Impact Factor 2.089

The world's most-cited Multidisciplinary Psychology journal

Original Research ARTICLE

Front. Psychol., 01 May 2018 | https://doi.org/10.3389/fpsyg.2018.00637

Numerical Affordance Influences Action Execution: A Kinematic Study of Finger Movement

  • 1Department of General Psychology, University of Padua, Padua, Italy
  • 2Padova Neuroscience Center, University of Padua, Padua, Italy

Humans represent symbolic numbers as oriented from left to right: the mental number line (MNL). Up to now, scientific studies have mainly investigated the MNL by means of response times. However, the existing knowledge on the MNL can be advantaged by studies on motor patterns while responding to a number. Cognitive representations, in fact, cannot be fully understood without considering their impact on actions. Here we investigated whether a motor response can be influenced by number processing. Participants seated in front of a little soccer goal. On each trial they were visually presented with a numerical (2, 5, 8) or a non-numerical ($) stimulus. They were instructed to kick a small ball with their right index toward a frontal soccer goal as soon as a stimulus appeared on a screen. However, they had to refrain from kicking when number five was presented (no-go signal). Our main finding is that performing a kicking action after observation of the larger digit proved to be more efficient: the trajectory path was shorter and lower on the surface, velocity peak was anticipated. The smaller number, instead, specifically altered the temporal and spatial aspects of trajectories, leading to more prolonged left deviations. This is the first experimental demonstration that the reaching component of a movement is influenced by number magnitude. Since this paradigm does not require any verbal skill and non-symbolic stimuli (array of dots) can be used, it could be fruitfully adopted to evaluate number abilities in children and even preschoolers. Notably, this is a self-motivating and engaging task, which might help children to get involved and to reduce potential arousal connected to institutional paper-and-pencil examinations.

Introduction

The propensity to spatially represent environmental information is a core characteristic of human cognitive system (Gevers et al., 2003). Numbers are coded into space along a left-right oriented continuum (Fias and Fischer, 2005; Bueti and Walsh, 2009; Dehaene, 2011). The seminal insight of such a spatial-numerical association goes back to 1880, when Galton (1880) firstly proposed that humans describe and think numbers as increasingly oriented from left to right along a mental number line (MNL), where small numbers are located on the left and large numbers on the right side of space. The first scientific demonstration of this spatial representation of number has been reported more than 100 years later, when Dehaene et al. (1993) discovered that humans respond faster to smaller numbers on the left space and to larger numbers on the right space; the Spatial Numerical Association of Response Codes (SNARC) effect. A large body of literature supports this effect. Humans show a left bias when indicating the center of a string composed of repeated “1”, and a right bias when it is composed of “9” (Fischer, 2001). This indicates that an automatic activation of the left or right space automatically occurs during number processing: the elaboration of small numbers pre-activates the left space and the elaboration of large numerical magnitudes pre-activates the right space.

Complementary results have been obtained in a pseudo-random number generation task. Loetscher et al. (2008) asked participants to report random numbers in the 1–30 numerical range. Participants were systematically influenced by the side (left or right) their head was turned. When they faced toward their left, they produced comparatively more small numbers with respect to when they faced toward their right (Loetscher et al., 2008; see also Winter et al., 2015 for similar results along both near/far space and vertical dimensions, and Hartmann et al., 2012 for a whole body condition). Passive observation of leftward or downward gaze similarly induced participants to generate smaller than large numbers, compared to observing color changes or rightward gaze (Grade et al., 2013). Such biases are explained by a shifting of the attention compatible with the MNL, which facilitates the accessibility to small numbers turning the left and to large numbers turning the right. More recently, the effect reported by Loetscher et al. (2008) has been replicated in a condition of lateral arm turns. The effect was present when two congruent body’s movements were required (e.g., right-turns of both arm and head), but it disappeared whenever the two movements were incongruent (e.g., left-turns of arm and right-turns of head). This reveals that the spatial bias induced by the two sensorimotor locations on numerical processing can annihilate each other (Cheng et al., 2015). All together, these findings show that numbers and motor actions influence each other. This interaction is not limited to laboratory experiences but it emerges also in everyday activities. Numerical magnitude influences directional decisions while walking. In a recent study, healthy adults were required to stand and to produce random numbers as they made lateral turns. Lateral turn decisions could be predicted by the magnitude of random numbers produced before the turn: participants turned left more often when they had just produced small numbers, vice-versa they turned right more often when they had just produced large numbers (Shaki and Fischer, 2014).

Since cognitive representations of perceptual and semantic information are fully understood only when considering their impact on actions (Gallese and Lakoff, 2005), the existing knowledge on the MNL should be extended to studies that analyze motor actions while responding to a number (see for example Girelli et al., 2016). An emerging literature of hand-tracking and computer-mouse tracking nicely depict how motor actions can be better understood while performing number related tasks (Song and Nakayama, 2008; Santens et al., 2011; Dotan and Dehaene, 2013; Faulkenberry, 2014; Faulkenberry et al., 2016, 2017).

