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.


Introduction
Children typically use their fingers when learning to count, understand numerical magnitudes, and calculate (e.g., [1]). This close association of fingers and numbers during early numerical development is reflected in finger-based strategies observed for counting, magnitude understanding including part-whole-relations, as well as arithmetic (for reviews see [2][3][4]).
As regards the working mechanism for finger-based numerical representations, it may not be accidental that our ten fingers reflect a base of 10, on which the place-value structure of the Arabic number system is built. The subdivision into five fingers on each hand adds a structural subbase-5 to finger-based numerical representations which allows to specifically evaluate finger-based numerical representations, particularly in the context of arithmetic performance. For instance, Domahs et al. [5] observed that children committed In the present study, we set out to investigate neural associations of fingers with number processing in children following a finger-based intervention. We pursued the idea that if children are intensively trained on using their fingers systematically for counting and calculations, this should facilitate the development of finger-based numerical representations. The finger-based intervention trained the systematic use of fingers for counting and initial calculation over the course of first grade [22]. We evaluated the neural correlates of mental arithmetic after this finger-based intervention in children, with a specific focus on activation in the sensorimotor cortex and the IPS, because these areas-but not frontal areas [12,23]-have been previously found to be associated with finger-based numerical representations. Specifically, we explored whether trained children differed in their sensorimotor and IPS activation for single-digit arithmetic from control children who did not complete the training by focusing on the subbase-5 effect in single-digit addition. To assess brain activation after the intervention, functional near-infrared spectroscopy (fNIRS) was used, since it tolerates movements, allows for an upright body position, can be applied in natural settings, and thus is appropriate for children [24].

Participants
A total of 46 children were recruited from the experimental and control groups of a large-scale finger-based intervention study [22], in which children were trained in finger-based numerical representations (i.e., systematic use of fingers for counting and initial calculation) during their math instruction in first grade. All participants were right-handed (except for two children), with no history of neurological or mental disorders, and without a disease that influences brain metabolism. Two children did not participate in the study due to technical problems (n = 1) or withdrawal from participation (n = 1). The intervention group (N = 22; 12 boys, 10 girls; age: M = 7;6 years, SD = 4.0 months, Range = [6;11-8;4] years) was assessed at the end of grade 1 after the intervention, while the control group (N = 22; 9 boys, 13 girls; age: M = 7;10 years, SD = 5.8 months, Range = [7;1-8;10] years) was assessed seven months later due to organizational constraints, when children already attended second grade. (Please note that information on age is missing for two children in the control group; they attended the same grade and thus have approximately a similar age.) Written informed consent was provided by the children's parents or legal guardians, and oral assent was obtained from all children prior to testing. The study was approved by the local ethics committee of the Medical Faculty of the University of Tuebingen (620/2012BO2).

Finger-Based Intervention
Based on the model of Roesch and Moeller [3], (i) basic numerical skills (e.g., exact number word sequence combined with basic counting), (ii) quantity-number concept (e.g., finger pattern reflects specific cardinality of the counted set), and (iii) number relations (e.g., number composition, comparison, calculation) were trained. Additionally, finger gnosis was strengthened. The finger-based training included different tasks and mini-games, whereby a special focus was to instruct children to use their fingers in a consistent and systematic way. The finger-based intervention was targeted at number relations, including addition and subtraction procedures. A total of 18 training sessions of about 30 min each were administered by the experimenters over the duration of the first school year during regular school lessons for trained children. Control children attended the regular math curriculum in school without a special focus on the use of fingers. In the intervention study, all children in a classroom were assigned to either the training or the control group in a quasi-experimental manner based on the willingness of teachers to participate in the finger-based training.

