The Impact of Symbolic and Non-Symbolic Quantity on Spatial Learning

An implicit mapping of number to space via a “mental number line” occurs automatically in adulthood. Here, we systematically explore the influence of differing representations of quantity (no quantity, non-symbolic magnitudes, and symbolic numbers) and directional flow of stimuli (random flow, left-to-right, or right-to-left) on learning and attention via a match-to-sample working memory task. When recalling a cognitively demanding string of spatial locations, subjects performed best when information was presented right-to-left. When non-symbolic or symbolic numerical arrays were embedded in these spatial locations, and mental number line congruency prompted, this effect was attenuated and in some cases reversed. In particular, low-performing female participants who viewed increasing non-symbolic number arrays paired with the spatial locations exhibited better recall for left-to-right directional flow information relative to right-to-left, and better processing for the left side of space relative to the right side of space. The presence of symbolic number during spatial learning enhanced recall to a greater degree than non-symbolic number—especially for female participants, and especially when cognitive load is high—and this difference was independent of directional flow of information. We conclude that quantity representations have the potential to scaffold spatial memory, but this potential is subtle, and mediated by the nature of the quantity and the gender and performance level of the learner.     

Operational Momentum in Multiplication and Division?

Biases are commonly seen in numerical cognition. The operational momentum (OM) effect shows that responses to addition and subtraction problems are biased in the whole-number direction of the operation. It is not known if this bias exists for other arithmetic operations. To determine whether OM exists in scalar operations, we measured response bias in adults performing symbolic (Arabic digits) and non-symbolic (dots) multiplication and division problems. After seeing two operands, with either a multiplication (×) or division (÷) sign, participants chose among five response choices. Both non-random performance profiles and the significant contribution of both operands in a multiple regression analysis predicting the chosen values, suggest that adults were able to use numerical information to approximate the outcomes in both notations, though they were more accurate on symbolic problems. Performance on non-symbolic problems was influenced by the size of the correct choice relative to alternatives. Reminiscent of the bias in addition and subtraction, we found a significant response bias for non-symbolic problems. Non-symbolic multiplication problems were overestimated and division problems were underestimated. These results indicate that operational momentum is present in non-symbolic multiplication and division. Given the influence of the size of the correct choice relative to alternatives, an interaction between heuristic bias and approximate calculation is possible.     

Functional imaging of numerical processing in adults and 4-y-old children

Adult humans, infants, pre-school children, and non-human animals appear to share a system of approximate numerical processing for non-symbolic stimuli such as arrays of dots or sequences of tones. Behavioral studies of adult humans implicate a link between these non-symbolic numerical abilities and symbolic numerical processing (e.g., similar distance effects in accuracy and reaction-time for arrays of dots and Arabic numerals). However, neuroimaging studies have remained inconclusive on the neural basis of this link. The intraparietal sulcus (IPS) is known to respond selectively to symbolic numerical stimuli such as Arabic numerals. Recent studies, however, have arrived at conflicting conclusions regarding the role of the IPS in processing non-symbolic, numerosity arrays in adulthood, and very little is known about the brain basis of numerical processing early in development. Addressing the question of whether there is an early-developing neural basis for abstract numerical processing is essential for understanding the cognitive origins of our uniquely human capacity for math and science. Using functional magnetic resonance imaging (fMRI) at 4-Tesla and an event-related fMRI adaptation paradigm, we found that adults showed a greater IPS response to visual arrays that deviated from standard stimuli in their number of elements, than to stimuli that deviated in local element shape. These results support previous claims that there is a neurophysiological link between non-symbolic and symbolic numerical processing in adulthood. In parallel, we tested 4-y-old children with the same fMRI adaptation paradigm as adults to determine whether the neural locus of non-symbolic numerical activity in adults shows continuity in function over development. We found that the IPS responded to numerical deviants similarly in 4-y-old children and adults. To our knowledge, this is the first evidence that the neural locus of adult numerical cognition takes form early in development, prior to sophisticated symbolic numerical experience. More broadly, this is also, to our knowledge, the first cognitive fMRI study to test healthy children as young as 4 y, providing new insights into the neurophysiology of human cognitive development.     

