Numbers within Our Hands: Modulation of Corticospinal Excitability of Hand Muscles during Numerical Judgment

Recruitment of the premotor cortex during arithmetic operations by the monkey

Arithmetic operations are complex mental processes rooted in the abstract concept of numerosity. Despite the significance, the neural architecture responsible for these operations has remained largely uncharted. In this study, we explored the presence of specific neuronal activity in the dorsal premotor cortex of the monkey dedicated to numerical addition and subtraction. Our findings reveal that many of these neural activities undergo a transformation, shifting their coding from arithmetic to motor representations. These motor representations include information about which hand to use and the number of steps involved in the action. We consistently observed that cells related to the right-hand encoded addition, while those linked to the left-hand encoded subtraction, suggesting that arithmetic operations and motor commands are intertwining with each other. Furthermore, we used a multivariate decoding technique to predict the monkey's behaviour based on the activity of these arithmetic-related cells. The classifier trained to discern arithmetic operations, including addition and subtraction, not only predicted the arithmetic decisions but also the subsequent motor actions of the right and left-hand. These findings imply a cognitive extension of the motor cortex's function, where inherent neural systems are repurposed to facilitate arithmetic operations.

Changes in the superior longitudinal fasciculus and anterior thalamic radiation in the left brain are associated with developmental dyscalculia

Developmental dyscalculia is a neurodevelopmental disorder specific to arithmetic learning even with normal intelligence and age-appropriate education. Difficulties often persist from childhood through adulthood lowering the individual's quality of life. However, the neural correlates of developmental dyscalculia are poorly understood. This study aimed to identify brain structural connectivity alterations in developmental dyscalculia. All participants were recruited from a large scale, non-referred population sample in a longitudinal design. We studied 10 children with developmental dyscalculia (11.3 ± 0.7 years) and 16 typically developing peers (11.2 ± 0.6 years) using diffusion-weighted magnetic resonance imaging. We assessed white matter microstructure with tract-based spatial statistics in regions-of-interest tracts that had previously been related to math ability in children. Then we used global probabilistic tractography for the first time to measure and compare tract length between developmental dyscalculia and typically developing groups. The high angular resolution diffusion-weighted magnetic resonance imaging and crossing-fiber probabilistic tractography allowed us to evaluate the length of the pathways compared to previous studies. The major findings of our study were reduced white matter coherence and shorter tract length of the left superior longitudinal/arcuate fasciculus and left anterior thalamic radiation in the developmental dyscalculia group. Furthermore, the lower white matter coherence and shorter pathways tended to be associated with the lower math performance. These results from the regional analyses indicate that learning, memory and language-related pathways in the left hemisphere might be related to developmental dyscalculia in children.

Cultural similarities and specificities of finger counting and montring: Evidence from Amazon Tsimane' people

Numerical cognition might be embodied, that is, grounded in bodily actions. This claim is supported by the observation that, potentially due to our shared biology, finger counting is prevalent among a variety of cultures. Differences in finger counting are apparent even within Western cultures. Relatively few indigenous cultures have been systematically analyzed in terms of traditional finger counting and montring (i.e., communicating numbers with fingers) routines. Even fewer studies used the same protocols across cultures, allowing for a systematic comparison of indigenous and Western finger counting routines. We analyze the finger counting and montring routines of Tsimane' (N = 121), an indigenous people living in the Bolivian Amazon rainforest, depending on handedness, education level, and exposure to mainstream, industrialized Bolivian culture. Tsimane' routines are compared with those of German and British participants. Tsimane' reveal a greater variation in finger counting and montring routines, which seems to be modified by their education level. We outline a framework on how different factors such as handedness and reading direction might affect cross-cultural and within-cultural variation in finger counting.

A sensorimotor perspective on numerical cognition

Numbers are present in every part of modern society and the human capacity to use numbers is unparalleled in other species. Understanding the mental and neural representations supporting this capacity is of central interest to cognitive psychology, neuroscience, and education. Embodied numerical cognition theory suggests that beyond the seemingly abstract symbols used to refer to numbers, their underlying meaning is deeply grounded in sensorimotor experiences, and that our specific understanding of numerical information is shaped by actions related to our fingers, egocentric space, and experiences with magnitudes in everyday life. We propose a sensorimotor perspective on numerical cognition in which number comprehension and numerical proficiency emerge from grounding three distinct numerical core concepts: magnitude, ordinality, and cardinality.

How can transforming representation of mathematical entities help us employ more cognitive resources?