From this fascinating perspective, adopting kinematic measures is a state-of-art methodology in order to provide a fine-tuned analysis of movement, a large range of degrees of freedom and a highly sensitive investigation. In fact, a mounting number of studies are now using 3-D motion capture and detailed kinematic analyses to measure behavior and to deeply examine questions relating to cognitive processing in naturalistic protocols (for reviews, see Castiello, 2005; Krishnan-Barman et al., 2017). A growing number of studies on prehension movements is proving that semantic information related to magnitude can indeed influence movement kinematics. In particular, it has been shown that grip aperture varies according to the dimension indicated by a label put on a target object: it is larger for the large-labeled object and smaller for the small-labeled object (Gentilucci et al., 2000, 2012; Andres et al., 2008a,b; Namdar et al., 2014). Precision grip movements are faster in response to small numbers and power grips are faster in response to large numbers (Lindemann et al., 2007). These studies clearly show the influence of numbers on motor patterns. However, this effect could also reflect a highly overlearned motor association between magnitude labels (e.g., small, medium, large) and manual responses (e.g., grasping a small or large glass of coke, a 0.5 kg or a 1 kg flour packet). These frequent experiences, though allowing to perform very efficient actions in everyday life (Schwarz and Keus, 2004), could bias to perform smaller grasping actions in relation to smaller digits and vice versa (for review, see Rugani and Sartori, 2016). Notably, two components characterize prehension movements (Jeannerod, 1981; Jakobson and Goodale, 1991; Chieffi and Gentilucci, 1993; Castiello, 1996; Smeets and Brenner, 1999). The reaching component extracts information regarding the object’s spatial location and activates those muscles relevant to approach it. The grasping component extracts information on the object’s intrinsic properties such as size and shape. The open question is whether number processing influences only the grip component or the preceding reaching movement as well (grasp and transport components). To pursue this question in an unbiased way, we recently adopted a new and not-overlearned paradigm (Rugani et al., 2017; see also Betti et al., 2015 for a previous application of this paradigm). We specifically combined a “free response” task with the kinematic analysis of a finger movement and we provided the first demonstration that numerical processing affect not only the grasping, but also the reaching component of movements. This finding particularly depicts the novelty of our approach: instead of measuring the grasping component – which might be affected by previous experience – we adopted a culturally unbiased index (i.e., the transport component). Participants were seated in front of two little soccer goals, one on their left and one on their right side, and they were instructed to kick a small ball with their right index toward the goal indicated by an arrow on the monitor. In a few crucial 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 then segmented in two temporal phases (i.e., Kick Preparation and Kick Finalization) in order to make a fine-grained analysis of action execution timing. Results showed that in responding to small numbers toward the left and to large numbers toward the right, participants were faster to finalize the action. Moreover, the small number specifically altered the temporal and spatial aspects of left kick’s trajectories, whereas the large number specifically modified right kick’s trajectories. However, a limit of that study is that data concerning the two different movements (i.e., left and right kicks) had to be considered separately due to mechanical and anatomical differences (i.e., the degrees of freedom of the right index finger in relation with the anatomy of the right hand). Here, we adopted a unique action – a straight kick – for all the experimental conditions to avoid any anatomical bias. This means that we expected all the kicks to differ in terms of temporal features of trajectory path, rather than spatial features (i.e., a general leftward deviation was expected across conditions given the degrees of freedom of the right index during the kicking).

Extensive literature on reach-to-grasp consistently showed a general anticipation in hand kinematics when a target object has to be carefully approached (e.g., with the intention to pour vs. to place it, see Schuboe et al., 2008; or with the intention to throw it vs. to lift it, see Armbrüster and Spijkers, 2006). Moreover, it is known that object weight influences motor planning and control of reach-to-grasp actions as to guarantee a stable final grip placement on the object (Weir et al., 1991; Brouwer et al., 2006; Eastough and Edwards, 2007). In particular, Ansuini et al. (2016) recently found that peak velocity between 10 and 40% of normalized movement time was greater when reaching an heavy than a light object. Interestingly, object weight can also influence simply pantomimed reach-to-grasp actions, thus reflecting a link between cognitive representations of the weight and distinctive features of a motor act.

Since the standard parameters utilized for characterizing the reaching component are essentially trajectory and velocity, here we expect that a functional connection between numerical cognition and action planning will translate into different spatial and temporal patterns across conditions. Since numerical priming has two features: (i) spatiality (small numbers are associated with left space and large numbers with right space) and (ii) weight (small numbers are associated with light objects and large numbers with heavy objects), these two features should jointly influence hand movement kinematics. In particular, we predict that the smaller number will influence the temporal aspects of left trajectory deviations, in line with our previous study (Rugani et al., 2017). Whereas the larger number will produce a more direct route, as indexed by lower and shorter trajectory path, and anticipated peak velocity. This innovative approach combining number presentation with action execution with will allow us to measure number-related information transmitted by the hand movements over time.

Materials and Methods

Participants

Twenty-three students (10 males and 13 females, mean age = 22.74 years, SD = 0.75) took part in the experiment. A statistical power analysis for sample size estimation was previously performed (GPower 3.1), based on data from a published study (Rugani et al., 2017). The mean effect size (ES) of paired t-test in that study (0.65) was considered to be large/medium according to Cohen’s (1988) criteria. Here, since we planned to use a repeated-measure ANOVA, for sample size estimation we inserted these values: η2 = 0.20; α = 0.01; 1-β = 0.99; number of measures = 3; groups = 1; supposed correlation among measures = 0.45. The projected sample size needed with this effect size is N = 23 for within group comparisons. All participants were right handed, had normal or corrected-to-normal vision, and were naive about the purpose of the experiment. Participants gave their written consent before the experiment. The experimental procedures were approved by the Ethics Committee of the University of Padova and were carried out in accordance with the principles of the 1964 Declaration of Helsinki (Sixth revision, 2008).

Stimuli

Stimuli consisted in three symbolic numbers: a small digit (2), an intermediate digit (5), and a large digit (8), plus a symbolic character semantically associated with numbers, though not a number in itself ($, see Figure 1). This character was specifically selected on the basis of its symmetry, in order to avoid any indication of direction (as compared to #, for example, which is slightly tilted to the right). The stimulus 5 was adopted as a no-go signal to ensure that reaching movements were not initiated before the number was processed. Hereafter, stimuli will be referred to as S2, S5, S8, and S$. Digits were in Arial font, black color and 160 size. On each trial, a black fixation cross (7.5 cm by 7.5 cm, in Arial font, black color) appeared on the screen before stimulus presentation.

FIGURE 1
www.frontiersin.org

FIGURE 1. Stimuli adopted in the experiment. A small digit (2), an intermediate digit (5; no-go signal), a large digit (8), and a non-numerical symbol ($).

Apparatus and Procedure

Participants sat on a chair in front of a table (90 cm × 90 cm) with the left hand resting on their left leg and the right hand located in the designated start position. The experimental apparatus consisted in a green velvet surface (93.5 cm × 74 cm). Participants’ right index was introduced in the plastic sock (4.5 cm high, 2.5 cm diameter) of a small plastic soccer shoe (3 cm long, 1.5 cm wide; for a schematic representation of the apparatus see Figure 2). At the beginning of each trial, participants were instructed to position the shoe on a footprint (3 cm long, 1.5 cm wide) painted on the velvet cloth. A plastic ball (2.3 cm of diameter) was positioned on a plastic ring (1.5 cm diameter) located at 1 cm away from the footprint. In the start position, participants rested their right wrist on a pillow (16 cm long, 11 cm wide and 6.5 cm high), which was shaped to guarantee a comfortable and repeatable posture of the hand, allowing them to effortlessly kick the ball. A small soccer goal (18 cm long 16 cm high) was located 50 cm away from the footprint. A 24” monitor (resolution 1920 × 1080 pixels, refresh frequency 120 Hz) set at eye level (the eye–screen distance was 80 cm) was used to present the experimental stimuli. Participants underwent two sessions (i.e., Training and Testing) and were instructed to kick the ball toward the soccer goal following stimulus presentation, at their own pace. No instruction was given concerning the speed of movement. A black fixation cross appeared for 100 ms and was replaced with a stimulus after 1000 ms. During the Training session S$ was presented for 15 trials. During the Testing session participants kicked the ball upon random presentation of either a symbolic number or a symbolic character: S2, S8, and S$ were shown 10 times each. Whenever S5 was presented (n = 10 trials), participants were required to refrain from kicking the ball.