Impact of high mathematics education on the number sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.     

Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children’s mathematical development. This mapping ability has been mainly examined indirectly by looking at children’s performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children’s mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills.     

Human Infants' Preference for Left-to-Right Oriented Increasing Numerical Sequences

While associations between number and space, in the form of a spatially oriented numerical representation, have been extensively reported in human adults, the origins of this phenomenon are still poorly understood. The commonly accepted view is that this number-space association is a product of human invention, with accounts proposing that culture, symbolic knowledge, and mathematics education are at the roots of this phenomenon. Here we show that preverbal infants aged 7 months, who lack symbolic knowledge and mathematics education, show a preference for increasing magnitude displayed in a left-to-right spatial orientation. Infants habituated to left-to-right oriented increasing or decreasing numerical sequences showed an overall higher looking time to new left-to-right oriented increasing numerical sequences at test (Experiment 1). This pattern did not hold when infants were presented with the same ordinal numerical information displayed from right to left (Experiment 2). The different pattern of results was congruent with the presence of a malleable, context-dependent baseline preference for increasing, left-to-right oriented, numerosities (Experiment 3). These findings are suggestive of an early predisposition in humans to link numerical order with a left-to-right spatial orientation, which precedes the acquisition of symbolic abilities, mathematics education, and the acquisition of reading and writing skills.     

Impaired parietal magnitude processing in developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability affecting the acquisition of school-level mathematical abilities in the context of otherwise normal academic achievement, with prevalence estimates in the order of 3-6%. Behavioural studies show deficits in elementary numerical processing among individuals with pure DD, indicating that deficits in higher-level mathematical skills may stem from impaired representation and processing of basic numerical magnitude. Adult neuropsychological and neuroimaging research points to the intraparietal sulcus as a key region for the representation and processing of numerical magnitude. This raises the possibility of a parietal dysfunction as a root cause of DD. We show that, in children with pure DD, the right intraparietal sulcus is not modulated in response to numerical processing demands to the same degree as in typically developing children. This finding provides the first direct evidence for a specific impairment of parietal magnitude systems in DD during non-symbolic numerosity processing.     

Acquisition of the Cardinal Principle Coincides with Improvement in Approximate Number System Acuity in Preschoolers

Human mathematical abilities comprise both learned, symbolic representations of number and unlearned, non-symbolic evolutionarily primitive cognitive systems for representing quantities. However, the mechanisms by which our symbolic (verbal) number system becomes integrated with the non-symbolic (non-verbal) representations of approximate magnitude (supported by the Approximate Number System, or ANS) are not well understood. To explore this connection, forty-six children participated in a 6-month longitudinal study assessing verbal number knowledge and non-verbal numerical acuity. Cross-sectional analyses revealed a strong relationship between verbal number knowledge and ANS acuity. Longitudinal analyses suggested that increases in ANS acuity were most strongly related to the acquisition of the cardinal principle, but not to other milestones of verbal number acquisition. These findings suggest that experience with culture and language is intimately linked to changes in the properties of a core cognitive system.     

Stay Tuned: What Is Special About Not Shifting Attention?

Background

When studying attentional orienting processes, brain activity elicited by symbolic cue is usually compared to a neutral condition in which no information is provided about the upcoming target location. It is generally assumed that when a neutral cue is provided, participants do not shift their attention. The present study sought to validate this assumption. We further investigated whether anticipated task demands had an impact on brain activity related to processing symbolic cues.

Methodology/Principal Findings

Two experiments were conducted, during which event-related potentials were elicited by symbolic cues that instructed participants to shift their attention to a particular location on a computer screen. In Experiment 1, attention shift-inducing cues were compared to non-informative cues, while in both conditions participants were required to detect target stimuli that were subsequently presented at peripheral locations. In Experiment 2, a non-ambiguous “stay-central” cue that explicitly required participants not to shift their attention was used instead. In the latter case, target stimuli that followed a stay-central cue were also presented at a central location. Both experiments revealed enlarged early latency contralateral ERP components to shift-inducing cues compared to those elicited by either non-informative (exp. 1) or stay-central cues (exp. 2). In addition, cueing effects were modulated by the anticipated difficulty of the upcoming target, particularly so in Experiment 2. A positive difference, predominantly over the posterior contralateral scalp areas, could be observed for stay-central cues, especially for those predicting that the upcoming target would be easy. This effect was not present for non-informative cues.

