Influences of cognitive control on number processing: New evidence from switching between two numerical tasks

A growing body of research suggests that basic numerical abilities such as number magnitude and number parity processing are influenced by cognitive control. So far, however, evidence for number processing being influenced by cognitive control came primarily from observed adaptations to stimulus set characteristics (e.g., ratio or order of specific stimulus types) and switches between a numerical and non-numerical task. Complementing this previous research, the present study employed a task switching paradigm exclusively involving numerical tasks (i.e., magnitude comparisons and parity judgements) to examine how cognitive control processes influence number processing. Participants were presented with a single-digit number and had to either judge its parity or compare its magnitude with a standard of 5, depending on a preceding cue. Based on previous results, we expected the numerical distance effect and the spatial-numerical association of response codes (SNARC) effect to be modulated in switch trials requiring the exertion of cognitive control. Partly in line with our expectations, the numerical distance effect was reduced in switch trials. However, no modulation of the SNARC effect was observed. The results pattern suggests that number processing is influenced by cognitive control, depending on task requirements and the type of numerical information (i.e., numerical magnitude vs spatial association of numbers) that is processed. To reconcile the present and previous results, we propose an information prioritisation account, suggesting that cognitive control primarily influences the processing of the information type that requires the most explicit processing.

Spatial-numerical associations without a motor response? Grip force says 'Yes'

In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., "two"), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

Transcoding counts: Longitudinal contribution of number writing to arithmetic in different languages

Number writing involves transcoding from number words (e.g., "thirty-two") to written digit strings (32) and is an important unique predictor of arithmetic. The existing longitudinal evidence about the relation between transcoding and arithmetic is mostly language specific. In languages with number word inversion (e.g., German), the order of tens and units is transposed in spoken number words compared with Arabic numbers. This makes transcoding more challenging than in languages without number word inversion (e.g., English). In the current study, we aimed to understand whether the contribution of number writing to the development of arithmetic is similar in languages with and without number word inversion. German-speaking children (n = 166) and English-speaking children (n = 201) were followed over the first 3 years of primary school. In a series of multiple linear regressions, we tested whether number writing of multi-digit numbers was a significant unique predictor of arithmetic after controlling for well-known non-numerical predictors (nonverbal reasoning and working memory) and numerical predictors (symbolic and nonsymbolic magnitude comparison). Number writing in Grade 1 predicted arithmetic in Grades 1, 2, and 3 over and above the other predictors. Crucially, number writing performance was of comparable importance for arithmetic development in German- and English-speaking children. Our findings extend previous evidence by showing that transcoding predicts the development of arithmetic skills during the first 3 years of primary school in languages with and without number word inversion.

Number symbols are processed more automatically than nonsymbolic numerical magnitudes: Findings from a Symbolic-Nonsymbolic Stroop task

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (N_Study1 = 80, N_Study2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.

Cognitive control in number processing: new evidence from number compatibility effects in task-switching

A growing body of research suggests that basic numerical abilities such as number magnitude processing are influenced by cognitive control processes. So far, evidence for number processing being affected by cognitive control processes stems primarily from observed adaptations of numerical effects to stimulus set characteristics (e.g. order or ratio of specific stimulus types). Complementing previous research on adaptation to stimulus set characteristics as an index of influences of cognitive control, the present study employed a task-switching paradigm to examine how cognitive control processes influence number processing. Participants were presented with a two-digit number and had to either judge its parity or compare its magnitude to a standard depending on a preceding cue. We expected numerical congruency effects (i.e. the unit-decade compatibility effect for magnitude comparisons and the parity congruity effect for parity judgements) to be larger in switch trials, as persisting activation of the task set of the preceding trial should increase interference. In contrast to our expectations, both numerical congruity effects were reduced following task switches as compared to repetitions. This interaction of task-switching with numerical congruency effects suggests an influence of cognitive control on basic number processing in form of persisting inhibition of previously abandoned task sets, so that these exert less influence on current number processing demands.