Experimental Task
All computerized tasks were programmed in Presentation (NeuroBehavioral Systems, Inc., Berkeley, CA, USA). The stimuli were presented in the center of the screen using white font against a black background (font size of 100). Instructions emphasized both speed and accuracy. Responses were noted by the experimenter and reaction times (RT) were recorded by voice key or button press. The addition task consisted of 40 single-digit addition problems. Each item consisted of two single-digit operands with a single-digit result ranging from 3 to 9. Half of the items did not require a subbase-5 carry operation (e.g., 3 + 1; 6 + 2), so that they could be solved within the same hand from a finger counting perspective. The other half did require a subbase-5 carry operation (e.g., 4 + 3; 1 + 8), so that their solution would require crossing from one hand to the other when applying a finger-based approach. The numerical size of the result (problem size) was matched between conditions. Numbers 5 and 10 were not used as either operands or results [6]. In an event-related design (see Figure 1A), the stimuli were presented in Arabic notation in random order for 4 s, followed by an interstimulus-interval of 4-7 s (jittered in steps of 0.150 s, mean of 5.5 s). Participants solved the addition problems by mental calculation and responded orally by saying "is [number]". the regular math curriculum in school without a special focus on the use of fingers. In the intervention study, all children in a classroom were assigned to either the training or the control group in a quasi-experimental manner based on the willingness of teachers to participate in the finger-based training.
Before the intervention, the intervention and control group did not significantly differ in finger gnosis, t(40) = −0.59, p = 0.561. Furthermore, the groups did not significantly differ in their early numerical abilities as assessed by a standardized math test administered at the beginning of first grade (i.e., four subtests on ordinality, symbolicnonsymbolic mapping, nonsymbolic set comparison, and symbolic magnitude comparison of the ERT 0+, Eggenberger Rechentest 0+ [25]), F(1, 37) = 2.83, p = 0.101. Additionally, there were no significant group differences in custom built tasks on addition, F(1, 37) = 2.45, p = 0.126, subtraction, F(1, 37) = 0.004, p = 0.949, number line estimation from 0 to 10, F(1, 37) = 0.038, p = 0.846, or number line estimation from 0 to 20, F(1, 37) < 0.001, p = 0.988. All comparisons of numerical abilities controlled for influences of general cognitive abilities (i.e., two subtests on continuing rows and matrices of the CFT 1-R, Culture Fair Intelligence Test-Revised [26]). Note that for some children pretest data was missing (n = 2 for finger gnosis and n = 4 for numerical and/or general cognitive abilities).

Experimental Task
All computerized tasks were programmed in Presentation (NeuroBehavioral Systems, Inc., Berkeley, CA, USA). The stimuli were presented in the center of the screen using white font against a black background (font size of 100). Instructions emphasized both speed and accuracy. Responses were noted by the experimenter and reaction times (RT) were recorded by voice key or button press. The addition task consisted of 40 single-digit addition problems. Each item consisted of two single-digit operands with a single-digit result ranging from 3 to 9. Half of the items did not require a subbase-5 carry operation (e.g., 3 + 1; 6 + 2), so that they could be solved within the same hand from a finger counting perspective. The other half did require a subbase-5 carry operation (e.g., 4 + 3; 1 + 8), so that their solution would require crossing from one hand to the other when applying a finger-based approach. The numerical size of the result (problem size) was matched between conditions. Numbers 5 and 10 were not used as either operands or results [6]. In an event-related design (see Figure 1A), the stimuli were presented in Arabic notation in random order for 4 s, followed by an inter-stimulus-interval of 4-7 s (jittered in steps of 0.150 s, mean of 5.5 s). Participants solved the addition problems by mental calculation and responded orally by saying "is [number]".

Procedure
After the finger-based intervention, trained and control children were tested individually in a dimly lit separate room in their school during regular school hours. At the beginning, instructions for all tasks and two practice items per task were provided. During Brain Sci. 2022, 12, 637 5 of 13 the fNIRS measurement, three numerical tasks related to finger counting were conducted: the addition task, the number partner task, and a (non-) symbolic number magnitude comparison task. The focus of the present study is on the addition task because it was conducted with an event-related design leading to a better signal-to-noise ratio as compared to the other tasks with a block design. The results of the number partner task are reported in the Supplementary Material. The number comparison was not analyzed, since it was too difficult for the children. Task order was counterbalanced across participants. All measurements were jointly performed by two experimenters, one responsible for monitoring the fNIRS measurement and the other for instructing participants and documenting their responses.