Conclusions/Significance

We interpret our result in terms of a more rapid engagement of attention occurring in the presence of a more predictive instruction (i.e. stay-central easy target). Our results indicate that the human brain is capable of very rapidly identifying the difference between different types of instructions.     

Effects of development and enculturation on number representation in the brain

A striking way in which humans differ from non-human primates is in their ability to represent numerical quantity using abstract symbols and to use these 'mental tools' to perform skills such as exact calculations. How do functional brain circuits for the symbolic representation of numerical magnitude emerge? Do neural representations of numerical magnitude change as a function of development and the learning of mental arithmetic? Current theories suggest that cultural number symbols acquire their meaning by being mapped onto non-symbolic representations of numerical magnitude. This Review provides an evaluation of this contention and proposes hypotheses to guide investigations into the neural mechanisms that constrain the acquisition of cultural representations of numerical magnitude.     

Anodal tDCS over the Motor Cortex on Prepared and Unprepared Responses in Young Adults

Anodal transcranial direct current stimulation (tDCS) over the primary motor cortex (M1) has been proposed as a possible therapeutic rehabilitation technique for motor impairment. However, despite extensive investigation into the effects of anodal tDCS on motor output, there is little information on how anodal tDCS affects response processes. In this study, we used a cued go/nogo task with both directional and non-directional cues to assess the effects of anodal tDCS over the dominant (left) primary motor cortex on prepared and unprepared motor responses. Three experiments explored whether the effectiveness of tDCS varied with timing between stimulation and test. Healthy, right-handed young adults participated in a double-blind randomised controlled design with crossover of anodal tDCS and sham stimulation. In Experiment 1, twenty-four healthy young adults received anodal tDCS over dominant M1 at least 40 mins before task performance. In Experiment 2, eight participants received anodal tDCS directly before task performance. In Experiment 3, twenty participants received anodal tDCS during task performance. In all three experiments, participants responded faster to directional compared to non-directional cues and with their right hand. However, anodal tDCS had no effect on go/nogo task performance at any stimulation – test interval. Bayesian analysis confirmed that anodal stimulation had no effect on response speed. We conclude that anodal tDCS over M1 does not improve response speed of prepared or unprepared responses of young adults in a go/nogo task.     

The role of highlighting in visual search through maps

Two experiments were conducted in which participants performed a vehicle dispatching task. The intensity of one information source (vehicles in Experiment 1, destinations in Experiment 2) was varied to examine the effects of salience and discrimination on both searching for and processing the information in a cluttered display. Response times were recorded for questions either requiring focused attention on or divided attention between the different information domains in the map. The results of the present experiments indicate that it is possible to declutter a display without erasing any information. By 'lowlighting' one information domain and keeping the other domain at a fairly high intensity level, dividing attention between the information sources is optimal, as is focusing attention on either of the information domains exclusively. These results are discussed in conjunction with a computational model of confusion and salience which serves to predict search and integration performance in a cluttered display with separate domains of information displayed at different intensities.     

Numerical magnitude in the human parietal lobe; tests of representational generality and domain specificity

Behavioral evidence suggests that human adults have a single system for representing the numerical magnitude of both symbolic numbers (e.g., Arabic digits) and nonsymbolic number stimuli (e.g., dot arrays). Brain imaging studies have implicated a specific parietal region in symbolic number processing, leading to the influential hypothesis that this region is the locus of a dedicated, domain-specific number system. Here we evaluated a prediction of this hypothesis, that this region should be activated not only by symbolic but also nonsymbolic number processing. Using nonsymbolic stimuli, we tested for higher parietal activations for number than for nonnumber comparison tasks (experiment 1), fMRI adaptation for numerosity repetition (experiment 2), and greater fMRI increases with increasing task difficulty for number than nonnumber tasks (experiment 3). None of these predictions were supported by the data, posing a serious challenge to the hypothesis that a single, domain-specific parietal region underlies both symbolic and nonsymbolic number representation.     