Further insights into the operation of the Chinese number system: Competing effects of Arabic and Mandarin number formats

Here we report the results of a speeded relative quantity task with Chinese participants. On each trial a single numeral (the probe) was presented and the instructions were to respond as to whether it signified a quantity less than or greater than five (the standard). In separate blocks of trials, the numerals were presented either in Mandarin or in Arabic number formats. In addition to the standard influence of numerical distance, a significant predictor of performance was the degree of physical similarity between the probe and the standard as depicted in Mandarin. Additionally, competing effects of physical similarity, defined in terms of the Arabic number format, were also found. Critically the size of these different effects of physical similarity varied systematically across individuals such that larger effects of one compensated for smaller effects of the other. It is argued that the data favor accounts of processing that assume that different number formats access different format-specific representations of quantities. Moreover, for Chinese participants the default is to translate numerals into a Mandarin format prior to accessing quantity information. The efficacy of this translation process is itself influenced by a competing tendency to carry out a translation into Arabic format.

The relationship between the height dimension and numerical processing

It is well documented that the ability to perceive numbers depends on perception of size. However, size consists of two different dimensions: height and width. In previous size-congruency experiments, the changes in the size dimension were confounded by changes in both the height and width dimensions. Hence, it is not clear if two digits that are equal in size but with different width and height produce a congruency effect and if so, which dimension (height or width) will be associated with quantity more prominently. In fact, different theories might predict different outcomes for the association of height versus width with numbers. To resolve this issue, this study included two experiments in which two equal-size digits that differed from each other in the height and width dimensions were presented and participants were asked to decide which digit is numerically larger. The results revealed a novel congruency effect in which larger numbers are associated more prominently with the height dimension when compared with the width dimension. This effect has important implications for understanding the relationship between number processing and the spatial perception system.

Investigating the respective contribution of sensory modalities and spatial disposition in numerical training

Recent studies have suggested that multisensory redundancy may improve cognitive learning. According to this view, information simultaneously available across two or more modalities is highly salient and, therefore, may be learned and remembered better than the same information presented to only one modality. In the current study, we wanted to evaluate whether training arithmetic with a multisensory intervention could induce larger learning improvements than a visual intervention alone. Moreover, because a left-to-right-oriented mental number line was for a long time considered as a core feature of numerical representation, we also wanted to compare left-to-right-organized and randomly organized arithmetic training. Therefore, five training programs were created and called (a) multisensory linear, (b) multisensory random, (c) visual linear, (d) visual random, and (e) control. A total of 85 preschoolers were randomly assigned to one of these five training conditions. Whereas children were trained to solve simple addition and subtraction operations in the first four training conditions, story understanding was the focus of the control training. Several numerical tasks (arithmetic, number-to-position, number comparison, counting, and subitizing) were used as pre- and post-test measures. Although the effect of spatial disposition was not significant, results demonstrated that the multisensory training condition led to a significantly larger performance improvement than the visual training and control conditions. This result was specific to the trained ability (arithmetic) and is discussed in light of the multisensory redundancy hypothesis.

Asymmetries in flanker-target interference at different levels of number processing

Visual stimuli presented in peripheries can be barely recognized when they are surrounded by flankers (crowding). The target-flanker interference can be asymmetrical, and this asymmetry depends on a stimulus type. In particular, recognition of a letter or a number is more disturbed by the presence of a leftward flanker, reflecting the direction of reading. So far, such reading-related asymmetry has been observed with visual recognition tasks. In the following studies, we used numbers as stimuli to examine whether the leftward asymmetry in crowding extends to other levels of information processing, i.e. whether it is present when more abstract, semantic features are extracted. We presented participants with numerical triplets in the left or right visual field, and asked them to classify the middle number according to its magnitude (Experiment 1), physical characteristics (Experiment 2) or parity (Experiment 3). We observed that the leftward flanker interfered stronger with the target than the rightward flanker, but only when magnitude and physical characteristics were classified. Our findings suggest that the leftward asymmetry in crowding extends up to the semantic level of number processing, but only selectively, i.e. when a certain sort of information (magnitude) is extracted.