FIGURE 2
www.frontiersin.org

FIGURE 2. Experimental set up. Participants sat in front of a monitor, wearing with their right index a small soccer shoe positioned on a footprint, in front of a plastic ball. A small goal was placed centrally with respect to the participant’s position. A 3D-Optoelectronic SMART-D system was used to track the kinematics of the participant’s right index finger and the position of the ball by means of six video cameras and two infrared reflective markers taped to the participant’s index finger and to the ball.

Kinematic Recording

A 3D-Optoelectronic SMART-D system (Bioengineering Technology and Systems, B|T|S|) was used to track the kinematics of the participant’s right index. One light-weight infrared reflective marker (0.25 mm in diameter; B|T|S|) was taped on the index finger’s proximal phalange to measure the kicking movement (see Figure 2). A second marker was located on the ball to compute the midline virtually connecting index finger and target object and to segment the whole movement in a Pre-Contact and a Post-Contact Phase. Six infrared video cameras (sampling rate 140 Hz) detecting the markers’ positions in a 3-D space were placed in a semicircle at a distance of 1–1.2 meters from the table. Each camera position, roll angle, zoom, focus, threshold and brightness were calibrated and adjusted to optimize data collection before each experimental session. For the dynamic calibration, a three-marker wand was moved throughout the workspace of interest for 60 s. The measurements were made along the three Cartesian axes [i.e., x (left–right), y (up–down), and z (anterior–posterior)].The spatial resolution of the recording system was 0.3 mm over the field of view. The standard deviation of the reconstruction error was 0.2 mm for the x, y, and z axes.

Data Processing

Following kinematic data collection, the SMART-D Tracker software package (B|T|S|) was used to provide a 3-D reconstruction of the marker positions of each trial as a function of time. The data were then filtered using a finite impulse response linear filter (transition band = 1 Hz, sharpening variable = 2, cut-off frequency = 10 Hz; D’Amico and Ferrigno, 1990, 1992). Movement onset was defined as the time at which the tangential velocity of the finger marker crossed a threshold (5 mm/s) and remained above it for longer than 500 ms. End of movement was defined as the time at which the tangential velocity of the finger marker dropped below the threshold (5 mm/s) after the ball was kicked. The following kinematic parameters were extracted for each individual movement using a custom Protocol run in Matlab, 2014b (The 4 Math Works, Natick, MA, United States):

Movement Time: the time interval between movement onset and end of movement (ms);

Trajectory Path: the length of the index trajectory (mm);

Maximum Trajectory Height: the maximum height of the index trajectory on the y-axis (mm);

Contact Time: the time at which the tangential velocity of the ball crossed a threshold (2 mm/s) and remained above it for longer than 500 ms;

Time to Maximum Velocity: the time at which index velocity was maximum, with respect to movement onset (ms);

Time to Maximum Trajectory Height: the time at which index trajectory was higher, with respect to movement onset (ms);

Time to Maximum Trajectory Deviation: the time at which index trajectory reached the maximum perpendicular deviation from the virtual line linking the starting position with the target object, with respect to movement onset (ms).

The temporal peaks were then normalized with respect to movement time, so that individual speed differences were accounted for:

Contact Time (%): the percentage of movement time at which the tangential velocity of the ball crossed a threshold (2 mm/s) and remained above it for longer than 500 ms;

Time of Maximum Velocity (%): the percentage of movement time at which the index trajectory was at maximum velocity (%);

Time to Maximum Trajectory Height (%): the percentage of movement time at which the index trajectory reached its higher peak (%).

Time to Maximum Trajectory Deviation (%): the percentage of movement time at which index trajectory reached the maximum deviation from the midline (%).

For each participant and kinematic index, we calculated means and relative standard deviations for each type of stimulus (S2, S8, and S$).

Data Analysis

The mean values for each parameter of interest were determined for each participant and entered into separate repeated-measures ANOVAs with Stimulus (S2, S8, and S$) as within-subjects factor.

Preliminary analyses were conducted to check for normality, sphericity (Mauchly test), univariate and multivariate outliers, with no violations noted. For the ANOVA the alpha level of p was set <0.01, in accordance with our power analysis. Main effects were used to explore the means of interest (post hoc t-test) and Bonferroni correction was applied (alpha level of p < 0.05) to prevent Type-1 errors. Statistical analyses were performed with SPSS 23 (SPSS Inc., Chicago, IL, United States) software.

Results

All the means, medians and standard errors are summarized in Table 1.

TABLE 1
www.frontiersin.org

TABLE 1. Statistically significant key kinematic parameters (mean, standard errors, and median per condition) across stimuli.

Movement Time (ms): The ANOVA performed on MT revealed a non-significant effect of Stimulus [F(2,44) = 3.48, p = 0.04, ηp2 = 0.14].

Trajectory Path (mm): The ANOVA performed on the length of the index trajectory revealed a significant effect of Stimulus [F(2,44) = 4.75, p = 0.01, ηp2 = 0.18]. Observing S8 led to a shorter trajectory with respect to observing S2 (p = 0.01). This effect was significant also for S8 compared to S$ (p = 0.02).

Maximum Trajectory Height (mm): The ANOVA performed on the maximum height of the index trajectory revealed a significant effect of Stimulus [F(2,44) = 323.98, p < 0.001, ηp2 = 0.94]. Observing S8 led to a lower trajectory with respect to observing S2 (p < 0.001). This effect was significant also for S8 compared to S$ (p < 0.001).

Contact Time (%): The ANOVA performed on CT revealed a non-significant effect of Stimulus [F(2,44) = 0.55, p = 0.58, ηp2 = 0.02].

