraparietal representations of number preferentially supports a verbal transitive series soon after learning, the basal ganglia are engaged when the series is well practiced. This finding suggests that the transient activation of number representations supports the representation of verbal transitive series until their late encoding in the basal ganglia-dopamine system by associative reinforcement mechanisms.