Finger-counting observation interferes with number processing

Aim of this study was to investigate the association between finger and number representation in a task in which students had to perform arithmetic calculations and decide whether the provided solution was correct or incorrect, while a pair of task-irrelevant hands gesturally expressed the same or a different number. In particular we aimed at investigating whether irrelevant finger-counting might interfere with arithmetic computing, thus showing the existence of a strict neural association between the two processes. 20 volunteers took part to the investigation and EEG/ERPs were recorded from 128 scalp sites. P300 amplitude was greater to correct than incorrect solutions. Accuracy was higher when there was no conflict between the two sets of information A numerical error-related negativity (nERN) was elicited by incorrect solutions, and also by correct solutions when the finger-counting was incongruent. Source analysis applied to the incongruent minus congruent difference showed that when finger-counting was incorrect nERN mostly derived from medial and superior prefrontal cortex activity (supporting action monitoring and suppression). Conversely, when finger-counting indicated the correct solution brain activation included occipital areas, somatosensory regions and visuomotor mirror areas, inferior and superior temporal cortex, reflecting attentional orienting toward the hands. In both cases, the left angular gyrus (BA39) was found active during conjoined digit/number processing, suggesting a strict neural association between finger and digit processing. The present findings help explaining why a lesion in the left parietal cortex may simultaneously lead to finger apraxia and acalculia (Gertsmann syndrome).

The neural association between arithmetic and basic numerical processing depends on arithmetic problem size and not chronological age

The intraparietal sulcus (IPS) is thought to be an important region for basic number processing (e.g. symbol-quantity associations) and arithmetic (e.g. addition). Evidence for shared circuitry within the IPS is largely based on comparisons across studies, and little research has investigated number processing and arithmetic in the same individuals. It is also unclear how the neural overlap between number processing and arithmetic is influenced by age and arithmetic problem difficulty. This study investigated these unresolved questions by examining basic number processing (symbol-quantity matching) and arithmetic (addition) networks in 26 adults and 42 children. Number processing and arithmetic elicited overlapping activity in the IPS in children and adults, however, the overlap was influenced by arithmetic problem size (i.e. which modulated the need to use procedural strategies). The IPS was recruited for number processing, and for arithmetic problems more likely to be solved using procedural strategies. We also found that the overlap between number processing and small-problem addition in children was comparable to the overlap between number processing and large-problem addition in adults. This finding suggests that the association between number processing and arithmetic in the IPS is related to the cognitive operation being performed rather than age.

Disentangling the Mechanisms of Symbolic Number Processing in Adults' Mathematics and Arithmetic Achievement

A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial-accessing underlying magnitude representation of symbols (i.e., symbol-magnitude associations), processing relative order of symbols (i.e., symbol-symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots-number word matching task-thought to be a measure of symbol-magnitude associations (numerical magnitude processing)-a numeral-ordering task that focuses on symbol-symbol associations (numerical order processing), and a digit-number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain-general factors (intellectual ability, working memory, inhibitory control, and non-numerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults' arithmetic skills build upon symbol-magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition.

Functionally distinct contributions of parietal cortex to a numerical landmark task: An fMRI study

This study aimed at establishing the neural basis of magnitude processing of multiple numbers from working memory. We designed a numerical landmark task and embedded it in a fragmented trial event-related fMRI design, allowing to separate encoding from decision processing. An attentional localiser task not involving numbers allowed further functional specification. The results show that in a numerical landmark task the right anterior intraparietal sulcus is involved in number encoding while more posterior parietal regions, bilateral superior parietal lobule and right inferior parietal lobule, provide domain-general support in the form of constructing a working memory representation or orienting spatial attention within that mental representation during number comparison. The results are in line with earlier studies reporting a functional distinction between anterior and posterior parietal contributions to number processing and further specify their role at a functional level.

A Mathematical Model of How People Solve Most Variants of the Number-Line Task

Current understanding of the development of quantity representations is based primarily on performance in the number-line task. We posit that the data from number-line tasks reflect the observer's underlying representation of quantity, together with the cognitive strategies and skills required to equate line length and quantity. Here, we specify a unified theory linking the underlying psychological representation of quantity and the associated strategies in four variations of the number-line task: the production and estimation variations of the bounded and unbounded number-line tasks. Comparison of performance in the bounded and unbounded number-line tasks provides a unique and direct way to assess the role of strategy in number-line completion. Each task produces a distinct pattern of data, yet each pattern is hypothesized to arise, at least in part, from the same underlying psychological representation of quantity. Our model predicts that the estimated biases from each task should be equivalent if the different completion strategies are modeled appropriately and no other influences are at play. We test this equivalence hypothesis in two experiments. The data reveal all variations of the number-line task produce equivalent biases except for one: the estimation variation of the bounded number-line task. We discuss the important implications of these findings.

