Passive hand movements disrupt adults' counting strategies

The effect of target detection task on memory encoding varies in different stimulus onset asynchronies

The attentional boost effect (ABE) and action-induced memory enhancement (AIME) suggest that memory performance for target-paired items is superior to that for distractor-paired items when participants performed a target detection task and a memory encoding task simultaneously. Though the memory enhancement has been well established, the temporal dynamics of how the target detection task influenced memory encoding remains unclear. To investigate this, we manipulated the stimulus onset asynchrony (SOA) between detection stimuli and the words to be memorized using a remember/know study-test paradigm, and we focused primarily on memory performance for the words that appeared after the detection response. The results showed that target-paired memory enhancement was robust from SOA = 0 s to SOA = 0.75 s, but was not significant when examined by itself in Experiment 1A or weakened in Experiment 2 and the conjoint analysis when SOA = 1 s, which were only observed in R responses. The post-response memory enhancement still existed when there was no temporal overlap between the word and target, similar to the magnitude of memory enhancement observed with temporal overlap. These results supported the view that target-paired memory enhancement (recollection rather than familiarity) occurred irrespective of whether the items appeared simultaneously with the targets or within a short period after the response, and the temporal overlap of the word and target was not necessary for post-response memory enhancement.

Early Gray Matter Structural Covariance Predicts Longitudinal Gain in Arithmetic Ability in Children

Previous neuroimaging studies on arithmetic development have mainly focused on functional activation or functional connectivity between brain regions. It remains largely unknown how brain structures support arithmetic development. The present study investigated whether early gray matter structural covariance contributes to later gain in arithmetic ability in children. We used a public longitudinal sample comprising 63 typically developing children. The participants received structural magnetic resonance imaging scanning when they were 11 years old and were tested with a multiplication task at 11 years old (time 1) and 13 years old (time 2), respectively. Mean gray matter volumes were extracted from eight brain regions of interest to anchor salience network (SN), frontal-parietal network (FPN), motor network (MN), and default mode network (DMN) at time 1. We found that longitudinal gain in arithmetic ability was associated with stronger structural covariance of the SN seed with frontal and parietal regions and stronger structural covariance of the FPN seed with insula, but weaker structural covariance of the FPN seed with motor and temporal regions, weaker structural covariance of the MN seed with frontal and motor regions, and weaker structural covariance of the DMN seed with temporal region. However, we did not detect correlation between longitudinal gain in arithmetic ability and behavioral measure or regional gray matter volume at time 1. Our study provides novel evidence for a specific contribution of gray matter structural covariance to longitudinal gain in arithmetic ability in childhood.

Fine motor skills and finger gnosia contribute to preschool children's numerical competencies

Facets of fine motor skills (FMS) and finger gnosia have been reported to predict young children's numerical competencies, possibly by affecting early finger counting experiences. Furthermore, neuronal connections between areas involved in finger motor movement, finger gnosia, and numerical processing have been posited. In this study, FMS and finger gnosia were investigated as predictors for preschool children's performance in numerical tasks. Preschool children (N = 153) completed FMS tasks measuring finger agility and finger dexterity as well as a non-motor finger gnosia task. Furthermore, children completed numerical tasks that involved finger use (i.e., finger counting and finger montring), and tasks that did not (i.e., picture-aided calculation and number line estimation). To control for possible confounding influences of domain general skills, we included measures of reasoning and spatial working memory. We found associations between FMS and both finger counting and calculation, but not finger montring. In contrast, finger gnosia was only associated with finger montring, but not finger counting and calculation. Surprisingly, there were no associations between FMS or finger gnosia with number line estimation. Findings highlight that the relationship between finger gnosia, FMS, and numerical skills is specific to task requirements. Possible implications are discussed.

