Learning and development of embodied numerosity

You can count on your fingers: Finger-based intervention improves first-graders' arithmetic learning

The question of whether finger use should be encouraged or discouraged in early mathematics instruction remains a topic of debate. Scientific evidence on this matter is scarce due to the limited number of systematic intervention studies. Accordingly, we conducted an intervention study in which first-graders (Mage = 6.48 years, SD = 0.35) completed a finger-based training (18 sessions of ∼ 30 min each) over the course of the first school year. The training was integrated into standard mathematics instruction in schools and compared with business-as-usual curriculum teaching. At the end of first grade and in a follow-up test 9 months later in second grade, children who received the finger training (n = 119) outperformed the control group (n = 123) in written addition and subtraction. No group differences were observed for number line estimation tasks. These results suggest that finger-based numerical strategies can enhance arithmetic learning, supporting the idea of an embodied representation of numbers, and challenge the prevailing skepticism about finger use in primary mathematics education.

Combining virtual reality and tactile stimulation to investigate embodied finger-based numerical representations

Finger-based representation of numbers is a high-level cognitive strategy to assist numerical and arithmetic processing in children and adults. It is unclear whether this paradigm builds on simple perceptual features or comprises several attributes through embodiment. Here we describe the development and initial testing of an experimental setup to study embodiment during a finger-based numerical task using Virtual Reality (VR) and a low-cost tactile stimulator that is easy to build. Using VR allows us to create new ways to study finger-based numerical representation using a virtual hand that can be manipulated in ways our hand cannot, such as decoupling tactile and visual stimuli. The goal is to present a new methodology that can allow researchers to study embodiment through this new approach, maybe shedding new light on the cognitive strategy behind the finger-based representation of numbers. In this case, a critical methodological requirement is delivering precisely targeted sensory stimuli to specific effectors while simultaneously recording their behavior and engaging the participant in a simulated experience. We tested the device's capability by stimulating users in different experimental configurations. Results indicate that our device delivers reliable tactile stimulation to all fingers of a participant's hand without losing motion tracking quality during an ongoing task. This is reflected by an accuracy of over 95% in participants detecting stimulation of a single finger or multiple fingers in sequential stimulation as indicated by experiments with sixteen participants. We discuss possible application scenarios, explain how to apply our methodology to study the embodiment of finger-based numerical representations and other high-level cognitive functions, and discuss potential further developments of the device based on the data obtained in our testing.

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.

Finger-Based Numerical Training Increases Sensorimotor Activation for Arithmetic in Children—An fNIRS Study

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers.

Mental simulation and its influence on finger-based numerical representations

BACKGROUND

There is evidence indicating beneficial effects of mental simulation on athletic and musical performance. We evaluated whether such beneficial effects of mental simulation generalize to the cognitive domain in terms of embodied (finger-based) numerical representations.

METHODS

We assessed 70 preschoolers (36 girls, mean age 5;9) on tasks assessing different basic numerical skills (e.g., counting, cardinality understanding, number composition, etc.) as well as different aspects of finger-based numerical representations. A subgroub completed a mental simulation phase prior to testing finger-based representations.

RESULTS

Children who completed the mental simulation phase, performed better on the tasks assessing finger-based representations compared to, children who did not complete the simulation phase. This held even when controlling for performance in basic numerical skills.

CONCLUSION

This study provides evidence that beneficial effects of mental simulation generalize to embodied (finger-based) numerical representations. Mental simulation may be useful to integrate in the instruction of basic numerical skills.

A Developmental Embodied Choice Perspective Explains the Development of Numerical Choices

The goal of this paper is to explore how an embodied view can redirect our understanding of decision making. To achieve this goal, we contribute a developmental embodied choice perspective. Our perspective integrates embodiment and bounded rationality from a developmental view in which the body provides cues that are used in abstract choices. Hereby, the cues evolve with the body that is not static and changes through development. To demonstrate the body’s involvement in abstract choices, we will consider choices in numerical settings in which the body is not necessarily needed for the solution. For this, we consider the magnitude-judgment task in which one has to choose the larger of two magnitudes. In a nutshell, our perspective will pinpoint how the concept of embodied choices can explain the development of numerical choices.