A large-scale survey on finger counting routines, their temporal stability and flexibility in educated adults

A strong link between bodily activity and number processing has been established in recent years. Although numerous observations indicate that adults use finger counting (FC) in various contexts of everyday life for different purposes, existing knowledge of FC routines and their use is still limited. In particular, it remains unknown how stable the (default) FC habits are over time and how flexible they can be. To investigate these questions, 380 Polish participants completed a questionnaire on their FC routines, the stability of these routines, and the context of FC usage, preceded by the request to count on their fingers from 1 to 10. Next, the test-retest stability of FC habits was examined in 84 participants 2 months following the first session. To the best of our knowledge, such a study design has been adopted for the first time. The results indicate that default FC routines of the majority of participants (75%) are relatively stable over time. At the same time, FC routines can flexibly adapt according to the situation (e.g., when holding an object). As regards prevalence, almost all participants, in line with previous findings on Western individuals, declared starting from the closed palm and extending consecutive fingers. Furthermore, we observed relations between FC preferences and handedness (more left-handers start from the left hand) and that actual finger use is still widespread in healthy adults for a variety of activities (the most prevalent uses of FC are listing elements, presenting arguments and plans, and calendar calculations). In sum, the results show the practical relevance of FC in adulthood, the relative stability of preferences over time along with flexible adaptation to a current situation, as well as an association of FC routines with handedness. Taken together our results suggest that FC is the phenomenon, which is moderated or mediated by multiple embodied factors.

Discriminability of numerosity-evoked fMRI activity patterns in human intra-parietal cortex reflects behavioral numerical acuity

Areas of the primate intraparietal cortex have been identified as an important substrate of numerical cognition. In human fMRI studies, activity patterns in these and other areas have allowed researchers to read out the numerosity a subject is viewing, but the relation of such decodable information with behavioral numerical proficiency remains unknown. Here, we estimated the precision of behavioral numerosity discrimination (internal Weber fraction) in twelve adult subjects based on psychophysical testing in a delayed numerosity comparison task outside the scanner. FMRI data were then recorded during a similar task, to obtain the accuracy with which the same sample numerosities could be read out from evoked brain activity patterns, as a measure of the precision of the neuronal representation. Sample numerosities were decodable in both early visual and intra-parietal cortex with approximately equal accuracy on average. In parietal cortex, smaller numerosities were better discriminated than larger numerosities of the same ratio, paralleling smaller behavioral Weber fractions for smaller numerosities. Furthermore, in parietal but not early visual cortex, fMRI decoding performance was correlated with behavioral number discrimination acuity across subjects (subjects with a more precise behavioral Weber fraction measured prior to scanning showed greater discriminability of fMRI activity patterns in intraparietal cortex, and more specifically, the right LIP region). These results suggest a crucial role for intra-parietal cortex in supporting a numerical representation which is explicitly read out for numerical decisions and behavior.

The neural circuits of number and letter copying: an fNIRS study

In our daily lives, we are constantly exposed to numbers and letters. However, it is still under debate how letters and numbers are processed in the brain, while information on this topic would allow for a more comprehensive understanding of, for example, known influences of language on numerical cognition or neural circuits shared by numerical cognition and language processing. Some findings provide evidence for a double dissociation between numbers and letters, with numbers being represented in the right and letters in the left hemisphere, while the opposing view suggests a shared neural network. Since processing may depend on the task, we address the reported inconsistencies in a very basic symbol copying task using functional near-infrared spectroscopy (fNIRS). fNIRS data revealed that both number and letter copying rely on the bilateral middle and left inferior frontal gyri. Only numbers elicited additional activation in the bilateral parietal cortex and in the left superior temporal gyrus. However, no cortical activation difference was observed between copying numbers and letters, and there was Bayesian evidence for common activation in the middle frontal gyri and superior parietal lobules. Therefore, we conclude that basic number and letter processing are based on a largely shared cortical network, at least in a simple task such as copying symbols. This suggests that copying can be used as a control condition for more complex tasks in neuroimaging studies without subtracting stimuli-specific activation.

Neural correlates of quantity processing of Chinese numeral classifiers

Linguistic analysis suggests that numeral classifiers carry quantity information. However, previous neuroimaging studies have shown that classifiers did not elicit higher activation in the intraparietal sulcus (IPS), associated with representation of numerical magnitude, than tool nouns did. This study aimed to control the semantic attributes of classifiers and reexamine the underlying neural correlates. Participants performed a semantic distance comparison task in which they judged which one of the two items was semantically closer to the target. Processing classifiers elicited higher activation than tool nouns in the bilateral inferior parietal lobules (IPL), middle frontal gyri (MFG), right superior frontal gyrus (SFG), and left lingual gyrus. Conjunction analysis showed that the IPS was commonly activated for classifiers, numbers, dots, and number words. The results support that classifiers activate quantity representations, implicating that the system of classifiers is part of magnitude cognition. Furthermore, the results suggest that the IPS represents magnitude independent of notations.