Time to Maximum Velocity (%): The ANOVA performed on the time at which index velocity was maximum revealed a significant effect of Stimulus [F(2,44) = 13.35, p < 0.001, ηp2 = 0.38]. Observing S8 led to an earlier peak with respect to observing S2 (p < 0.001). This effect was significant also for S8 compared to S$ (p < 0.001).

Time to Maximum Trajectory Height (%): The ANOVA performed on the time at which index trajectory was higher revealed a significant effect of Stimulus [F(2,44) = 9.07, p < 0.001, ηp2 = 0.29]. Observing S8 led to an earlier peak with respect to observing S2 (p < 0.001). This effect was significant also for S8 compared to S$ (p = 0.02).

Time to Maximum Trajectory Deviation (%): The ANOVA performed on the time at which index trajectory reached the maximum deviation from the midline revealed a significant effect of Stimulus [F(2,44) = 9.07, p < 0.001, ηp2 = 0.29]. Observing S2 led to a delayed leftward deviation with respect to observing S8 (p < 0.001; see Figure 3).

FIGURE 3
www.frontiersin.org

FIGURE 3. Graphical representation of % of Time to Maximum Deviation results. Leftward trajectory deviations following S2 and S8 presentation (red and blue lines, respectively) show a delayed peak for the small number presentation (51%) compared to the larger number (44%).

Discussion

The aim of this study was to determine whether number processing affects the performance of executed movements. Participants were asked to perform a kicking action with their right hand after observing a small/large digit (2, 8) or a symbolic character ($). Our main finding is that although executed actions were exactly the same across conditions, a decrease in Trajectory Path, Trajectory Height, Time to Maximum Velocity and Time to Maximum Trajectory Height occurred for the large compared to the small digit. Our results are in line with previous studies demonstrating a general anticipation when an object is approached more carefully (e.g., Armbrüster and Spijkers, 2006; Schuboe et al., 2008) and an early velocity peak when reaching a heavy than a light object (Ansuini et al., 2016). In our study, performing a finger kicking action after observation of a large digit was indeed highly efficient: the trajectory path was shorter and lower on the surface and the velocity peak was anticipated. In particular, we found an anticipation of the Time of Maximum Velocity ranging from S8 (56%) to S$ (64%) and S2 (65%), despite the executed movement was the same. Since a statistically significant effect on Time to Maximum Velocity was specifically connected to the observation of S8, this might suggests the activation of an association between larger numbers and weight. By combining knowledge regarding numerical magnitude and weight dynamics, the motor system might be able to adjust kick kinematics accordingly.

A crucial data arising from the present data is the temporal aspect of trajectory deviations. Given the very short distance between footprint and ball (1 cm) and the constrained end-goal (i.e., straight kick), no effect was expected in terms of trajectory deviations before contact. However, a longer tilt leftwards for the S2 condition during the post-contact phase seems to indicate that participants were aiming towards the left following small number presentation compared to large number presentation. Similar results were obtained with an index finger pointing task (Fischer, 2003). Participants were faster when pointing leftward after a small digit presentation and rightward after a large digit presentation (Fischer, 2003). Subsequent studies in adults (Ishihara et al., 2006) and in 7 year-old children (Möhring et al., 2017) revealed that this bias could be explained by a contamination of motor preparation by a direct activation of number magnitude whit the congruent spatial location.

Our data show for the first time that the control mechanisms underlying reaching formation are affected by number processing beyond the – already demonstrated – grasping component. Since the effect of numerical magnitude on grip aperture kinematics (Gentilucci et al., 2000, 2012; Andres et al., 2004, 2008a,b; Lindemann et al., 2007; Moretto and di Pellegrino, 2008; Chiou et al., 2012; Namdar et al., 2014) and object affordances (Badets et al., 2007; Chiou et al., 2009) is well known, the present data significantly extend previous literature. The impact of numerical magnitude on both reaching and grasping kinematics would corroborate the theory that representations of number and actions share common codes within a magnitude representation’s system (Lindemann et al., 2007).

The ATOM Theory and Numerical Affordance

From a neuropsychological viewpoint, the modulation of numerical cognition on action control could be explained by the “A Theory of Magnitude”, or “ATOM theory” (Walsh, 2003; see also Bueti and Walsh, 2009 for an updated proposal). The ATOM theory postulates that the intra-parietal sulcus (IPS) serves as the cortical center for time, space, and numbers estimation. The IPS would be equipped with an analog system that constantly computes magnitudes for action execution (Bueti and Walsh, 2009). It is therefore plausible that beyond object affordances related to the physical features of an object (Gibson, 1979; Tucker and Ellis, 1998), a “numerical affordance” might link objects’ extension and numerousness to specific motor dynamics. Here we specifically demonstrated that two features related to numbers (spatiality and weight) are interrelated and affect movement kinematics. From this perspective, the ATOM theory may explain the interaction between numerical information and non-numerical magnitude, such as time and space, and especially how numbers prompt spatially oriented actions (SNARC effect).

In neural terms, reaching and grasping components are mediated by two separate anatomical pathways (for review see Filimon, 2010). Grasping is organized by a lateral parieto-frontal circuit and reaching by a more medial parieto-frontal circuit including medial intraparietal area and dorsal premotor area (Filimon, 2010; Di Bono et al., 2015). Notably, the MLN is linked to a parietal network: Consistent with the ATOM theory (Walsh, 2003; Bueti and Walsh, 2009), the brain regions dedicated to number processing and to reach-to-grasp movements are closely linked by a generalized magnitude system, which transforms quantitative information into actions. In this connection, it would be important to consider the neural mechanism linking number and reaching movement. Functional neuroimaging studies will help to clarify the differential contribution of the reaching and the grasping components to number processing in action execution.

Embodied Number Processing

Our evidence, highlighting spatial and temporal properties of finger movements responding to numbers, fits with the embodied theory of numerical representation. From this perspective, numbers are not abstract, but embodied, i.e., rooted in bodily experiences. The way in which we use our bodies to act can influence our cognition (for an overview see Wilson, 2002; Barsalou, 2008; Patro et al., 2015). For example, the sensory-motor activations which occur during learning shape the newly learnt representation (Fischer and Zwaan, 2008; Fischer, 2012). Since number acquisition usually implies concomitant body-movements, like finger counting (Brissiaud, 1992; Domahs et al., 2010), such embodied space-motor-number relations have also been used for training. For example it has been shown that playing games eliciting an embodied experience of the spatial layout of the MNL improves numerical competences (Ramani and Siegler, 2008; Whyte and Bull, 2008; Siegler and Ramani, 2009).