[Effectiveness of a Manual Dexterity Training in German Kindergarten]

Effectiveness of a Manual Dexterity Training in German Kindergarten The present study examines effects of a manual dexterity training with cup stacking/speed stacking exercises for children in the last year of German kindergarten. Between pre- and posttest, nine trainings sessions were conducted within two weeks. The training group consisted of N = 20 children, the waiting control group of N = 17 children. Pre- and posttest consisted of the manual dexterity scale of the Movement ABC-2 (Petermann, 2011). Compared to the control group, the training group showed significantly lower pretest scores but higher posttest scores. Results were discussed in the light of need for replications. The importance of early prevention and intervention of motor coordination problems is highlighted.

Effect of Finger Gnosis on Young Chinese Children's Addition Skills

Evidence has revealed an association between finger gnosis and arithmetic skills in young Western children, however, it is unknown whether such an association can be generalized to Chinese children and what mechanism may underlie this relationship. This study examines whether finger gnosis is associated with addition skills in young Chinese children and, if so, what numerical skills could explain this correlation. A total of 102 Chinese children aged 5–6 years were asked to complete finger gnosis and addition tasks in Study 1. Results showed that finger gnosis was significantly associated with addition performance. However, no significant correlation was found between finger gnosis and the use of finger counting in solving addition problems. Moreover, girls’ finger gnosis was better than boys’, and children with musical training demonstrated better finger gnosis than those without. In Study 2, 16 children with high finger gnosis and 20 children with low finger gnosis were selected from the children in Study 1 and asked to perform enumeration, order judgment, number sense, and number line estimation. Children with high finger gnosis performed better in number line estimation than their counterparts with low finger gnosis. Moreover, the number line estimation fully mediated the relationship between finger gnosis and addition performance. Together, these studies provide evidence of a correlation between finger gnosis and addition skills. They also highlight the importance of number line estimation in bridging this association.

Mechanisms for the Approach/Avoidance Decision Applied to Autism

As a neurodevelopmental disorder with serious lifelong consequences, autism has received considerable attention from neuroscientists and geneticists. We present a hypothesis of mechanisms plausibly affected during brain development in autism, based on neural pathways that are associated with social behavior and connect the prefrontal cortex (PFC) to the basal ganglia (BG). We consider failure of social approach in autism as a special case of imbalance in the fundamental dichotomy between behavioral approach and avoidance. Differential combinations of genes mutated, differences in the timing of their impact during development, and graded degrees of hormonal influences may help explain the heterogeneity in symptomatology in autism and predominance in boys.

Executive Functions and Fine Motor Skills in Kindergarten as Predictors of Arithmetic Skills in Elementary School

The present longitudinal study focused on domain-general predictors of arithmetics in elementary school. The role of executive functions (EFs) and fine motor skills for the prediction of arithmetic skills in 1st/2nd grade was examined. Data from N = 173 kindergarten children were included. Age, socioeconomic status, fluid intelligence, and processing speed were controlled. Regression analyses revealed that fine motor skills predicted arithmetic skills. When EFs were added, fine motor skills did not contribute to the prediction of arithmetic skills. Visuospatial working memory and interference control were significant predictors. Findings indicate an important role of EF as predictors of arithmetic skills.

Tactile Enumeration and Embodied Numerosity Among the Deaf

Representations of the fingers are embodied in our cognition and influence performance in enumeration tasks. Among deaf signers, the fingers also serve as a tool for communication in sign language. Previous studies in normal hearing (NH) participants showed effects of embodiment (i.e., embodied numerosity) on tactile enumeration using the fingers of one hand. In this research, we examined the influence of extensive visuo-manual use on tactile enumeration among the deaf. We carried out four enumeration task experiments, using 1-5 stimuli, on a profoundly deaf group (n = 16) and a matching NH group (n = 15): (a) tactile enumeration using one hand, (b) tactile enumeration using two hands, (c) visual enumeration of finger signs, and (d) visual enumeration of dots. In the tactile tasks, we found salient embodied effects in the deaf group compared to the NH group. In the visual enumeration of finger signs task, we controlled the meanings of the stimuli presentation type (e.g., finger-counting habit, fingerspelled letters, both or neither). Interestingly, when comparing fingerspelled letters to neutrals (i.e., not letters or numerical finger-counting signs), an inhibition pattern was observed among the deaf. The findings uncover the influence of rich visuo-manual experiences and language on embodied representations. In addition, we propose that these influences can partially account for the lag in mathematical competencies in the deaf compared to NH peers. Lastly, we further discuss how our findings support a contemporary model for mental numerical representations and finger-counting habits.