Data-driven heterogeneity in mathematical learning disabilities based on the triple code model

Many classifications of heterogeneity in mathematical learning disabilities (MLD) have been proposed over the past four decades, however no empirical research has been conducted until recently, and none of the classifications are derived from Triple Code Model (TCM) postulates. The TCM proposes MLD as a heterogeneous disorder, with two distinguishable profiles: a representational subtype and a verbal subtype. A sample of elementary school 3rd to 6th graders was divided into two age cohorts (3rd - 4th grades, and 5th - 6th grades). Using data-driven strategies, based on the cognitive classification variables predicted by the TCM, our sample of children with MLD clustered as expected: a group with representational deficits and a group with number-fact retrieval deficits. In the younger group, a spatial subtype also emerged, while in both cohorts a non-specific cluster was produced whose profile could not be explained by this theoretical approach.

Quantifying a threat: Evidence of a numeric processing bias

Humans prioritize the processing of threats over neutral stimuli; thus, not surprisingly, the presence of threats has been shown to alter performance on both perceptual and cognitive tasks. Yet whether the quantification process is disrupted in the presence of threat is unknown. In three experiments, we examined numerical estimation and discrimination abilities in adults in the context of threatening (spiders) and non-threatening (e.g., flowers) stimuli. Results of the numerical estimation task (Experiment 1) showed that participants underestimated the number of threatening relative to neutral stimuli. Additionally, numerical discrimination data reveal that participants' abilities to discriminate between the number of entities in two arrays were worsened when the arrays consisted of threatening entities versus neutral entities (Experiment 2). However, discrimination abilities were enhanced when threatening content was presented immediately before neutral dot arrays (Experiment 3). Together, these studies suggest that threats impact our processing of visual numerosity via changes in attention to numerical stimuli, and that the nature of the threat (intrinsic or extrinsic to the stimulus) is vital in determining the direction of this impact. Intrinsic threat content in stimuli impedes its own quantification; yet threat that is extrinsic to the sets to be enumerated enhances numerical processing for subsequently presented neutral stimuli.

Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection

Number interval bisection consists of estimating the mid-number within a pair (1-9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants' verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective.

Creating semantics in tool use

This article presents the first evidence for a functional link between tool use and the processing of abstract symbols like Arabic numbers. Participants were required to perform a tool-use task after the processing of an Arabic number. These numbers represented either a small (2 or 3) or a large magnitude (8 or 9). The tool-use task consisted in using inverse pliers for gripping either a small or a large object. The inverse pliers enable to dissociate the hand action from the tool action in relation to the object (i.e., closing the hand led to an opening of the tool and vice versa). The number/tool hypothesis predicts that the quantity representation associated with Arabic numbers will interact with the action of the tool toward the object. Conversely, the number/hand hypothesis predicts that the quantity associated with numbers will interact with the action of the hand toward the tool. Results confirmed the first hypothesis and rejected the second. Indeed, large numbers interacted with the action of the tool, such that participants were longer to perform an "opening-hand/closing-tool" action after the processing of large numbers. Moreover, no effect was detected for small numbers, confirming previous studies which used only finger movements. Altogether, our finding suggests that the well-known finger/number interaction can be reversed with tool use.

Rapid proportion comparison with spatial arrays of frequently used meaningful visual symbols

It has been shown that when two arrays of Arabic numerals were briefly presented, observers could accurately indicate which array contained the larger number of a target numeral. This study investigated whether this rapid proportion comparison can be extended to other meaningful symbols that share some of notable properties of Arabic numerals. We tested mainly several Japanese Kanji letters, each of which represents a meaning and can work as a word. Using physically identical stimulus sets that could be interpreted as different types of letters, Experiment 1 first confirmed the rapid proportion comparison with Arabic numerals for Japanese participants. Experiment 2 showed that the rapid proportion comparison can be extended to Kanji numerals. Experiment 3 successfully demonstrated that rapid proportion judgments can be found with non-quantitative Kanji letters that are used frequently. Experiment 4 further demonstrated the rapid proportion comparison with frequently used meaningful non-letter symbols (gender icons). The rapid processing cannot be attributed to fluent processing of familiar items, because it was not found with familiar phonograms (Japanese Kana letters). These findings suggest that the rapid proportion comparison can be commonly found with frequently used meaningful symbols, even though their meaning is not relevant to the task.