Differences in event-related potential (ERP) responses to small tie, non-tie and 1-problems in addition and multiplication

Using ERP, we investigated the cause of the tie advantage according to which problems with repeated operands are solved faster and more accurately than non-tie problems. We found no differences in early or N400 ERP components between problems, suggesting that tie problems are not encoded faster or suffer from less interference than non-tie problems. However, a lesser negative amplitude of the N2 component was found for tie than non-tie problems. This suggests more working-memory and attentional resource requirements for non-tie problems and therefore more frequent use of retrieval for tie than non-tie problems. The possible peculiarity of problems involving a 1 was also investigated. We showed less negative N2 amplitudes for these problems than for other non-tie problems, suggesting less working-memory resources for 1-problems than other non-tie problems. This could be explained either by higher reliance on memory retrieval for 1-problems than non-1 problems or by the application of non-arithmetical rules for 1-problems.

Effect of Mental Calculation and Number Comparison on a Manual-Pointing Movement

The present study aimed at examining the effect of mental calculation and number comparison on motor performance measured as the movement time of a fast manual-pointing movement. Three experiments, involving a total number of 65 undergraduate subjects, examined the effect of mental subtraction (complex) and, respectively, of (a) mental addition (simple or complex), (b) mental multiplication (simple or complex), and (c) the comparison of dot sets and number comparison. Each number was written in Arabic. The movement times were analyzed by using a multilevel linear mixed-effect model. The results showed significant improvement of manual-pointing movement performance only after the complex calculations and after number comparison. Possible implication of attentional mechanisms specific to this arithmetical activity is further discussed.

Processing of numerical representation of fingers depends on their location in space

Fingers can express quantities and thus contribute to the acquisition and manipulation of numbers as well as the development of arithmetical skills. As embodied entities, the processing of finger numerical configurations should, therefore, be facilitated when they match shared cultural representations and are presented close to the body. To investigate these issues, the present study investigated whether canonical finger configurations are processed faster than noncanonical configurations or spatially matched dot configurations, taking into account their location in the peripersonal or the extrapersonal space. Analysis of verbal responses to the enumeration of small and large numerosities showed that participants (N = 30) processed small numerosities faster than large ones and dots faster than finger configurations despite visuo-spatial matching. Canonical configurations were also processed faster than noncanonical configurations but for finger numerical stimuli only. Furthermore, the difference in response time between dots and fingers processing was greater when the stimuli were located in the peripersonal space than in the extrapersonal space. As a whole, the data suggest that, due to their motor nature, finger numerical configurations are not processed as simple visual stimuli but in relation to corporal and cultural counting habits, in agreement with the embodied framework of numerical cognition.

Embodied numerical representations and their association with multi-digit arithmetic performance

There is a well-documented association between fingers and numbers, which was claimed to stem from the use of finger-based strategies for counting and calculating during childhood. Recently, it has been argued that this may lead to a concomitant activation of finger-based alongside other numerical representations when encountering single-digit numbers. Indeed, the occurrence of such a co-activation is supported by observed influences of finger counting habits on different numerical tasks, including single-digit arithmetic problem solving. In this study, we pursued the question whether the influence of finger-based representations on arithmetic generalizes to multi-digit arithmetic by investigating the association between the recognition of canonical and non-canonical finger patterns and multi-digit arithmetic in adults. Results indicated that canonical finger-based numerical representations were significantly associated with addition performance only, whereas non-canonical finger-based representations were associated significantly with all four arithmetic operations. We argue that, because non-canonical patterns do not benefit from the iconicity of canonical patterns, their magnitude may need to be constructed through magnitude manipulation which may in turn increase associations with mental arithmetic. In sum, our findings provide converging evidence for a functional association between finger-based representations and arithmetic performance.

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.