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.

A Finger-Based Numerical Training Failed to Improve Arithmetic Skills in Kindergarten Children Beyond Effects of an Active Non-numerical Control Training

It is widely accepted that finger and number representations are associated: many correlations (including longitudinal ones) between finger gnosis/counting and numerical/arithmetical abilities have been reported. However, such correlations do not necessarily imply causal influence of early finger-number training; even in longitudinal designs, mediating variables may be underlying such correlations. Therefore, we investigated whether there may be a causal relation by means of an extensive experimental intervention in which the impact of finger-number training on initial arithmetic skills was tested in kindergarteners to see whether they benefit from the intervention even before they start formal schooling. The experimental group received 50 training sessions altogether for 10 weeks on a daily basis. A control group received phonology training of a similar duration and intensity. All children improved in the arithmetic tasks. To our surprise and contrary to most accounts in the literature, the improvement shown by the experimental training group was not superior to that of the active control group. We discuss conceptual and methodological reasons why the finger-number training employed in this study did not increase the initial arithmetic skills beyond the unspecific effects of the control intervention.

Functional lateralization of arithmetic processing in the intraparietal sulcus is associated with handedness

Functional lateralization is established for various cognitive functions, but was hardly ever investigated for arithmetic processing. Most neurocognitive models assume a central role of the bilateral intraparietal sulcus (IPS) in arithmetic processing and there is some evidence for more pronounced left-hemispheric activation for symbolic arithmetic. However, evidence was mainly obtained by studies in right-handers. Therefore, we conducted a functional near-infrared spectroscopy (fNIRS) study, in which IPS activation of left-handed adults was compared to right-handed adults in a symbolic approximate calculation task. The results showed that left-handers had a stronger functional right-lateralization in the IPS than right-handers. This finding has important consequences, as the bilateral IPS activation pattern for arithmetic processing seems to be shaped by functional lateralization and thus differs between left- and right-handers. We propose three possible accounts for the observed functional lateralization of arithmetic processing.

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.

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.

Spatial Presentations, but Not Response Formats Influence Spatial-Numerical Associations in Adults

According to theories of embodied numerosity, processing of numerical magnitude is anchored in bodily experiences. In particular, spatial representations of number interact with movement in physical space, but it is still unclear whether the extent of the movement is relevant for this interaction. In this study, we compared spatial-numerical associations over response movements of differing spatial expansion. We expected spatial-numerical effects to increase with the extent of physical response movements. In addition, we hypothesized that these effects should be influenced by whether or not a spatial representation of numbers was presented. Adult participants performed two tasks: a magnitude classification (comparing numbers to the fixed standard 5), from which we calculated the Spatial Numerical Association of Response Codes (SNARC) effect; and a magnitude comparison task (comparing two numbers against each other), from which we calculated a relative numerical congruity effect (NCE), which describes that when two relatively small numbers are compared, responses to the smaller number are faster than responses to the larger number; and vice versa for large numbers. A SNARC effect was observed across all conditions and was not influenced by response movement extent but increased when a number line was presented. In contrast, an NCE was only observed when no number line was presented. This suggests that the SNARC effect and the NCE reflect two different processes. The SNARC effect seems to represent a highly automated classification of numbers as large or small, which is further emphasized by the presentation of a number line. In contrast, the NCE likely results from participants not only classifying numbers as small or large, but also processing their relative size within the relevant section of their mental number line representation. An additional external presentation of a number line might interfere with this process, resulting in overall slower responses. This study follows up on previous spatial-numerical training studies and has implications for future spatial-numerical trainings. Specifically, similar studies with children showed contrasting results, in that response format but not number line presentation influenced spatial-numerical associations. Accordingly, during development, the relative relevance of physical experiences and presentation format for spatial-numerical associations might change.

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.

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.