Age-related differences in sequential modulations of problem-size and rule-violation effects during arithmetic problem verification tasks

Young and older adults were asked to verify true (e.g., 5 × 61 = 305) and false (5 × 61 = 315) arithmetic problems. Half the problems were small (e.g., 5 × 17 = 85) and half were large problems (e.g., 5 × 93 = 465). Half the false problems respected the five rule (i.e., the product of an operand multiplied by five ends with either 5 or 0), and half violated this rule (e.g., 21 × 5 = 115 vs. 21 × 5 = 113). Both young and older adults showed problem-size effects (i.e., they verified small problems more quickly than large problems) and five-rule violation effects (i.e., they verified problem violating five rule more quickly than problems respecting five rule). Moreover, we found sequential modulations of these problem-size and five-rule effects. Problem-size effects were larger on current problems following large problems than after small problems, and five-rule violation effects were larger after problems violating the five rule than after no-rule violation problems. Finally, sequential modulations of problem-size effects were larger in older adults than in young adults, and there were no age-related differences in sequential modulations of five-rule violation effects. These findings speak to the determiners of arithmetic performance, as to how well arithmetic calculation and non-calculation strategies are executed and selected on current problems depends on strategies used with preceding problems.

[fMRI and DTI in delayed development of number processing]

The neuronal correlate of the current cultural performance arose from developmental processes that can be observed by functional and anatomical magnetic resonance imaging. The velocity of these maturation processes occurs differently between adolescents, causing implications for both school career and academic performance. Regarding spatial-numerical cognition the myelinization of the superior longitudinal bundle appears to be crucial because this fiber connection intermediates between the linguistic nature of number words and conception of their spatial-numerical magnitude. The neuroscientific observation of anatomical brain maturation and its influence on school-relevant number processing may be helpful for educational purposes as well as for school psychology.

Eye movements reflect and shape strategies in fraction comparison

The comparison of fractions is a difficult task that can often be facilitated by separately comparing components (numerators and denominators) of the fractions—that is, by applying so-called component-based strategies. The usefulness of such strategies depends on the type of fraction pair to be compared. We investigated the temporal organization and the flexibility of strategy deployment in fraction comparison by evaluating sequences of eye movements in 20 young adults. We found that component-based strategies could account for the response times and the overall number of fixations observed for the different fraction pairs. The analysis of eye movement sequences showed that the initial eye movements in a trial were characterized by stereotypical scanning patterns indicative of an exploratory phase that served to establish the kind of fraction pair presented. Eye movements that followed this phase adapted to the particular type of fraction pair and indicated the deployment of specific comparison strategies. These results demonstrate that participants employ eye movements systematically to support strategy use in fraction comparison. Participants showed a remarkable flexibility to adapt to the most efficient strategy on a trial-by-trial basis. Our results confirm the value of eye movement measurements in the exploration of strategic adaptation in complex tasks.

Parietal dysfunction during number processing in children with fetal alcohol spectrum disorders

Number processing deficits are frequently seen in children prenatally exposed to alcohol. Although the parietal lobe, which is known to mediate several key aspects of number processing, has been shown to be structurally impaired in fetal alcohol spectrum disorders (FASD), effects on functional activity in this region during number processing have not previously been investigated. This fMRI study of 49 children examined differences in activation associated with prenatal alcohol exposure in five key parietal regions involved in number processing, using tasks involving simple addition and magnitude comparison. Despite generally similar behavioral performance, in both tasks greater prenatal alcohol exposure was related to less activation in an anterior section of the right horizontal intraparietal sulcus known to mediate mental representation and manipulation of quantity. Children with fetal alcohol syndrome and partial fetal alcohol syndrome appeared to compensate for this deficit by increased activation of the angular gyrus during the magnitude comparison task.