This article discusses the cognitive process of transforming one representation of mathematical entities into another representation. This process, which has been called mathematical metaphor, allows us to understand and embody a difficult-to-understand mathematical entity in terms of an easy-to-understand entity. When one representation of a mathematical entity is transformed into another representation, more cognitive resources such as the visual and motor systems can come into play to understand the target entity. Because of their nature, some curves, which are one group of visual representations, may have a great motor strength. It is suggested that directedness, straightness, length, and thinness are some possible features that determine degree of motor strength of a curve. Another possible factor that can determine motor strength of a curve is the strength of association between shape of the curve and past experiences of the observer (and her/his prior knowledge). If an individual has had the repetitive experience of observing objects moving along a certain curve, the shape of the curve may have a great motor strength for her/him. In fact, it can be said that some kind of metonymic relationship may be formed between the shapes of some curves and movement experiences.

Mental arithmetic modulates temporal variabilities of finger-tapping tasks in a tempo-dependent manner

Background

Several psychiatric diseases impair temporal processing. Temporal processing is thought to be based on two domains: supra-second intervals and sub-second intervals. Studies show that temporal processing in sub-second intervals is mainly an automated process. However, the brain functions involved in temporal processing at each time scale remain unclear. We hypothesized that temporal processing in supra-second intervals requires several brain areas, such as the ventrolateral prefrontal cortex, intraparietal sulcus (IPS), and inferior parietal lobe, corresponding to various cognitions in a time scale-dependent manner. We focused on a dual-task paradigm (DTP) involving simultaneous performance of cognitive and motor tasks, which is an effective method for screening psychomotor functions; we then designed a DTP comprising finger tapping at various tempi as the temporal processing task and two cognitive tasks (mental arithmetic and reading) that might affect temporal processing. We hoped to determine whether task-dependent interferences on temporal processing in supra-second intervals differed depending on the cognitive tasks involved.

Methods

The study included 30 participants with no history of neuromuscular disorders. Participants were asked to perform a DTP involving right index finger tapping at varying tempi (0.33, 0.5, 1, 2, 3, and 4 s inter-tapping intervals). Cognitive tasks comprised mental arithmetic (MA) involving three-digit addition, mental reading (MR) of three- to four-digit numbers, and a control (CTL) task without any cognitive loading. For comparison between tasks, we calculated the SDs of the inter-tapping intervals. Participants' MA abilities in the three-digit addition task were evaluated.

Results

The MA and MR tasks significantly increased the SDs of the inter-tapping intervals compared to those of the CTL task in 2-3 s and 3-4 s for the MA and MR tasks, respectively. Furthermore, SD peaks in the finger-tapping tasks involving MA were normalized by those in the CTL task, which were moderately correlated with the participants' MA ability (r = 0.462, P = 0.010).

Discussion

Our results established that DTP involving the temporal coordination of finger-tapping and cognitive tasks increased temporal variability in a task- and tempo-dependent manner. Based on the behavioral aspects, we believe that these modulations of temporal variability might result from the interaction between finger function, arithmetic processing, and temporal processing, especially during the "pre-semantic period". Our findings may help in understanding the temporal processing deficits in various disorders such as dementia, Parkinson's disease, and autism.

More Thumbs Than Rules: Is Rationality an Exaptation?

The literatures on bounded and ecological rationality are built on adaptationism-and its associated modular, cognitivist and computational paradigm-that does not address or explain the evolutionary origins of rationality. We argue that the adaptive mechanisms of evolution are not sufficient for explaining human rationality, and we posit that human rationality presents exaptive origins, where exaptations are traits evolved for other functions or no function at all, and later co-opted for new uses. We propose an embodied reconceptualization of rationality-embodied rationality-based on the reuse of the perception-action system, where many neural processes involved in the control of the sensory-motor system, salient in ancestral environments have been later co-opted to create-by tinkering-high-level reasoning processes, employed in civilized niches.

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

One of the most critical skills behind consumer's behavior is the ability to assess whether a price after a discount is a real bargain. Yet, the neural underpinnings and cognitive mechanisms associated with such a skill are largely unknown. While there is general agreement that the posterior parietal cortex (PPC) on the left is critical for mental calculations, and there is also recent repetitive transcranial magnetic stimulation (rTMS) evidence pointing to the supramarginal gyrus (SMG) of the right PPC as crucial for consumer-like arithmetic (e.g., multi-digit mental addition or subtraction), it is still unknown whether SMG is involved in calculations of sale prices. Here, we show that the neural mechanisms underlying discount arithmetic characteristic for shopping are different from complex addition or subtraction, with discount calculations engaging left SMG more. We obtained these outcomes by remodeling our laboratory to resemble a shop and asking participants to calculate prices after discounts (e.g., $8.80-25 or $4.80-75%), while stimulating left and right SMG with neuronavigated rTMS. Our results indicate that such complex shopping calculations as establishing the price after a discount involve SMG asymmetrically, whereas simpler calculations such as price addition do not. These findings have some consequences for neural models of mathematical cognition and shed some preliminary light on potential consumer's behavior in natural settings.