Counting on fine motor skills: links between preschool finger dexterity and numerical skills

Finger counting is widely considered an important step in children's early mathematical development. Presumably, children's ability to move their fingers during early counting experiences to aid number representation depends in part on their early fine motor skills (FMS). Specifically, FMS should link to children's procedural counting skills through consistent repetition of finger-counting procedures. Accordingly, we hypothesized that (a) FMS are linked to early counting skills, and (b) greater FMS relate to conceptual counting knowledge (e.g., cardinality, abstraction, order irrelevance) via procedural counting skills (i.e., one-one correspondence and correctness of verbal counting). Preschool children (N = 177) were administered measures of procedural counting skills, conceptual counting knowledge, FMS, and general cognitive skills along with parent questionnaires on home mathematics and fine motor environment. FMS correlated with procedural counting skills and conceptual counting knowledge after controlling for cognitive skills, chronological age, home mathematics and FMS environments. Moreover, the relationship between FMS and conceptual counting knowledge was mediated by procedural counting skills. Findings suggest that FMS play a role in early counting and therewith conceptual counting knowledge.

Finger-Based Numerical Skills Link Fine Motor Skills to Numerical Development in Preschoolers

Previous studies investigating the association between fine-motor skills (FMS) and mathematical skills have lacked specificity. In this study, we test whether an FMS link to numerical skills is due to the involvement of finger representations in early mathematics. We gave 81 pre-schoolers (mean age of 4 years, 9 months) a set of FMS measures and numerical tasks with and without a specific finger focus. Additionally, we used receptive vocabulary and chronological age as control measures. FMS linked more closely to finger-based than to nonfinger-based numerical skills even after accounting for the control variables. Moreover, the relationship between FMS and numerical skill was entirely mediated by finger-based numerical skills. We concluded that FMS are closely related to early numerical skill development through finger-based numerical counting that aids the acquisition of mathematical mental representations.

Act on Numbers: Numerical Magnitude Influences Selection and Kinematics of Finger Movement

In the past decade hand kinematics has been reliably adopted for investigating cognitive processes and disentangling debated topics. One of the most controversial issues in numerical cognition literature regards the origin - cultural vs. genetically driven - of the mental number line (MNL), oriented from left (small numbers) to right (large numbers). To date, the majority of studies have investigated this effect by means of response times, whereas studies considering more culturally unbiased measures such as kinematic parameters are rare. Here, we present a new paradigm that combines a "free response" task with the kinematic analysis of movement. Participants were seated in front of two little soccer goals placed on a table, one on the left and one on the right side. They were presented with left- or right-directed arrows and they were instructed to kick a small ball with their right index toward the goal indicated by the arrow. In a few test trials participants were presented also with a small (2) or a large (8) number, and they were allowed to choose the kicking direction. Participants performed more left responses with the small number and more right responses with the large number. The whole kicking movement was segmented in two temporal phases in order to make a hand kinematics' fine-grained analysis. The Kick Preparation and Kick Finalization phases were selected on the basis of peak trajectory deviation from the virtual midline between the two goals. Results show an effect of both small and large numbers on action execution timing. Participants were faster to finalize the action when responding to small numbers toward the left and to large number toward the right. Here, we provide the first experimental demonstration which highlights how numerical processing affects action execution in a new and not-overlearned context. The employment of this innovative and unbiased paradigm will permit to disentangle the role of nature and culture in shaping the direction of MNL and the role of finger in the acquisition of numerical skills. Last but not least, similar paradigms will allow to determine how cognition can influence action execution.

Counting on the mental number line to make a move: sensorimotor ('pen') control and numerical processing

Mathematics is often conducted with a writing implement. But is there a relationship between numerical processing and sensorimotor 'pen' control? We asked participants to move a stylus so it crossed an unmarked line at a location specified by a symbolic number (1-9), where number colour indicated whether the line ran left-right ('normal') or vice versa ('reversed'). The task could be simplified through the use of a 'mental number line' (MNL). Many modern societies use number lines in mathematical education and the brain's representation of number appears to follow a culturally determined spatial organisation (so better task performance is associated with this culturally normal orientation-the MNL effect). Participants (counter-balanced) completed two consistent blocks of trials, 'normal' and 'reversed', followed by a mixed block where line direction varied randomly. Experiment 1 established that the MNL effect was robust, and showed that the cognitive load associated with reversing the MNL not only affected response selection but also the actual movement execution (indexed by duration) within the mixed trials. Experiment 2 showed that an individual's motor abilities predicted performance in the difficult (mixed) condition but not the easier blocks. These results suggest that numerical processing is not isolated from motor capabilities-a finding with applied consequences.