Finger-counting habits, not finger movements, predict simple arithmetic problem solving

Previous research in embodied mathematical cognition has found differences between those who start counting on their left hand and those who start counting on the right hand. However, if starting hand is a finger-embodied effect, then finger-specific interference may affect these differences between left and right starters. Furthermore, cultures that demonstrate different finger-counting habits may also be differently affected by this interference. In the current study, a total of 66 Canadians and 60 Chinese participants completed a single/dual-task paradigm and were also assessed on their starting hand for counting. The primary task was to verbally answer simple arithmetic problems, while the dual task was to either sequentially tap their fingers or their foot. Contrary to predictions, a specific finger-movement interference pattern that had previously been reported was not evident in this study, despite a much larger sample. Nevertheless, Canadians left starters outperformed right starters for every operation type, which may be further evidence of individual differences in the lateralization of arithmetic processes. Derived from a combination of a replication, a conceptual replication, and a cross-cultural comparison, this investigation suggests that embodied effects in the published literature are in need of both independent replication as well as investigation of individual differences. This study also further validates the differences between left and right starters, and suggests that more research is needed to understand the influence of embodied cognition on mathematical understanding.

Stimulating numbers: signatures of finger counting in numerosity processing

Finger counting is one of the first steps in the development of mature number concepts. With a one-to-one correspondence of fingers to numbers in Western finger counting, fingers hold two numerical meanings: one is based on the number of fingers raised and the second is based on their ordinal position within the habitual finger counting sequence. This study investigated how these two numerical meanings of fingers are intertwined with numerical cognition in adults. Participants received tactile stimulation on their fingertips of one hand and named either the number of fingers stimulated (2, 3, or 4 fingers; Experiment 1) or the number of stimulations on one fingertip (2, 3, or 4 stimulations; Experiment 2). Responses were faster and more accurate when the set of stimulated fingers corresponded to finger counting habits (Experiment 1) and when the number of stimulations matched the ordinal position of the stimulated finger (Experiment 2). These results show that tactile numerosity perception is affected by individual finger counting habits and that those habits give numerical meaning to single fingers.

Intrinsic insula network engagement underlying children's reading and arithmetic skills

The neural substrates of children's reading and arithmetic skills have long been of great interest to cognitive neuroscientists. However, most previous studies have focused on the contrast between these skills as specific domains. Here, we investigate the potentially shared processes across these domains by focusing on how the neural circuits associated with cognitive control influence reading and arithmetic proficiency in 8-to-10-year-old children. Using a task-free resting state approach, we correlated the intrinsic functional connectivity of the right anterior insula (rAI) network with performance on assessments of Chinese character recognition, reading comprehension, subtraction, and multiplication performance. A common rAI network strengthened for reading and arithmetic skill, including the right middle temporal gyrus (MTG) and superior temporal gyrus (STG) in the lateral temporal cortex, as well as the inferior frontal gyrus (IFG). In addition, performance measures evidenced rAI network specializations. Single character recognition was uniquely associated with connectivity to the right superior parietal lobule (SPL). Reading comprehension only, rather than character recognition, was associated with connectivity to the right IFG, MTG and angular gyrus (AG). Furthermore, subtraction was associated with connectivity to premotor cortex whereas multiplication was associated with the supramarginal gyrus. Only reading comprehension and multiplication were associated with hyper connectivity within local rAI network. These results indicate that during a critical period for children's acquisition of reading and arithmetic, these skills are supported by both intra-network synchronization and inter-network connectivity of rAI circuits. Domain-general intrinsic insular connectivity at rest contained also, functional components that segregated into different sets of skill-related networks. The embedded components of cognitive control may be essential to understanding the interplay of multiple functional circuits necessary to more fully characterize cognitive skill acquisition.

The effects of training on tactile enumeration

Subitizing is a fast and accurate process of enumerating small quantities. Whether subitizing carried out in the tactile modality is under debate. We previously found a moderately increasing RT slope from one to four stimuli and a large decrease in RT for five stimuli when using one hand. Yet, a high error rate was observed, making it difficult to determine if the RT pattern found was indeed subitizing. To increase accuracy, we carried out training of the tactile enumeration task using one hand for 6 days. We compared performance in the trained and additional non-trained tasks between two groups-the 6-day training group (6DT) and the non-trained controls (C)-after three periods (1 week, 1 and 6 months after the training of the 6DT group ended). Results showed an increase in accuracy rates for both groups but a decrease in RT for the 6DT group only for the trained task. This RT improvement was present even after 6 months. Importantly, the RT slope of one-hand enumeration did not change after training, showing a moderately increased slope up to four stimuli and a decrease for five stimuli. Our study shows the training long-term effect on tactile enumeration and emphasizes the embodiment of finger counting on enumeration. Two possible enumeration processes are discussed-accelerated counting and subitizing-both based on spatial cues and pattern recognition of familiarized finger-counting patterns.