The agent is right: when motor embodied cognition is space-dependent

The role of embodied mechanisms in processing sentences endowed with a first person perspective is now widely accepted. However, whether embodied sentence processing within a third person perspective would also have motor behavioral significance remains unknown. Here, we developed a novel version of the Action-sentence Compatibility Effect (ACE) in which participants were asked to perform a movement compatible or not with the direction embedded in a sentence having a first person (Experiment 1: You gave a pizza to Louis) or third person perspective (Experiment 2: Lea gave a pizza to Louis). Results indicate that shifting perspective from first to third person was sufficient to prevent motor embodied mechanisms, abolishing the ACE. Critically, ACE was restored in Experiment 3 by adding a virtual "body" that allowed participants to know "where" to put themselves in space when taking the third person perspective, thus demonstrating that motor embodied processes are space-dependent. A fourth, control experiment, by dissociating motor response from the transfer verb's direction, supported the conclusion that perspective-taking may induce significant ACE only when coupled with the adequate sentence-response mapping.     

Brain Correlates of Non-Symbolic Numerosity Estimation in Low and High Mathematical Ability Children

Previous studies have implicated several brain areas as subserving numerical approximation. Most studies have examined brain correlates of adult numerical approximation and have not considered individual differences in mathematical ability. The present study examined non-symbolic numerical approximation in two groups of 10-year-olds: Children with low and high mathematical ability. The aims of this study were to investigate the brain mechanisms associated with approximate numerosity in children and to assess whether individual differences in mathematical ability are associated with differential brain correlates during the approximation task. The results suggest that, similarly to adults, multiple and distributed brain areas are involved in approximation in children. Despite equal behavioral performance, there were differences in the brain activation patterns between low and high mathematical ability groups during the approximation task. This suggests that individual differences in mathematical ability are reflected in differential brain response during approximation.     

Temporal brain dynamics of multiple object processing: the flexibility of individuation

The ability to process concurrently multiple visual objects is fundamental for a coherent perception of the world. A core component of this ability is the simultaneous individuation of multiple objects. Many studies have addressed the mechanism of object individuation but it remains unknown whether the visual system mandatorily individuates all relevant elements in the visual field, or whether object indexing depends on task demands. We used a neural measure of visual selection, the N2pc component, to evaluate the flexibility of multiple object individuation. In three ERP experiments, participants saw a variable number of target elements among homogenous distracters and performed either an enumeration task (Experiment 1) or a detection task, reporting whether at least one (Experiment 2) or a specified number of target elements (Experiment 3) was present. While in the enumeration task the N2pc response increased as a function of the number of targets, no such modulation was found in Experiment 2, indicating that individuation of multiple targets is not mandatory. However, a modulation of the N2pc similar to the enumeration task was visible in Experiment 3, further highlighting that object individuation is a flexible mechanism that binds indexes to object properties and locations as needed for further object processing.     

Unravelling developmental disregard in children with unilateral cerebral palsy by measuring event-related potentials during a simple and complex task

Background

In a subset of children with unilateral Cerebral Palsy (CP) a discrepancy between capacity and performance of the affected upper limb can be observed. This discrepancy is known as Developmental Disregard (DD). Though the phenomenon of DD has been well documented, its underlying cause is still under debate. DD has originally been explained based on principles of operant conditioning. Alternatively, it has been proposed that DD results from a diminished automaticity of movements, resulting in an increased cognitive load when using the affected hand. To investigate the amount of involved cognitive load we studied Event-Related Potentials (ERPs) preceding task-related motor responses during a single-hand capacity and a dual-hand performance task. It was hypothesised that children with DD show alterations related to long-latency ERP components when selecting a response with the affected upper limb, reflecting increased cognitive load in order to generate an adequate response and especially so within the dual-hand task.

Methods

Fifteen children with unilateral CP participated in the study. One of the participants was excluded due to major visual impairments. Seven of the remaining participants displayed DD. The other seven children served as a control group. All participants performed two versions of a cue-target paradigm, a single-hand capacity and a dual-hand performance task. The ERP components linked to target presentation were inspected: the mid-latency P2 component and the consecutive long-latency N2b component.