Learning-Challenged Youth Show an Abnormal Relationship Between Fronto-Parietal Myelination and Mathematical Ability

BACKGROUND AND PURPOSE

Differences in the microstructure of fronto-parietal white matter tracts have been associated with mathematical achievement. However, much of the supporting evidence relies on nonspecific diffusion-weighted magnetic resonance imaging, making it difficult to isolate the role of myelin in math ability.

METHODS

We used myelin water imaging to measure brain myelin. We related myelin water fraction (MWF) to Woodcock-Johnson III (WJ-III) basic math scores using region of interest (ROI) and tract-based spatial statistics (TBSS) analyses, in 14 typically developing and 36 learning challenged youth aged 9-17 years.

RESULTS

The ROI analysis found a positive relationship between fronto-parietal MWF and math in typically developing youth, but not in learning challenged youth. The relationship between fronto-parietal MWF and math observed in typically developing youth was fully mediated by age. No group differences in fronto-parietal MWF were found between typically developing and learning challenged youth. TBSS also found no group differences in MWF values. TBSS indicated math-MWF relationships extend beyond fronto-parietal tracts to descending and ascending projection tracts in typically developing youth. TBSS identified math-MWF relationships in the cerebral peduncles of learning challenged youth.

CONCLUSIONS

Our results suggest that in typically developing youth, brain myelination contributes to individual differences in basic math achievement. In contrast, youth with learning challenges appear to have less capacity to leverage myelin to improve math achievement.

Putting a Finger on Numerical Development - Reviewing the Contributions of Kindergarten Finger Gnosis and Fine Motor Skills to Numerical Abilities

The well-documented association between fingers and numbers is not only based on the observation that most children use their fingers for counting and initial calculation, but also on extensive behavioral and neuro-functional evidence. In this article, we critically review developmental studies evaluating the association between finger sensorimotor skills (i.e., finger gnosis and fine motor skills) and numerical abilities. In sum, reviewed studies were found to provide evidential value and indicated that both finger gnosis and fine motor skills predict measures of counting, number system knowledge, number magnitude processing, and calculation ability. Therefore, specific and unique contributions of both finger gnosis and fine motor skills to the development of numerical skills seem to be substantiated. Through critical consideration of the reviewed evidence, we suggest that the association of finger gnosis and fine motor skills with numerical abilities may emerge from a combination of functional and redeployment mechanisms, in which the early use of finger-based numerical strategies during childhood might be the developmental process by which number representations become intertwined with the finger sensorimotor system, which carries an innate predisposition for said association to unfold. Further research is nonetheless necessary to clarify the causal mechanisms underlying this association.

Exploring the interactions among SNARC effect, finger counting direction and embodied cognition

The Spatial Numerical Association of Response Code (SNARC) is the preferential association between smaller/larger magnitudes and left/right side, respectively. Some evidence suggest a link between SNARC and a left-to-right finger counting habit. We asked 268 participants to show how they use the hands to count from 1 to 10. By means of this ecological task, 80% of the sample use first the right hand (to count from 1 to 5) and the majority of them use a palm-up posture. In Experiment 2 (N = 46) right-starters were asked to categorize 1-to-5 magnitudes as even or odd, using the left and right hand. Stimuli were presented both as Arabic numbers and by means of left and right hand photographs in palm-up and palm-down posture. Results confirmed the expected SNARC effect in the Arabic condition. With hand images we found that right hand responses were better for larger than for smaller magnitudes (SNARC, mainly for left hand palm-up stimuli), showing that the SNARC can be generalized to different codes. Finally, the interactions between magnitudes and left/right hand images in palm-up and palm-down posture suggest that embodied cognition can influence numerical processing.

Incidental Counting: Speeded Number Naming Through Finger Movements

The first steps in numerical cognition are usually done in conjunction with fingers. Following the assumption that abstract concepts stay associated with the sensory-motor information that was present during their acquisition and consolidation, mental number representations should always be associated with the respective finger counting components. We tested whether finger movements that imply finger counting actually prime the corresponding number concepts in adults. All participants counted number 1 with their thumb and incremented sequentially to number 5 with their pinky. In the experiment, participants sequentially and repeatedly pressed five buttons from thumb to pinky. Each button press triggered the visual presentation of a random number between 1 and 5 that had to be named aloud, resulting in 20% counting-congruent and 80% counting-incongruent finger-number mappings. Average naming latencies were significantly shorter for congruent than incongruent finger-number combinations. Furthermore, there was a distance effect where primes partly co-activated numerically close target numbers and with decreasing priming for more distant prime-target pairs. Overall, these results provide further evidence that number representations are strongly associated with finger counting experience, making fingers an effective tool for number comprehension.