The challenging perspective of embodied cognition offers a stimulating approach to the study of mathematical competences. The analysis of finger movements indeed is considered a powerful method to assess numerical representations (Dotan and Dehaene, 2013). Paradigms focused on finger trajectories could be used to assess mental computations, and might offer a diagnostic instrument for measuring both normal and pathological development of mathematical competences (Booth and Siegler, 2006).

Conclusion

This study aimed at deepens our knowledge on the link between spatial numerical association and action execution. From an evolutive perspective, it could extend existing evidence on the origin of the spatial numerical association (de Hevia and Spelke, 2009; de Hevia et al., 2012; McCrink and Opfer, 2014; Nuerk et al., 2015; Rugani and de Hevia, 2016; Möhring et al., 2017). Moreover, it could allow to clarify whether and how symbolic and non-symbolic numbers (see Rugani et al., 2017 for a definition) affect the sensorimotor transformations related to the motor control of the hand. This is particularly relevant considering the role of finger counting in number processing (Di Luca et al., 2006; Fischer, 2008; Sixtus et al., 2017), which survives in adults and seems to help the associations between numbers and hand actions (Hatano et al., 1977; Hubbard et al., 2005). The important relation between finger counting and mathematical abilities is scientifically documented. Abacus experts spontaneously move their hands while solving arithmetic calculation (Hatano et al., 1977). The manumerical cognition hypothesis (Hubbard et al., 2005) claims that this relation could explicate why dyscalculia, left–right confusion and finger agnosia often co-occur in the Gerstmann syndrome.

Last but not least, our protocol – based on a self-motivating and engaging task – would allow to investigate numerical cognition and its relation with space without the anxiety which usually disadvantages children with problems in mathematical comprehension (for the use of an innovative approach on mathematical learning with Touchscreen Tablets, see Duijzer et al., 2017). Highly math-anxious persons have a common and strong tendency to avoid math, which reduces their possibility to increase their math competences (Ashcraft, 2002).

This paradigm, characterized by a new and not-overlearned task, could therefore be used to study the relation between number processing and motor action over development, before and during mathematical learning. Movements kinematics not only provides an accurate measure of the association between numbers and actions, but could also offer a novel tool for the diagnosis of potential mathematical deficits.

Author Contributions

RR and LS designed the study, created the stimuli, collected, analyzed the data, and wrote the manuscript. LS did the statistical analyses. RR, SB, and LS interpreted the data discussed the results. SB created the figures.

Funding

This work was supported by SIR grant (Scientific Independence of Young Researchers – No. RBSI141QKX) to LS and by “German Academic Exchange Service or DAAD (German: Deutscher Akademischer Austauschdienst),” Funding program: Research Stays for University Academics and Scientists, 2017 – No. 91644645 to RR.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The authors would like to thank Elena Carlotta Borile for her help in conducting the experiments.

References

Andres, M., Davare, M., Pesenti, M., Olivier, E., and Seron, X. (2004). Number magnitude and grip aperture interaction. Neuroreport 15, 2773–2777.

Google Scholar

Andres, M., Olivier, E., and Badets, A. (2008a). Actions, words, and numbers: a motor contribution to semantic processing? Curr. Dir. Psychol. Sci. 17, 313–317. doi: 10.1111/j.1467-8721.2008.00597.x

CrossRef Full Text | Google Scholar

Andres, M., Ostry, D. J., Nicol, F., and Paus, T. (2008b). Time course of number magnitude interference during grasping. Cortex 44, 414–419. doi: 10.1016/j.cortex.2007.08.007

PubMed Abstract | CrossRef Full Text | Google Scholar

Ansuini, C., Cavallo, A., Campus, C., Quarona, D., Koul, A., and Becchio, C. (2016). Are we real when we fake? Attunement to object weight in natural and pantomimed grasping movements. Front. Hum. Neurosci. 10:471. doi: 10.3389/fnhum.2016.00471

PubMed Abstract | CrossRef Full Text | Google Scholar

Armbrüster, C., and Spijkers, W. (2006). Movement planning in prehension: do intended actions influence the initial reach and grasp movement? Motor Control 10, 311–329. doi: 10.1123/mcj.10.4.311

PubMed Abstract | CrossRef Full Text | Google Scholar

Ashcraft, M. H. (2002). Math anxiety: personal, educational, and cognitive consequences. Curr. Dir. Psychol. Sci. 11, 181–185. doi: 10.1111/1467-8721.00196

CrossRef Full Text | Google Scholar

Badets, A., Andres, M., Di Luca, S., and Pesenti, M. (2007). Number magnitude potentiates action judgements. Exp. Brain Res. 180, 525–534. doi: 10.1007/s00221-007-0870-y

PubMed Abstract | CrossRef Full Text | Google Scholar

Barsalou, L. W. (2008). Grounded cognition. Annu. Rev. Psychol. 59, 617–645. doi: 10.1146/annurev.psych.59.103006.093639

CrossRef Full Text | Google Scholar

Betti, S., Castiello, U., and Sartori, L. (2015). Kick with the finger: symbolic actions shape motor cortex excitability. Eur. J. Neurosci. 42, 2860–2866. doi: 10.1111/ejn.13067

PubMed Abstract | CrossRef Full Text | Google Scholar

Booth, J. L., and Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Dev. Psychol. 42, 189–201. doi: 10.1037/0012-1649.41.6.189

PubMed Abstract | CrossRef Full Text | Google Scholar

Brissiaud, R. (1992). “A tool for number construction: finger symbol sets,” in Pathways to Number: Children’s Developing Numerical Abilities, eds J. Bideaud, C. Meljac, and J.-P. Fischer (Hillsdale, NJ: Erlbaum), 41–65.