Results

In the dual-hand performance task children with DD showed an enhancement in mean amplitude of the long-latency N2b component when selecting a response with their affected hand. No differences were found regarding the amplitude of the mid-latency P2 component. No differences were observed regarding the single-hand capacity task. The control group did not display any differences in ERPs linked to target evaluation processes between both hands.

Conclusion

These electrophysiological findings show that DD is associated with increased cognitive load when movements are prepared with the affected hand during a dual-hand performance task. These findings confirm behavioural observations, advance our insights on the neural substrate of DD and have implications for therapy.     

Is the self always better than a friend? Self-face recognition in Christians and atheists

Early behavioral studies found that human adults responded faster to their own faces than faces of familiar others or strangers, a finding referred to as self-face advantage. Recent research suggests that the self-face advantage is mediated by implicit positive association with the self and is influenced by sociocultural experience. The current study investigated whether and how Christian belief and practice affect the processing of self-face in a Chinese population. Christian and Atheist participants were recruited for an implicit association test (IAT) in Experiment 1 and a face-owner identification task in Experiment 2. Experiment 1 found that atheists responded faster to self-face when it shared the same response key with positive compared to negative trait adjectives. This IAT effect, however, was significantly reduced in Christians. Experiment 2 found that atheists responded faster to self-face compared to a friend's face, but this self-face advantage was significantly reduced in Christians. Hierarchical regression analyses further showed that the IAT effect positively predicted self-face advantage in atheists but not in Christians. Our findings suggest that Christian belief and practice may weaken implicit positive association with the self and thus decrease the advantage of the self over a friend during face recognition in the believers.     

Fast or Slow? Compressions (or Not) in Number-to-Line Mappings

We investigated, in a university student population, spontaneous (non-speeded) fast and slow number-to-line mapping responses using non-symbolic (dots) and symbolic (words) stimuli. Seeking for less conventionalized responses, we used anchors 0–130, rather than the standard 0–100. Slow responses to both types of stimuli only produced linear mappings with no evidence of non-linear compression. In contrast, fast responses revealed distinct patterns of non-linear compression for dots and words. A predicted logarithmic compression was observed in fast responses to dots in the 0–130 range, but not in the reduced 0–100 range, indicating compression in proximity of the upper anchor 130, not the standard 100. Moreover, fast responses to words revealed an unexpected significant negative compression in the reduced 0–100 range, but not in the 0–130 range, indicating compression in proximity to the lower anchor 0. Results show that fast responses help revealing the fundamentally distinct nature of symbolic and non-symbolic quantity representation. Whole number words, being intrinsically mediated by cultural phenomena such as language and education, emphasize the invariance of magnitude between them—essential for linear mappings, and therefore, unlike non-symbolic (psychophysical) stimuli, yield spatial mappings that don’t seem to be influenced by the Weber-Fechner law of psychophysics. However, high levels of education (when combined with an absence of standard upper anchors) may lead fast responses to overestimate magnitude invariance on the lower end of word numerals.     

Task attention facilitates learning of task-irrelevant stimuli

Attention plays a fundamental role in visual learning and memory. One highly established principle of visual attention is that the harder a central task is, the more attentional resources are used to perform the task and the smaller amount of attention is allocated to peripheral processing because of limited attention capacity. Here we show that this principle holds true in a dual-task setting but not in a paradigm of task-irrelevant perceptual learning. In Experiment 1, eight participants were asked to identify either bright or dim number targets at the screen center and to remember concurrently presented scene backgrounds. Their recognition performances for scenes paired with dim/hard targets were worse than those for scenes paired with bright/easy targets. In Experiment 2, eight participants were asked to identify either bright or dim letter targets at the screen center while a task-irrelevant coherent motion was concurrently presented in the background. After five days of training on letter identification, participants improved their motion sensitivity to the direction paired with hard/dim targets improved but not to the direction paired with easy/bright targets. Taken together, these results suggest that task-irrelevant stimuli are not subject to the attentional control mechanisms that task-relevant stimuli abide.