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.

Tactile enumeration: A case study of acalculia

Enumeration is one of the building blocks of arithmetic and fingers are used as a counting tool in early steps. Subitizing-fast and accurate enumeration of small quantities-has been vastly studied in the visual modality, but less in the tactile modality. We explored tactile enumeration using fingers, and gray matter (GM) changes using voxel-based morphometry (VBM), in acalculia. We examined JD, a 22-year-old female with acalculia following a stroke to the left inferior parietal cortex. JD and a neurologically healthy normal comparison (NC) group reported how many fingers were stimulated. JD was tested at several time points, including at acute and chronic phases. Using the sensory intact hand for tactile enumeration, JD showed deficit in the acute phase, compared to the NC group, and improvement in the chronic phase of (1) the RT slope of enumerating up to four stimuli, (2) enumerating neighboring fingers, and (3) arithmetic fluency performance. Moreover, VBM analysis showed a larger GM volume for JD relative to the NC group in the right middle occipital cortex, most profoundly in the chronic phase. JD's performance serves as a first glance of tactile enumeration in acalculia. Pattern-recognition-based results support the suggestion of subitizing being the enumeration process when using one hand. Moreover, the increase in GM in the occipital cortex lays the groundwork for studying the innate and primitive ability to perceive and evaluate sizes or amounts-"sense of magnitude"- as a multisensory magnitude area and as part of a recovery path for deficits in basic numerical abilities.

Examining the Triple Code Model in numerical cognition: An fMRI study

The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N = 46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.

Configured-groups hypothesis: fast comparison of exact large quantities without counting

Our innate number sense cannot distinguish between two large exact numbers of objects (e.g., 45 dots vs 46). Configured groups (e.g., 10 blocks, 20 frames) are traditionally used in schools to represent large numbers. Previous studies suggest that these external representations make it easier to use symbolic strategies such as counting ten by ten, enabling humans to differentiate exactly two large numbers. The main hypothesis of this work is that configured groups also allow for a differentiation of large exact numbers, even when symbolic strategies become ineffective. In experiment 1, the children from grade 3 were asked to compare two large collections of objects for 5 s. When the objects were organized in configured groups, the success rate was over .90. Without this configured grouping, the children were unable to make a successful comparison. Experiments 2 and 3 controlled for a strategy based on non-numerical parameters (areas delimited by dots or the sum areas of dots, etc.) or use symbolic strategies. These results suggest that configured grouping enables humans to distinguish between two large exact numbers of objects, even when innate number sense and symbolic strategies are ineffective. These results are consistent with what we call "the configured group hypothesis": configured groups play a fundamental role in the acquisition of exact numerical abilities.

(Lack of) Corticospinal facilitation in association with hand laterality judgments

In recent years, mental practice strategies have drawn much interest in the field of rehabilitation. One form of mental practice particularly advocated involves judging the laterality of images depicting body parts. Such laterality judgments are thought to rely on implicit motor imagery via mental rotation of one own's limb. In this study, we sought to further characterize the involvement of the primary motor cortex (M1) in hand laterality judgments (HLJ) as performed in the context of an application designed for rehabilitation. To this end, we measured variations in corticospinal excitability in both hemispheres with motor evoked potentials (MEPs) while participants (n = 18, young adults) performed either HLJ or a mental counting task. A third condition (foot observation) provided additional control. We hypothesized that HLJ would lead to a selective MEP facilitation when compared to the other tasks and that this facilitation would be greater on the right than the left hemisphere. Contrary to our predictions, we found no evidence of task effects and hemispheric effects for the HLJ task. Significant task-related MEP facilitation was detected only for the mental counting task. A secondary experiment performed in a subset of participants (n = 6) to further test modulation during HLJ yielded the same results. We interpret the lack of facilitation with HLJ in the light of evidence that participants may rely on alternative strategies when asked to judge laterality when viewing depictions of body parts. The use of visual strategies notably would reduce the need to engage in mental rotation, thus reducing M1 involvement. These results have implications for applications of laterality tasks in the context of the rehabilitation program.

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".

Finger posing primes number comprehension

Canonical finger postures, as used in counting, activate number knowledge, but the exact mechanism for this priming effect is unclear. Here we dissociated effects of visual versus motor priming of number concepts. In Experiment 1, participants were exposed either to pictures of canonical finger postures (visual priming) or actively produced the same finger postures (motor priming) and then used foot responses to rapidly classify auditory numbers (targets) as smaller or larger than 5. Classification times revealed that manually adopted but not visually perceived postures primed magnitude classifications. Experiment 2 obtained motor priming of number processing through finger postures also with vocal responses. Priming only occurred through canonical and not through non-canonical finger postures. Together, these results provide clear evidence for motor priming of number knowledge. Relative contributions of vision and action for embodied numerical cognition and the importance of canonicity of postures are discussed.