fNIRS Data Acquisition
The fNIRS data was measured using the continuous wave ETG-4000 Optical Topography System (Hitachi Medical Corporation, Tokyo, Japan). This system uses wavelengths of 695 ± 20 nm and 830 ± 20 nm as light sources and continuously measures data at a sampling rate of 10 Hz. The optodes (16 sources, 14 detectors) were arranged in two 3 × 5 arrays with a fixed inter-optode distance of 30 mm covering the left and right hemisphere, respectively, embedded in a cap (Brain Products GmbH, Herrsching, Germany). The probesets were localized at P3/P4 for the upper channels in the back and oriented towards F3/F4 for this channel row according to the 10-20 system (see Figure 1B); for more details on the location about the probeset, see [27]. The correspondence of fNIRS channels to the underlying cortical areas was estimated based on a virtual registration method [28][29][30].

Data Analysis
Data exclusion. In the addition task, participants were excluded due to drop out from all analysis (n = 1), and due to missing data from behavioral data analysis (n = 2) or RT analysis only (n = 2). For the RT analysis, RTs of incorrectly solved trials, missing RTs, RTs below 200 ms, and RTs deviating more than three median absolute deviations from the participant's median were excluded. The same trials were excluded from the fNIRS analysis since the addition task followed an event-related design.
fNIRS data preprocessing. fNIRS data were analyzed with custom MATLAB (The MathWorks, Inc., Natick, MA, USA) scripts. Relative concentration changes of oxygenated (O 2 Hb) and deoxygenated hemoglobin (HHb) were calculated for each fNIRS channel according to the modified Beer-Lambert law. The fNIRS signal was preprocessed by using the temporal derivative distribution repair (TDDR) [31] to correct for high-amplitude motion artifacts and by applying a bandpass filter of 0.01-0.5 Hz. The correlation-based signal improvement (CBSI) [32] was used to reduce low-amplitude motion artifacts; CBSI is based on the negative correlation between O 2 Hb and HHb and considered as one of the best artifact correction methods [33]. CBSI was necessary since the signal of the relatively young children in this study was quite noisy due to movement artifacts. The remaining noisy channels were interpolated by surrounding channels (13.22% in the addition task). In the addition task, trials that were excluded from the RT analysis (13.60%) as well as trials containing uncorrectable artifacts (1.89%) were further excluded from analysis. The eventrelated fNIRS data of the addition task was analyzed in a model-based approach. Based on the standard hemodynamic response function, a general linear model was computed for each channel, participant, and condition.
Two regions of interest (ROIs) were defined for either hemisphere: the sensorimotor cortex and the areas around the IPS (see Figure 1B; cf. Figure 1 in [27]). The sensorimotor cortex (consisting of the primary somatosensory cortex, primary motor cortex, pre-motor cortex, and supplementary motor cortex) was chosen to reflect the finger localizer in the study of Tschentscher et al. [15] and is represented by the channel 16  Statistical data analysis. Statistical analyses were conducted using JASP (Jeffreys's Amazing Statistics Program, Version 0.13.1, JASP Team, 2016). The behavioral data of the addition task was analyzed using ANOVAs discerning the factors group (trained vs. control children) and carry 5 (without vs. with) for both RT and accuracy. For the fNIRS data, ANOVAs were conducted for each ROI (sensorimotor cortex and IPS) discerning the factors group (trained vs. control children), carry 5 (without vs. with), and hemisphere (left vs. right). Post-hoc tests were added when necessary. As this study was exploratory with open hypotheses, we did not apply statistical corrections for multiple comparisons. Nevertheless, we focused on only two ROIs rather than evaluating brain activation through all channels of the fNIRS probeset. Violin and bar plots were created using the R package ggplot2 [34].