Google Scholar

Brouwer, A. M., Georgiou, I., Glover, S., and Castiello, U. (2006). Adjusting reach to lift movements to sudden visible changes in target’s weight. Exp. Brain Res. 173, 629–636. doi: 10.1007/s00221-006-0406-x

PubMed Abstract | CrossRef Full Text | Google Scholar

Bueti, D., and Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philos. Trans. R. Soc. Lond. B Biol. Sci. 364, 1831–1840. doi: 10.1098/rstb.2009.0028

PubMed Abstract | CrossRef Full Text | Google Scholar

Castiello, U. (1996). Grasping a fruit: selection for action. J. Exp. Psychol. Hum. Percept. Perform. 22, 582–603. doi: 10.1037/0096-1523.22.3.582

PubMed Abstract | CrossRef Full Text | Google Scholar

Castiello, U. (2005). The neuroscience of grasping. Nat. Rev. Neurosci. 6, 726–736. doi: 10.1038/nrn1744

PubMed Abstract | CrossRef Full Text | Google Scholar

Cheng, X., Ge, H., Andoni, D., Ding, X., and Fan, Z. (2015). Composite body movements modulate numerical cognition: evidence from the motion numerical compatibility effect. Front. Psychol. 6:1692. doi: 10.3389/fpsyg.2015.01692

PubMed Abstract | CrossRef Full Text | Google Scholar

Chieffi, S., and Gentilucci, M. (1993). Coordination between the transport and the grasp components during prehension movements. Exp. Brain Res. 94, 471–477. doi: 10.1007/BF00230205

CrossRef Full Text | Google Scholar

Chiou, R. Y. C., Chang, E. C., Tzeng, O. J. L., and Wu, D. H. (2009). The common magnitude code underlying numerical and size processing for action but not for perception. Exp. Brain Res. 194, 553–562. doi: 10.1007/s00221-009-1730-8

PubMed Abstract | CrossRef Full Text | Google Scholar

Chiou, R. Y. C., Wua, D. H., Tzeng, O. J. L., Hung, D. L., and Chang, E. C. (2012). Relative size of numerical magnitude induces a size-contrast effect on the grip scaling of reach-to-grasp movements. Cortex 48, 1043–1051. doi: 10.1016/j.cortex.2011.08.001

PubMed Abstract | CrossRef Full Text | Google Scholar

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd Edn. Hillsdale, NJ: Lawrence Erlbaum Associates.

Google Scholar

D’Amico, M., and Ferrigno, G. (1990). Technique for the evaluation of derivatives from noisy biomechanical displacement data using a model-based bandwidth-selection procedure. Med. Biol. Eng. Comput. 28, 407–415. doi: 10.1007/BF02441963

PubMed Abstract | CrossRef Full Text | Google Scholar

D’Amico, M., and Ferrigno, G. (1992). Comparison between the more recent techniques for smoothing and derivative assessment in biomechanics. Med. Biol. Eng. Comput. 30, 193–204. doi: 10.1007/BF02446130

PubMed Abstract | CrossRef Full Text | Google Scholar

de Hevia, M. D., and Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition 110, 198–207. doi: 10.1016/j.cognition.2008.11.003

PubMed Abstract | CrossRef Full Text | Google Scholar

de Hevia, M. D., Vanderslice, M., and Spelke, E. S. (2012). Cross dimensional mapping of number, length and brightness by preschool children. PLoS One 7:e35530. doi: 10.1371/journal.pone.0035530

PubMed Abstract | CrossRef Full Text | Google Scholar

Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics, Revised and Updated. New York, NY: Oxford University Press.

Google Scholar

Dehaene, S., Bossini, S., and Giraux, P. (1993). The mental representation of parity and number magnitude. J. Exp. Psychol. Gen. 122, 371–396. doi: 10.1037/0096-3445.122.3.371

CrossRef Full Text | Google Scholar

Di Bono, M. G., Begliomini, C., Castiello, U., and Zorzi, M. (2015). Probing the reaching-grasping network in humans through multivoxel pattern decoding. Brain Behav. 5:e00412. doi: 10.1002/brb3.412

PubMed Abstract | CrossRef Full Text | Google Scholar

Di Luca, S., Granà, A., Semenza, C., Seron, X., and Pesenti, M. (2006). Finger–digit compatibility in Arabic numeral processing. Q. J. Exp. Psychol. 59, 1648–1663. doi: 10.1080/17470210500256839

PubMed Abstract | CrossRef Full Text | Google Scholar

Domahs, F., Moeller, K., Huber, S., Willmes, K., and Nuerk, H. C. (2010). Embodied numerosity: implicit hand-based representations influence symbolic number processing across cultures. Cognition 116, 251–266. doi: 10.1016/j.cognition.2010.05.007

PubMed Abstract | CrossRef Full Text | Google Scholar

Dotan, D., and Dehaene, S. (2013). How do we convert a number into a finger trajectory? Cognition 129, 512–529. doi: 10.1016/j.cognition.2013.07.007

PubMed Abstract | CrossRef Full Text | Google Scholar

Duijzer, C. A., Shayan, S., Bakker, A., Van der Schaaf, M. F., and Abrahamson, D. (2017). Touchscreen tablets: coordinating action and perception for mathematical cognition. Front. Psychol. 8:144. doi: 10.3389/fpsyg.2017.00144

PubMed Abstract | CrossRef Full Text | Google Scholar

Eastough, D., and Edwards, M. G. (2007). Movement kinematics in prehension are affected by grasping objects of different mass. Exp. Brain Res. 176, 193–198. doi: 10.1007/s00221-006-0749-3

PubMed Abstract | CrossRef Full Text | Google Scholar

Faulkenberry, T. J. (2014). Hand movements reflect competitive processing in numerical cognition. Can. J. Exp. Psychol. 68, 147–151. doi: 10.1037/cep0000021

PubMed Abstract | CrossRef Full Text | Google Scholar

Faulkenberry, T. J., Cruise, A., Lavro, D., and Shaki, S. (2016). Response trajectories capture the continuous dynamics of the size congruity effect. Acta Psychol. 163, 114–123. doi: 10.1016/j.actpsy.2015.11.010

PubMed Abstract | CrossRef Full Text | Google Scholar

Faulkenberry, T. J., Cruise, A., and Shaki, S. (2017). Reversing the manual digit bias in two-digit number comparison. Exp. Psychol. 64, 191–204. doi: 10.1027/1618-3169/a000365

PubMed Abstract | CrossRef Full Text | Google Scholar

Fias, W., and Fischer, M. H. (2005). “Spatial representation of number,” in Handbook of Mathematical Cognition, ed. J. Campbell (New York, NY: Psychology Press), 43–54.