A helping hand putting in order: Visuomotor routines organize numerical and non-numerical sequences in space

Theories of embodied cognition emphasize the importance of sensorimotor schemas linked to external world experience for representing conceptual knowledge. Accordingly, some researchers have proposed that the spatial representation of numerical and non-numerical sequences relies on visuomotor routines, like reading habit and finger counting. There is a growing interest in how these two routines contribute to the spatial representation of ordinal sequences, although no investigation has so far directly compared them. The present study aims to investigate how these routines contribute to represent ordinal information in space. To address this issue, bilingual participants reading either from left-to-right or right-to-left were required to map ordinal information to all fingers of their right dominant hand. Critically, we manipulated both the direction of the mapping and the language of the verbal information. More specifically, a finger-mapping compatibility task was adopted in three experiments to explore the spatial representation of numerical (digit numbers and number words) and non-numerical (days of the week, presented in Hebrew and in English) sequences. Results showed that numerical information was preferentially mapped according to participants' finger counting habits, regardless of hand posture (prone and supine), number notation and reading habit. However, for non-numerical ordinal sequences, reading and finger counting directions both contributed to determine a preferential spatial mapping. These findings indicate that abstract knowledge representation relies on multiple over-trained visuomotor routines. More generally, these results highlight the capacity of our cognitive system to flexibly represent abstract ordered information, by relying on different directional experiences (finger counting, reading direction) depending on the stimuli and on the task at hand.

Finger counting habit and spatial-numerical association in children and adults

Sensory-motor experiences are known to build up concrete and abstract concepts during the lifespan. The present study aimed to test how finger counting habits (right-hand vs. left-hand starters) could influence the spatial-numerical representation in number-to-position (explicit) and digit-string bisection (implicit) tasks. The subjects were Italian primary school children (N=184, from the first to the fifth year) and adults (N=42). No general preference for right- or left-starting in the finger counting was found. In the explicit task, right- or left-starting did not affect performance. In the implicit task, the right-hand starters shifted from the left to the right space when bisecting small and large numbers respectively, while the left-hand starters shifted from the right to the left space with higher leftward bias for large numbers. The finger configuration in Italian children and adults influences the spatial-numerical representation, but only when implicit number processing is required by the task.

Composite body movements modulate numerical cognition: evidence from the motion-numerical compatibility effect

A recent hierarchical model of numerical processing, initiated by Fischer and Brugger (2011) and Fischer (2012), suggested that situated factors, such as different body postures and body movements, can influence the magnitude representation and bias numerical processing. Indeed, Loetscher et al. (2008) found that participants’ behavior in a random number generation task was biased by head rotations. More small numbers were reported after leftward than rightward head turns, i.e., a motion-numerical compatibility effect. Here, by carrying out two experiments, we explored whether similar motion-numerical compatibility effects exist for movements of other important body components, e.g., arms, and for composite body movements as well, which are basis for complex human activities in many ecologically meaningful situations. In Experiment 1, a motion-numerical compatibility effect was observed for lateral rotations of two body components, i.e., the head and arms. Relatively large numbers were reported after making rightward compared to leftward movements for both lateral head and arm turns. The motion-numerical compatibility effect was observed again in Experiment 2 when participants were asked to perform composite body movements of congruent movement directions, e.g., simultaneous head left turns and arm left turns. However, it disappeared when the movement directions were incongruent, e.g., simultaneous head left turns and arm right turns. Taken together, our results extended Loetscher et al.’s (2008) finding by demonstrating that their effect is effector-general and exists for arm movements. Moreover, our study reveals for the first time that the impact of spatial information on numerical processing induced by each of the two sensorimotor-based situated factors, e.g., a lateral head turn and a lateral arm turn, can cancel each other out.

What Is the Role of Manual Preference in Hand-Digit Mapping During Finger Counting? A Study in a Large Sample of Right- and Left-Handers

The goal of the present study was to test whether there is a relationship between manual preference and hand-digit mapping in 369 French adults with similar numbers of right- and left-handers. Manual laterality was evaluated with the finger tapping test to evaluate hand motor asymmetry, and the Edinburgh handedness inventory was used to assess manual preference strength (MPS) and direction. Participants were asked to spontaneously "count on their fingers from 1 to 10" without indications concerning the hand(s) to be used. The results indicated that both MPS and hand motor asymmetry affect the hand-starting preference for counting. Left-handers with a strong left-hand preference (sLH) or left-hand motor asymmetry largely started to count with their left hand (left-starter), while right-handers with a strong right-hand preference (sRH) or right-hand motor asymmetry largely started to count with their right hand (right-starter). Notably, individuals with weak MPS did not show a hand-starting preference. These findings demonstrated that manual laterality contributes to finger counting directionality. Lastly, the results showed a higher proportion of sLH left-starter individuals compared with sRH right-starters, indicating an asymmetric bias of MPS on hand-starting preference. We hypothesize that the higher proportion of sLH left-starters could be explained by the congruence between left-to-right hand-digit mapping and left-to-right mental number line representation that has been largely reported in the literature. Taken together, these results indicate that finger-counting habits integrate biological and cultural information.