Transcranial random noise stimulation and cognitive training to improve learning and cognition of the atypically developing brain: A pilot study

Learning disabilities that affect about 10% of human population are linked to atypical neurodevelopment, but predominantly treated by behavioural interventions. Behavioural interventions alone have shown little efficacy, indicating limited success in modulating neuroplasticity, especially in brains with neural atypicalities. Even in healthy adults, weeks of cognitive training alone led to inconsistent generalisable training gains, or "transfer effects" to non-trained materials. Meanwhile, transcranial random noise stimulation (tRNS), a painless and more direct neuromodulation method was shown to further promote cognitive training and transfer effects in healthy adults without harmful effects. It is unknown whether tRNS on the atypically developing brain might promote greater learning and transfer outcomes than training alone. Here, we show that tRNS over the bilateral dorsolateral prefrontal cortices (dlPFCs) improved learning and performance of children with mathematical learning disabilities (MLD) during arithmetic training compared to those who received sham (placebo) tRNS. Training gains correlated positively with improvement on a standardized mathematical diagnostic test, and this effect was strengthened by tRNS. These findings mirror those in healthy adults, and encourage replications using larger cohorts. Overall, this study offers insights into the concept of combining tRNS and cognitive training for improving learning and cognition of children with learning disabilities.

Think3d!: Improving mathematics learning through embodied spatial training

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students’ spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains – specifically for problem types expected to show gains from spatial training – and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.

Support of mathematical thinking through embodied cognition: Nondigital and digital approaches

Research on mathematics education has shown that learners’ actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical thinking. This is especially crucial given the increasing accessibility of technology—such as digital touch devices, 3D printers, and location sensors—for constructing embodied experiences. Providing guidance for incorporating those tools, we focus on the role that embodied cognition can play in communicating mathematical concepts as well as in allowing learners to experiment and evolve their ideas. To inspire future integration of theory in the development of technologically enhanced embodied mathematics experiences, we provide examples of how this can be done. Finally, we outline future directions in the areas of design, implementation, and assessment of embodied learning of mathematics.

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 gnosis predicts a unique but small part of variance in initial arithmetic performance

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes.

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.

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.

Mathematics anxiety reduces default mode network deactivation in response to numerical tasks

Mathematics anxiety is negatively related to mathematics performance, thereby threatening the professional success. Preoccupation with the emotional content of the stimuli may consume working memory resources, which may be reflected in decreased deactivation of areas associated with the default mode network (DMN) activated during self-referential and emotional processing. The common problem is that math anxiety is usually associated with poor math performance, so that any group differences are difficult to interpret. Here we compared the BOLD-response of 18 participants with high (HMAs) and 18 participants with low mathematics anxiety (LMAs) matched for their mathematical performance to two numerical tasks (number comparison, number bisection). During both tasks, we found stronger deactivation within the DMN in LMAs compared to HMAs, while BOLD-response in task-related activation areas did not differ between HMAs and LMAs. The difference in DMN deactivation between the HMA and LMA group was more pronounced in stimuli with additional requirement on inhibitory functions, but did not differ between number magnitude processing and arithmetic fact retrieval.

How space-number associations may be created in preliterate children: six distinct mechanisms

The directionality of space-number association (SNA) is shaped by cultural experiences. It usually follows the culturally dominant reading direction. Smaller numbers are generally associated with the starting side for reading (left side in Western cultures), while larger numbers are associated with the right endpoint side. However, SNAs consistent with cultural reading directions are present before children can actually read and write. Therefore, these SNAs cannot only be shaped by the direction of children’s own reading/writing behavior. We propose six distinct processes – one biological and five cultural/educational – underlying directional SNAs before formal reading acquisition: (i) Brain lateralization, (ii) Monitoring adult reading behavior, (iii) Pretend reading and writing, and rudimentary reading and writing skills, (iv) Dominant attentional directional preferences in a society, not directly related to reading direction, (v) Direct spatial-numerical learning, (vi) Other spatial-directional processes independent of reading direction. In this mini-review, we will differentiate between these processes, elaborate when in development they might emerge, discuss how they may create the SNAs observed in preliterate children and propose how they can be studied in the future.