Language influences number processing--a quadrilingual study

Reading/writing direction or number word formation influence performance even in basic numerical tasks such as magnitude comparison. However, so far the interaction of these language properties has not been evaluated systematically. In this study we tested English, German, Hebrew, and Arab participants realizing a natural 2 × 2 design of reading/writing direction (left-to-right vs. right-to-left) and number word formation (non-inverted vs. inverted, i.e., forty-seven vs. seven-and-forty). Symbolic number magnitude comparison was specifically influenced by the interaction of reading/writing direction and number word formation: participants from cultures where reading direction and the order of tens and units in number words are incongruent (i.e., German and Hebrew) exhibited more pronounced unit interference in place-value integration. A within-group comparison indicated that this effect was not due to differences in education. Thus, basic cultural differences in numerical cognition were driven by natural language variables and their specific combination.

Concurrent validity of approximate number sense tasks in adults and children

Reasoning with non-symbolic numerosities is suggested to be rooted in the Approximate Number System (ANS) and evidence pointing to a relationship between the acuity of this system and mathematics is available. In order to use the acuity of this ANS as a screening instrument to detect future math problems, it is important to model ANS acuity over development. However, whether ANS acuity and its development have been described accurately can be questioned. Namely, different tasks were used to examine the developmental trajectory of ANS acuity and studies comparing performances on these different tasks are scarce. In the present study, we examined whether different tasks designed to measure the acuity of the ANS are comparable and lead to related ANS acuity measures (i.e., the concurrent validity of these tasks). We contrasted the change detection task, which is used in infants, with tasks that are more commonly used in older children and adults (i.e., comparison and same-different tasks). Together, our results suggest that ANS acuity measures obtained with different tasks are not related. This poses serious problems for the comparison of ANS acuity measures derived from different tasks and thus for the establishment of the developmental trajectory of ANS acuity.

Relating numeric cognition and language processing: do numbers and words share a common representational platform?

Numerical processing and language processing are both grounded in space. In the present study we investigated whether these are fully independent phenomena, or whether they share a common basis. If number processing activates spatial dimensions that are also relevant for understanding words, then we can expect that processing numbers may influence subsequent lexical access to words. Specifically, if high numbers relate to upper space, then they can be expected to facilitate understanding of words such as bird that are having referents typically found in the upper vertical space. The opposite should hold for low numbers. These should facilitate the understanding of words such as ground referring to entities with referents in the lower vertical space. Indeed, in two experiments we found evidence for such an interaction between number and word processing. By eliminating a contribution of linguistic factors gained from additional investigations on large text corpora, this strongly suggests that understanding numbers and language is based on similar modal representations in the brain. The implications of these findings for a broader perspective on grounded cognition will be discussed.

The number processing and calculation system: evidence from cognitive neuropsychology

INTRODUCTION

Cognitive neuropsychology focuses on the concepts of dissociation and double dissociation. The performance of number processing and calculation tasks by patients with acquired brain injury can be used to characterise the way in which the healthy cognitive system manipulates number symbols and quantities. The objective of this study is to determine the components of the numerical processing and calculation system.

METHODS

Participants consisted of 6 patients with acquired brain injuries in different cerebral localisations. We used Batería de evaluación del procesamiento numérico y el cálculo, a battery assessing number processing and calculation. Data was analysed using the difference in proportions test.

RESULTS

Quantitative numerical knowledge is independent from number transcoding, qualitative numerical knowledge, and calculation. Recodification is independent from qualitative numerical knowledge and calculation. Quantitative numerical knowledge and calculation are also independent functions.

CONCLUSIONS

The number processing and calculation system comprises at least 4 components that operate independently: quantitative numerical knowledge, number transcoding, qualitative numerical knowledge, and calculation. Therefore, each one may be damaged selectively without affecting the functioning of another. According to the main models of number processing and calculation, each component has different characteristics and cerebral localisations.

TEST: a tropic, embodied, and situated theory of cognition

TEST is a novel taxonomy of knowledge representations based on three distinct hierarchically organized representational features: Tropism, Embodiment, and Situatedness. Tropic representational features reflect constraints of the physical world on the agent's ability to form, reactivate, and enrich embodied (i.e., resulting from the agent's bodily constraints) conceptual representations embedded in situated contexts. The proposed hierarchy entails that representations can, in principle, have tropic features without necessarily having situated and/or embodied features. On the other hand, representations that are situated and/or embodied are likely to be simultaneously tropic. Hence, although we propose tropism as the most general term, the hierarchical relationship between embodiment and situatedness is more on a par, such that the dominance of one component over the other relies on the distinction between offline storage versus online generation as well as on representation-specific properties.