Finger Counting and (2D:4D) Digit Ratio in Spatial-Numerical Association

It is reported that a canonical and cultural finger counting habit influences the spatial-numerical association. The digit ratio (the ratio between the lengths of the index and ring fingers as a putative indicator of prenatal androgen exposure) also plays an effect on space-number representation, reflecting a stronger left-to-right number representation in people with a short index finger and longer ring finger (i.e., 2D:4D ratio). It is unknown whether the finger counting habit and digit ratio have an effect on spatial-numerical association independently from each other or whether they interact with each other. In Study 1, the digit ratio and finger counting mapping were recorded in right handers. The participants performed number-to-position, digit string bisection, and physical line bisection tasks. In the number-to-position task, a finger counting effect was found, as well as a significant interaction between factors. A digit ratio effect was observed in the digit string bisection task. In Study 2, digit ratio and finger counting mapping were recorded in right and left handers. The results showed that the finger counting habit influenced the spatial biases in both numerical tasks. A significant interaction between finger counting and digit ratio was found in both numerical tasks when only the left hand was considered. The results are discussed considering the embodied nature of the spatial-numerical association.

Mental representations of magnitude and order: a dissociation by sensorimotor learning

Numbers and spatially directed actions share cognitive representations. This assertion is derived from studies that have demonstrated that the processing of small- and large-magnitude numbers facilitates motor behaviors that are directed to the left and right, respectively. However, little is known about the role of sensorimotor learning for such number-action associations. In this study, we show that sensorimotor learning in a serial reaction-time task can modify the associations between number magnitudes and spatially directed movements. Experiments 1 and 3 revealed that this effect is present only for the learned sequence and does not transfer to a novel unpracticed sequence. Experiments 2 and 4 showed that the modification of stimulus-action associations by sensorimotor learning does not occur for other sets of ordered stimuli such as letters of the alphabet. These results strongly suggest that numbers and actions share a common magnitude representation that differs from the common order representation shared by letters and spatially directed actions. Only the magnitude representation, but not the order representation, can be modified episodically by sensorimotor learning.

Perceiving fingers in single-digit arithmetic problems

In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.

Tactile enumeration of small quantities using one hand

Our study explores various aspects of enumerating small quantities in the tactile modality. Fingertips of one hand were stimulated by a vibro-tactile apparatus (for 100/800 ms). Between 1 and 5 stimuli were presented to the right or the left hand and applied to neighboring (e.g., thumb-index-middle) or non-neighboring (e.g., thumb-middle-pinkie) fingers. The results showed a moderate increase in RT up to 4 stimuli and then a decrease for 5 stimuli. Right hand stimulation evoked more accurate performance than left hand stimulation only under short exposures (100 ms). Importantly, when the stimuli were presented to neighboring fingers, the accuracy rate was higher and the RT was faster than when presented to non-neighboring fingers. We discuss the results and suggest that when the stimuli are presented to one hand the subitizing range is 4 rather than 3. Furthermore, the right hand advantage and the efficiency for neighboring fingers are further support for the association between number and spatial arrangement of the fingers.

Eating tools in hand activate the brain systems for eating action: a transcranial magnetic stimulation study

There is increasing neuroimaging evidence suggesting that visually presented tools automatically activate the human sensorimotor system coding learned motor actions relevant to the visual stimuli. Such crossmodal activation may reflect a general functional property of the human motor memory and thus can be operating in other, non-limb effector organs, such as the orofacial system involved in eating. In the present study, we predicted that somatosensory signals produced by eating tools in hand covertly activate the neuromuscular systems involved in eating action. In Experiments 1 and 2, we measured motor evoked response (MEP) of the masseter muscle in normal humans to examine the possible impact of tools in hand (chopsticks and scissors) on the neuromuscular systems during the observation of food stimuli. We found that eating tools (chopsticks) enhanced the masseter MEPs more greatly than other tools (scissors) during the visual recognition of food, although this covert change in motor excitability was not detectable at the behavioral level. In Experiment 3, we further observed that chopsticks overall increased MEPs more greatly than scissors and this tool-driven increase of MEPs was greater when participants viewed food stimuli than when they viewed non-food stimuli. A joint analysis of the three experiments confirmed a significant impact of eating tools on the masseter MEPs during food recognition. Taken together, these results suggest that eating tools in hand exert a category-specific impact on the neuromuscular system for eating.