Behavioral Data
The RT analysis revealed a significant main effect of carry 5, F(1, 37) = 16.28, p < 0.001, η 2 p = 0.306, that was qualified by a significant interaction of group and carry 5, F(1, 37) = 8.67, p = 0.006, η 2 p = 0.190 (see Figure 2). The subbase-5 effect, reflecting that the children solved addition problems without carry 5 faster than addition problems with carry 5, was more pronounced in trained children than control children, t(37)  Statistical data analysis. Statistical analyses were conducted using JA Amazing Statistics Program, Version 0.13.1, JASP Team, 2016). The behavio addition task was analyzed using ANOVAs discerning the factors group control children) and carry 5 (without vs. with) for both RT and accuracy. F The analysis of accuracy revealed a significant main effect of carry 5, F(1, 39) = 9.90, p = 0.003, η 2 p = 0.202, indicating that children solved addition problems without carry 5 more accurately than addition problems with carry 5. Neither the main effect of group, F(1, 39) = 0.433, p = 0.514, η 2 p = 0.011, nor the interaction of group and carry 5 were significant, F(1, 39) = 2.05, p = 0.161, η 2 p = 0.050.

Discussion
This study set off to explore the neural signature of finger-based numerical representations by comparing neural activation in the sensorimotor cortex and IPS during arithmetic between children who completed a finger-based intervention and a control