Considering digits in a current model of numerical development

Numerical cognition has long been considered the perfect example of abstract information processing. Nevertheless, there is accumulating evidence in recent years suggesting that the representation of number magnitude may not be entirely abstract but may present a specific case of embodied cognition rooted in the sensory and bodily experiences of early finger counting and calculating. However, so far none of the existing models of numerical development considers the influence of finger-based representations. Therefore, we make first suggestions on (i) how finger-based representations may be integrated into a current model of numerical development; and (ii) how they might corroborate the acquisition of basic numerical competencies at different development levels.

Developmental dyscalculia

Numerical skills are essential in our everyday life, and impairments in the development of number processing and calculation have a negative impact on schooling and professional careers. Approximately 3 to 6 % of children are affected from specific disorders of numerical understanding (developmental dyscalculia (DD)). Impaired development of number processing skills in these children is characterized by problems in various aspects of numeracy as well as alterations of brain activation and brain structure. Moreover, DD is assumed to be a very heterogeneous disorder putting special challenges to define homogeneous diagnostic criteria. Finally, interdisciplinary perspectives from psychology, neuroscience and education can contribute to the design for interventions, and although results are still sparse, they are promising and have shown positive effects on behaviour as well as brain function.

CONCLUSION

In the current review, we are going to give an overview about typical and atypical development of numerical abilities at the behavioural and neuronal level. Furthermore, current status and obstacles in the definition and diagnostics of DD are discussed, and finally, relevant points that should be considered to make an intervention as successful as possible are summarized.

Walking boosts your performance in making additions and subtractions

Previous research demonstrates that the processing of spatial information and numerical magnitude are strictly interwoven. Recent studies also provide converging evidence that number processing is influenced by body movements. In the present study we further investigate this issue by focusing on whether and how motions experienced with the whole body can influence arithmetical calculations. We asked participants to make additions or subtractions while experiencing leftward and rightward motions. Data revealed the emergence of a congruency effect between the orientation inferred by the type of arithmetical calculations and the type of motions experienced along an horizontal axis.

Making fingers and words count in a cognitive robot

Evidence from developmental as well as neuroscientific studies suggest that finger counting activity plays an important role in the acquisition of numerical skills in children. It has been claimed that this skill helps in building motor-based representations of number that continue to influence number processing well into adulthood, facilitating the emergence of number concepts from sensorimotor experience through a bottom-up process. The act of counting also involves the acquisition and use of a verbal number system of which number words are the basic building blocks. Using a Cognitive Developmental Robotics paradigm we present results of a modeling experiment on whether finger counting and the association of number words (or tags) to fingers, could serve to bootstrap the representation of number in a cognitive robot, enabling it to perform basic numerical operations such as addition. The cognitive architecture of the robot is based on artificial neural networks, which enable the robot to learn both sensorimotor skills (finger counting) and linguistic skills (using number words). The results obtained in our experiments show that learning the number words in sequence along with finger configurations helps the fast building of the initial representation of number in the robot. Number knowledge, is instead, not as efficiently developed when number words are learned out of sequence without finger counting. Furthermore, the internal representations of the finger configurations themselves, developed by the robot as a result of the experiments, sustain the execution of basic arithmetic operations, something consistent with evidence coming from developmental research with children. The model and experiments demonstrate the importance of sensorimotor skill learning in robots for the acquisition of abstract knowledge such as numbers.

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.

The role of fingers in number processing in young children

The aim of the present study was to investigate the relationship between finger counting and numerical processing in 4-7-year-old children. Children were assessed on a variety of numerical tasks and we examined the correlations between their rates of success and their frequency of finger use in a counting task. We showed that children's performance on finger pattern comparison and identification tasks did not correlate with the frequency of finger use. However, this last variable correlated with the percentages of correct responses in an enumeration task (i.e., Give-N task), even when the age of children was entered as a covariate in the analysis. Despite this correlation, we showed that some children who never used their fingers in the counting task were able to perform optimally in the enumeration task. Overall, our results support the conclusion that finger counting is useful but not necessary to develop accurate symbolic numerical skills. Moreover, our results suggest that the use of fingers in a counting task is related to the ability of children in a dynamic enumeration task but not to static tasks involving recognition or comparison of finger patterns. Therefore, it could be that the link between fingers and numbers remain circumscribed to counting tasks and do not extent to static finger montring situations.