Aspects of situated cognition in embodied numerosity: the case of finger counting

Numerical cognitions such as spatial-numerical associations have been observed to be influenced by grounded, embodied and situated factors. For the case of finger counting, grounded and embodied influences have been reported. However, situated influences, e.g., that reported counting habits change with perception and action within a given situation, have not been systematically examined. To pursue the issue of situatedness of reported finger-counting habits, 458 participants were tested in three separate groups: (1) spontaneous condition: counting with both hands available, (2) perceptual condition: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) perceptual and proprioceptive condition: counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand. Report of typical counting habits differed strongly between the three conditions. 28 % reported to start counting with the left hand in the spontaneous counting condition (1), 54 % in the perceptual condition (2) and 62 % in the perceptual and proprioceptive condition (3). Additionally, all participants in the spontaneous counting group showed a symmetry-based counting pattern (with the thumb as number 6), while in the two other groups, a considerable number of participants exhibited a spatially continuous counting pattern (with the pinkie as number 6). Taken together, the study shows that reported finger-counting habits depend on the perceptual and proprioceptive situation and thus are strongly influenced by situated cognition. We suggest that this account reconciles apparently contradictory previous findings of different counting preferences regarding the starting hand in different examination situations.

Habilidades matemáticas iniciais em crianças surdas e ouvintes

O presente estudo tem como objetivo investigar o conhecimento de procedimentos e conceitos matemáticos em crianças surdas da educação infantil. Até o momento, existe uma grande escassez de estudos sobre o desenvolvimento de conceitos e procedimentos matemáticos em crianças surdas de idade pré-escolar. Os poucos trabalhos existentes sugerem que as crianças surdas têm dificuldades em aprender a sequência numérica. Contudo, não há qualquer evidência conclusiva a respeito das causas desta dificuldade. Os resultados deste estudo revelaram que as diferenças de desempenho entre crianças surdas e ouvintes estão relacionadas com a demanda linguística.

Neural connectivity patterns underlying symbolic number processing indicate mathematical achievement in children

In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis to investigate the neural substrates for symbolic number processing in young children. We hypothesized that, as children solidify the mapping between symbols and underlying magnitudes, important developmental changes occur in the neural communication between the right parietal region, important for the representation of non-symbolic numerical magnitudes, and other brain regions known to be critical for processing numerical symbols. To test this hypothesis, we scanned children between 4 and 6 years of age while they performed a magnitude comparison task with Arabic numerals (numerical, symbolic), dot arrays (numerical, non-symbolic), and lines (non-numerical). We then identified the right parietal seed region that showed greater blood-oxygen-level-dependent signal in the numerical versus the non-numerical conditions. A psychophysiological interaction method was used to find patterns of effective connectivity arising from this parietal seed region specific to symbolic compared to non-symbolic number processing. Two brain regions, the left supramarginal gyrus and the right precentral gyrus, showed significant effective connectivity from the right parietal cortex. Moreover, the degree of this effective connectivity to the left supramarginal gyrus was correlated with age, and the degree of the connectivity to the right precentral gyrus predicted performance on a standardized symbolic math test. These findings suggest that effective connectivity underlying symbolic number processing may be critical as children master the associations between numerical symbols and magnitudes, and that these connectivity patterns may serve as an important indicator of mathematical achievement.

The impact of finger counting habits on arithmetic in adults and children

Here, we explored the impact of finger counting habits on arithmetic in both adults and children. Two groups of participants were examined, those that begin counting with their left hand (left-starters) and those that begin counting with their right hand (right-starters). For the adults, performance on an addition task in which participants added 2 two-digit numbers was compared. The results revealed that left-starters were slower than right-starters when adding and they had lower forward and backward digit-span scores. The children (aged 5-12) showed similar results on a single-digit timed addition task-right-starters outperformed left-starters. However, the children did not reveal differences in working memory or verbal and non-verbal intelligence as a function of finger counting habit. We argue that the motor act of finger counting influences how number is represented and suggest that left-starters may have a more bilateral representation that accounts for the slower processing.

Fine-grained semantic categorization across the abstract and concrete domains

A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related) and abstract (mental state-, emotion-, mathematics-related) categories, with respect either to different semantic domain-related scales (rating study 1), or to concreteness, familiarity, and context availability (rating study 2). Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains.