Discussion
This study set off to explore the neural signature of finger-based numerical representations by comparing neural activation in the sensorimotor cortex and IPS during arithmetic between children who completed a finger-based intervention and a control group. Differences due to the finger-based intervention were found in the sensorimotor cortex with a different lateralization of the subbase-5 effect in mental addition. Importantly, this was observed in the absence of overt finger movements. Activation differences in the IPS between trained and control children were less conclusive.
Activation associated with the subbase-5 effect showed a different lateralization in the sensorimotor cortex of children after the finger-based intervention as compared to control children. While the subbase-5 effect was more pronounced in the right sensorimotor cortex in trained children, it was also found in the left sensorimotor cortex in control children. The right-lateralized activation in the sensorimotor cortex, which is typically associated with finger and hand movements, was observed during addition in trained children and thus seems to be an intervention effect: Over the course of their first school year, children were trained in using their fingers for counting and initial arithmetic with their dominant hand for small numbers up to five and with both hands for larger numbers. Since most children participating in the study were right-handed, they would have started with their right hand and used their left hand when crossing the 5 boundary (for evidence that free counting mostly starts with the preferred hand in children see [35], in adults see [36]). In turn, this may have led to more contralateral (right-hemispheric) activation in the sensorimotor cortex when contrasting addition with vs. without crossing the 5 boundary (for contralateral activation depending on the hand to start finger counting in adults see also [15]). While all addition problems that require subbase-5 carries have results above 5 (i.e., using the second hand additionally to the first hand, which is the left hand in right starters), addition problems that do not require subbase-5 carries equally consist of both problems calculated within the second hand (e.g., 6 + 3) and problems calculated within the first hand (e.g., 1 + 3). Although this is necessary to avoid confounds of carry with problem size, it may add some noise to the data as concerns activation of the second hand in finger-number representations: The second hand may be activated in 100% of the addition problems with crossing the subbase-5 boundary, but also in 50% of the other addition problems.
Nevertheless, we found more pronounced right sensorimotor activation in the absence of overt finger movements during single-digit arithmetic for trained children as compared to control children. We suggest that this might reflect traces of the finger-based intervention, which was designed to strengthen the association between fingers and numbers. The significant effects on lateralization, depending on whether the left or right hand is predominantly involved in the respective finger movements, was observed for the sensorimotor cortex (not for the parietal cortex), which is in line with previous findings in adults [12,15]. As such, these data allow for the generalization of such lateralization signatures to children who were trained to use their fingers for counting and initial calculations. In sum, the observed activation pattern in the sensorimotor cortex during mental arithmetic seems to reflect strengthened embodied numerical representations after a finger-based intervention. Whether or not these embodied representations facilitate arithmetic processing is a question for future research.
Besides finger-related sensorimotor activation, a neural overlap for fingers and numbers was previously also reported for the IPS in adults [12] and children [13]. In the current study, however, differences in IPS activation between trained and control children need to be interpreted with caution. Trained children tended to show a stronger subbase-5 effect in the left IPS, but the direct comparison to control children was not significant. This finding might reflect a representation of a finger-related effect in mental arithmetic in a typical brain region for number magnitude processing. This finger-related numerical representation might be established in children who were trained to use their fingers for single-digit arithmetic, comparable to what was previously found for adults [12]. Children at this early age begin to establish this representation leading to a subbase-5 effect in both solution times and accuracy (as in adults, cf. [6]); whether an explicit finger-based numerical training facilitates this development in the core region of number processing -the IPS -could not be clarified in the current study due to insufficient power. Future studies would be desirable to further evaluate the neural overlap of fingers and numbers in the IPS in longitudinal or intervention studies in children involving different age groups.
When interpreting the results of the current study, there are limitations to be considered. First, sample sizes in the present study were comparably small and the statistical power to detect small effects was accordingly low. Thus, we were careful in interpreting the absence of effects that might be detected with sufficient power. Note that the small sample sizes were caused by the special populations recruited (in particular an experimental and a control group of children from an intensive intervention study running over an entire school year, cf. [22]), meaning that the present study is nonetheless the largest neurocognitive intervention study investigating finger-based numerical representations in children to date. Second, constraints on the time available for reliable fNIRS measurements in such young children further resulted in low numbers of trials per task. This can affect the reliability of the data. Third, data quality was not optimal, with missing behavioral data and low signal-to-noise ratio in the fNIRS data, potentially due to the measurements in a natural setting at children's schools. This was primarily due to motion artifacts, as children of this age may hardly sit still over an extended period of time and as some of the paradigms required movements. Although fNIRS can tolerate motion artifacts to a certain extent, motion artifact correction without the use of short channels was not optimal for this sample and setting. Fourth, concerning the control-group design, it needs to be taken into account that the neural activation was only assessed after the finger-based intervention took place (and not in a to-be-preferred pre-post design). Because children differ considerably in their numerical development at that age, this leads to additional error variance within groups. In the absence of general performance differences, the specificity of group differences in the subbase 5 effect seems to reflect a training effect rather than rather than being due to general differences between groups independent of the training. Supporting this interpretation, the trained and control groups of the larger intervention study did not significantly differ in numerical precursor abilities, general cognitive abilities and finger gnosis before the intervention. Moreover, due to constraints on study planning (ensuring testing of the trained children directly after the training, which was close to summer holidays) and logistics (bringing the fNIRS device to schools), the testing of the control group was delayed so that the groups differed in about half a year of age and education. Although differences in sensorimotor activation might not simply be explained by age differences, they are a serious confound, especially for the inconclusive results on IPS activation, because finger-based training and development might lead to similar activation changes in the IPS. Nevertheless, we are confident that the present data are meaningful because the children did not differ in their behavioral performance. Additionally, Krinzinger et al. [13] did not find age-related changes in the neural overlap of areas associated with finger movements and mental arithmetic in an even larger age range (6-12 years) than in the current study. Finally, methodological limitations also need to be mentioned. Even though fNIRS theoretically can reach activation in areas around the IPS, the specific location of the overlap of numbers and fingers in the IPS might not be covered (for further explanations see [37]).
In conclusion, we found converging neural evidence for the strengthening of fingerbased numerical representations following a finger-based intervention in children in their first year of school. In particular, single-digit mental arithmetic elicited activation in the sensorimotor cortex associated with using the respective hand for solving the task-even in the absence of overt finger movements (cf. [15]). This suggests enhanced embodied representations following sensorimotor experiences made in the training. However, whether finger-based instruction also leads to a more pronounced neural association of fingers and numbers in the IPS needs to be clarified in future research. In conclusion, the present results indicate that training finger-based numerical strategies, i.e., the use of fingers for counting, base-10 representations, and initial calculations, seems to leave learning traces in the brain. As such, the current exploratory study may-despite its limitations-well serve as a starting point for better controlled future (intervention) studies substantiating the beneficial role of finger-based numerical representations for children's numerical development.
Supplementary Materials: The supporting information on the number partner task can be downloaded at: https://www.mdpi.com/article/10.3390/brainsci12050637/s1. References [38][39][40][41]   Informed Consent Statement: Written informed consent was provided by the children's parents or legal guardians, and oral assent was obtained from all children prior to testing.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to ethical restrictions.