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.

The role of fingers in the development of counting and arithmetic skills

Interactions between fingers and numbers have been reported in the existing literature on numerical cognition. The aim of the present research was to test whether hand interference movements might have an impact on children performance in counting and basic arithmetic problem solving. In Experiment 1, 5-year-old children had to perform both a one-target and a two-target counting task in three different conditions: with no constraints, while making interfering hand movements or while making interfering foot movements. In Experiment 2, first and fourth graders were required to perform addition problems under the same control and sensori-motor interfering conditions. In both tasks, the hand movements caused more disruption than the foot movements, suggesting that finger-counting plays a functional role in the development of counting and arithmetic.

Random walks on the mental number line

The direction of influence between conceptual and motor activation, and its relevance for real-life activities, is still unclear. Here, we use the frequently reported association between small/large numbers and left/right space to investigate this issue during walking. We asked healthy adults to generate random numbers as they made lateral turns and found that (1) lateral turn decisions are predicted by the last few numbers generated prior to turning; (2) the intention to turn left/right makes small/large numbers more accessible; and (3) magnitude but not order of auditorily presented numbers influences the listener's turn selection. Our findings document a bidirectional influence between conceptual and motor activation and point to a hierarchically organized conceptual-motor activation.

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.

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.

Common substrate for mental arithmetic and finger representation in the parietal cortex

The history of mathematics provides several examples of the use of fingers to count or calculate. These observations converge with developmental data showing that fingers play a critical role in the acquisition of arithmetic knowledge. Further studies evidenced specific interference of finger movements with arithmetic problem solving in adults, raising the question of whether or not finger and number manipulations rely on common brain areas. In the present study, functional magnetic resonance imaging (fMRI) was used to investigate the possible overlap between the brain areas involved in mental arithmetic and those involved in finger discrimination. Solving subtraction and multiplication problems was found to increase cerebral activation bilaterally in the horizontal part of the intraparietal sulcus (hIPS) and in the posterior part of the superior parietal lobule (PSPL). Finger discrimination was associated with increased activity in a bilateral occipito-parieto-precentral network extending from the extrastriate body area to the primary somatosensory and motor cortices. A conjunction analysis showed common areas for mental arithmetic and finger representation in the hIPS and PSPL bilaterally. Voxelwise correlations further showed that finger discrimination and mental arithmetic induced a similar pattern of activity within the parietal areas only. Pattern similarity was more important for the left than for the right hIPS and for subtraction than for multiplication. These findings provide the first evidence that the brain circuits involved in finger representation also underlie arithmetic operations in adults.

The influence of implicit hand-based representations on mental arithmetic

Recently, a strong functional relationship between finger counting and number processing has been suggested. It has been argued that bodily experiences such as finger counting may influence the structure of the basic mental representations of numbers even in adults. However, to date it remains unclear whether the structure of finger counting systems also influences educated adults' performance in mental arithmetic. In the present study, we pursued this question by examining finger-based sub-base-five effects in an addition production task. With the standard effect of a carry operation (i.e., base-10 crossing) being replicated, we observed an additional sub-base-five effect such that crossing a sub-base-five boundary led to a relative response time increase. For the case of mental arithmetic sub-base-five effects have previously been reported only in children. However, it remains unclear whether finger-based numerical effects in mental arithmetic reflect an important but transitory step in the development of arithmetical skills. The current findings suggest that even in adults embodied representations such as finger counting patterns modulate arithmetic performance. Thus, they support the general idea that even seemingly abstract cognition in adults may at least partly be rooted in our bodily experiences.