Objects, numbers, fingers, space: clustering of ventral and dorsal functions in young children and adults

In the primate brain, sensory information is processed along two partially segregated cortical streams: the ventral stream, mainly coding for objects' shape and identity, and the dorsal stream, mainly coding for objects' quantitative information (including size, number, and spatial position). Neurophysiological measures indicate that such functional segregation is present early on in infancy, and that the two streams follow independent maturational trajectories during childhood. Here we collected, in a large sample of young children and adults, behavioural measures on an extensive set of functions typically associated with either the dorsal or the ventral stream. We then used a correlational approach to investigate the presence of inter-individual variability resulting in clustering of functions. Results show that dorsal- and ventral-related functions follow two uncorrelated developmental trajectories. Moreover, within each stream, some functions show age-independent correlations: finger gnosis, non-symbolic numerical abilities and spatial abilities within the dorsal stream, and object and face recognition abilities within the ventral stream. This pattern of clear within-stream cross-task correlation seems to be lost in adults, with two notable exceptions: performance in face and object recognition on one side, and in symbolic and non-symbolic comparison on the other, remain correlated, pointing to distinct shape recognition and quantity comparison systems.

The Body of Evidence: What Can Neuroscience Tell Us about Embodied Semantics?

Semantic knowledge is based on the way we perceive and interact with the world. However, the jury is still out on the question: to what degree are neuronal systems that subserve acquisition of semantic knowledge, such as sensory-motor networks, involved in its representation and processing? We will begin with a critical evaluation of the main behavioral and neuroimaging methods with respect to their capability to define the functional roles of specific brain areas. Any behavioral or neuroscientific measure is a conflation of representations and processes. Hence, a combination of behavioral and neurophysiological interactions as well as time-course information is required to define the functional roles of brain areas. This will guide our review of the empirical literature. Most research in this area has been done on semantics of concrete words, where clear theoretical frameworks for an involvement of sensory-motor systems in semantics exist. Most of this evidence still stems from correlational studies that are ambiguous with respect to the behavioral relevance of effects. Evidence for causal effects of sensory-motor systems on semantic processes is still scarce but evolving. Relatively few neuroscientific studies so far have investigated the embodiment of abstract semantics for words, numbers, and arithmetic facts. Here, some correlational evidence exists, but data on causality are mostly absent. We conclude that neuroimaging data, just as behavioral data, have so far not disentangled the fundamental link between process and representation. Future studies should therefore put more emphasis on the effects of task and context on semantic processing. Strong conclusions can only be drawn from a combination of methods that provide time-course information, determine the connectivity among poly- or amodal and sensory-motor areas, link behavioral with neuroimaging measures, and allow causal inferences. We will conclude with suggestions on how this could be accomplished in future research.

Selective Interference of Finger Movements on Basic Addition and Subtraction Problem Solving

Fingers offer a practical tool to represent and manipulate numbers during the acquisition of arithmetic knowledge, usually with a greater involvement in addition and subtraction than in multiplication. In adults, brain-imaging studies show that mental arithmetic increases activity in areas known for their contribution to finger movements. It is unclear, however, if this truly reflects functional interactions between the processes and/or representations controlling finger movements and those involved in mental arithmetic, or a mere anatomical proximity. In this study we assessed whether finger movements interfere with basic arithmetic problem solving, and whether this interference is specific for the operations that benefit the most from finger-based calculation strategies in childhood. In Experiment 1, we asked participants to solve addition, subtraction, and multiplication problems either with their hands at rest or while moving their right-hand fingers sequentially. The results showed that finger movements induced a selective time cost in solving addition and subtraction but not multiplication problems. In Experiment 2, we asked participants to solve the same problems while performing a sequence of foot movements. The results showed that foot movements produced a nonspecific interference with all three operations. Taken together, these findings demonstrate the specific role of finger-related processes in solving addition and subtraction problems, suggesting that finger movements and mental arithmetic are functionally related.

Your actions in my cerebellum: subclinical deficits in action observation in patients with unilateral chronic cerebellar stroke

Empirical evidence indicates that cognitive consequences of cerebellar lesions tend to be mild and less important than the symptoms due to lesions to cerebral areas. By contrast, imaging studies consistently report strong cerebellar activity during tasks of action observation and action understanding. This has been interpreted as part of the automatic motor simulation process that takes place in the context of action observation. The function of the cerebellum as a sequencer during executed movements makes it a good candidate, within the framework of embodied cognition, for a pivotal role in understanding the timing of action sequences. Here, we investigated a cohort of eight patients with chronic, first-ever, isolated, ischemic lesions of the cerebellum. The experimental task consisted in identifying a plausible sequence of pictures from a randomly ordered group of still frames extracted from (a) a complex action performed by a human actor ("biological action" test) or (b) a complex physical event occurring to an inanimate object ("folk physics" test). A group of 16 healthy participants was used as control. The main result showed that cerebellar patients performed significantly worse than controls in both sequencing tasks, but performed much worse in the "biological action" test than in the "folk physics" test. The dissociation described here suggests that observed sequences of simple motor acts seem to be represented differentially from other sequences in the cerebellum.