Google Scholar

Filimon, F. (2010). Human cortical control of hand movements: parietofrontal networks for reaching, grasping, and pointing. Neuroscientist 16, 388–407. doi: 10.1177/1073858410375468

PubMed Abstract | CrossRef Full Text | Google Scholar

Fischer, M. H. (2001). Number processing induces spatial performance biases. Neurology 57, 822–826. doi: 10.1212/WNL.57.5.822

CrossRef Full Text | Google Scholar

Fischer, M. H. (2003). Spatial representations in number processing—Evidence from a pointing task. Vis. Cogn. 10, 493–508. doi: 10.1080/13506280244000186

CrossRef Full Text | Google Scholar

Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex 44, 386–392. doi: 10.1016/j.cortex.2007.08.004

PubMed Abstract | CrossRef Full Text | Google Scholar

Fischer, M. H. (2012). A hierarchical view of grounded, embodied, and situated numerical cognition. Cogn. Process. 13, 161–164. doi: 10.1007/s10339-012-0477-5

PubMed Abstract | CrossRef Full Text | Google Scholar

Fischer, M. H., and Zwaan, R. A. (2008). Embodied language: a review of the role of the motor system in language comprehension. Q. J. Exp. Psychol. 61, 825–850. doi: 10.1080/17470210701623605

PubMed Abstract | CrossRef Full Text | Google Scholar

Gallese, V., and Lakoff, G. (2005). The brain’s concepts: the role of the sensory-motor system in conceptual knowledge. Cogn. Neuropsychol. 22, 455–479. doi: 10.1080/02643290442000310

PubMed Abstract | CrossRef Full Text | Google Scholar

Galton, F. (1880). Visualised numerals. Nature 21, 252–256. doi: 10.1038/021252a0

CrossRef Full Text | Google Scholar

Gentilucci, M., Benuzzi, F., Bertolani, L., Daprati, E., and Gangitano, M. (2000). Recognising a hand by grasp. Cogn. Brain Res. 9, 125–135. doi: 10.1016/S0926-6410(99)00049-X

CrossRef Full Text | Google Scholar

Gentilucci, M., Campione, G. C., De Stefani, E., and Innocenti, A. (2012). Is the coupled control of hand and mouth postures precursor of reciprocal relations between gestures and words? Behav. Brain Res. 233, 130–140. doi: 10.1016/j.bbr.2012.04.036

PubMed Abstract | CrossRef Full Text | Google Scholar

Gevers, W., Reynvoet, B., and Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition 87, B87–B95. doi: 10.1016/S0010-0277(02)00234-2

CrossRef Full Text | Google Scholar

Gibson, J. J. (1979). The Ecological Approach to Visual Perception. Hillsdale, NJ: Lawrence Erlbaum.

Google Scholar

Girelli, L., Perrone, G., Croccolo, F., Roman, E. H., Bricolo, E., Mancin, M., et al. (2016). Manual actions cover symbolic distances at different speed. Acta Psychol. 169, 56–60. doi: 10.1016/j.actpsy.2016.05.002

PubMed Abstract | CrossRef Full Text | Google Scholar

Grade, S., Lefèvre, N., and Pesenti, M. (2013). Influence of gaze observation on random number generation. Exp. Psychol. 60, 122–130. doi: 10.1027/1618-3169/a000178

PubMed Abstract | CrossRef Full Text | Google Scholar

Hartmann, M., Grabherr, L., and Mast, F. W. (2012). Moving along the number line: interactions between whole-body motion and numerical cognition. J. Exp. Psychol. Hum. Percept. Perform. 38, 1416–1427. doi: 10.1037/a0026706

PubMed Abstract | CrossRef Full Text | Google Scholar

Hatano, G., Miyake, Y., and Binks, M. G. (1977). Performance of expert abacus operators. Cognition 5, 47–55. doi: 10.1016/0010-0277(77)90016-6

CrossRef Full Text | Google Scholar

Hubbard, E. M., Piazza, M., Pinel, P., and Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nat. Rev. Neurosci. 6, 435–448. doi: 10.1038/nrn1684

PubMed Abstract | CrossRef Full Text | Google Scholar

Ishihara, M., Jacquin-Courtois, S., Flory, V., Salemme, R., Imanaka, K., and Rossetti, Y. (2006). Interaction between space and number representations during motor preparation in manual aiming. Neuropsychologia 44, 1009–1016. doi: 10.1016/j.neuropsychologia.2005.11.008

PubMed Abstract | CrossRef Full Text | Google Scholar

Jakobson, L. S., and Goodale, M. A. (1991). Factors affecting higher-order movement planning: a kinematic analysis of human prehension. Exp. Brain Res. 86, 199–208. doi: 10.1007/BF00231054

PubMed Abstract | CrossRef Full Text | Google Scholar

Jeannerod, M. (1981). “Intersegmental coordination during reaching at natural visual objects,” in Attention and Performance IX, eds J. Long and A. Baddeley (Hillsdale, NY: Erlbaum), 153–168.

Google Scholar

Krishnan-Barman, S., Forbes, P. A., and Hamilton, A. F. C. (2017). How can the study of action kinematics inform our understanding of human social interaction? Neuropsychologia 105, 101–110. doi: 10.1016/j.neuropsychologia.2017.01.018

PubMed Abstract | CrossRef Full Text | Google Scholar

Lindemann, O., Abolafia, J. M., Girardi, G., and Bekkering, H. (2007). Getting a grip on numbers: numerical magnitude priming in object grasping. J. Exp. Psychol. Hum. Percept. Perform. 33, 1400–1409. doi: 10.1037/0096-1523.33.6.1400

PubMed Abstract | CrossRef Full Text | Google Scholar

Loetscher, T., Schwarz, U., Schubiger, M., and Brugger, P. (2008). Head turns bias the brain’s internal random generator. Curr. Biol. 18, R60–R62. doi: 10.1016/j.cub.2007.11.015

PubMed Abstract | CrossRef Full Text | Google Scholar

McCrink, K., and Opfer, J. E. (2014). Development of spatial-numerical associations. Curr. Dir. Psychol. Sci. 23, 439–445. doi: 10.1177/0963721414549751

PubMed Abstract | CrossRef Full Text | Google Scholar

Möhring, W., Ishihara, M., Curiger, J., and Frick, A. (2017). Spatial-numerical associations in first-graders: evidence from a manual-pointing task. Psychol. Res. doi: 10.1007/s00426-017-0904-4 [Epub ahead of print].

PubMed Abstract | CrossRef Full Text | Google Scholar

Moretto, G., and di Pellegrino, G. (2008). Grasping numbers. Exp. Brain Res. 188, 505–515. doi: 10.1007/s00221-008-1386-9

PubMed Abstract | CrossRef Full Text | Google Scholar

Namdar, G., Tzelgov, J., Algom, D., and Ganel, T. (2014). Grasping numbers: evidence for automatic influence of numerical magnitude on grip aperture. Psychon. Bull. Rev. 21, 830–835. doi: 10.3758/s13423-013-0550-9

PubMed Abstract | CrossRef Full Text | Google Scholar

Nuerk, H.-C., Patro, K., Cress, U., Schild, U., Friedrich, C. K., and Goebel, S. M. (2015). How space-number associations may be created in preliterate children: six distinct mechanisms. Front. Psychol. 6:215. doi: 10.3389/fpsyg.2015.00215

PubMed Abstract | CrossRef Full Text | Google Scholar

Patro, K., Nuerk, H. C., and Cress, U. (2015). Does your body count? Embodied influences on the preferred counting direction of preschoolers. J. Cogn. Psychol. 27, 413–425. doi: 10.1080/20445911.2015.1008005

CrossRef Full Text | Google Scholar

Ramani, G. B., and Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Dev. 79, 375–394. doi: 10.1111/j.1467-8624.2007.01131.x

PubMed Abstract | CrossRef Full Text | Google Scholar

Rugani, R., Betti, S., Ceccarini, F., and Sartori, L. (2017). Act on numbers: numerical magnitude influences selection and kinematics of finger movement. Front. Psychol. 8:1481. doi: 10.3389/fpsyg.2017.01481

PubMed Abstract | CrossRef Full Text | Google Scholar

Rugani, R., and de Hevia, M. D. (2016). Number-space associations without language. Evidence from preverbal human infants and non-human animal species. Psychon. Bull. Rev. 24, 352–369. doi: 10.3758/s13423-016-1126-2

PubMed Abstract | CrossRef Full Text | Google Scholar

Rugani, R., and Sartori, L. (2016). Numbers in action. Front. Hum. Neurosci. 10:388. doi: 10.3389/fnhum.2016.00388

PubMed Abstract | CrossRef Full Text | Google Scholar

Santens, S., Goossens, S., and Verguts, T. (2011). Distance in motion: response trajectories reveal the dynamics of number comparison. PLoS One 6:e25429. doi: 10.1371/journal.pone.0025429

PubMed Abstract | CrossRef Full Text | Google Scholar

Schuboe, A., Maldonado, A., Stork, S., and Beetz, M. (2008). “Subsequent actions influence motor control parameters of a current grasping action,” in Proceedings of the 17th IEEE International Symposium on Robot and Human Interactive Communication, RO-MAN, Yokohama, 389–394. doi: 10.1109/ROMAN.2008.4600697

CrossRef Full Text | Google Scholar

Schwarz, W., and Keus, I. M. (2004). Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses. Percept. Psychophys. 66, 651–664. doi: 10.3758/BF03194909

PubMed Abstract | CrossRef Full Text | Google Scholar

Shaki, S., and Fischer, M. H. (2014). Random walks on the mental number line. Exp. Brain Res. 232, 43–49. doi: 10.1007/s00221-013-3718-7

PubMed Abstract | CrossRef Full Text | Google Scholar

Siegler, R. S., and Ramani, G. B. (2009). Playing linear number board games—but not circular ones—improves low-income preschoolers’ numerical understanding. J. Educ. Psychol. 101, 545–560. doi: 10.1037/a0014239

CrossRef Full Text | Google Scholar

Sixtus, E., Fischer, M. H., and Lindemann, O. (2017). Finger posing primes number comprehension. Cogn. Process. 18, 237–248. doi: 10.1007/s10339-017-0804-y

PubMed Abstract | CrossRef Full Text | Google Scholar

Smeets, J. B. J., and Brenner, E. (1999). A new view on grasping. Motor Control 3, 237–271. doi: 10.1123/mcj.3.3.237

CrossRef Full Text | Google Scholar

Song, J.-H., and Nakayama, K. (2008). Numeric comparison in a visually-guided manual reaching task. Cognition 106, 994–1003. doi: 10.1016/j.cognition.2007.03.014

PubMed Abstract | CrossRef Full Text | Google Scholar

Tucker, M., and Ellis, R. (1998). On the relations between seen objects and components of potential actions. J. Exp. Psychol. Hum. Percept. Perform. 24, 830–846. doi: 10.1037/0096-1523.24.3.830

CrossRef Full Text | Google Scholar

Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn. Sci. 7, 483–488. doi: 10.1016/j.tics.2003.09.002

PubMed Abstract | CrossRef Full Text | Google Scholar

Weir, P. L., MacKenzie, C. L., Marteniuk, R. G., Cargoe, S. L., and Frazer, M. B. (1991). The effects of object weight on the kinematics of prehension. J. Mot. Behav. 23, 192–204. doi: 10.1080/00222895.1991.10118362

PubMed Abstract | CrossRef Full Text | Google Scholar

Whyte, J. C., and Bull, R. (2008). Number games, magnitude representation, and basic number skills in preschoolers. Dev. Psychol. 44, 588–596. doi: 10.1037/0012-1649.44.2.588

PubMed Abstract | CrossRef Full Text | Google Scholar

Wilson, M. (2002). Six views of embodied cognition. Psychon. Bull. Rev. 9, 625–636. doi: 10.3758/BF03196322

CrossRef Full Text | Google Scholar

Winter, B., Matlock, T., Shaki, S., and Fischer, M. H. (2015). Mental number space in three dimensions. Neurosci. Biobehav. Rev. 57, 209–219. doi: 10.1016/j.neubiorev.2015.09.005

PubMed Abstract | CrossRef Full Text | Google Scholar

Keywords: mental number line, spatial-numerical association, kinematics, reaching, action execution, finger movement, numerical cognition

Citation: Rugani R, Betti S and Sartori L (2018) Numerical Affordance Influences Action Execution: A Kinematic Study of Finger Movement. Front. Psychol. 9:637. doi: 10.3389/fpsyg.2018.00637

Received: 13 December 2017; Accepted: 16 April 2018;
Published: 01 May 2018.

Edited by:

Hans-Christoph Nuerk, Universität Tübingen, Germany

Reviewed by:

Samuel Shaki, Ariel University, Israel
Thomas J. Faulkenberry, Tarleton State University, United States

Copyright © 2018 Rugani, Betti and Sartori. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Rosa Rugani, rosa.rugani@unipd.it Luisa Sartori, luisa.sartori@unipd.it